Design procedures for tall buildings with dynamic modification devices

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Design procedures for tall buildings with dynamic modification devices

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CHAPTER OUTLINE 5.1 Available Codes and Design Tools.....................................................................236 5.1.1 Codes and Guidelines .....................................................................236 5.1.2 Practical Design Aspects .................................................................248 5.1.3 Structural Analyses.........................................................................251 5.2 Passive Damping Systems ................................................................................264 5.2.1 Step-by-Step Procedure for Distributed Dampers...............................265 5.2.2 Step-by-Step Procedure for Mass Dampers .......................................321 5.3 Isolation Systems.............................................................................................347 5.3.1 Step-by-Step Procedure for Base Isolation ........................................347 5.4 Active, Semiactive, and Hybrid Systems ............................................................365 5.4.1 Literature Review ...........................................................................365 5.4.2 Step-by-Step Procedure ..................................................................367 5.5 Retrofit of Existing Buildings.............................................................................400 5.5.1 Code Requirements ........................................................................400 5.5.2 Evaluation Procedures Based on ASCE 41-13 (ASCE, 2013) .............402 5.5.3 Step-by-Step Procedure ..................................................................403 5.5.4 Case Study: Retrofitting Examples of High-Rise Building with Damping Systems...........................................................................422 5.6 Dynamic Modification Devices Strategy Optimization..........................................429 5.6.1 Introduction ...................................................................................429 5.6.2 Algorithm-Based Optimization Procedures ........................................430 5.6.3 Nonalgorithm-Based Optimization Procedures...................................433

This chapter of the book gives a general overview of the current state-of-the-art design procedures for tall building with dynamic modification devices under wind/ seismic loading. Code prescriptive procedures are reviewed, by examining national and international codes/standards available worldwide. US codes are discussed in detail since they are arguably the most advanced standards for the design of dynamic modification devices. Practical design and structural analysis aspects are also discussed based on the structural engineering office experience in the design of tall buildings with dynamic modification systems. Subsequently, detailed stepby-step procedures, based on code requirements, are then outlined for the major devices categories as discussed in Chapter 4. It is important to note that code Damping Technologies for Tall Buildings. DOI: https://doi.org/10.1016/B978-0-12-815963-7.00005-1 Copyright © 2019 Council on Tall Buildings and Urban Habitat (CTBUH). Published by Elsevier Inc. All rights reserved.

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prescriptive procedures are not available for all devices, such as mass dampers (i.e., tuned mass dampers (TMDs), tuned liquid dampers (TLDs), tuned liquid column dampers (TLCDs)). In these cases, an extensive literature review is carried out to summarize alternative noncode prescriptive design procedures.

5.1 AVAILABLE CODES AND DESIGN TOOLS In the following sections, the major codes and guidelines available worldwide for the design of structures with dynamic modification devices are reviewed. In most of the cases, these were not written exclusively for tall buildings. For this reason, when reviewing the step-by-step procedures, in addition to code-based prescriptive procedures (where available), relevant literature is reviewed.

5.1.1 CODES AND GUIDELINES Despite the large variety of research and applications of dynamic modification technology for the seismic design, wind design, and rehabilitation of buildings, not many guidelines have been developed. In reality, most guidelines appear to focus on providing simple recommendations for testing procedures of devices, without any specification for their design. The European code (Eurocode 8 (CEN, 2003)), Italian standards (NTC, 2008), Japanese building code (BCJ, 2013; JSSI, 2003, 2005, 2007), and New Zealand standards (NZS, 2006) provide basic recommendations for structures with added damping, but have no specific recommendations for practitioners. In contrast, in the United States, there are guidelines available for both new (ASCE 7-16 (ASCE, 2017a)) and existing buildings (ASCE41-17 (ASCE, 2017b)). For these reasons, and for most devices, the requirements from US guidelines are utilized as the basis for the design of structures with dynamic modification devices, as will be shown later.

5.1.1.1 European code Eurocode treats dynamic modification system only in the seismic portion (CEN, 2003). In particular, in Part 1 (CEN, 2003), the requirements for base-isolated structures as a means to protect buildings against earthquake actions are discussed. Other types of dynamic modification system are not treated even if they are allowed in Part 3 (CEN, 2003) for the seismic rehabilitation and retrofit of buildings. The code allows to use different types of isolation devices, such as elastomeric bearings and friction pendulum bearings, as long as they are capable of providing one of the following functions (or a combination of them): • • • •

Sustaining vertical loads with high vertical and low horizontal stiffness, allowing large horizontal displacements Energy dissipation through hysteretic and/or viscous mechanisms System recentering Restraining lateral movement for service conditions (not seismic)

5.1 Available Codes and Design Tools

In addition, CEN (2003) provides several general design recommendations, such as: • •

• • •

•

Only the isolation system may reach the ultimate capacity while the structure above and below has to remain elastic at all times. The isolation system should be positioned such that its center of rigidity should be in proximity to the center of rigidity of the structure, above the isolation system itself. A rigid diaphragm shall be provided below and above the isolation interface. No part of the isolation system shall be in tension. Increased reliability is required when isolation devices are utilized. For this reason, an amplification factor of the seismic design displacement is considered. Restrictions are also placed on the soil and the differential movements of the surrounding systems.

For the modeling and analysis of structures with isolation systems, the code (CEN, 2003) emphasizes the importance of estimating and modeling the property variation during the life span of the devices, with a maximum variation of 20%, which is considered acceptable. For these reasons, isolators should be modeled with appropriate constitutive properties. However, a simplified linear model can be utilized when the following requirements are satisfied: • • • •

The equivalent stiffness of the system is greater than 50% of the secant stiffness at 20% of the design displacement. The equivalent total viscous damping is less than 30%. The force
displacement characteristics of the isolation system have a variation less than 10% of the design values for a range of around 30%. The increase in the restoring force between 50% and 100% of the design displacement is not less than 2.5% of the total gravity load on the isolation system.

If these requirements are satisfied, the isolation system can be modeled with an equivalent stiffness at the design displacement, for the considered limit states (of the base-isolated building) into account the dissipation energy of the devices. For higher modes, no additional supplemental viscous damping shall be included. In case both stiffness and damping are highly dependent on the design displacement, an iterative procedure should be carried out until a difference of 5% between assumed and calculated damping is reached. The type of analysis permitted for structures with isolation devices depends on the satisfaction of the following criteria: •

Static linear analysis is allowed when the following conditions are satisfied: • Isolation system can be linearly modeled. • Isolated structure equivalent period is in between 3 times the fixed-base building period and 3 seconds.

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•

•

Vertical stiffness is greater than 800 times the horizontal stiffness of the isolation system. • Vertical period is less than 0.1 second. • There is no tension in any of the isolation devices. • The structural system is regular. • Height of the structure above the isolation system is less than 20 m or 5 floors. • Structure below the isolation can be considered rigid, if the period is less than 0.05 second. • Major plan dimension is less than 50 m. • Eccentricity shall be less than 3% in any direction. If all of these requirements are satisfied, two models can be developed: one for the superstructure and one for the substructure. Dynamic linear analysis is allowed when the isolation system can be modeled as a linear system subject to the requirement that follows: • The model shall consider both the substructure and the superstructure unless the substructure is just the foundation system. • Response-spectrum (RSA) or response-history analyses (RHA) can be utilized. For RSA a bidirectional combination shall be utilized and the vertical component is required when the vertical stiffness is less than 800 times the horizontal stiffness of the isolation system. The spectrum can be reduced based on the total damping. For the RHA the total damping shall be defined for each mode, when a modal decomposition approach is utilized, or through modifying the damping matrix.

As can be seen the requirements for utilizing static linear analysis exclude the possibility of applying it to tall buildings. Therefore, for tall buildings, only the dynamic linear analyses or nonlinear analyses (both static and dynamic) can be utilized.

5.1.1.2 Italian code The Italian building code, called NTC (2008) (“Nuove Norme Tecniche”), does not give specific design criteria for dynamic modification systems, but Section 7.10 provides some general guidelines for the design of isolation systems positioned underneath the main building. These guidelines follow the same requirements as Eurocode 8 (CEN, 2003) as reviewed in the previous section.

5.1.1.3 Japanese code The Japanese Building Standard Law (BSL) (BCJ, 2013) provides some general guidelines for added damping systems and relative calculations based on energy balance theory (see Chapters 3 and 4). The main concept is that dissipation devices should absorb enough energy to not to reach the main structural damage limit state. However, the Japan Society of Seismic Isolation (JSSI, 2003, 2005, 2007) proposed simplified procedures for four different damper types (Fig. 4.1 (Kasai et al., 2008)) and nine different frame configurations (Fig. 5.1 (Symans et al., 2008)). The proposed analyses consider the building being modeled as a multiple

5.1 Available Codes and Design Tools

FIGURE 5.1 Possible JSSI frame configurations. Adapted from Kasai, K., Kibayashi, M., 2004. JSSI manual for building passive control technology part-1 manual contents and design/analysis methods. In: 13th World Conference on Earthquake Engineering, Vancouver, BC, Canada, August 1 6, 2004 Paper No. 2989.

FIGURE 5.2 MDOF shear beam model for flexural behavior.

degree-of-freedom (MDOF) stick frame system, which allows it to also be utilized if significant flexural behavior is present in the building (Fig. 5.2 (Kasai et al., 2008)). Structures equipped with these dissipative devices can be idealized at each story, according to JSSI (2003, 2005, 2007), with an equivalent single

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FIGURE 5.3 SDOF-added component models.

degree-of-freedom (SDOF) system (Fig. 5.2) consisting of damper, supporting member (e.g., brace), and frame. The damper and relative supporting members are called the “added components” (Kasai and Kibayashi, 2004). Fig. 5.3 shows the model for four different dampers: steel, viscoelastic, and viscous/oil. The models are composed of a spring with stiffness (K), dashpot, and viscous coefficient (C). Furthermore, the subcaption b refers to the brace and d to the damper. All the models have elements in series except the viscoelastic device, where the damper stiffness and viscous parts are in parallel. The elastic stiffnesses of the oil and that of the viscous dampers are due to the compressive modulus of the oil and viscous liquid, respectively. In these cases, the equivalent brace stiffness is given by adding the brace and damper stiffness. The only different case is the steel damper, where a unique stiffness is defined. It is important to note that the Japanese code states the importance of modeling the frequency dependency of the viscoelastic properties. JSSI (Kasai and Kibayashi, 2004) also provides recommendations for the hysteretic characteristics of each device for the peak deformations of the damper, the added component, and the whole system (Fig. 5.4). From the hysteresis loop, it is 0 00 possible to compute the storage (K ) and loss (K ) stiffnesses computed by dividing peak force by the corresponding displacement (black dot) and zero displacement force (white dot) to the peak displacement, respectively. The response and design of structures equipped with these devices have been simplified by JSSI (2003, 2005, 2007) by proposing performance curves (Fig. 5.5 (Kasai and Kibayashi, 2004)). These are a continuous function of an SDOF system based on damper properties, storage, and loss stiffness for an idealized response spectrum. The curves show both the displacement (Rd ) and the force (acceleration) reduction ratio (Ra ), defined as ratio between the peak responses with and without damper. In Fig. 5.5, Kf is the frame stiffness, μ is the ductility 00 of the steel damper, and Kd1 is the damper loss stiffness. The curves show how, up to a certain point, larger dampers lead to more reduction, at which point

FIGURE 5.4 JSSI dampers hysteretic properties for three different peak deformations. Adapted from Kasai, K., Kibayashi, M., 2004. JSSI manual for building passive control technology part-1 manual contents and design/analysis methods. In: 13th World Conference on Earthquake Engineering, Vancouver, BC, Canada, August 1
6, 2004 Paper No. 2989.

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FIGURE 5.5 Performance curves for four different damper types. Adapted from Kasai, K., Kibayashi, M., 2004. JSSI manual for building passive control technology part-1 manual contents and design/analysis methods. In: 13th World Conference on Earthquake Engineering, Vancouver, BC, Canada, August 1
6, 2004 Paper No. 2989.

they become no longer beneficial. Moreover, when a brace has low stiffness and large damper forces, the energy dissipation becomes smaller. Based on the performance curves, as shown in Fig. 5.5, dampers can be designed as an SDOF system. This can be extended to multistory systems, in case the story-to-damper stiffness ratio satisfies the SDOF system model. This should be obtained by considering 80% of the total mass of the building and the effective height is based on the first mode deflected shape. Kasai and Kibayashi (2004) show a design step-by-step procedure as shown in Fig. 5.6. It is important to note that design validation should be carried out through time-history analyses with modeling of damper devices (Kasai and Kibayashi, 2004).

5.1 Available Codes and Design Tools

FIGURE 5.6 Damper and system design procedure. Adapted from Kasai, K., Kibayashi, M., 2004. JSSI manual for building passive control technology part-1 manual contents and design/analysis methods. In: 13th World Conference on Earthquake Engineering, Vancouver, BC, Canada, August 1
6, 2004 Paper No. 2989.

5.1.1.4 Chinese code The Chinese seismic code, GB 50011 (GB50011, 2010), provides design recommendations for seismic isolation and seismic energy
dissipating systems, in Chapters 3.8 and 12, respectively. Isolation systems are permitted for multistory masonry and reinforced concrete (RC) frame buildings, if the following requirements are satisfied: • • • •

Regular structures can be designed according to provision of Section 5.1.2 of GB 50011 (GB50011, 2010). Irregular structures adopting seismic isolation need to be verified by model tests. Nonseismic lateral action shall not be greater than 10% of the total structural weight. Components of the seismic-isolated story have enough stiffness and damping to avoid interrupting any mechanical equipment.

Energy dissipation systems are permitted for steel and RC structures. These systems must provide sufficient damping and shall be designed per the provisions for each structural type. Moreover, these systems can be utilized for the buildings having special performance requirements or with a seismic intensity between 8 (20:2=0:3 g) and 9 (0.40 g).

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The following is a brief overview of the requirements for both seismicisolation and energy dissipation systems. It is important to note that GB50111 (2010) requires to carry out performance-based design (PBD) for structures equipped with both damper and isolation systems according to the requirements for seismic performance objectives (POs) (as reviewed in Chapter 3).

5.1.1.4.1 Base-isolated buildings The code defines as isolation stories where isolators and related elements are positioned in within the structure. The general requirements for the design of these systems are as follows: •

A shear-type model can be utilized for the structure above the isolation system. Time-history analyses shall be performed with near-fault input accelerations, and in case near-field accelerograms are not available, the analyses shall be performed with standard acceleration with the following multiplication factors: 1.5 when the site is located within 5 km from the fault and 1.25 when the site is located beyond 5 km from the fault. In the case of masonry structures, a simplified procedure can be utilized [Appendix L of GB50011 (2010)].

•

•

The provisions allow the use of rubber isolator units with the following requirements: •

The ultimate displacement, under the compression stress limits given in Table 5.1, shall not exceed the maximum of either 0.55 times the effective diameter or 3 times the total rubber isolator thickness. In case the secondary form factor (ratio of the diameter and the total rubber thickness) of the isolator unit is less than five, the stress limits shall be reduced as follows: by 20% if between four and five, and by 40% if between three and four. Moreover, in case the outer diameter of the isolator unit is less than 300 mm, a stress limit of 12 MPa shall be used for Category C. The isolator property variation shall not be greater than 20% of the nominal properties, and creep shall not exceed 5% of the total thickness.

•

Table 5.1 Compression Stress Limits of Rubber Isolator (GB50011, 2010) Building Category

Aa

Bb

Cc

Compression stress limit (MPa)

10

12

15

a

Major buildings that are not damaged during an earthquake event. Functional buildings that could be slightly damaged during an earthquake event. c Buildings that are not part of A and B. b

5.1 Available Codes and Design Tools

In addition to what is stated earlier, the isolator units shall meet the following additional requirements: •

•

Under rare earthquake occurrence, the isolation plane shall be stable and should not have permanent deformations. Moreover, the isolation units should not have any tension load. This is particularly difficult to be achieved for high-rise buildings; see Chapter 4 for same example applications. The stiffness (kd ) and damping (ζ d ) of the isolation plane can be computed as follows: X kd 5 kdi P kdi ζ di ζd 5 kd

•

•

(5.1) (5.2)

where kdi and ζ di are, respectively, the stiffness and equivalent viscous damping of the ith isolator unit that should be determined by testing. Horizontal stiffness shall be based on the shear force considered for rarely occurring earthquakes (2%
3% probability of exceeding the force within 50 years, as defined in GB-50011 (GB50011, 2010)). Torsional stiffness shall be taken into consideration in case torsional effects are present. The displacement of the ith isolator unit (udi ), under rare earthquake occurrence, should be limited as follows: udi 5 Ati udc # u i

(5.3)

where udc is the center of the isolation story displacement without torsion included, Ati is the ith isolator unit torsion factor (in the case of no torsion, a minimum torsion factor of 1.15 shall be used), u i is the displacement limit computed by the minimum between 0.55 times the effective diameter and 3 times the total thickness.

5.1.1.4.2 Buildings with energy dissipation devices GB 50011 (GB50011, 2010) allows two different types of devices: displacementdependent (metallic, friction, etc.) and velocity-dependent devices (viscous, viscoelastic, etc.). The following provisions are provided in the code: • • • •

•

Devices shall be provided at the story where the drifts are significant. Linear and nonlinear analyses can be utilized depending on the behavior of the energy dissipated system. A limiting value of 1=80 is required for the elasto-plastic interstory drift ratio. The device supplemental damping ratio can be estimated from the ratio between dissipated and potential energy as was shown in Eq. (3.60). The dissipated energy, for each device, can be computed similarly to what was shown in Chapter 4 and the potential energy as was shown in Eq. (3.61). The maximum supplemental damping is 20%.

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5.1.1.5 New Zealand code The New Zealand Concrete Structure Standard (NZS, 2006) provides simple guidelines for the seismic design of concrete structures equipped with added damping devices when utilized in base-isolated systems, which can also be applied to other structural systems. The standard states that the major advantages from inserting added damping devices as part of a base isolation approach can be gained in stiff structures rigidly connected to the ground (e.g., low-rise buildings or nuclear power plants). These devices are permitted if, at the ultimate limit states (ULS), the following requirements are satisfied: • • •

Device performance is supported by testing. Protection against the yielding of structural members is the same as the one considered for building without dissipation devices. Structural details allow the control of the deformation for demands greater than the design demands.

The design of the dissipation and main structural members should consider three earthquake intensity levels (and associated limit states): •

•

•

Moderate: the source of energy dissipation should be only from damping devices, that is, no damage to the structural members. This is considered a serviceability limit state (SLS). Design: the structural members could yield and typical standard design procedures (i.e., for structures without dampers) should apply, even if the structural system is subject to lower ductility demand as a result of the utilization of the dissipation devices. This is considered an ULS. Extreme: capacity design principles should be applied in order to prevent brittle failures and collapses. This is considered an extreme limit state.

The NZ standard (NZS, 2006) additionally suggests undertaking nonlinear time-history analyses (NLTHAs) for design purposes, since the knowledge and the experience in utilizing these systems are not well developed or established.

5.1.1.6 US codes In North America, the first attempt to apply a code to the design of structure with dissipation devices was undertaken in 1993 (Whittaker et al., 1991) by the Energy Dissipation Working Group (EDWG) of the Base-Isolation Subcommittee of the Structural Engineers Association of Northern California (SEAONC). Subsequently, in FEMA 222A (FEMA, 1994), NEHRP provided an appendix (not considered a code (Hanson and Miyamoto, 2002)) by introducing the utilization of these new techniques. The idea was to utilize an equivalent viscous damping approach with NLTHAs, when nonlinear velocity proportional devices were utilized. The first technical guideline available was Chapter 9 of FEMA 273 (FEMA, 1997a). This guideline was immediately superseded by the appendix to Chapter 13 of FEMA 302 (FEMA, 1997b). In this appendix, only general guidelines were provided.

5.1 Available Codes and Design Tools

A deeper insight in the utilization and design of energy dissipation devices were then provided in FEMA 356 (FEMA, 2000) and FEMA 450 (FEMA, 2003) (formerly FEMA 368 (FEMA, 2001)). These standards were a joint effort between ASCE and FEMA. The first document (FEMA, 2000) refers to the assessment of existing structures and the second (FEMA, 2003) examines the design of new structures. FEMA 450 (FEMA, 2003) was developed by Technical Subcommittee 12 (TS 12) of the Provision Update Committee (PUC). The proposed design philosophy was applicable to different dissipation systems (displacement- and velocity-dependent types). These standards specified the requirements on the type of analyses, design procedures, and testing protocols to utilize in the design process. The requirements of FEMA 450 were then included in ASCE 7-02 (ASCE, 2002) and subsequently in ASCE 7-05 (ASCE, 2005) and ASCE 7-10 (2010). A major revision has been just realized with ASCE 7-16 (ASCE, 2017a). This revision was based on the work conducted by TS 12, ASCE 41 committee members, and the NEHRP committee. The resulting work was based on the ASCE 41-13 (ASCE, 2013) and NEHPR (2015) recommendations and divided into two independent chapters: base isolated structures and structures with damping systems. In regard to existing buildings, TS 12 revised FEMA 356 (FEMA, 2000) in 2006 with ASCE 41-06 (ASCE, 2006) “Seismic Rehabilitation of Existing Buildings,” where guidelines for the seismic rehabilitation of structures with seismic isolation and energy dissipation devices are provided in Chapter 9. A major revision to this guideline was conducted in the 2013 edition of ASCE 41 (ASCE, 2013), where Chapter 13 goes into great detail for both seismic isolation and dissipative devices. The criteria selection between the two systems is based on the POs. Indeed, energy dissipation systems are usually preferred for several reasons: they are more suitable for a wider range of building heights; and they can also control other sources of excitation (like wind or mechanical loads). ASCE 41-13 (ASCE, 2013) also provides the possibility to utilize other control systems (e.g., active and hybrid control, and TMDs) as long as it is reviewed by an independent engineering review panel. However, no requirements for these devices are given. A new version of ASCE 41-17 (ASCE, 2017b) was just realized where, similar to ASCE 7-16 (ASCE, 2017a), base isolation and dissipation devices in two distinct chapters. Based on this historical review, in the proposed step-by-step procedures, the requirements of ASCE 7-16 (ASCE, 2017a), ASCE 41-17 (ASCE, 2017b), and NEHRP (2015) will be explained in detail with the relative design criteria that are the basis for the design of buildings equipped with dynamic modification technologies. These requirements will be applicable only to distributed dampers and base isolation systems, while for the other device categories the available literature will be reviewed for defining a design procedure. In addition, since the scope of this publication is on tall buildings, the requirements of ASCE (2017a) and NEHRP (2015) are integrated with the PEER/TBI (2017) and PEER/ATC (2010) guidelines that specify requirements for the performance-based seismic design (PBSD) of tall buildings.

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5.1.2 PRACTICAL DESIGN ASPECTS The design of tall buildings with additional dissipation devices requires the interaction of a number of professionals (wind tunnel laboratory, geotechnical engineer, damper manufacturer, owner, and architect), under the supervision of the structural designer. The professionals involved in the design process have different responsibilities from the characterization of the loads (wind, earthquake, vibrations), by means of numerical analyses or experimental activities, to the finalized design of the damping devices and the experimental characterization of all the mechanical components of the devices themselves and their behavior. During the structural analysis phase, specific assumptions are made by the structural engineer regarding the applied loads, the structural system, the boundary conditions, and the features of the damping devices; all of these modeling aspects, affecting the predictions of numerical analyses, are predefined and agreed upon together with the other professionals. Nevertheless, damping device characterization commonly requires an interactive process, involving different rounds of analyses with different sets of parameters. For this reason, it is important that wind tunnel tests, or the other analyses providing an estimate of the seismic action or vibration, shall be carried out in early stages in a way that they can provide reliable bases to modify the intensity of the external actions as a function of the considered return period and of the expected global damping. In fact, it is not uncommon for wind tunnel tests or seismic characterization studies to be carried out and completed well before the mechanical design of the damper is actually started, as an extensive interaction between the different professionals (i.e., climate and wind engineers, structural engineers, and manufacturers) is not always possible. In this scenario, the structural designer needs to make sure that, in the wind testing phase, the collected data provide tools for a robust evaluation of the relationship between the total damping ratio of the structure with additional devices (ζ T ) and the damping constant of the device (Cd ). Therefore, further interactions between the structural designer and the manufacturer can lead, in the following phase, to the finalized mechanical design of the devices.

5.1.2.1 Damper system from concept to production process Damping system installation in buildings is a straightforward process. Involvement of each stakeholder is necessary at the earliest design stage possible to understand the system as a whole. Strong interaction among the stakeholders plays a vital role in the success of the project. As soon as the building owner assigns an architect to design a building, architects must first consider whether this building will be built in a seismic and/or wind-prone area. This information will determine the shape and the dimension of building. They must also have general view of damping systems available in the market, so they can incorporate the appropriate system (if necessary) into their initial building design. Architects can seek advice from structural designers about what kind of damping system is suitable for their design. Both architects and

5.1 Available Codes and Design Tools

structural designers also need to give an explanation to the building owner about the importance of damping systems in a building to prevent unnecessary loss or damage. Building owners and architects must lead this crucial design stage. Certain aspects must be approved at the beginning of the design phase, such as additional cost, damper size, and location. The building owner can also assign other structural design firms to provide peer-review activities. Structural designers must gather as much information as possible from different damper manufacturers and check their track record and referral projects. Damper manufacturers need to provide their product specifications and required design parameters to the structural designer. Design assistance support by manufacturers will also help to verify good design practice for the structural designers. A detailed product specification is prepared based on good practice and international standards. However, the accuracy of input data is also very important. Correct measurement from wind laboratories, based on the proper model scale, will determine the quality of data. Site measurement will be required in order to understand the landscape and topography. This data will be a governing tool to make the decision on what type of damping system to use. Once the damping system is approved, it must be clearly specified through design drawings and tender documents, including a list of approved damper manufacturers. After tender approval by the owner, the damper is ready to be manufactured and shop drawings can be produced. These shop drawings will need to be checked thoroughly by the structural designer and building owner. Then, the damper is fabricated by the manufacturer. External supervision is necessary during this process to avoid any delay in schedule or defect in the product. Prototype and/or fabrication testing is done to check the accuracy and reliability before final delivery to site. Standard testing by an independent laboratory is also required to ensure the quality of the product (see Chapter 7 for more details about testing requirements for damping devices). During the construction stage, the contractor and structural designer must ensure that the damper installation follows the design assumptions. Installation must follow the standard procedure or method statement. On-site supervision is important in this case to minimize any mistakes in the installation and ensure optimal results. Final in situ measurements are recorded after installation to check the effectiveness of the damping system. See Chapter 7 for more details about inspection requirements.

5.1.2.2 Process of wind design and occupant comfort process Particularly for tall and slender buildings, occupant comfort (in the form of lateral accelerations) during wind events often controls the design of the lateral force
resisting system. The essential building characteristics under the control of the design team that affect a building’s response to wind include stiffness, mass, shape, and damping. The susceptibility of a building to experience large lateral accelerations may or may not be apparent to the structural engineer at the onset of the schematic

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design. Buildings with high height
width aspect ratios can be particularly challenging. For very slender buildings, it is often useful to engage the services of a wind tunnel laboratory during the schematic design phase. Performing an initial wind tunnel test can provide important information that can impact the design of the key elements during the schematic phase (e.g., the extent, location and size of the lateral force
resisting system components, the overall height of the building, or the shape of the tower). More often, with less challenging buildings, wind tunnel testing takes place during the design development phase, after the overall geometry of the building is set. However, stiffness, mass, and damping can still be adjusted to affect the building’s response. When performing either a high-frequency force balance study or a pressure integration study to determine the building response, the structural engineer will provide the wind tunnel laboratory with the building periods, in addition to the following properties for each floor of the building: • • • • •

Structural mode shapes Mass Location of the center of mass Mass moment of inertia Assumed level of intrinsic damping

The wind tunnel testing will yield results for equivalent static forces on a floor-by-floor basis, in addition to overall base shears and moments. Moreover, it is quite useful to produce spectra of along-wind and across-wind accelerations based on building period. The structural engineer will evaluate the results and iterate the process with the wind tunnel lab as necessary. During this process, a determination will be made as to whether a supplementary damping system needs to be incorporated into the design. Often, but not always, isolated damping systems are employed to mitigate wind effects. In such cases, the damper designer, and sometimes the wind tunnel lab, will be responsible for designing a system to provide the appropriate level of damping. From this point forward, the structural engineer merely has to keep the damper design apprised of any changes to the building dynamic properties as the design process moves toward completion.

5.1.2.3 Process of seismic design and strength requirements Whereas damping is generally considered in regard to serviceability issues, when designing for wind, damping affects strength requirements in seismic design. Obviously, based on the specific seismic demands, a building structure can be benefited greatly from higher levels of total damping. When the following prescriptive code approaches for the structural design, intrinsic levels of damping are built in to the code requirements (e.g., 2.5% ((ASCE 7-16 (ASCE, 2017a))), 3% (NEHRP, 2015)), as discussed in Section 3.2.

5.1 Available Codes and Design Tools

In cases where a PBD approach (PEER/TBI, 2017) is implemented using a supplementary damping system, the structural engineer must work together with the geotechnical engineer and damper manufacturer to develop the final design. A site-specific response spectrum may be developed, based on a range of total damping levels by the geotechnical engineer. The structural engineer can evaluate the lateral force
resisting system via modal response analysis for varied levels of seismic demand to understand the relative value of total damping. The geotechnical engineer will generally develop site-specific time-history ground motions to be incorporated in the structural engineer’s time-history analysis. A damper manufacturer can provide characteristics of specific damping elements to be incorporated into the analysis. While coordinating with the damper manufacturer, the structural engineer must iterate through his analysis to hone in on the specific characteristics required for the damping elements.

5.1.2.4 Properties of damping devices In order to correctly identify the basic parameters of damping devices, it is important to gather the best possible knowledge of the structural system and of all the factors affecting the efficiency of the dampers, such as construction tolerances, friction, additional stiffness, and temperature effects (see Section 5.1.3.3.3). The parameters used to define the constitutive law of dampers need to be specified and experimentally validated for different operational conditions, temperature ranges, and frequencies of excitation. In the case of dampers under wind loads, due to the nature of the load, all of the specifications for the materials used in manufacturing must be calibrated to take into account fatigue and deterioration issues. The service life of the device is specified and guaranteed by continuous monitoring and/or periodic inspection and maintenance; the maintenance plan is generally drafted by the manufacturer with the supervision of the structural designer (see Chapter 7 for further details).

5.1.3 STRUCTURAL ANALYSES Dynamic modification systems are holistic devices or systems, which serve to improve the performance of structures as a whole under dynamic excitation. By virtue of their height, tall buildings experience dynamic excitation caused by structure
wind interaction. Similarly, in geographic regions with relatively high seismicity, tall buildings are probably at risk of experiencing dynamic base excitation caused by intense ground shaking created by seismic events (earthquakes). Due to both of the aforementioned excitations, the response of the structure is primarily a function of mechanical properties unique to each building, such as natural frequencies, stiffness, mass, and damping. Input excitations themselves are functions of geometric profile/orientation, surface roughness, and geographic location (wind profile and seismicity), and act primarily in a lateral direction (parallel to the building’s floors).

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Consequently, an analytical framework, which approximates both the threedimensional (3D) dynamic properties of the structure and its site-specific loading history, must be employed when evaluating the implementation of dynamic modification systems. Commonly, this framework requires collaboration between different engineering consultants and is, by nature, iterative.

5.1.3.1 Computational structural analysis modeling Tall building systems inherently contain a large number of individual components acting together to form a lateral load
resisting system, which acts in opposition to dynamic excitation and loads created by wind and earthquakes. Taller buildings often have multiple lateral load
resisting typologies combined in a way to maximize lateral stiffness by engaging the individual stiffness of many structural members. Finite element analysis (FEA) techniques are well suited to determine the global, 3D, dynamic properties created by assemblies of large numbers of structural elements. Many modern commercial FEA software packages, specifically tailored to building analysis, exist and implement a variety of common analysis techniques/methodologies. Inherently, structural analysis models are mathematical approximations of the expected behavior of a physical system over time. Since buildings experience a complex loading history over their design life, the engineer must ensure that boundary condition sensitivity changes in system stiffness due to loading magnitude/displacement amplitude, material nonlinearity, and material property variability are accounted for. Therefore, the idea to bound the structural system’s response through multiple model runs should be employed. It is crucial that the engineer recognizes the approximate and iterative nature of structural analysis/modeling and, therefore, avoids attempting to capture complex behavior in one pass.

5.1.3.2 Analysis type The structural systems employed in tall buildings require the engineer to create multiple models when evaluating the performance of the structure. Different levels of analytical rigors are appropriate at different stages in the design process and models tend to evolve as design progresses and the structural system is refined. Common analytical methods (linear and nonlinear) are described in the following sections, in order of increasing rigor/complexity.

5.1.3.2.1 Linear analysis methods Linear analysis covers a broad range of methods, which use linear elastic material behavior to determine structural dynamic properties and responses. Linear analysis can be conducted using force-based approaches, such as linear static analysis and linear dynamic analysis (RSA); or it can be conducted using a linear timehistory approach (RHA). According to PEER/TBI (2017), linear analysis (RSA or RHA) is appropriate for service-level earthquake (SLE) evaluation and for design

5.1 Available Codes and Design Tools

earthquake (DE) when required by ASCE 7-16 (2017a). Some considerations for each linear approach are as follows: •

Linear static analysis is a design approach where equivalent static story forces, due to wind or earthquakes, are applied to the structure. The computation of story forces is prescriptive, and formulations for calculating these forces are provided within the applicable building code (Section 5.1.1). Linear static analysis is typically restricted to use in regular structures, where dynamic behavior is dominated by the fundamental mode of vibration, without significant higher modes and torsion effects and in regions of low seismicity. Since tall buildings often exhibit significant higher mode effects and the effects of torsion are important, linear dynamic analysis, instead of linear static analysis, is typically conducted for the seismic design of tall buildings, even in regions of low seismicity. • Linear dynamic analysis methods are based on procedures which employ the concept of modal superposition and are often associated with seismic design. Many building codes employ prescriptive provisions for modal RSA, where design acceleration response spectra are used to computate the peak linear response for each mode of vibration (Section 5.1.1). Peak modal responses are then statically combined (with a complete quadratic combination (CQC) method (PEER/TBI, 2017)) to generate the overall response of the structure. For wind-governed tall buildings, equivalent static wind forces provided by the wind consultant are often used in conjunction with linear dynamic/modal RSA for earthquakes. The structural engineer is not directly performing linear dynamic analysis for wind effects within their computation model, because the wind consultant creates the response spectra upon which the static loading provided is determined. A force spectrum using wind tunnel test data is used in conjunction with dynamic properties provided by the structural engineer to create wind response spectra in frequency domain, which are then used to create equivalent static loading and the associated load combination factors for x-sway, y-sway, and torsion. • Linear time-history analysis methods determine the structural response using inputs which vary with time. Acceleration versus time input signals can be applied to above-grade stories for determining response under wind loading, and base excitation accelerograms (earthquake records) can be used for determining response under seismic ground motion. Linear time-history analysis is typically conducted using modal analysis methods; whereas NLTHA can be conducted using fast nonlinear analysis (FNA, also called a modal method) or using direct-integration (DI) time-history analysis (as discussed in Section 5.1.3.2.3). Linear methods for dynamic modification systems. When force-based approaches, such as linear static or linear dynamic analysis, are used, it is helpful to think of results as a snapshot in time corresponding to a certain moment in the building’s loading history. Commonly, linear analysis is used to determine the

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baseline building properties provided to the wind consultant for use in motion assessment and to determine the equivalent static forces used for the calculation of interstory drift and other serviceability criteria. When motion-activated devices, such as TMD or tuned sloshing dampers, are employed, linear dynamic analysis is often utilized throughout the design process, with material properties varied when assessing the supplemental damping system’s performance. This approach is reasonable because motion-activated devices are most commonly employed to control accelerations resulting from dynamic wind interaction with the structure and are typically not used to improve seismic response. In regions of low seismicity, tall structures are designed to remain essentially elastic under service-level wind loading when compared to the much larger inelastic behavior observed under intense ground shaking due to earthquakes (in areas of high seismicity) and, therefore, a bounded linear dynamic analysis with appropriate assumptions/empirical parameters could be employed. In this scenario, modal RSA or linear time-history analysis for seismic design would generally follow code prescriptive methodology and would not account for any supplemental damping effects created under the ground motions. Although supplemental damping effect created by the device would not be used to improve response, its additional mass must be considered when determining seismic forces and building frequencies. Similarly, some displacement- or velocity-activated supplemental damping systems may be modeled using linear methods, provided that their behavior can be adequately captured using linear links (springs and dashpots). Whether linear or nonlinear analysis is used, damper link formations should be based on full-scale testing conducted by the damper manufacturer and must be carefully integrated into structural analysis models to ensure the link formulations are validated for the range of frequencies, displacements, and temperatures being investigated. If supplemental damping is ignored for earthquake response (i.e., wind serviceability only), the stiffness of the links must still be considered when determining seismic forces and building frequencies. It should be noted that when displacement- or velocity-activated distributed damping systems are approximated using linear analysis, supplemental damping produced is typically smeared over the entire model and equivalent modal damping is reported (for Eigen analysis to be employed, see the different step-bystep procedures as described in the later sections). When linear analysis methods are used, it is critical that appropriate effective element stiffness is considered for particular bounds, since, for example, concrete cracking, structural steel connection fixity, and foundation
soil interaction are not varied during a given model solution. Empirical stiffness modifiers are typically used to account for material nonlinear behavior for each analysis. The codes (e.g., ASCE, 2017a; PEER/ATC, 2010; AISC, 2016a; PEER/TBI, 2017; CSA, 2014) usually propose property modifiers for both material strength and effective stiffness, depending on the criteria the building needs to be designed for. Material strength shall be based on project-specific data. When these are not available, it is permissible to use expected properties instead of nominal or

5.1 Available Codes and Design Tools

Table 5.2 Expected Material Strengths (PEER/TBI, 2017) Material

Expected Yield Strength

Expected Ultimate Strength

482 MPa 565 MPa 476 MPa 586 MPa 1.1
1.5 fya

731 MPa 786 MPa 655 MPa 772 MPa 1.1
1.2 fua

Reinforcing Steel A615 Grade 60 A615 Grade 75 A706 Grade 60 A706 Grade 80 Structural Steel Concrete

1.3 fc

a

For structural steel the expected strength factors are different depending on the type of steel section utilized (i.e., hot rolled structural shapes and bars, hollow structural sections, steep pipe, and plates).

specified properties (see Table 5.2 for an example valid for US material (PEER/ TBI, 2017)). However, for evaluation and retrofit design of existing buildings, ASCE 41-13 (ASCE, 2013) specifies lower bound properties ( nominal properties) in force-based checks of elements that are prone to experiencing nonductile behavior, whereas it requires the use of “expected strength” when the element is expected to experience ductile behavior. Material stiffness shall take into account the effects of axial, flexural, and shear cracking. For steel members the elastic stiffness is determined by the full cross-sectional properties and the elastic modulus of steel (200,000 MPa) (PEER/ TBI, 2017). However, concrete member stiffness can be estimated with effective values as given in Table 5.3 (ASCE, 2017a), in Table 5.4 (PEER/TBI, 2017), and Table 5.5 (CSA, 2014), in lieu of detailed analysis. As it can be seen in the tables multipliers are less than one in most of the cases since they represent the effective linear branch of the inelastic model (PEER/TBI, 2017). In the tables, EC is the concrete elastic modulus; Ig is the cross-sectional gross moment of inertia; Aw is the cross-sectional web nominal area; and Ag is the cross-sectional gross area.

5.1.3.2.2 Nonlinear analysis methods Nonlinear analysis is a broad category of methods which use nonlinear material behavior (as well as geometrical) to determine the structural response. Depending on the specifics of a particular project, the level of detail of a nonlinear analysis can vary significantly. Where nonlinear analysis is used, it is common practice to begin analytical work with simpler linear models to establish baseline dynamic properties and global structural response. Understanding the basic system parameters and behavior will allow for informed decision making for what level of nonlinear analysis is warranted. As mentioned, modeling practices should be viewed as an evolution in rigor and detail. Multiple models with increasing levels of nonlinearity are typically employed until sufficient convergence is achieved.

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Table 5.3 Effective Stiffnesses of RC Structural Elements (for DE and MCER Demands) According to ASCE 41-17 (ASCE, 2017b) Component

Flexural Rigidity

Shear Rigidity

Axial Rigidity

Beams (nonprestressed)a Beams (prestressed)a Columnsb with compression 0 under gravity load $ 0:5Ag fc b Columns with compression 0 under gravity load # 0:1Ag fc or with tension

0:3Ec Ig Ec Ig 0:7Ec Ig

0:4Ec AW 0:4Ec AW 0:4Ec Aw



Ec Ag

0:3Ec Ig

0:4Ec Aw

Walls (cracked)

0:5Ec Ig

0:4Ec Aw

0:4Ec Ag

Ec Ag (compression) Es As (tension) Ec Ag (compression) Es As (tension) Ec Ag

0:4Ec Ag

Ec Ag

Flat slabs (nonprestressed) Flat slabs (prestressed)



   4c1 =l1 Ec Ig $ 1=3 Ec Ig

0:5Ec Ig

Note: c1 is size of the equivalent column in the direction of the span. l1 is the length of the slab in the direction of the seismic force. a For T-beams, Ig can be taken as twice the value of Ig of the web alone. For coupling beams in coupled shear walls, the effective stiffness values given for nonprestressed beams should be considered, unless alternative stiffness is determined by more detailed analysis (ASCE 41-17 (ASCE, 2017b)). b For columns with axial compression falling between the limits provided, flexural rigidity should be determined by linear interpolation. If interpolation is not performed, the more conservative effective stiffness should be used.

Note that this section is limited to discussion of the use of nonlinear elements for modeling components of the dynamic modification system itself. These nonlinear elements can be used in conjunction with an approximation of the main building structure which uses elastic elements. Bounding material properties of both the supplemental damping system and the main building structure to account for nonlinear behavior is an effective technique to integrate a dynamic modification system in structural engineering design. However, more advanced analysis can be undertaken where the main building structure is modeled using nonlinear elements. Nonlinear modeling of the total system, particularly for concrete structures, is very complex and is outside the scope of this book. Many of the seismic references cited in this publication offer limited guidance on how to appropriately undertake these analyses. Moreover, it is important to note that whenever undertaking comprehensive nonlinear analysis of the total building system, peer review should be undertaken. When displacement- or velocity-activated supplemental damping systems, such as metallic dampers, friction dampers, viscous damping devices, and viscoelastic damping devices, or base isolation are employed, nonlinear analysis is often utilized because it can capture the behavior of dampers modeled using link elements. Moreover, two common nonlinear time-history methodologies can be utilized: FNA and DI analysis. FNA is more commonly employed when modeling

Table 5.4 Effective Stiffnesses of RC Structural Elements According to PEER/TBI (2017) MCER-Level Nonlinear Models

Service-Level Linear Model Component a

Structural walls (in-plane) Structural walls (out-of-plane) Basement walls (in-plane) Basement walls (out-of-plane) Coupling beams with conventional or diagonal reinforcement Composite steel/reinforced concrete coupling beamsb Non-post-tension (PT) transfer diaphragms (in-plane only) PT transfer diaphragms (in-plane only) Beams Columns Mat (in-plane) Mat (out-of-plane) a

Axial

Flexural

Shear

Axial

Flexural

Shear

1:0Ec Ag
1:0Ec Ag
1:0Ec Ag

0:75Ec Ig 0:25Ec Ig 1:0Ec Ig 0:25Ec Ig  0:07 hl Ec Ig # 0:3Ec Ig

0:4Ec Ag
0:4Ec Ag
0:4Ec Ag

0:75Ec Ag
1:0Ec Ag
1:0Ec Ag

0:35Ec Ig 0:25Ec Ig 0:8Ec Ig 0:25Ec Ig  0:07 hl Ec Ig # 0:3Ec Ig

0:2Ec Ag
0:2Ec Ag
0:4Ec Ag

1:0ðEAÞtrans

0:07

1:0Es Asw

1:0ðEAÞtrans

0:07

0:5Ec Ag

0:5Ec Ig

0:4Ec Ag

0:25Ec Ag

0:25Ec Ig

0:1Ec Ag

0:8Ec Ag 1:0Ec Ag 1:0Ec Ag 0:8Ec Ag


0:8Ec Ig 0:5Ec Ig 0:7Ec Ig 0:8Ec Ig 0:8Ec Ig

0:4Ec Ag 0:4Ec Ag 0:4Ec Ag 0:8Ec Ag


0:5Ec Ag 1:0Ec Ag 1:0Ec Ag 0:5Ec Ag


0:5Ec Ig 0:3Ec Ig 0:7Ec Ig 0:5Ec Ig 0:5Ec Ig

0:2Ec Ag 0:4Ec Ag 0:4Ec Ag 0:5Ec Ag


When modeled as line elements and not as fiber elements. ðEIÞtrans is the cracked trasformed sections.

b

l h

ðEIÞtrans

l h ðEIÞtrans

1:0Es Asw

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Table 5.5 Effective Stiffnesses of RC Structural Elements According to Canadian Standard Association (CSA) A23.3 (CSA, 2004) Ranges for Linear Elastic Analysis Load Type Wind

Component Nondiagonally reinforced coupling beams Diagonally reinforced coupling beams Shear walls Shear walls in net tension Slabs with mild reinforcement Posttensioned slabs Beams (excluding coupling beams) Columns Columns in net tension

Seismic

Beams (excluding coupling beams) Columns (Nondiagonally reinforced) coupling beams (Diagonally reinforced) coupling beams Slab frame element Wall

Serviceability (SLS)

Strength (ULS)

0:50Ig Ave 5 0:40Ag 0:45Ig Ave 5 0:45Ag 0:95Ig Ave 5 0:95Ag

0:40Ig Ave 5 0:25Ag 0:35Ig Ave 5 0:40Ag 0:75Ig Ave 5 0:75Ag

Refined calculation required 0:35Ig 0:60Ig 0:50Ig Ave 5 0:75Ag 1:0Ig Ave 5 1:0Ag

0:20Ig 0:45Ig 0:40Ig Ave 5 0:50Ag 0:70Ig Ave 5 0:70Ag

Refined calculation required 0:40Ig a c Ig 0:40Ig Ave 5 0:15Ag 0:25Ig Ave 5 0:45Ag 0:20Ig aw Ig Axe 5 aw Ag

0:40Ig ac Ig 0:40Ig Ave 5 0:15Ag 0:25Ig Ave 5 0:45Ag 0:20Ig aw Ig Axe 5 aw Ag

Note: From CSA A23.3 (CSA, 2014) Table N9.2.1.2 and Table 21.1.

distributed supplemental damping systems because it is found to be generally more accurate and efficient than DI methods. Additionally, typically only FNA allows for the generation of energy plots which can be used to evaluate the performance/damping generated by link elements. However, if the model has many DOFs and large number of link elements are utilized, DI may be more straightforward and efficient than FNA (this is true if limited number of response-history runs is expected). Moreover, FNA solver do not provide the nonlinear geometry—large displacement option and such effects cannot be studied unless DI methods are utilized.

5.1 Available Codes and Design Tools

When modeling distributed supplemental damping systems, additional modes of vibration need to be considered to capture the damping produced by (nonlinear) link elements. Ritz vectors require much fewer additional modes of vibration to capture link damping than eigenvectors and therefore it is commonly recommended to use them. Further, attempting to use eigenvectors with nonlinear link elements may result in capturing the incomplete or inaccurate behavior since nonlinear analysis does not smear damping globally. Therefore, it is strongly recommended that before undertaking complex structural analysis which integrates the effects of a supplemental damping system, the engineer should thoroughly review the various analytical methods available. When conducting FNA using Ritz vectors, as recommended, an additional mode of vibration must be provided for each nonlinear link used in the model. In general, prior to implementing a model with nonlinear links, the engineer will have run baseline models to determine dynamic properties ignoring the effects of the dynamic modification system. This baseline model should be used to determine the minimum number of modes required to achieve appropriate amount of mass participation (a requirement in many building codes for seismic design). Once the number of modes required to quantify global building behavior is established, additional modes should be included to capture each nonlinear link in the supplemental damping system. Convergence studies should be employed to ensure appropriate number of modes are provided and the hysteretic plots of each link should be reviewed to ensure the links are active in the model. Since FNA does not report lumped equivalent modal damping, log-decrement displacement versus time plots are commonly used to compute supplemental damping. As recommended previously, models should evolve in complexity as the behavior of the system is better understood/refined. For distributed supplement damping systems, linear links with eigenvectors can be used to provide a preliminary (unconservative) upper bound of the supplemental damping provided. When more advanced nonlinear links are used with Ritz vectors, the supplemental damping produced in a distributed system should be marginally lower than predicted using the linear links. Caution: Where the supplemental damping system is not a distributed system, but is rather concentrated in a small number of elements, linear analysis with eigenvectors will not provide realistic preliminary level results and the engineer should begin by using Ritz vectors. Damped outriggers or belt trusses would be an example of such a concentrated system, whereas distributed viscoelastic coupling dampers replacing a significant number of coupling beams is an example of a “distributed” system. Caution: Related with “damping leakage” phenomenon with FNA. This effect produces an overestimation of damping when high values of linear effective are utilized in certain software (Sarlis and Constantinou, 2010). Common computational methods for calculating supplemental damping. Classical linear modal analysis with eigenvectors is a classical modal

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analysis and assumes that the damping provided by the dynamic modification system is proportional to velocity. If the damping matrix can be decoupled using the mode shapes, the mth modal damping coefficient can be obtained by pre- and postmultiplying the damping matrix by the mth mode shape. The damping ratio in the mth mode is obtained as a function of the mth circular frequency and modal mass. Most commercial software packages will report damping values mode by mode numerically in their output files. As noted previously, this technique can overestimate or underestimate the added damping; however, it is accurate if the damping matrix can be decoupled using the mode shapes. It is therefore recommended to be used only for preliminary analysis wherever appropriate (as noted previously). Nonlinear modal analysis with Ritz vectors requires the use of free vibration study, which is produced by a ramp load followed by an instantaneous removal of the load (this is valid for SDOF since for MDOF the shape of load is also important). Structural response output data are used to calculate damping using the logdecrement technique as the average of the ratio of the positive peak and negative peak amplitude of each peak followed by the mth following cycle. It is common to discard the first several damping value estimations because they are typically more variable (since the response get more stable after a couple of cycles). Subsequently, the total damping is taken as the average of remaining damping values. Supplemental damping matrix is determined by subtracting the inherent damping matrix, which is commonly an input parameter in FEA software, from the total computed damping matrix. P-delta analysis. Modern commercial FEA software packages used for the lateral analysis of buildings have features/functions which include P-delta effects. The destabilizing gravity loads shall be considered for P-delta effects over the entire building. In case only the lateral resisting system is modeled, leaning columns shall be considered to provide realistic gravity load distribution (PEER/ATC, 2010; PEER/TBI, 2017).

5.1.3.2.3 Preliminary analyses Although static and dynamic analyses of tall building structural systems can be nowadays be performed with the aid of commercial finite element packages, in early stages of design, it is still a common practice to adopt simplified models. For example, the adoption of continuum models, the so-called replacement beam (RB) models, can help designers to more properly deal with the analysis and preliminary design of building structures. The dominant behavior of tall building structural systems can be captured with clamped (cantilever) RB models (Euler Bernoulli beam (EBB), shear beam, Timoshenko beam, coupled two beams, and sandwich beam (SWB)) by considering the stiffness properties (Fig. 5.7 (Faridani, 2015)). The damping phenomenon can also be studied by means of distributedparameter models (Lavan, 2012; Faridani and Capsoni, 2016a,b). In order to take into account the additional damping, distributed-parameter damping formulations

5.1 Available Codes and Design Tools

FIGURE 5.7 Damper synthesis of the RB idealization process from the 3D model to a 1D model.

have been developed for the EBB frame to approximately analyze shear wall systems including supplementary viscous damping (Lavan, 2012).

5.1.3.3 Boundary conditions and common assumptions When undertaking global structural analyses, it is often necessary to perform sensitivity analysis to bound uncertainty/variability using several different models. The approach of bounding the probable behavior of a structure when approximating it in FEA should also be employed when integrating damper elements in analysis. As structural complexity increases, determining the governing criteria globally and locally becomes increasingly difficult, and it therefore becomes critical to be able to process large volumes of data efficiently. Adopting a framework of automated postprocessing of data allows the engineer to quickly determine the sensitivity of selected variables. The following subsections briefly discuss some potential parameters which commonly require sensitivity analysis/bounding.

5.1.3.3.1 Soil
structure interaction Soil
structure interaction (SSI) is commonly accounted for by a bounded analysis employing several different models. Where floor plan enlarges below grade a virtual outrigger is created by foundation walls engaged laterally by slab diaphragms, and this virtual outrigger action is commonly referred to as the “backstay effect” (PEER/ATC, 2010). Backstay effects are particularly sensitive to diaphragm rigidity and to the surrounding soil interacting with the foundation walls. It is common to run upper and lower bounds of slab diaphragm stiffness to conservatively envelope forces in the diaphragms (collectors), foundation walls, and the tower’s primary lateral load
resisting system as it passes through the below-grade structure.

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Modeling SSI and bounding backstay effects are outside the scope of this book but are thoroughly covered in PEER ATC-72-1 (PEER/ATC, 2010) (Appendix A), PEER Guidelines for Performance-Based Design of Tall Buildings (PEER/TBI, 2017), and LATBSDC Alternative Analysis and Design Procedure (LATBSDC, 2017).

5.1.3.3.2 Effective stiffness for RC components Effective stiffness parameters for RC components are commonly bounded to account for increased cracking at high-load levels (ULS) and for lower cracking at service load levels used for wind serviceability (drifts and building motions). As shown earlier, Tables 5.3
5.5 provide guidance on concrete cracking-related stiffness parameters for various elements and different demand levels (SLE, DE, and maximum considered earthquake (MCER)). Typically, a supplemental damping system’s efficiency is evaluated at both service and ultimate load levels; and for seismic design for a wide range of ground motion intensities when conducting PBSD. Generally cracking modification factors are employed in linear elastic models to obtain baseline structural dynamic properties (from FEA). Sensitivity analysis of high-demand RC elements can be conducted by extracting forces and rotations from a linear elastic model and employing nonlinear concrete models such as modified compression field theory (Vecchio and Collins, 1986) or other constitutive models to determine cracking at a particular load level and updating effective stiffness parameters in linear FEA models iteratively, thereby creating a quasi-nonlinear model at that load level. This approach creates discrete models for a particular time in a structure’s loading time history. For advanced analysis, particularly in the high seismicity area, nonlinear timehistory FEA is often used when modeling the total building system at relatively high-load levels. Since these models are complex and tend to have relatively long analysis time, bounding effective stiffness in linear elastic or quasi-nonlinear models is an effective way to begin to understand the behavior of the system prior to running full nonlinear models. Moreover, for the design of wind-governed supplemental damping systems/in areas of low seismicity, it is often common practice to bound concrete nonlinear material properties in quasi-nonlinear models. When bounding the effects of concrete cracking, particular attention should be paid to high-demand elements and concentrated stiffness systems such as: • • • • •

Coupling beams Outrigger walls Belt walls Columns used to couple outriggers and belts to the rest of the lateral load
resisting system Diaphragms/collectors engaging secondary lateral load
resisting elements/ systems (such as foundation walls)

5.1 Available Codes and Design Tools

Other mechanical and material properties which may require the use of bounding/sensitivity analysis: • • •

•

Young’s modulus of concrete Joint rigidity and fixity in steel and concrete structures Foundation bearing strata stiffness; particularly on soft strata: • Raft foundation rotation • Pile
soil interaction Effect of secondary elements

Note: secondary elements such as slabs (out-of-plane flexural rigidity), gravity beams, and continuous drop panels may affect the lateral stiffness and frequencies of the tower. However, the stiffness of these elements is often ignored when determining the demand on the primary lateral load
resisting system. In this approach, the design of the secondary elements would consider gravity and lateral forces (determined from a model where their stiffness is not ignored).

5.1.3.3.3 Modification factors of dynamic modification properties Nominal properties of dynamic modification system shall take into account the variation due to different factors, such as temperature, aging, and environmental exposure (ASCE, 2017a; NEHRP, 2015). In general, to account for property variation factors in modeling, there are three methods: 1. Using advanced software packages which explicitly models property variation due to environmental conditions (e.g., temperature and velocity). More detail about this approach is outside the scope of this book. 2. Through testing data (see Chapter 7). 3. Use of property modification factors (λ) (see subsequent discussion). Property modifications factors (λ) should be defined for each category of dynamic modification devices. US codes provide different expressions to calculate them: •

NEHRP (2015) and ASCE 7-16 (ASCE, 2017a) recommend that a minimum, λmin , and a maximum, λmax , variation factor shall be employed in damper modeling, analysis, and design. These two factors are functions of minimum and maximum values of three parameters: aging/environmental factors (λae ), testing (λtest ), and specifications (λspec ), as follows:     λmax 5 1 1 0:75 λae;max 2 1 λtest;max 3 λspec;max $ λmax;lim     λmin 5 1 2 0:75 12λae;min λtest;min 3 λspec;min # λmin;lim

(5.4) (5.5)

Practical ranges are (NEHRP, 2015; ASCE, 2017a): 0:85 # λmin # 0:95 and 1:05 # λmax # 1:15. The limiting values for distributed dampers are: λmax;lim 5 1.2 and λmin;lim 5 0.85; while for base isolation the following values are recommended: λmax;lim = 1.8 and λmin;lim 5 0.8 or 0.6 for NEHRP (2015) and ASCE (2017a) respectively.

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Maximum and minimum design properties can be obtained by multiplying nominal design properties of dampers by the property variation factors λmin and λmax , as follows:

•

Maximum property 5 Nominal property 3 λmax

(5.6)

Minimum property 5 Nominal property 3 λmin

(5.7)

Then, separate analyses and design for the building with maximum and minimum properties should be performed under external excitation (e.g., wind and SLE/DE/MCER earthquake conditions). ASCE 41-17 (2017b): similar to NEHRP (2015) and ASCE (2017a) recommendations the minimum, λmin , and maximum, λmax , modification factors can be computed as follows:     λmax 5 1 1 SPAF λPM;max 2 1 λspec;max $ λmax;lim     λmin 5 1 2 SPAF 12λPM;min λspec;min # λmin;lim

(5.8) (5.9)

where λspec is the ower and upper specification tolerance, which is the permissible variation between the average production test values and the nominal values (in the range of 1 10% to 1 15%); λPM is the global property modification factor, which is the product of all the factors for environmental and testing effects (typical values are provided in ASCE (2017a) based on AASHTO recommendations (AASHTO, 2010)); SPAF is the system property adjustment factor, which takes into account that each property modification factor does not occur at the same time (taken as 0.67 for all performance levels). ASCE 41-17 (ASCE, 2017b) provides guidance on this factor based on AASHTO recommendations (AASHTO, 2010); λmax;lim is the maximum limit value equals to 1.15 or 1.3 for distributed dampers and base isolation, respectively; and λmin;lim is the minimum limit value equals to 0.85 for both distributed dampers and base isolation. Multiplying nominal design properties of dampers by property variation factors λmin and λmax leads to maximum (Eq. 5.6) and minimum (Eq. 5.7) design properties.

5.2 PASSIVE DAMPING SYSTEMS Including passive damping systems as part of a structural design scheme is based on a well-maintained balance between performance targets, construction costs, and complexities of their implementation in an actual building. Every tall building or dynamically sensitive structure has unique characteristics and constraints that must be carefully investigated by the design team in order to determine which

5.2 Passive Damping Systems

type of damping system can best achieve the target performance in terms of cost, construction schedule, constructability, etc. The up-front implementation assessment of a dynamic modification system should consider a wide range of factors that are critical in achieving the desired performance, such as: • • • • • • • • •

Source of the external dynamic excitation (e.g., vortex shedding, turbulent buffeting, seismic) Anticipated dynamic behavior of the structure Performance level required based on the occupancy or usage Damper
structure interaction Load magnitude at the damper
structure interface Available space Construction material, method, and schedule Lifting capabilities at the site during installation Maintenance and inspection requirements

At early design stages, careful consideration of the above factors are fundamental to the successful implementation of dynamic modification systems, and to assure that the desired performance of the building is achieved. As shown in the previous chapters, within the category of the passive damping systems, mass damping systems (i.e., TMDs and TLDs) have become increasingly popular solutions to enhance the serviceability performance of tall buildings and other wind-sensitive structures. However, the implementation of distributed damping systems (i.e., viscoelastic dampers, viscous dampers, and friction dampers) has been primarily aimed at providing earthquake protection for structures in high seismic regions. Basic design considerations and practical suggestions for implementing these systems are described with a step-by-step procedure (Fig. 5.8) for the different damping devices discussed in Chapter 4. Ten main steps are defined (Fig. 5.8) and detailed explanations of each step are given in the following sections.

5.2.1 STEP-BY-STEP PROCEDURE FOR DISTRIBUTED DAMPERS In Section 4.1.1, the basics principles of design for distributed dampers were introduced. In this section, the design procedure for a building with distributed dampers will be reviewed. In the literature, there are several methods available for both code/guidelines and noncode/guidelines prescriptive procedures, as summarized in Table 5.6. The majority of these procedures refer to design of structures under seismic loading without dealing with wind design (except the work by McNamara et al. (1999)). The main reason for this could be related to the dominance of the design procedures based on low-rise buildings that usually are dominated by seismic excitations. Indeed, while looking at tall buildings, wind loading can become the predominant concern as shown in Chapter 3. Another important consideration is related to the type of analyses allowed by these procedures. Standard building

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FIGURE 5.8 Step-by-step procedure for implementing passive damping systems.

5.2 Passive Damping Systems

Table 5.6 Distributed Damper: Available Design Procedures Code/Guidelines Prescriptive

Noncode/Guidelines Prescriptive

FEMA-356 (FEMA, 2000d) FEMA-368 (FEMA, 2001) FEMA-450 (FEMA, 2003) ASCE 41-13 (ASCE, 2013) ASCE 41-17 (ASCE, 2017b) ASCE 7-10 (ASCE, 2010) ASCE 7-16 (ASCE, 2017a) TBI (PEER/TBI, 2017) FEMA P-751 (NEHRP, 2012) FEMA P-1050-1 (NEHRP, 2015) Ramirez et al. (2001) Liang et al. (2012) Chinese Code (GB50011, 2010) Japanese Code (BCJ, 2013) JSSI Manual (2003, 2005, 2007)

Gluck et al. (1996) Soong and Dargush (1997) Peckan et al. (1999a,b) Lopez-Garcia (2001) Yang et al. (2002a,b) Kim et al. (2003) Uetani et al. (2003) Lin et al. (2003) Christopoulos and Filiatrault (2006) Lin et al. (2008) Lomiento et al. (2010) Silvestri et al. (2010) Lago (2011); Sullivan and Lago (2012) Zhou et al. (2012) Pettinga et al. (2013) Guo and Christopoulos (2013) Diotallevi et al. (2014) Palermo et al. (2016)

codes, such as the Chinese (GB50011, 2010), Japanese (BCJ, 2013), and US codes (ASCE, 2017a), permit the use simplified analysis procedures only for regular and low-rise buildings and, in the case of tall buildings, more complicated approaches are required, including dynamic analyses (for seismic design) and wind-tunnel tests (for wind design) (e.g., ASCE 7-16 (ASCE, 2017a) and PEER/TBI (2017)). Given the scope of this book, only the most reliable and generally recognized design approaches are examined. Code-prescriptive procedures are the most suitable procedures for design, since they are based on current national standards. For these reasons, in the following sections, the step-by-step procedure provided is mostly based on US design codes (ASCE 7-16 (ASCE, 2017a), ASCE 41-17 (ASCE, 2017b), NEHRP (2009, 2015), PEER/TBI (2017)). However, reference to other methods is given to underline the current trends in the research field. The procedure has been developed for both seismic and wind design. Moreover, this approach has been made as broad as possible, so that it can be applicable to different types of distributed dampers (e.g., viscous, viscoelastic, metallic, and friction) and building heights. In the following sections, every step, as shown in Fig. 5.8, is developed in detail for four different types of damping devices: viscous, viscoelastic, metallic (hysteretic), and friction.

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Table 5.7 Risk Category of Tall Buildings for Flood, Wind, Snow, Earthquake, and Ice Loads (ASCE, 2017a) Importance Factors Occupancy of Tall Buildings Buildings that represent a low risk to human life in the event of failure All buildings except those listed in risk categories I, III, and IV Buildings which could present a significant risk to human life under failure Buildings designated as essential facilities

Risk Category

Earthquake Loads (Ie )

Ice-Wind Loads (Iw )

I

1

1

II

1

1

III

1.25

1

IV

1.5

1

5.2.1.1 Step 1: Building and site categorization This step is subdivided into three subsections. The first subsection (Step 1.1) is devoted to the categorization of tall building sites in which the building is located. The second subsection (Step 1.2) relates only to buildings that need to be designed for seismic activity and it differentiates between the code prescriptive RSA and ground motion hazard analysis for the MCER. The third subsection (Step 1.3) is devoted to the determination of basic wind design loads.

5.2.1.1.1 Step 1.1: Risk category and occupancy importance factor Buildings are categorized to determine flood, wind, snow, ice, and earthquake loads, based on the risk associated with different performance levels (ASCE, 2017a). The building risk category and relative occupancy importance factor can be found using Table 5.7, depending on the priority of minimum design loads (e.g., seismic and wind) for the building. These values will be used to determine the seismic and wind loading that the building needs to sustain, as is shown in subsequent steps.

5.2.1.1.2 Step 1.2: Site spectral response acceleration, response spectrum, and time histories For the seismic design of buildings with dynamic modification systems, different seismic levels are considered (ASCE 7-16 (ASCE, 2017a), NEHRP (2015)): (1) DE and (2) MCER. The responses to the first set are suggested (NEHRP 2015) to be used for the design of structural systems, equipped with dynamic modification devices, and the responses to the second set are to be employed for the design of dynamic modification systems (ASCE, 2010; NEHRP, 2015). However, for tall buildings the TBI (PEER, 2017) recommends to use a PBD procedure according to the following two seismic levels: SLE (instead of DE) and MCER. Tall buildings as per PEER (2017) have the following characteristics: • •

Fundamental period greatly above 1 second. Higher mass participation for higher modes of vibration.

5.2 Passive Damping Systems

• •

Drift ratio from axial (from walls and columns) and shear (from frames or walls) deformation is comparable. Slender aspect ratio for the seismic force-resisting system.

The seismic demand on a building is based on the risk-targeted MCER, a site characteristic, of where the building will be constructed. According to ASCE 716 (ASCE, 2017a) the spectra for both DE and MCER levels can be determined according to the following procedures depending on the MCER spectral response acceleration at 1 second (S1 ): • •

If S1 , 0:6, consider an MCER based on mapped values and determine the corresponding spectra for the site DE and MCER levels. If S1 $ 0:6, perform an MCER ground motion hazard analysis in accordance with Section 21.2 of ASCE 7-16 (ASCE, 2017a) and then construct the relevant spectra for the site DE and MCER levels.

Buildings with risk categories I, II, III, or IV, located in a site where S1 $ 0:75, should not be constructed, where there is a known potential for an active fault to cause a rupture in the ground surface at the structure. The spectral acceleration for both the short period (SS ) and at 1 second (S1 ), given the site location, should be computed according to one of the following methods: 1. Directly determined using Figs. 22-1
22-6, presented in ASCE 7-16 (ASCE, 2017a). These values refer to site class B and for other soil site class values shall be modified through correction factors (ASCE, 2017a). 2. Using the online tool available through the USGS website. Note: this S1 categorization is not valid for tall buildings since for ground motion characterization only hazard analysis is allowed (i.e., mapped values cannot be considered) (PEER, 2017). However, in the following both mapped values and hazard analysis are reviewed for completeness. S1 , 0:6 Risk-targeted maximum considered earthquake (MCER)-based on mapped values (not applicable to high-rise buildings according to PEER (2017)). According to ASCE (2017a), the response spectrum is constructed based on the following five steps: 1. Site class: Based on the site-soil properties, the site can be classified into six categories A, B, C, D, E, or F. The most appropriate parameter that determines the site class is the average value of the shear-wave velocity, vs , of the upper 100 ft (30.48 m) of soil at the site, which is expressed as follows: Pn di vs 5 Pi51 n di

(5.10)

i51 vsi

Here, n is the number of layers of similar soil materials, where data are available; di is the depth of layer i; and vsi is the shear-wave velocity of the soil in n P layer i. It should be noted that di equals 100 ft (30.48 m). i51

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Table 5.8 Site Class Classification Based on Site Material and Average Shear Wave Velocity v s (ASCE, 2017a) Site Class A B C D E F

Range of v s (m/s)

Site Material Hard rock Rock Very dense soil and soft rock Stiff soil Any profile with more than 3 m of soft clay Liquefiable soils; quick and highly sensitive clays; collapsible weakly cemented soils; peats or highly organic clays; very high plasticity clays; very thick soft or medium-stiff clays

.1524 762
1524 366
762 183
366 ,183 _

Having determined v s using Eq. (5.10), the site classes can be easily selected from Table 5.8. According to ASCE 7-16 (ASCE, 2017a) there are two exceptions when using Eq. (5.10): a. If the average value of shear-wave velocity, v s , is not known for a site, two other parameters, the standard penetration test blow count, N , and the undrained shear strength, s u , of the upper 100 ft (30.48 m) of soil at the site, can be applied. b. If the soil properties are not known in sufficient detail to determine the site class, class D can be used, unless the expert consultant (geotechnical engineer) determines that site class E or F is existing at the site. 2. Design spectral response acceleration parameters: The design spectral response acceleration parameters (SDS and SD1 ), at short period, TS , and at a 1-second period, T1 , can be estimated as follows: 2 SDS 5 Fa SS 3

(5.11)

2 SD1 5 Fv S1 3

(5.12)

Here, Fa and FV are site coefficients, which are defined in Tables 5.9 and 5.10, respectively. To determine these coefficients, site class and mapped MCER spectral response acceleration parameters (SS and S1 ) are required (ASCE, 2017a). c. Seismic design category: The building can be assigned to a seismic design category (use Table 5.11) based upon their risk category and the severity of the DE at the site (i.e., design spectral response acceleration parameters, SDS and SD1 , determined previously). d. Design response spectrum: If site-specific ground motion procedures are not employed, a design response-spectrum curve can be developed (see Fig. 5.9) as:

5.2 Passive Damping Systems

Table 5.9 Values of Site Coefficient Fa (ASCE, 2017a) Range of SS a

Site Class

SS # 0.25

SS 5 0.5

SS 5 0.75

SS 5 1.0

SS 5 1.25

SS $ 1.5

A B C D E

0.8 0.9 1.3 1.6 2.4

0.8 0.9 1.3 1.4 1.7

0.8 0.9 1.2 1.2 1.3

F

Site analysis required

Site analysis required

Site analysis required

0.8 0.9 1.2 1.1 Site analysis required Site analysis required

0.8 0.9 1.2 1.0 Site analysis required Site analysis required

0.8 0.9 1.2 1.0 Site analysis required Site analysis required

a

Use straight-line interpolation for intermediate values of Ss .

Table 5.10 Values of Site Coefficient Fv (ASCE, 2017a) Site Class A B C D E

F

a

Range of S1 a S1 # 0.1

S1 5 0.2

S1 5 0.3

S1 5 0.4

S1 5 0.5

S1 $ 0.6

0.8 0.8 1.5 2.4 4.2

0.8 0.8 1.5 2.2b Site analysis required Site analysis required

0.8 0.8 1.5 2.0b Site analysis required Site analysis required

0.8 0.8 1.5 1.9b Site analysis required Site analysis required

0.8 0.8 1.5 1.8b Site analysis required Site analysis required

0.8 0.8 1.4 1.7b Site analysis required Site analysis required

Site analysis required

Use straight-line interpolation for intermediate values of S1 . Also see requirements for site analysis.

b

SA 5

0 1 8 > > T > > SDS @0:4 1 0:6 A for T , T0 > > T0 > > > > > > S for T $ T0 ; T # TS > DS < SD1 > > > > > > T > > > SD1 TL > > > > : T2

for T . TS ; T # TL

(5.13)

for T . TL

where T is the fundamental period of the structure; T0 equals to 0:2ðSD1 =SDS Þ; TS equals to SD1 =SDS ; and TL is the long-period transition parameter obtained from published maps on ASCE 7-16 (ASCE, 2017a), or site-specific response

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Table 5.11 Seismic Design Category Based on SDS and SD1 (ASCE, 2017a) Risk Category Range of SD

I or II or III

IV

SDS , 0.167 or SD1 , 0.067 0.167 # SDS , 0.33 or 0.067 # SD1 , 0.133 0.33 # SDS , 0.5 or 0.133 # SD1 , 0.2 SDS $ 0.5 or SD1 $ 0.2

A B C D

A C D D

FIGURE 5.9 Design response spectrum.

analysis, or any other methods approved by the authority having jurisdiction. The details of the procedure and rationale used in determining the TL maps in ASCE 7-16 (ASCE, 2017a) and in NEHRP (2009) can be found in Crouse et al. (2006). e. Risk-targeted maximum considered response spectrum: Given the design response spectrum (Fig. 5.9), the MCER response spectrum can be simply determined by multiplying the design response spectrum by 1.5 (ASCE, 2017a; NEHRP, 2015). S1 $ 0:6 Risk-targeted maximum considered earthquake (MCER) ground motion hazard analysis (ASCE, 2017a) (for any value of S1 for tall buildings according to PEER (2017)). An hazard analysis shall be conducted for tall buildings (according to PEER (2017)) and for any other structures in the case S1 , previously obtained, is greater than 0.6 second. This shall account for the geological and seismic characteristic of the site to be provided in a report (ASCE, 2017a). The site-specific MCER is determined from two different procedures: (1) probabilistic and (2) deterministic ground motions. Based on these, the site-specific

5.2 Passive Damping Systems

spectral response accelerations (SAM ) shall be defined, at any period, as the lesser of the values computed from the probabilistic and deterministic methods. In the following, the two different procedures are briefly reviewed: 1. Probabilistic risk-targeted MCER ground motions: the response spectrum for this method has a return period of 1% probability of collapse within a 50-year period. The spectral acceleration coordinate can be determined from either of the two following methods: a. The acceleration at each spectral response period can be computed from the spectral response acceleration for a 5% damped response spectrum with 2% probability of exceedance within a 50-year period, multiplied by the risk coefficient, CR : defined at short, CRS , and 1-second period, CR1 . The values of the response coefficient can be determined from Figs. 22-18 and 22-19 in ASCE (2017a). For periods less than 0.2 second, CR 5 CRS , and for periods greater than 1.0 s, CR 5 CR1 : For periods in between a linear interpolation between the risk coefficients is allowed. When dealing with tall buildings, where the fundamental period is usually long enough (e.g., T . 1 s), considering CR 5 CR1 is acceptable. b. Spectral ordinate from iterative integration of a site-specific hazard that has collapsed fragility probability density function lognormally distributed. The ordinate of the probabilistic ground motion response spectrum at each period shall achieve a 1% probability of collapse within a 50-year period for a collapse fragility having a 10% probability of collapse at said, and a logarithmic standard deviation of 0.6 (ASCE, 2017a). 2. Deterministic risk-targeted MCER ground motions: at each period, the spectral response acceleration shall be calculated as the 84th-percentile of 5% damped spectral response acceleration in the direction of maximum horizontal response computed at that period. The maximum value of such acceleration calculated for the characteristic earthquakes on all known active faults within the region shall be used. (ASCE, 2017a) Each ordinate shall not be less than the MCER response spectrum as determined for S1 , 0.6, constructed with SS 5 1:5 and S1 5 0:6. Having calculated the site-specific MCER acceleration, SAM , the design spectrum values, SA , can then be calculated as follows: 2 SA 5 SAM 3

(5.14)

Subsequently, the spectral displacement shall be defined as: • • •

SDS as the maximum between SDS determined at 0.2-second period and 90% of SDS determined for any period longer than 0.2-second. SD1 as the maximum between SDS determined 1-second period and double of SDS at 2-second period. SMS and SM1 as 1.5 times SDS and SD1 , respectively.

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CHAPTER 5 Design procedures for tall buildings

•

Design and maximum response displacement values shall not be less than 80% of those determined for S1 , 0.6.

The above-explained site-specific earthquake hazard analysis can be performed with computer software, such as EZFRISK (Risk Engineering, 2012). This is based on the models by Cornell (1973) and McGuire (1976) on probabilistic seismic hazards. This method allows the modeling of the faults, in the vicinity of the building site, as linear sources with fault earthquake activities based on historical and geologic data. Selection and scaling of ground motion records. In the case of nonlinear response procedures, the selection and scaling of appropriate horizontal ground motion acceleration time histories, for MCER, are essential to produce meaningful results (ASCE, 2017a). According to design standards (ASCE, 2017a; PEER, 2017), the following points can be explored: •

• •

•

•

•

At least 11 pairs of ground motions shall be selected for each target spectrum. The chosen events shall have similar characteristics and spectral shape of the target spectrum. In the case of near-fault sites the proportion of ground motion having these effects shall be such that they represent the probability that MCER will have these effects (ASCE, 2017a). Synthetic/simulate ground motions while permitted by ASCE (2017a) shall not be utilized based on design practice. Ground motion modification can be carried out through amplitude-scale or spectral matching (not possible for near-fault site unless the pulse characteristics are maintained after matching) (ASCE, 2017a). The period bounds for scaling or matching are defined as follows (ASCE, 2017a): • Upper-bound period shall be greater or equal to 2 times the largest first mode of the building among the two principal directions (a lower value of 1.5 can be used if justified by dynamic analysis under MCER). • Lower-bound period shall be defined such that it includes a sufficient number of building modes to reach 90% of mass participation in each principle direction. Moreover, it shall not exceed 20% of the lowest first mode among the two principal directions. Instead, in case vertical component is considered, the lower bound period shall not be taken less than 0.1 second or the lowest period (among the two principal directions) which mass participation contribution. Amplitude scaling: for each ground motion pair a maximum-direction spectra shall be constructed. The same factor shall be applied for each ground motion pair such that the average maximum-direction spectra from all ground motion match or exceed the target response spectrum. In any case, it shall not fall below 90% for any period within the selected period range. In case vertical response is considered, each component shall be scaled to envelope the target vertical response spectrum over the period range specified. Spectrum matching: each pair of ground motions shall be modified such that the suite average maximum-direction spectra equal or exceed 110% of the

5.2 Passive Damping Systems

•

target spectrum over the period range specified. For the vertical component the ground motion shall be spectrally matched such as the average of the suite never falls below the target vertical spectrum for the period range specified. Ground motions shall be applied to the support of the model in the building orthogonal direction “such that the average of the component response spectrum for the records applied in each direction is within 10% of the mean of the component response spectra of all the records applied in the period range specified” (ASCE, 2017a). In the design process, the average of the peak responses among a set of ground can be utilized. However, some criteria require to use the maximum of peak response, such as per PEER (2017) in which the peak drift has to be less than 4.5%.

5.2.1.1.3 Step 1.3: Wind demand The design wind load according to ASCE 7-16 (ASCE, 2017a) can be determined based on wind speed that is tabulated (based on risk category, Table 5.7) in the wind hazard map (just for US regions). Except for cases in which regional climate data show unusual wind conditions, the following categories are used in code: • • • •

Risk Risk Risk Risk

category I, Fig. 26.5-1.A (ASCE, 2017a) category II, Fig. 26.5-1.B (ASCE, 2017a) category III, Fig. 26.5-1.C (ASCE, 2017a) category IV, Fig. 26.5-1.D (ASCE, 2017a)

Two procedures are commonly utilized for determining wind loads for static analysis: directional and wind-tunnel procedures (ASCE, 2017a). The latter procedure can be applied to all types of buildings while the former has several limitations (i.e., applicable only to regular-shaped buildings, no effects on building due to cross-wind loading, vortex shedding and instability due to galloping or flutter, and building site location with no channeling effect or buffeting in the wake of upwind obstructions). These requirements show that dynamically sensitive buildings (i.e., tall buildings) might require wind-tunnel testing. Directional wind procedure. This procedure can be applied to all types of buildings that are regular shaped and are not subject to a cross-wind loading (ASCE, 2017a). In all other cases, the designer shall use the wind-tunnel procedure, as explained in the next substep. The code provides two different procedures depending on the height: above or below the limit of 48.8 m (160 ft). In this book, only the procedure for structures with height above 48.8 m will be reviewed. The procedure proposed by the ASCE 7-16 (ASCE, 2017a) considers the application of wind in each direction as an independent action: windward, leewar, and side walls. There are eight different steps in the procedure, as shown in Fig. 5.10. 1. Have been already discussed in Section 5.2.1.1.1. 2. Have been already discussed in Section 5.2.1.1.3.

275

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CHAPTER 5 Design procedures for tall buildings

FIGURE 5.10 ASCE (2017a) directional wind procedure steps.

3. The different wind-load parameters to be calculated are the following: • Wind directionality factor, Kd : determined from Table 5.12. • Exposure category: for each wind direction, shall be based on the surface roughness and exposure categories. These need to be determined for the two upwind section extending 45 degrees on each side. For further details, refer to Section 26.7 of ASCE 7-16 (ASCE, 2017a). • The topographic factor, K zt : it takes into account the changes in the topography of the proximity of the structure under analysis. For further details, refer to Section 26.8 of ASCE 7-16 (ASCE, 2017a). • Gust effect factor, Gef : it takes into account the wind turbulence
structure interaction, as well as the dynamic amplification due to building flexibility. This factor is computed differently for rigid (,1 Hz) and flexible (.1 Hz) buildings. For rigid buildings, it is permitted to be simply taken as 0.85 or computed as follows:  1 1 1:7gQ Iz Q Gef 5 0:925 1 1 1:7gv Iz

(5.15)

5.2 Passive Damping Systems

Table 5.12 Wind Directionality Factor (ASCE, 2017a) Directionality Factor, Kd

Structure Type Buildings Main wind force-resisting system Components cladding Arched roofs

0.85 0.85 0.85

Chimneys, Tanks, and Similar Structures Square Hexagonal Round

0.90 0.95 1.00

Solid freestanding walls and solid freestanding and attached sign

0.85

Open signs and lattice framework

0.85



10 1=6 z vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u 1 Q5u  0:63 u t 1 1 0:63 L2L1H z Iz 5 gc

 A z Lz 5 gl 10

(5.16)

(5.17)

(5.18)

where Iz is the intensity turbulence at the equivalent height of the building, z is defined as 0:6H (but not less than zmin , Table 5.13); Q is the background response; the constants gQ and gv shall be taken as 3.4; the constants gc , gl , and A are shown in Table 5.13; L2 is the building horizontal dimension perpendicular to the wind direction; and H is the mean roof height. Instead, for flexible buildings the gust factor, Gef , can be computed as follows: qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1 0 1 1 1:7Iz g2Q Q2 1 g2R R2G A Gf 5 0:925@ 1 1 1:7gv Iz

(5.19)

The constants gQ and gv shall be taken as 3.4 and gR as follows: gR 5

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 0:577 2 lnð3600f1 Þ 1 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 lnð3600f1 Þ

(5.20)

277

Table 5.13 Gust Effect Factor Constants (ASCE, 2017a) Exposure

α

zg (m)

a^

b^

α

b

gc

gl (m)

A

zmin (m)a

B C D

7.0 9.5 11.5

365.76 274.32 213.36

1/7.0 1/9.5 1/11.5

0.84 1.00 1.07

1/4.0 1/6.5 1/9.0

0.45 0.65 0.80

0.30 0.20 0.15

97.54 152.4 198.12

1/3.0 1/5.0 1/8.0

9.14 4.57 2.13

The equivalent height z is equal to the greater of 0:6H and zmin and for building with H # zmin is equal to zmin .

a

5.2 Passive Damping Systems

where f1 is the building fundamental frequency and RG is the resonant factor: sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 RG 5 Rn Rh RB ð0:53 1 0:047RL Þ ζT Rn 5

7:47N1

(5.22)

ð1110:3N1 Þ5=3 n1 Lz Vz

(5.23)

 1 1  2 1 2 e22η for η . 0 η 2η2

(5.24)

N1 5 Rl 5

(5.21)

Rl 5 1 for η 5 0

(5.25)

where the subscript l in Eqs. (5.24) and (5.25) shall be taken as H, L2 , and L1 (building horizontal dimension perpendicular and parallel to wind direction); ζ T is the total damping ratio; and η is a constant equal to: Rl 5 RH -η 5 4:6f1 H=V z

(5.26)

Rl 5 RL2 -η 5 4:6f1 L2 =V z

(5.27)

Rl 5 RL1 -η 5 15:4f1 L1 =V z

(5.28)

where V z is the mean hourly wind speed at height z:  α z V Vz 5b 10

• •

(5.29)

where b, α, and z are defined in Table 5.13 and V is the basic wind speed. Enclosure classification: categorized buildings as enclosed, partially enclosed and open. Internal pressure coefficient, GC pi : based on the enclosure classification, as shown in Table 5.14. For large volume building, partially enclosed, a reduction factor can be utilized as: 0

1

1 B C RGCpi 5 0:5@1 1 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiA Vvi 1 1 22;800Aog

(5.30)

where Aog is the opening total area in the building envelope (walls and roof in ft2) and Vvi is the unpartitioned internal volume (in ft3). 4. The velocity pressure exposure coefficients, Kz or Kh , are determined from the following equation (Table 5.15):  2=α 4:57m # z # zg -Kz 5 2:01 z=zg  2=α z , 4:57m-Kz 5 2:01 15=zg

(5.31)

where zg and α are tabulated in Table 5.13. Linear interpolation for intermediate values of z is allowed (ASCE, 2017a).

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Table 5.14 Internal Pressure Coefficient (ASCE, 2017a) Enclosure Classification

GCpi

Open buildings Partially enclosed buildings

0.00 1 0.55 20.55 1 0.18 20.18

Enclosed buildings

Note: Plus and minus signs indicate pressure acting toward and away from the surface, respectively. Two cases shall be considered: one with positive value of GCpi applied to all surfaces and one with negative values.

Table 5.15 Velocity Pressure Exposure Coefficients (ASCE, 2017a) Exposure Height Above Ground Level (m)

B

C

D

0
4.6 6.1 7.6 9.1 12.2 15.2 18 21.3 24.4 27.4 30.5 36.6 42.7 48.8 54.9 61.0 76.2 91.4 106.7 121.9 137.2 152.4

0.57 0.62 0.66 0.70 0.76 0.81 0.85 0.89 0.93 0.96 0.99 1.04 1.09 1.13 1.17 1.20 1.28 1.35 1.41 1.47 1.52 1.56

0.85 0.90 0.94 0.98 1.04 1.09 1.13 1.17 1.21 1.24 1.26 1.31 1.36 1.39 1.43 1.46 1.53 1.59 1.64 1.69 1.73 1.77

1.03 1.08 1.12 1.16 1.22 1.27 1.31 1.34 1.38 1.40 1.43 1.48 1.52 1.55 1.58 1.61 1.68 1.73 1.78 1.82 1.86 1.89

5.2 Passive Damping Systems

5. The velocity pressure, qz, can be determined at height z and at the mean roof height H, qH , as follows: qz 5 0:613Kz Kzt Kd V 2

(5.32)

where V is the basic wind speed in m/s, Kz is the velocity pressure coefficient, Kzt is the topographic factor, and Kd is the wind directionality factor, as previously defined. In case z 5 H, the velocity pressure, qH , is computed at the roof height. 6. The external pressure coefficient, Cp and CN , can be determined based on the charts provided in Section 27.3 of ASCE 7-16 (ASCE, 2017a). 7. The wind pressure, p, can be determined on each building surface depending on the type of building: • Enclosed and partially enclosed rigid buildings: p 5 qGCp 2 qi GCpi

(5.33)

•

where q 5 qz for windward walls at height z; q 5 qH for leeward and side walls, and roofs at height H; qi 5 qH for windward, leeward, and side walls, and roofs at height H of enclosed buildings and for negative internal pressure for partially enclosed buildings; and qi 5 qz internal pressure for partially enclosed buildings with z evaluated at the highest opening influencing the positive internal pressure. Conservatively, qi 5 qH can be taken. Enclosed and partially enclosed flexible buildings:

•

Open buildings:

p 5 qGf Cp 2 qi GCpi

(5.34)

p 5 GCN

(5.35)

where CN is net pressure coefficient as determined in step 6. The wind pressure as calculated above shall not be less than the following requirements: • For enclosed and partially enclosed buildings: 0.77 kN/m2 for walls and 0.38 kN/m2 for roofs. • For open buildings: 0.77 kN/m2. 8. The action on each surface shall be applied concurrently on windward walls, leeward walls, and roofs, as shown for the load cases of Fig. 5.11. The figure shows how the influence of eccentricity is a crucial element and the values provided refer to rigid buildings calculated for each main direction (ex and ey ). Instead, flexible buildings shall be computed as follows, for each main direction: e5

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi  2 gQ QeQ 1 ðgR RG eR Þ2 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 gQ Q 1 ðgR RG Þ2 1 1 1:7Iz

eq 1 1:7Iz

(5.36)

where eQ is the eccentricity, e, for rigid structures (Fig. 5.11), and eR is the distance between the elastic shear center and the center of mass of each floor. Wind-tunnel procedure. In case the previously described directional procedure is not applicable, wind-tunnel tests are required to determine the wind pressure on

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CHAPTER 5 Design procedures for tall buildings

FIGURE 5.11 Design wind load cases. Adapted from ASCE, 2017a. ASCE7-16: Minimum Design Loads for Buildings and Other Structures. American Society of Civil Engineers, Reston, VA.

the building, and also for testing the efficiency of dynamic modification system (see Chapter 7 for more details). The conditions, for the tunnel testing protocol, required by ASCE 7-16 (ASCE, 2017a) and ASCE 49 (ASCE, 2012) are as follows: • •

•

Modeling of wind-speed variation with height is necessary (i.e., atmospheric boundary layer). Accurate scale modeling is essential to model atmospheric turbulence and the geometric characteristics of the surrounding environment, as well as the building under study. The model’s projected area is less than 8% of the total test section area, unless a correction is considered for blockage.

5.2 Passive Damping Systems

• • • •

Accounting for longitudinal pressure gradient is necessary. Must attempt to minimize the Reynolds number of pressures and forces. Response parameters are estimated, based on the required measurements of the tests. The structural model of the building under study shall take into account a correct distribution of mass, stiffness, and damping.

The load effects on buildings shall have the same recurrence interval as that for analytical methods recognized in the existing literature. These methods would allow the combination of the wind-tunnel test data with meteorological data or a probabilistic model.

5.2.1.1.4 Step 1.4: Load combinations The effects of gravity loads and seismic/wind forces can be combined as follows (ASCE; 2017a): •

Basic load combinations for strength design Earthquake: 

ð1:2 1 0:2SDS ÞDL 1 LL 1 EL 1 0:2SL ð0:9 2 0:2SDS ÞDL 1 EL 1 1:6HL

(5.37)

Wind: 

•

1:2DL 1 LL 1 WL 1 0:5SL 0:9DL 1 WL

(5.38)

Basic load combinations for allowable stress design Earthquake: 8 <

ð1 1 0:14SDS ÞDL 1 HL 1 FL 1 0:7EL ð1 1 0:1SDS ÞDL 1 0:75LL 1 HL 1 FL 1 0:525EL : ð0:6 2 0:14SDS ÞDL 1 HL 1 0:7EL

Wind:

(5.39)

8 <

DL 1 0:6WL DL 1 0:75L 1 0:45WL : 0:6D 1 HL 1 0:6WL

(5.40)

where DL is the dead load; LL is the live load; SL is the snow load; HL is the load due to lateral earth pressure, ground water pressure, or pressure of bulk materials; FL is the load due to fluids with well-defined pressures and maximum heights; EL is the earthquake force; and WL is the wind force. Having set the load combinations, it is important to define the sequence in which they are applied: first gravity (DL and LL ) and then lateral loads (EL and WL ). Note: these combinations are rarely applied when site-specific hazard information and nonlinear seismic analyses are performed; refer to ASCE 7-16 (2017a) and TBI 2.0 (PEER, 2017). Similarly, when wind tunnel is utilized for a tall

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CHAPTER 5 Design procedures for tall buildings

building the load combinations are sometimes modified by recommendation from the wind consultant.

5.2.1.2 Step 2: Select lateral force
resisting system For tall buildings, several structural systems have been used in the past, depending on several considerations, such as building height, loading criteria, and uses (Ali and Moon, 2007; CTBUH, 2010) (Fig. 5.12). ASCE 7-16 (ASCE, 2017a) provides some criteria for the selection of lateral force
resisting system. Depending on if the building under consideration is a new or an existing one, the lateral structural system can be properly chosen based on the code high limitations and soil type as given in Table 5.16. In the table, there are also relevant seismic design parameters (i.e., response modification coefficient, R, deflection amplification factor, Cda , and overstrength factor, Ω0 ) that shall be used for determining the base shear, member design forces, and design story drift (see ASCE (2017a) for further details). The code also allows the use of structural systems not contained in the table provided that analytical and experimental studies have been carried out. Furthermore, a combination of different structural systems (both vertical and horizontal) is allowed (see ASCE 7-16 (ASCE, 2017a) for further details). Note: it is important to understand that many tall building applications are nonprescriptive design and required PBSD to be shown in conformance with building code intent or project-specific enhanced objectives. For these reasons, the values provided in Table 5.16 are in most of the case not directly applicable to tall buildings.

5.2.1.3 Step 3: Building fundamental properties and preliminary structural analyses The primary building characteristics that need to be estimated are the modal properties: periods, Tn , and mode shapes, φn . ASCE (2017a) permits to use two methods to determine the fundamental building period: approximated and through numerical analysis. Different approximation methods for seismic- and wind-based design procedures are presented. These procedures are limited by building height and types and are typically not applicable for tall buildings (refer to ASCE (2017a) for further information). For these reasons, the most common approach for tall buildings is to perform numerical modal analyses utilizing any of the available commercial software. To determine modal periods and mode shapes, the analyses should include enough modes to obtain at least 90% mass participation of the actual mass in each horizontal direction (and torsional mode) of the building. In addition, it is current practice to target as much as 99% participation (given the computer capabilities). The building total participating mass is computed as the summation of dead load above the base, total operating weight of permanent equipment, and at least 25% of the required live loads in areas utilized as storage, with a minimum of 5% of the total dead load (ASCE, 2017a).

5.2 Passive Damping Systems

FIGURE 5.12 Classification of tall building structural systems: (A) exterior and (B) interior structures.

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CHAPTER 5 Design procedures for tall buildings

Table 5.16 Suitable Load-Resisting Systems and Design Coefficients for Tall Buildings (ASCE, 2017a) Limitations Including Structural Height (m) Seismic Design Category

Structural System Bearing walls systems

Frame systems

Framed concrete shear walls Steel and concrete composite braced frames

Momentresisting frames

Special RC Ordinary RC Detailed plain concrete Ordinary plain concrete Steel eccentrically braced frames Steel special concentrically braced frames Steel ordinary concentrically braced frames Special reinforced Ordinary reinforced Detailed plain Ordinary plain Eccentrically braced frames Special concentrically braced frames Ordinary concentrically braced frames Plate shear walls Special shear walls Ordinary shear walls Steel special Steel special truss Steel intermediate Steel ordinary Special RC Intermediate RC Ordinary RC Steel and concrete composite special

R

Ω0

Cda

B

C

D

E

F

5 4 2

2.5 2.5 2.5

5 4 2

NL NL NL

NL NL NP

49 NP NP

49 NP NP

31 NP NP

1.5

2.5

1.5

NL

NP

NP

NP

NP

8

2

4

NL

NL

49

49

31

6

2

5

NL

NL

49

49

31

3.25

2

3.25

NL

NL

11

11

NP

6 5 2 1.5 8

2.5 2.5 2.5 2.5 2.5

5 4.5 2 1.5 4

NL NL NL NL NL

NL NL NP NP NL

49 NP NP NP 49

49 NP NP NP 49

31 NP NP NP 31

5

2

4.5

NL

NL

49

49

31

3

2

3

NL

NL

NP

NP

NP

6.5 6 5 8 7 4.5 3.5 8 5 3 8

2.5 2.5 2.5 3 3 3 3 3 3 3 3

5.5 5 4.5 5.5 5.5 4 3 5.5 4.5 2.5 5.5

NL NL NL NL NL NL NL NL NL NL NL

NL NL NL NL NL NL NL NL NL NP NL

49 49 NP NL 49 11 NP NL NP NP NL

49 49 NP NL 31 NP NP NL NP NP NL

31 31 NP NL NP NP NP NL NP NP NL

(Continued)

5.2 Passive Damping Systems

Table 5.16 Suitable Load-Resisting Systems and Design Coefficients for Tall Buildings (ASCE, 2017a) Continued Limitations Including Structural Height (m) Seismic Design Category

Structural System

Dual systems with special moment frames

Dual systems with intermediate moment frames

Steel and concrete composite intermediate Steel and concrete composite ordinary Steel eccentrically braced frames Steel special concentrically braced frames Special RC shear walls Ordinary RC shear walls Steel/concrete composite eccentrically braced frames Steel/concrete composite special concentrically braced frames Steel/concrete composite plate shear walls Steel/concrete composite special shear walls Steel/concrete composite ordinary shear walls Steel special concentrically braced frames Special RC shear walls Steel/concrete composite special concentrically braced frames Steel/concrete composite ordinary braced frames

R

Ω0

Cda

B

C

D

E

F

5

3

4.5

NL

NL

NP

NP

NP

3

3

2.5

NL

NP

NP

NP

NP

8

2.5

4

NL

NL

NL

NL

NL

7

2.5

5.5

NL

NL

NL

NL

NL

7

2.5

5.5

NL

NL

NL

NL

NL

6

2.5

5

NL

NL

NP

NP

NP

8

2.5

4

NL

NL

NL

NL

NL

6

2.5

5

NL

NL

NL

NL

NL

7.5

2.5

6

NL

NL

NL

NL

NL

7

2.5

6

NL

NL

NL

NL

NL

6

2.5

5

NL

NL

NP

NP

NP

6

2.5

5

NL

NL

11

NP

NP

6.5

2.5

5

NL

NL

49

31

31

5.5

2.5

4.5

NL

NL

49

31

NP

3.5

2.5

3

NL

NL

NP

NP

NP

(Continued)

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CHAPTER 5 Design procedures for tall buildings

Table 5.16 Suitable Load-Resisting Systems and Design Coefficients for Tall Buildings (ASCE, 2017a) Continued Limitations Including Structural Height (m) Seismic Design Category

Structural System Steel/concrete composite ordinary shear walls Ordinary RC shear walls Shear wall frame with ordinary RC moment frames and ordinary RC shear walls 

R

Ω0

Cda

B

C

D

E

F

5

3

4.5

NL

NL

NP

NP

NP

5.5

2.5

4.5

NL

NL

NP

NP

NP

4.5

2.5

4

NL

NP

NP

Note: NL, not limited; NP, not permitted.

Moreover, the mathematical model of the building structure should explicitly define the structural member effective stiffness, mass properties, and inherent damping behavior (Chapter 3, Section 3.2). Structural member effective stiffness (see Tables 5.3
5.5) and expected strength (see Table 5.2) were already discussed in Section 5.1.3.2. The designer should analyze and design the bare structural system based on code requirements (ASCE, 2017a), loading criteria (Section 5.2.1.1), and analysis procedure (Section 5.2.1.4). From this analysis, the designer would understand if the bare structural system can resist the lateral loads without requiring excessive structural member sizes and detailing in order to satisfy strength, drift, and code acceleration requirements. Moreover, for seismic loading inelastic behavior is expected and this would induce damage to the structure causing reliability and economical concern as already explained in Chapter 3. Based on these analyses, the designer would understand the benefit of a dynamic modification system to be added to the main structural system selected in Step 2 (Section 5.2.1.2). In the following steps, the required procedure for the design of structures with passive distributed dynamic modification technologies will be reviewed in depth.

5.2.1.4 Step 4: Select a suitable analysis procedure Different procedures are provided depending on the dominant building external lateral excitation (i.e., seismic or wind) (ASCE, 2017a): 1. For seismic analysis, three procedures are commonly utilized (ASCE, 2017a; ASCE, 2017b; NEHRP, 2009, 2015): equivalent lateral force (ELF), response spectrum, and nonlinear response-history procedures. The relative corresponding acceptance criteria and limitations are given in Table 5.17. The ELF method is not allowed for tall buildings, because there is a limit on

5.2 Passive Damping Systems

Table 5.17 Analysis Procedures, Acceptance Criteria, and Limitations (ASCE, 2017a; NEHRP, 2009, 2015) Analysis Procedure

Criteria

Limitations for Tall Buildings

Equivalent lateral force

S1 , 0.6 Ndia $ 2 ζ Tb # 0.35 Hc # 30 m No irregularities Rigid diaphragms S1 , 0:6 Ndia $ 2 ζ Tb # 0.35 No criteria

Not permitted

Response-spectrum method

Nonlinear procedures

Permitted

Not limited

a

Nd is the number of damper per each story in each principal direction. ζ T is the total effective damping of the fundamental mode in the direction of interest (this is determined in Step 5). c The total height of the building. b

the maximum height of 30 m. Moreover, higher mode effects might become dominant in higher buildings (Lopez and Cruz, 1996; Chopra, 2007), and since the ELF procedure is based on a first-mode response, this might underestimate the design base shear and not accurately estimate the vertical distribution of seismic forces (ASCE, 2017a). Response-spectrum method is permitted if the criteria mentioned in Table 5.17 are satisfied. Except the first criterion (S1 , 0:6), which is related to the building site, the two other criteria (number of dampers per story, Nd , and total damping ratio, ζ T ) depend on the designer’s decision. Despite the other two procedures, nonlinear procedures are always acceptable for the design of tall buildings with dynamic modification devices. 2. For wind analysis, major standards (e.g., ASCE (2017a)) do not provide recommendations for structures equipped with distributed damping devices. However, linear static procedures are commonly utilized since the main structure response needs to remain elastic with the loads determined based on code procedures or wind-tunnel tests. In the following sections, different procedures are reviewed for structures with distributed damping technologies. Similar approaches can be applied to bare structure but this is outside the scope of this publication (see ASCE (2017a) for more details).

5.2.1.4.1 Step 4.1: Response-spectrum analysis procedure In this step the most important parameters for the design of a building with response-spectrum procedure, according to ASCE 7-16 (ASCE, 2017a), are reviewed. It is important to note that most of the commercial software available

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Table 5.18 Damping Factor (ASCE, 2017a) Effective Damping ζ (Percentage of Critical)

Bζ Factor (Where T . T 0 )

,2 5 10 20 30 40 50 60 70 80 90 $ 100

0.8 1.0 1.2 1.5 1.8 2.1 2.4 2.7 3.0 3.3 3.6 4.0

are capable of performing RSA but it is important that the designer has to be conscious on how the procedure is structured. Determine the numerical damping reduction factor Bζ . The response-spectrum procedure, when selected, requires the user to estimate the damping reduction factor, Bζ , which is based on damping, ζ, as selected in Step 5 (Section 5.2.1.5). In general, Bζ is defined, for a given period, as the ratio between the spectral value at 5% damping and at total damping ratio (Ramirez et al., 2001; Liang et al., 2012). ASCE 7-16 (ASCE, 2017a) provides estimate of Bζ factor for certain equivalent viscous damping levels (Table 5.18). The values in this table are presented for structures with natural periods, T , greater than or equal to T0 (Step 1.2, Section 5.2.1.1.2). If T is less than T0 , the factor Bζ can be interpolated linearly between Bζ 5 1 at T 5 0 and the value given by Table 5.18 at T0 . Alternately, in the literature several relationships have been proposed for Bζ as a function of the damping ratio, ζ: 1. Christopoulos and Filiatrault (2006) Bζ 5

4 1 2 lnðζ Þ

(5.41)

2. FEMA 440 (FEMA, 2005) and ASCE 41-17 (ASCE, 2017b) Bζ 5

4 5:6 2 lnð100ζ Þ

(5.42)

3. Eurocode 8 (CEN, 2003) Bζ 5

rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 0:05 1 ζ 0:1

(5.43)

These relationships are compared in Fig. 5.13. From the figure, it can be seen that all relationships are in good agreement for damping ratio values less than 40%.

5.2 Passive Damping Systems

FIGURE 5.13 Damping reduction factor Bζ versus effective damping ζ with various methods.

Calculate the seismic base shear (V ) of the building and compare it with the minimum value (Vmin ). The seismic base shear, V , used for the design of the force-resisting systems should not be less than Vmin , as expressed by (ASCE, 2017a): V 5 Cs W . Vmin 5 max

 Cs W ; 0:75Cs W Bζ

(5.44)

where 8 S > 0D11 for T1 # TL > > > > > R > > T@ A > > < Ie

8 9 0:044SDS Ie $ 0:01 > > > > > > > > < = 0:5SD1 I !e for S1 $ 0:6 # Cs 5 SDS # SD1 TL > > > R > > > 0 1 for T1 . TL > > > Ie > IRe > > : > ; > R > > 2 > > T @I A :

(5.45)

e

The important factor, Ie , is defined in Table 5.7 and the response modification coefficient, R, can be determined using Table 5.16; SD1 , SDS , and TL are determined previously in Step 1.2 (Section 5.2.1.1.2); T1 is the fundamental period of the building; and Bζ is the damping reduction factor. Note that in Eq. (5.44) the limit, 0:75Cs W, is not applicable in case less than two dampers per main direction in each story are provided and if horizontal and/ or vertical irregularities are present (ASCE, 2017a).

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CHAPTER 5 Design procedures for tall buildings

Determine the parameters of the lateral force
resisting system. ASCE 7-16 (ASCE, 2017a) allows the designer to take into account the inelastic behavior of the structural system and provides simplified formulas to estimate the relative hysteretic damping. It is important to note that buildings equipped with dynamic modification devices are usually designed to remain elastic for all the levels of excitation. In case inelastic deformations are considered, in the design process, it should be proven that these are not detrimental for the behavior of the damping system (ASCE, 2017a). In any case the parameters to take into consideration, when considering inelastic deformations, are the following: •

•

Effective ductility demands μD and μM : The effective ductility demand of the seismic force-resisting system of the building is defined as the ratio between the fundamental mode displacement, D1 ; and the displacement at the effective yield point of the system, Dy , both determined at the center of rigidity of the roof level in the direction of interest (ASCE, 2017a; NEHRP, 2015). Depending if D1 is estimated for the DE or the MCER, ground motions, the effective ductility is specified using symbol μD or μM , respectively. For the RSA of the damped structural system, the effective ductility demands are utilized for taking the inelastic (nonlinear) structural effects on the responses, as well as for updating the hysteretic and total damping contributions into account. As an initial phase, the designer may assume values of the effective ductility demands on the structure due to the DE (μD ) and MCER (μM ). These parameters may depend on the structural system and material type at hand. As discussed earlier, it is a general assumption to assume μD 5 μM 5 1, since the elastic behavior of the damped structure is desired. Effective fundamental mode period: In current building codes (ASCE, 2017a; NEHRP, 2015) nonlinearities are taken into account the global building behavior through the definition of the effective fundamental period. Depending upon the earthquake level (i.e., DE or MCER ground motions), this period can be explicitly computed by considering the postyield force
deflection characteristics of the structural system or can be obtained as follows: pffiffiffiffiffiffi T1D 5 T1 μD pffiffiffiffiffiffiffi T1M 5 T1 μM

•

(5.46) (5.47)

Modal seismic base shear and modal effective seismic weight: The modal base shear, Vm , of the mth mode in the desired direction can be readily calculated as: Vm 5 Csm Wm

(5.48)

where Csm is the modal seismic response coefficient (computed as shown below) and Wm is the modal effective seismic weight of the mth mode of structure given by the following:

5.2 Passive Damping Systems Pn

2 wi φim Wm 5 Pn  2 i51 wi φim i51

•

(5.49)

where φim is the mth modal displacement amplitude at the ith level of the structure (Section 5.2.1.3) in the direction of interest, normalized to unity at the roof level, and wi is the portion of the total effective seismic weight W, assigned to level i. Modal seismic response coefficients: these coefficients are computed for the fundamental and higher modes as follows: For fundamental modes: 

R SDS for T1D , TS Cd Ω0 Bζ1D

(5.50)

R SD1 for T1D $ TS Cd T1D Ω0 Bζ1D

(5.51)

Cs1 5  Cs1 5

For higher modes (m . 1): 

Csm 5

R SDS for Tm , TS Cd Ω0 BζmD

R SD1 for Tm $ TS Csm 5 Cd Tm Ω0 BζmD

(5.52)



•

(5.53)

Here, response modification coefficient R, deflection amplification factor Cd , and overstrength factor Ω0 were determined using Table 5.16; Tm is the period of the mth mode of vibration in the direction of interest (Step 3, Section 5.2.1.3); SD1 and SDS are determined in Step 1 (Section 5.2.1.1); and BζmD is the mth mode numerical damping reduction factor (see Table 5.18) for mth mode supplemental damping and Tm $ T0 5 0:2 SSD1 . As previously stated it DS is common practice to assume the same value of the supplemental damping for all modes. Total seismic base shear V and check its limit: ASCE (2017a) standard requires that the seismic base shear and its minimum value should be computed for a given direction of the interest. Provided that closely spaced modes do not have significant cross-correlation, the total base shear can be calculated with the square root of sum of the squares (SRSS) by: vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u Nm uX V 5t ðVm Þ2 $ Vmin

(5.54)

m51

where V min is calculated in Eq. (5.44). As an alternative, a CQC can be adopted to compute the base shear (refer to Chopra (2006) for further details).

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CHAPTER 5 Design procedures for tall buildings

•

Note: For a low-rise building with less number for mode shape, this procedure is practical. Instead, for tall building for which the analysis could include more than 100 mode shape, this method may be impractical. Design lateral force in modal form (Fim ): To determine the forces in the structural elements the design base shear needs to be distributed along the building height. ASCE 7-16 (ASCE, 2017a) proposed the calculation of the design lateral force, Fim , at ith level due to the mth mode in a given direction as follows: Fim 5 wi φim

Γm Vm Wm

(5.55)

where Γm is the modal participation factor associated for the mth mode of vibration in the direction under consideration that can be estimated as follows: Wm i51 wi φim

Γm 5 Pn

(5.56)

•

Design force in structural elements: Design forces in the structural elements can be determined using the SRSS or CQC of modal design forces (Chopra, 2006). To this end, the design lateral forces from the previous equation can be utilized in commercial software with static analysis. The alternative is to employ RSA directly, in a structural software with the parameters previously determined. Determine the parameters of distributed damping system. Based on the design and MCER seismic demands, the damper parameters can be separately determined with the use of the subsequent steps (ASCE, 2017a). •

DE roof displacement in modal forms (DmD m 5 1; 2; . . . ; n): For fundamental modes: D1D 5

2 g SDS T1D g SDS T12 Γ1 $ 2 Γ1 for T1D , TS 2 BζT1D BζT1E 4π 4π

(5.57)

D1D 5

g SD1 T1D g SD1 T1 Γ1 $ 2 Γ1 for T1D $ TS 4π2 4π BζT1D BζT1E

(5.58)

For higher modes (m . 1): DmD 5

•

g SD1 Tm g SDs Tm2 Γm # 2 Γm 2 4π 4π BζTmD BζTmD

(5.59)

where BζT1D and BζTmD are the total damping reduction factors for the fundamental and mth mode, respectively, at design displacement, and BζT1E is the total damping reduction factor for the fundamental mode at initial displacement (Table 5.18). DE floor deflection in modal δi;mD and total δiD forms: δi;mD 5DmD φim

(5.60)

5.2 Passive Damping Systems

vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u N uX  2 δiD 5 t δi;mD

(5.61)

m51

•

DE story drift in modal Δi;mD and total ΔiD forms: The story drift, Δi;mD , of mth mode and total drift, ΔiD , both associated with ith story can be computed as: Δi;mD 5 δi;mD 2 δi21;mD vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u Nm uX  2 Δi;mD ΔiD 5 t

(5.62) (5.63)

m51

•

DE story velocity in modal rimD and total forms riD : For fundamental modes: ri;1D 5 2π

Δi;1D T1D

(5.64)

ri;mD 5 2π

Δi;mD Tm

(5.65)

For higher modes (m . 1):

The total story velocity associated with ith story is: vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u Nm uX  2 riD 5 t ri;mD

(5.66)

m51

•

MCER roof displacement in modal forms (DmM form 5 1; 2; . . . ; n): For fundamental mode: D1M 5

2 g SMS T1M g SMS T12 Γ1 $ 2 Γ1 for T1M , TS 2 BζT1M BζT1E 4π 4π

(5.67)

D1M 5

g SM1 T1M g SM1 T1 Γ1 $ 2 Γ1 for T1M $ TS 4π2 4π BζT1M BζT1E

(5.68)

For higher modes (m . 1): DmM 5

g SM1 Tm g SMs Tm2 Γm # 2 Γm 2 BζTmM BζTmM 4π 4π

(5.69)

where BζT1M and BζTmM are the total damping reduction factors for the fundamental and mth mode, respectively, at maximum displacement (Table 5.18). In the subsequent steps, the structure inelastic behavior is taken into account while calculating the total damping (ASCE, 2017a; NEHRP, 2009, 2015). Using these steps causes iterations, and designers should repeat the calculations of this section until convergence.

295

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CHAPTER 5 Design procedures for tall buildings

Determine ductility demands. The maximum ductility associated with the structural system can be calculated as: " μ max 5 0:5

R Ω 0 Ie

μ max 5

#

2 11

for T1D # TS

R for T1 $ TS Ω 0 Ie

(5.70)

(5.71)

where Ie can be chosen from Table 5.7. This maximum value shall not be exceeded the ductility for DE, μ D , and MCER, μ M , levels, computed as follows: μD 5

4π2 RD1D $1 gCd Ω0 Γ1 CS1 T12

(5.72)

μM 5

4π2 RD1M $1 gCd Ω0 Γ1 CS1 T12

(5.73)

Note that, alternatively, it is permitted (ASCE, 2017a; NEHRP, 2015) to use nonlinear static (pushover) analysis, to develop a force
displacement curve of the system and to use this curve instead of the above equations in order to calculate the ductility demands. Determine hysteretic damping ratios ζ hD and ζ hM . In this step, with the use of inherent damping ratio, ζ i , specified in Step 3 (Section 5.2.1.3), the hysteretic damping ratio can be calculated, ζ hD and ζ hM , which are the damping contribution postyield hysteretic behavior for the DE and MCER levels, respectively, at effective ductility demands μD and μM , determined by: 8 0 > >   > > ζ hD 5 qH 0:64 2 ζ i @1 2 > > > < 0 > > >   > > ζ hM 5 qH 0:64 2 ζ i @1 2 > > :

1 1A μD 1 1 A μM

(5.74)

where 0:5 # qH 5 0:67

TS #1 T1

(5.75)

Determine the modal effective damping for design and maximum ground motions. This step gives the designer the opportunity to update the total effective damping by accounting for the ductility demands (μ D and μ M ) under DE and MCER ground motions, respectively. To this end, considering the hysteretic damping ratio (ζ h) and by including μ D and μ M , one can calculate the updated total damping ratio using Eqs. (5.76) and (5.77), respectively. Afterward, the

5.2 Passive Damping Systems

designer should refer to the above paragraphs to modify the structural and damping responses. In case nonlinear structural behavior is not considered, this step (as well the previous ones) is neglected. 

pffiffiffiffiffiffi ζ T1D 5 ζ i 1 ζ d1 μ D 1 ζ hD ζ TmD 5 ζ i 1 ζ dm 1 ζ hD for m . 1  pffiffiffiffiffiffiffi ζ T1M 5 ζ i 1 ζ d1 μ M 1 ζ hM ζ TmM 5 ζ i 1 ζ dm 1 ζ hM for m . 1

(5.76) (5.77)

Here, ζ hD and ζ hM are determined previously. The supplemental damping ratio, ζ d1 , at the fundamental mode is estimated in Step 5 (Section 5.2.1.5). It should be noted that the damping ratio, ζ dm , in higher modes may be assumed identical to that of the fundamental mode (i.e., ζ dm 5 ζ d1 ), or can be alternatively calculated using equations from other sources (see Lago (2011) for more information).

5.2.1.4.2 Step 4.2: Nonlinear procedure ASCE 7-16 (ASCE, 2017a) allows the utilization of nonlinear procedures for all types of buildings. Two different types of analyses are allowed: 1. Nonlinear response-history procedure 2. Nonlinear static procedure In both procedures, the structural and dynamic modification element’s nonlinear properties shall be explicitly modeled as verified by testing (ASCE, 2017a). The damper model shall also take into account the frequency and amplitude dependencies. However, this is not required when the properties vary during the loading history. In this case, an upper and a lower bound of the device properties can be used and the envelope of the dynamic response can be utilized (refer to Step 8 (Section 5.2.1.8.3) for more details). Nonlinear response-history procedure. This procedure considers the 3D numerical modeling of the whole building structural system, taking into account its intrinsic nonlinear hysteretic behavior, except for the elements of force-resisting system with ductility less than 1.5 that could be modeled as linear elements (ASCE, 2017a) (Note: careful consideration about modeling linear elements should be taken care since this is considered valid for systems with focused ductile behavior.) The nonlinear behavior should be consistent with test data and shall represent the overall cyclic behavior (i.e., yielding, strength and stiffness degradation, and pinching). The model shall be assumed as fixed based unless a realistic SSI model is used. Diaphragm flexibility shall be taken into account the case they are not rigid, compared to the vertical elements of the structural system. The numerical model should consider the actual spatial distribution of the mass throughout the structure. Nonlinear static procedure. Nonlinear static “pushover” procedure is used in addition to response-spectrum and ELF procedures in the case S1 . 0:6 to confirm

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the peak response (NEHRP, 2015). This procedure shall utilize a numerical model, similar to that of the nonlinear response-history procedure. The result of the analysis shall be a force
displacement curve that can be utilized for determining the ductility demand, as shown in Section 5.2.1.4.1.

5.2.1.5 Step 5: Select total target damping A trial supplemental equivalent damping ratio, ζ d , should be chosen by the designer. As shown in Chapter 3 (Section 3.2), this value is just one part of the building total damping that is made of this additional contribution: intrinsic, aerodynamic, and hysteretic. The intrinsic damping estimation is not trivial and ASCE 7-16 (ASCE, 2017a) specifies that it should be not greater than 3% for all the modes (detailed discussion on the different standard requirements was done in Chapter 3 (Section 3.2.2)). The hysteretic damping is commonly neglected (i.e., ζ h 5 0) in practice for buildings with dynamic modification devices, since it could be detrimental for the behavior of the dissipating system. In any case, a more detailed discussion on how to calculate structural hysteretic damping is given in Section 5.2.1.4.1. Similarly, the aerodynamic damping is neglected but it could become relevant with the next generation of slender supertall buildings. The amount of total damping is usually decided based on a combination of code requirements, economical, and practical aspects. Looking at code requirements, US code (NEHRP, 2015) allows a maximum total damping of 35%. Instead, the Chinese code (GB50011, 2010) recommends a total damping of less than 25%. In literature, other examples are found: Lee and Taylor (2001) suggest a value between 15% and 25%, while Zhou et al. (2012) suggested to use 15%. Note that this estimated damping value refers to the building fundamental mode of vibration and it is important to specify it also for higher modes. This is especially relevant for tall buildings that, in most cases, do not have single dominant modes. It is common practice to assume that the inherent damping is constant through all the modes, but this could be not conservative enough for the damping of the dissipation and hysteretic damping (see Lago (2011) for more information on different procedures available for estimating the higher mode damping). Starting from these recommendations, a designer can select a total damping value based on the required reduction of the building demand obtained from the target spectrum and the estimated predominant modal periods (Step 3, Section 5.2.1.3).

5.2.1.6 Step 6: Damper type, configuration, and distribution In this step, designers should choose the dynamic modification technology to utilize and this is obtained from the following three tasks: type of dampers, installation configuration of dampers, and distribution of devices over the building. 1. Selection of energy-dissipating devices: In general, distributed dampers can be classified into two categories: (1) velocity-dependent and (2) displacement-

5.2 Passive Damping Systems

dependent devices (for more details refer to Chapter 4 (Section 4.1.1)). The designer should select the appropriate type of distributed dampers with regard to several aspects, including: a. Type and form of tall building structural system: Depending on the type and form of the structure (e.g., frame, wall systems, combined systems) the type of damper may vary. For example, for coupled shear wall buildings friction dampers (Chung et al., 2009) and viscoelastic devices (Christopuolus and Montgomery, 2013) may be more suitable as coupling elements. b. Damper economics: In general, displacement-dependent devices are less expensive than velocity-dependent ones (e.g., Liang et al. (2012)). Also, the cost related to the availability of devices, depending on the site location, may be important. Moreover, displacement-dependent devices may need to be replaced after an event (see Chapter 3 (Sections 3.6) for further details about the economic aspects of damping devices). c. Target performance: Depending on the structural performance to be achieved, the selected type of devices may differ. For instance, velocitydependent dampers might slightly increase the base shear at the foundation level when the structure becomes inelastic, while displacement-based devices exhibit less of these problems (Symans et al., 2008). Furthermore, the use of viscous dampers more effectively reduces vibrations (Liang et al., 2012). d. Excitation force: Depending on which external lateral load (e.g., wind or earthquake) is exciting the tall buildings, the type of dampers applied may be different. For example, velocity-dependent dampers are usually preferred for wind-dominant excited buildings, rather than displacementbased ones. Additionally, displacement-dependent dampers, especially friction dampers, are more suitable for buildings located near high-seismic zones with long-period ground motion histories (Liang et al., 2012). Further details and guidelines about the selection of damper type are provided in Chapter 4 (Section 4.4). 2. Damper geometrical configuration: After selecting the type of energydissipating devices, the most suitable device configuration can be chosen by the designer, mainly depending on the type of lateral load
resisting structural system. The most common damper configurations are represented in Chapter 4 (Section 4.1.1). In case the tall building’s lateral system consists of a frame-like (shear-type) structure, the configurations illustrated in Fig. 4.2 may be adopted. Instead, if coupled walls are used, the installations shown in Fig. 4.16 or 4.19 could be more appropriate. In addition, diagonal or Chevron configurations could not be the preferred solution due to architectural constraints (see Chapter 6 (Section 6.1) for further details). Another reason could be the presence of stiff coupling beams and shear wall systems with relative small interstory drift velocities that might not be sufficient to activate diagonal or Chevron damper configurations (Lavan, 2012).

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3. Damper distribution: Given the type and damper geometrical configuration, the device distribution along the plan and height of the building can be determined by the designer, based on the following considerations: a. Plan distribution. Concerning the building plan, the distribution should be symmetrical (ASCE, 2017a) to the center of stiffness in such a way that no torsional effects could develop due to damper forces under seismic or wind loading. To control torsional effects, it is recommended (NEHRP, 2015) that at least four dampers are considered in each story and along each main direction of building, with at least two devices (per direction) on each side of the center of stiffness of any story. If these minimum conditions are not satisfied, all dampers must be capable of sustaining 1.3 times the maximum displacements obtained under MCER; moreover, velocity-dependent dampers must sustain displacements and forces associated with 1.3 times the maximum velocity under MCER. No additional requirements are given for wind design. Depending on the most critical direction under external excitations, the damping system may be assigned to one direction of the building plan or to more directions; the desirable direction to be equipped with dampers in existing buildings may sometimes depend upon the possible location for the device placement within the structural systems in that direction. For a case study example of this type, see San Diego Courthouse case study, in Chapter 8 (Section 8.1.6). b. Vertical distribution. Regarding the distribution in height, in general, these general aspects should be considered: interstory drifts and velocities profile, damper mechanical properties distribution in height, and the number of devices assigned in each story. Building codes usually provide general recommendations on how dampers distribute vertically. American standards (e.g., FEMA (2000d)) suggest that damper should be arranged evenly along the height of the building. In China, GB50011 (2010) suggests that energy dissipation devices can be positioned in those stories where the drift is larger. Its number and distribution should be decided reasonably by means of comprehensive analysis, so that it is beneficial to improve the energy dissipation capacity of the whole structure. However, GB50011 (2010) provides the formula for calculating the effective supplemental damping ratio, which is applicable only when the dampers are arranged evenly along the height of the building. Based on these considerations, the traditional arrangement scheme for dampers is to place them in the story with larger drifts or velocities, and at the same time, try to arrange them evenly along the height of the building. However, in practical high-rise projects, the two aspects above are hardly achievable. Current super tall buildings are mainly composed of framecore tube structures with outriggers at several floors along the height. In this case, dampers could be placed only at outriggers stories that usually

5.2 Passive Damping Systems

have the smallest story drift and velocity (see Section 5.6.2 for further distribution optimization criteria). In literature the major several vertical distribution methods can be found and the most common are the following: uniform, based on damper properties (Whittle et al., 2012) and inversely proportional distribution (Takewaki, 2009). The first approach has been successfully applied in several different buildings: uniform distribution of viscoelastic dampers within the original World Trade Center in New York City and the Santa Clara County Building in San Jose, California (Soong and Dargush, 1997, and see Chapter 8 for more case studies). However, this distribution method may not be the most effective one because it does not take into consideration the different demand at each floor. To overcome this, a partial distribution of identical dampers around the maximum shear deformation along the height could be utilized (Lago, 2011; Christopoulos and Montogomery, 2013). The second basic approach is based on distributing dampers based on their mechanical properties. The major methods are stiffness- and massproportional distribution. The former considers the distribution of the dampers with the relative constant, c, proportional to the ith story lateral stiffness, ki . The larger the story stiffness, ki , the greater the damping coefficient, ci . The stiffness can be estimated simply from applying a distributed static lateral load and the ratio of interstory shear force to interstory displacement at each level gives the lateral story stiffness for a typical structural system (Whittle et al., 2012). The other option can be based on mass-proportional distribution in which the damper constant is proportional to the mass. In this case, dampers are placed between the floor and a fix point (usually the ground), but this is quite impractical for tall buildings (Trombetti and Silvestri, 2006). The third approach is based on the work by Takewaki (2009) and Takewaki and Fujita (2009). They emphasized that the distribution of passive energy-dissipating devices is not efficient in upper stories of tall buildings. Moreover, Takewaki (2009) mentioned that the dampers are more effective for shear deformation; thus, the linear distribution of dampers, consistent with dominance of such a deformation along tall buildings, is proposed. The proposed simplified strategy (Takewaki, 2009) consists in multiplying a constant damping coefficient by a series of factors, defined by the user, to obtain an inverse-linear distribution (see Fig. 5.14). Only two coefficients, less than one, are needed: υ1 assigned to the first story and υN associated with the topmost story. In addition, to the above-mentioned distributions, some other advanced methods can be employed to get the optimal distribution of dampers along the building height. These include sequential search algorithm (SSA)-mode application (Lopez-Garcia, 2001) and analysis/redesign approach (Lavan and Levy,

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FIGURE 5.14 Fully linear distribution of damping along tall building height.

2006) (further details about more advanced techniques are described in detail in Section 5.6).

5.2.1.7 Step 7: Damping preliminary design In this step, the preliminary design of the major type of distributed damping devices (viscous, viscoelastic, and hysteretic/friction) is reviewed and discussed in detail.

5.2.1.7.1 Viscous dampers’ properties estimation Generally speaking, the main parameters to define in order to design a viscous damper are velocity exponent, α, damping coefficient, c, and damper power, ED . Velocity exponent. In case nonlinear viscous dampers are chosen, the velocity exponent, α, should be preliminarily selected by the designer. A viscous damper catalogue is commonly provided by manufacturers for several specified values of α (Zhou et al., 2012). Generally speaking, the suitable α value is smaller for the seismic design than wind-resistant design (Taylor, 2010). As discussed in Chapter 4 (Section 4.1.1.1.1), the main advantage of utilizing linear damper (i.e., α 5 1:0) is that the damping force has 90 degrees phase difference with the elastic restoring force of structure. For nonlinear viscous dampers, the phase difference diminishes as the velocity exponent gets smaller (see Fig. 5.15). Damping coefficient. The damping coefficient can be estimated knowing the velocity exponent, α, of viscous dampers and the supplemental target damping ratio, ζ d , chosen by the designer in Step 5 (Section 5.2.1.5). Additionally, to determine the damping coefficient, the type of damping distribution along the building height needs to be chosen. Hence, the designer can choose between different damping distributions, previously described in Step 6

5.2 Passive Damping Systems

FIGURE 5.15 Constitutive relation curves of different damping indeces.

(Section 5.2.1.6): uniform (Liang et al., 2012; Palermo et al., 2016), stiffnessproportional (ASCE, 2017a), and inversely linear (Takewaki, 2009). In the following, each distribution method is briefly reviewed. •

Uniform damping distribution. In case viscous dampers are uniformly distributed, Liang et al. (2012) have proposed a preliminary design method for estimating the damping coefficient according to different installation arrangements. Considering a nonlinear viscous damper with constant, Ci , associated with the ith story (if more than one damper per stories this is the total required damper constant per story), and velocity exponent, α, the generalized expression is developed as follows: Ci 5

12α 4πM1  0:8u_ di;max ζd 2 NT1 ðGah Þi

(5.78)

Here, N is the number of stories that are equipped with dampers; M1 is the fundamental mode effective mass, obtained from modal analysis performed in Step 3 (Section 5.2.1.3); u_ di;max is the damper maximum velocity at the ith floor; ðGah Þi is the geometrical magnification factor that relates to the ith floor to the (i 2 1)th floor (see some common relations of ðGah Þi , as illustrated in Chapter 4 (Fig. 4.2), according to various damper configurations and summarized in Table 5.19)). The maximum interstory velocity, u_ di;max , can be obtained from commercial software results or from empirical relations, as proposed by Palermo et al. (2016) for shear-type buildings. Alternatively, in response to spectrum procedure the maximum of interstory velocity can be calculated from Step 4 (Section 5.2.1.4.1). For preliminary design, Zhou et al. (2012) suggest that a velocity of 200
250 mm/s is usually appropriate for building viscous dampers. Moreover, Sinclair (2006) took a design velocity of 254 mm/s for viscous dampers.

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Table 5.19 Horizontal Magnification Factors for Various Damper Installation Schemes Damper Installation Type Diagonal Intradiagonal Scissor Chevron Bottom toggle

Geometrical Magnification Factor ðGah Þi   cos θj  a cos θj Hjj   sin θj1   tan θj2 1

  cos θj1   cos θj1 1 θj2

  sin θj2   cos θj1 1 θj2     aj :cos θj1   2 cos θj2 cos θj1 1 θj2 bj aj   sin θj1 1

Up-Toggle Modified Toggle Modified Chevron

In alternative to Eq. (5.78) a simplified relation (Silvestri et al., 2010; Palermo et al., 2016) can be utilized as follows: Ci 5

 12α N 11 2πm  0:8:u_ di;max ζd 2 nd T1 ðGah Þi

(5.79)

where nd is the total number of identical viscous dampers placed at each story; N is the number of building stories; and m is the total mass of the building. In the case of buildings with significant flexural deformation (e.g., tall buildings with wall systems) the vertical deformation could be comparable to the horizontal one (as already explained in Chapter 4 (Section 4.1.1.1)). For this reason, Hwang et al. (2008) propose an update of Eq. (5.78) to take into account the vertical deformations for linear viscous dampers with uniform distribution along the height:  2 m i φh i Ci 5 P h     i2 ζ d T1 j ðGah Þj φh rj 2 ðGav Þj φv rj 4π

P

i

(5.80)

where ðGah Þj and ðGav Þj are magnification factors in the horizontal and vertical directions, (see Table 5.20 for some damper-type configurations);   respectively  φh rj and φv rj are, respectively, the horizontal and vertical relative displacements between two ends of the jth damper associated with the fundamental   mode; φh i is the horizontal displacement of the fundamental mode at the ith floor. Note that the vertical mode displacements are known from the modal analysis carried out in Step 3 (Section 5.2.1.3).

5.2 Passive Damping Systems

Table 5.20 Vertical Magnification Factors for Various Damper Installation Schemes Magnification Factor of Vertical Direction ðGav Þi   sin θj

Damper Installation Type Diagonal

ðhj =bj Þ     cos θj2 cos θj4 2 θj1   cos θj1 1 θj2       cos θj2 cos θj1 1 θj3   2 sin θj3 cos θj1 1 θj2

Chevrona Up-Toggleb Bottom-Togglec

a

h is the interstory height and b is the length of a single bay. For this configuration, θ4 is the angle between damper direction and vertical direction. c For this configuration, θ3 is the angle between damper direction and vertical direction. b

In case the viscous dampers are nonlinear, the magnification factors, from Table 5.20, can be used with the following equation: Ci 5

•

P  2 ð2πÞ32α D12α 1D i m i φh i h     i11α ζ d P 22α T1 ψ ð G Þ φ 2 ð G Þ ah av h rj j j φh rj j

(5.81)

Here, D1D is the roof design displacement corresponding to fundamental mode (as calculated in Step 3 (Section 5.2.1.3)) and ψ is a constant defined in Chapter 4 (Section 4.1.1.1.1). Stiffness-proportional damping distribution. For linear viscous dampers, where a stiffness-proportional damping distribution is selected, the total added damping coefficient, Ctot , can calculated as follows (ASCE, 2017a): Ctot 5

T1

PN

2 i51 mi φ1i  2 2 j51 Kj ðGah Þj φ1j 2φ1;j21

4πKtot

PNd

ζd

(5.82)

where Kj is the jth lateral story stiffness (Step 2); Ktot is the sum of all the story stiffnesses; φ1j and φ1;j21 are, respectively, the horizontal modal displacements of the jth damper between the ith and ði 2 1Þth floor in the fundamental mode; and mi is the mass at the ith floor level. Consequently, the damping coefficient Ci for the ith story (this is the total damping needed per floor) can be directly calculated as: Ci 5 Ctot

Ki Ktot

(5.83)

If the dampers are nonlinear the following expression can be applied: Ci 5 Ctot

12α Ki  0:8u_ di;max Ktot

(5.84)

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CHAPTER 5 Design procedures for tall buildings

•

Inversely linear distribution. If dampers are distributed as inversely linear along the height (see Fig. 5.13), the following expression can be used: Ci 5

T1

PN

2 i51 mi φ1i  2 2 j51 ηj ðGah Þj φ1j 2φ1;j21

PNd

4π



0:8u_di;max

12α

ζ d ηi

(5.85)

where Ci 5 ηi C denotes the total damping coefficient assigned to the ith story and ηi is known from Step 6 (Section 5.2.1.6). Note that damping coefficient evaluation can be accompanied or verified with the average values from a series of experimental tests (e.g., prototype and production tests (NEHRP, 2015)) during the design or construction phase (ASCE, 2017a; NEHRP, 2009, 2015) (see Chapter 7 for further details about these testing procedures). Damper power. Controlling the damper power is one of the most critical aspects in the design of viscous dampers. For example, for wind resistance the power needs to be controlled to prevent the damper from damage under lingering-high temperature. Considering an SDOF stimulated by a sine function (u 5 u0 sinðωtÞ) load, the energy dissipated of nonlinear damper, based on the damper force (Chapter 4 (Eq. 4.6))], is: ð ED 5

Fd dud 5

ð 2π=ω 0

cju_ d j11α dt 5 ψcωα u11α 0

(5.86)

where ψ is a constant estimated as shown in Eq. (4.20); ω is the angular velocity; and u0 is the amplitude of damper (often be set equal to 0.2
0.3 times maximum displacement of damper). This expression is equivalent to the one for linear dampers as shown in Eq. (4.9). Then the damper power is equal to: PD 5 ED f1

(5.87)

where PD is damper power in watts and f1 in general is the primary frequency of structure for the direction which has arranged dampers. Eq. (5.86) shows how the damper power is greatly influenced by the damping exponent. Hence, for damper used in wind resistance, the basic principle is the damping exponent cannot be too small. Moreover, for most dampers, their permitted power is less than 1 HP (different tonnage dampers have different permitted powers). Therefore, for α 5 0:3 the damper power will be overlarge if the damper is used for wind resistance, and this will be worse for smaller damping exponent coefficients. Balancing this by repeated iteration is one of the main contents of damper parametric design of high-rise buildings.

5.2.1.7.2 Viscoelastic dampers’ property estimation The stiffness and damping coefficients of viscoelastic dampers may depend upon the frequency and temperature of the dampers which are consistent with

5.2 Passive Damping Systems

the fundamental frequency of the building and the working temperature range (ASCE, 2017a). The stiffness and loss factor (damping) of each viscoelastic damper must be chosen based on the available viscoelastic material and the geometry of the damper (Chapter 4 (Section 4.1.1.1.2)). In general, this can be a trial-and-error approach (Christopoulos and Filiatrault, 2006) and it can be accompanied or verified with the use of a series of experimental tests (see Chapter 7) (ASCE, 2017a). As an assumption, the ambient temperature of the viscoelastic material can be assumed invariant, for example, 21 C, during earthquake events and the shear strain to remain constant at 100% (Marko et al., 2006). Moreover, it has been shown that a large decrease in the material stiffness occurs in the 0%
50% strain range, whereas in the 50%
200% strain range the stiffness remains approximately constant (Aiken et al., 1990). In general, depending on the distribution type of devices along the height (i.e., uniform-proportional and stiffness-proportional), two procedures are presented to preliminarily determine the viscoelastic damper properties (note that both procedures do not take into account the stiffness of the brace supporting the viscoelastic damper): •

Uniform damping distribution. In case the viscoelastic dampers are distributed uniformly along the total height or a part of total height, based on the supplemental viscous damping, ζ d , created by Nd discrete devices (Constantinou et al., 1998; Christopuolos and Montgomery, 2013), the damping coefficient assigned to ith story is: Ci 5

T1

PN

2 i51 mi φ1i  2 2 j51 ðGah Þj φ1j 2φ1;j21

4π

PNd

ζd

(5.88)

where T 1 is the fundamental period of the viscoelastic-damped building. To quickly estimate this period, the following expression is proposed by Ramirez et al. (2001): ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi s 2ζ 12 d T 1 5 T1 η

(5.89)

where η is the loss factor of the viscoelastic material, as described in Chapter 4 (Section 4.1.1.1.2). For simplicity, ηD1 is suggested as an initial trial (Ramirez et al., 2001). Alternatively, this parameter can be more accurately calculated as shown in Appendix A (from Eq. 4.39) using the fundamental frequency, ω1 , and the operating design temperature of the building. A comprehensive database of viscoelastic material properties for a range of temperatures, strains, and frequencies is presented by Zimmer (1999). It is important to emphasize that the addition of viscoelastic dampers should not significantly alter the natural period of the building (Christopuolos and Montgomery, 2013). Consequently, based on the existing relation (Appendix A (Eq. 4.40)) between the stiffness and damping in viscoelastic

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materials, the viscoelastic damper stiffness property, kdi , of dampers associated with ith story can be estimated by: Ci kdi 5 η

•

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ω21 1 2 2ζ d =η

(5.90)

Stiffness-proportional damping distribution. The stiffness of viscoelastic dampers, kdi , added to the istory, can be set to be proportional to the story stiffness of the bare structure, Ki. The damper stiffness is then expressed, accounting for geometrical magnification factor ðGah Þi , expressed in Table 5.19, based on additional damping ratio, ζ d , at the fundamental mode of the structure, as (Soong and Dargush, 1997; Christopoulos and Filiatrault, 2006): 2ζ d Ki  kdi 5  η 2 2ζ d ðGah Þ2i

(5.91)

The viscoelastic damping coefficient can be calculated using Eq. (4.40) (as shown in Appendix A), and is also shown here: ηkdi Ci 5 qffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2

ω1 1 2 2ζ d =η

(5.92)

It should be noted that the response of the building may be assessed with multiple analyses, using limiting upper and lower bound amounts, for example, due to variation in temperature, for the stiffness and damping coefficients (ASCE, 2013). Designers can refer to Step 8 (Section 5.2.1.8.3) for more details about how to model changes in damper properties.

5.2.1.7.3 Displacement-dependent dampers’ properties estimation For displacement-dependent dampers the force is mainly a function of the relative displacement between two ends of the damper. Indeed, the response is independent of the relative velocity and the excitation frequency (see Chapter 4 (Section 4.1.1.3) for more details about this category of devices) (ASCE, 2017a; NEHRP, 2015). In this step, two kinds of displacement-dependent dampers are reviewed: •

Friction (coulomb) dampers are presented with three different damping distribution types (i.e., uniform-proportional, story shear-proportional, and inversely linear-proportional). Uniform-proportional to the story strength (shear) and triangle (inversely linear) distribution patterns of slips forces, in general, lead to a significantly better seismic performance (i.e., reduction in interstory drift and roof displacement). For example, Nadid et al. (2015) studied different pattern distributions for moment-resisting RC frames under seismic excitations retrofitted by friction dampers.

5.2 Passive Damping Systems

•

Hysteretic dampers with bilinear behavior (Liang et al., 2012) are reviewed. Two different distribution patterns are studied: uniform distribution along the height and story shear-proportional distribution. In addition, bracefriction (coulomb) damper systems (Lee et al., 2008a,b) are treated since they exhibit an elastic-perfectly plastic hysteretic model, similar to hysteretic dampers. Friction (coulomb) dampers. Depending on the distribution of friction dissipating devices along the building height, the frictional forces required for the design can be independently estimated using the effective supplemental damping ratio, ζ d . Assuming that the devices are pure friction dampers of a coulomb type (see Fig. 4.63 in Chapter 4), their mechanical behavior can be achieved ideally using zero velocity exponents, in the definition of the equivalent damping of nonlinear viscous dampers (as shown in the previous section). On this basis, different expressions are presented in the following, depending on damping distribution utilized. •

Uniform damping distribution. In case the damping force (coefficient) is associated with each of the Nd dampers, it is assumed to be identically distributed along the building height (Lee et al., 2008a,b), the following expression gives the preliminary design slip force of friction dampers: P d 2π3 ζ d D1M Ni51 mi φ21i Fdsi 5 2 PNm   T1 j51 fj φ1j 2 φ1;j21

•

(5.93)

where D1M is the maximum roof displacement under MCER associated with the fundamental mode that can be calculated from Eqs. (5.67) and (5.68). Story shear-proportional damping distribution. Friction dampers may be distributed proportional to the story shear forces, Vi (Pekcan et al., 1999a,b; Levy et al., 2001; Lee et al., 2008a,b). These forces can be estimated by applying a distributed (triangular) static lateral load on the structural system (Rao et al., 1995). Alternatively, if the story shear is unknown, the slip force with such a distribution type can be expressed by: Fdsi 5

P d 2π3 ζ d D1M Ni51 mi φ21i   Si PNm 2 T1 j51 Sj Gahj φ1j 2 φ1;j21

(5.94)

where the story shear force, Vi , assigned to ith story is proportional to the N P mi φ1i (Hwang et al., 2013). In alternative, the proportionalparameter Sj 5 i5j

ity of slip forces to story shears is defined based on the product of stiffness and peak interstory drift of the ith floor (Lee et al., 2008a,b). Additionally, the slip forces of friction dampers can also be distributed proportional to modal story shear forces (Levy et al., 2001).

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CHAPTER 5 Design procedures for tall buildings

•

Inversely linear damping distribution. Nabid et al. (2015) proposed to distributed friction dampers based on an inverse-linear manner, where the slip force at the ith story, Fdsi , is proportional to the total slip force, Fds;tot , as: Fdsi 5 ηi Fds;tot P 2π3 ζ d1 D1M Ni51 mi φ21i Fdsi 5 2 PNm   ηi T1 j51 ηj Gahj φ1j 2 φ1;j21

(5.95) (5.96)

where ηi , called the proportionality factor, is assigned to ith story in such a way a linear distribution of slip forces can be obtained along the height. Hysteretic dampers. In general, the behavior of a hysteretic damper can be idealized with a bilinear damping mechanism (as reviewed in detail in Chapter 4, Section 4.1.1.2.1). Hence, when a damper is incorporated in a structure, the damping force versus relevant structural response can be modeled as a parallelogram (see Fig. 4.32 in Chapter 4). Hysteretic (bilinear) dampers can be characterized with the use of three independent parameters, that is, yielding displacement, Dy , yielding ratio (i.e., rα 5 k0p =k0 ), initial stiffness, k0 , and postyield stiffness, k0p . These parameters, shown in Fig. 4.32 (Chapter 4), should be specified from the list of manufacturer’s products (Liang et al., 2012). In particular, a parallelogram-type hysteretic model can also be obtained with a pure friction damper (Fig. 4.63 in Chapter 4) in series with an additional supporting system, connected to main structural members (see Fig. 5.16). In this case, the frictional force Fds in the damper, and the shear force, in brace Fb , are equal from a mathematical viewpoint. The hysteretic loop of a bracing-friction damper is then defined as an elastic-perfectly plastic model (Fig. 4.31 (Chapter 4)). Four steps are presented in the following; in order to preliminary design the hysteretic dampers/spring-friction damper systems for each story, given the supplemental damping ratio, ζ d , from Step 5 (Section 5.2.1.5) and fundamental Eigen properties (i.e., T1 and φ1 , Step 3 (Section 5.2.1.3)) of the building. •

Selection of yielding displacement: The yielding displacement, Dy , in hysteretic (bilinear) dampers plays a greater role in response reduction than the initial stiffness, k0 . The selection of the yielding displacement is frequently predetermined in accordance with the specific type of damping materials and in general, smaller values of Dy may give better results.

FIGURE 5.16 Spring-friction damper system.

5.2 Passive Damping Systems

•

•

Concerning spring-friction damper systems, yielding displacement (maximum preslip displacement) is related to the yielding properties of the brace supporting the friction damper. This can be chosen by the designer (Levy et al., 2001) or with reference to the manufacturer. Selection of yielding ratio: The value of this parameter is usually much less than unity. Designers may select the yielding ratio, rα , from the information provided by the manufacturer. When the yielding stiffness of devices is significantly small (i.e., k0 -0) this leads to an elastic-perfectly plastic hysteretic behavior which results in negligible yielding ratio (i.e., rα -0). This assumption is also valid for spring-friction damper systems. Determination of characteristic strength (f0 ): For simplicity, since the strain energy of the main structure is much larger than that stored in the devices, the latter one can be neglected once devices are yielded (Liang et al., 2012). Accordingly, assuming all the dampers are activated simultaneously, the following relation gives the approximate characteristic strength as: f0 5

•

P 2π3 ζ d D21M Ni51 mi φ21i     P m T12 Nj51 Gahj D1M φ1j 2 φ1;j21 2 Dy

(5.97)

where the maximum roof displacement, D1M , under MCER can be estimated from Eqs. (5.67) and (5.68) or from the result of a RSA using commercial software. Gahj is the geometrical factor for hysteretic dampers as given in Table 5.19. It is better to limit the characteristic strength, f0 , to a certain range, especially when the damper yielding stiffness, kd , is small in comparison to the structural stiffness. Moreover, f0 should not be too large or too small for vibration reduction (Liang et al., 2012). For example, in tall buildings (i.e., large fundamental period) the choice of a small characteristic strength will reduce the displacement more effectively (Liang et al., 2012). Concerning spring-friction damper systems (Fig. 5.16), the slip force, Fds , of the friction (coulomb) damper can be simply replaced by the characteristic strength, f0 , of hysteretic bilinear dampers (Fig. 4.32 (Chapter 4)). Determination of yielding stiffness and unloading stiffness: Given the damper parameters, the value of initial stiffness, k0 , and yielding stiffness, k0p , can be, respectively, calculated as: k0 5

f0 ð1 2 rα ÞDy

k0p 5 rα k0

(5.98) (5.99)

If the yielding stiffness, k0 , is less than a certain threshold, the structural vibration cannot be reduced. Hence, one can increase the k0 when the threshold is reached. It should be noted that, although increasing k0 is beneficial, it is usually determined by manufacturers; hence, designers do not have a selection range for the yielding stiffness (Liang et al., 2012).

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For brace-friction damper systems, rα 5 0 and accordingly, the brace stiffness (kb 5 k0 ) can be calculated as: kb 5 k0 5

f0 Fds 5 Dy Dy

(5.100)

Consequently, given the length, Lbj , of the brace, its cross-sectional area reads (Levy et al., 2001): Aj 5

kb Lbj EB

(5.101)

where EB is the elastic modulus of the brace material. Note that the above steps are suitable for hysteretic dampers where they are identical in every story (i.e., uniform damping distribution). For other kinds of damping distribution, the expression of characteristic strength is slightly different, depending on the type of distribution. For example, dealing with the story shearproportional damping distribution replacing the characteristic strength (f0i ) assigned to the ith story with the slip force (Fdsi ) in Eq. (5.94), the following expression is obtained to calculate the damper forces: f0i 5

P 2π3 ζ d1 D21M Ni51 mi φ21i     Sj j51 Sj Gahj D1M φ1j 2 φ1;j21 2 Dy

PNm 2

T1

(5.102)

5.2.1.8 Step 8: Construct damped structural model and perform structural analyses After the mechanical properties of dampers are preliminarily determined, as shown in the previous step, the mathematical model of the building structure, initially constructed in Step 3 (Section 5.2.1.3), should be updated by including the damping systems. Then, the NLTHA of the mathematical model of the structure and damping systems constructed in this step can be carried out for one of the following reasons: • •

To verify the responses predicted with the response-spectrum procedure as shown in Step 4.1 (Section 5.2.1.4.1). To mainly analyze the damped building responses, if the nonlinear procedure is chosen for the design.

The following points should be noted when dealing with the explicit damper structural modeling (ASCE, 2017a; NEHRP, 2015) in commonly available software: •

Structural system
NLTHA should be accomplished at both the service and MCER levels.
Inherent damping shall not be greater than 3% (NEHRP, 2015) (see Step 5, Section 5.2.1.5, and Chapter 3 (Section 3.2) for more details about inherent damping estimation).

5.2 Passive Damping Systems




•

Inherent eccentricity, due to asymmetry in mass and stiffness, can be accounted for in the model in MCER analysis.
Accidental eccentricity, consisting the center-of-mass by an amount equal to 5% of the diaphragm dimension separately in two orthogonal directions of building, should be considered in the model.
P-delta effects should be considered during modeling.
Depending on the material behavior, the hysteretic behavior of the structural members should be properly assigned during modeling.
Per the preliminary analysis (Step 6, Section 5.2.1.6), every structural element can be modeled as linear if capacity/demand ratio is less than 1.5.
The structures that have significant horizontal structural irregularity (in plan) should be modeled using a 3D representation.
If the floor diaphragms are not considered as rigid ones, the model may include representation of the diaphragm’s stiffness characteristics and relevant additional degrees of freedom.
The SSI may be included through direct analysis (through finite element modeling of the SSI) or substructure approach (through representing the stiffness and damping of the soil
foundation interface). More details about this is outside the scope of this publication but interested readers should refer to NIST (2012). Damping system
Results under the MCER analysis should be used to design the dampers.
If damper properties change with time and/or temperature, such behavior should be explicitly accounted for in the model (further details in Section 5.2.1.8.3 and in Chapter 4 (Section 4.1.1) for general material damper behavior).
In the direction of interest, depending upon the suitable positions in the structural system, at least two dampers at each side of the center of rigidity shall be modeled along all stories of the structural system (NEHRP, 2015); the mechanical properties of all the dampers in each story can be assumed identical.
Displacement-dependent dampers (e.g., friction and hysteretic) should be modeled accounting for the hysteretic behavior of the devices consistent with test data (see Chapter 7 for more details about testing devices).
The stiffness (e.g., in viscoelastic dampers and if any in viscous dampers) and damping properties of the velocity-dependent damping devices can be explicitly assigned using the values specified in Step 7 (Section 5.2.1.7).

The major commercially available software capable of modeling dampers are the following: CSI (2016a,b,c), Opensees (2017), Abaqus (Dassualt, 2017), Midas (Harpaceas, 2017), Seismosoft (2017), and Ansys (2017). Other softwares are commercially available but they are more specific to analyze the mechanical behavior of the single device, such as Comsol (2017) and MSC Nastran (2016).

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FIGURE 5.17 Viscous/viscoelastic dampers modeling: (A) Kelvin model and (B) Maxwell model.

In the following, basics of dampers modeling are given. Interested readers should refer to the relevant literature on the subject for more details.

5.2.1.8.1 Modeling viscous/viscoelastic dampers Viscous/viscoelastic dampers can be modeled using the following two models: • •

Kelvin model (Fig. 5.17A). Mostly utilized for dampers with storage stiffness and weak frequency dependence, and discussed in detail in Chapter 4. Maxwell model (Fig. 5.17B). Mostly utilized for dampers with strong frequency dependency (this model ignores temperature dependence). CSI (2016b) suggests using this model for both viscous and viscoelastic dampers. The stiffness, kd , should be set to as large as possible. In order to guarantee this, it is recommended that the relaxation time (cd =kd ) to be an order of magnitude less than the loading time step, Δt. For example, a value of kd 5 100cd can be utilized.

Having the dampers always in series with the linkage of the damper-brace assembly will act as a Maxwell model. For this reason, the damper effectiveness is reduced as a function of structural properties and loading frequency (FEMA, 2006b). Nonlinear two-node link element (NLLINK), found in SAP2000 (CSI, 2016b), ETABS (CSI, 2016a), or OpenSees (2016) programs, can be utilized for modeling this type of dampers. This can be expressed as a Maxwell element with a dashpot and a spring in parallel (Fig. 5.17B (Christopoulos and Montgomery, 2013; DIS, 2017)). Note that SAP2000 (CSI, 2016b) has some numerical problems in case nonlinear viscous dampers with velocity exponents less than 0.4 are utilized.

5.2.1.8.2 Modeling friction and hysteretic dampers The nonlinear behavior of yielding and friction dampers can be modeled with a bilinear elastoplastic spring with hardening (Fig. 4.32 (Chapter 4)) and a bilinear rigid plastic (perfectly plastic, Fig. 4.31 (Chapter 4)) spring, respectively. For this

5.2 Passive Damping Systems

FIGURE 5.18 Plastic
Wen model.

purpose, a nonlinear link element available in most software, called Plastic
Wen (Fig. 5.18), can be used. This element has six DOFs and, for each DOF, the independent uniaxial plasticity properties (Bagheri et al., 2015) can be specified (Fig. 5.18).

5.2.1.8.3 Effects of variation in damper properties The design of dampers can include effects of environment (thermal conditions, aging, fatigue, and creep), production problems, and manufacturer test tolerances (velocity effects and first cycle effects). Hence, the nominal design properties specified and verified in previous steps may be modified using the property modification factors λ (ASCE, 2017a; NEHRP, 2009, 2015). Multiplying nominal design properties of dampers by property variation factors λmin and λmax (Section 5.1.3.3.3) leads to upper-bound (Equation 5.6) and lower-bound (Equation 5.7) design properties. Note that NEHRP (2015) allows to use an average value of λ, between λmin and λmax , for all the damping devices within a given type and size in lieu of each damper. These factors may be applied to whatever parameters (e.g., damping coefficient or velocity exponent) of the damper. The design temperature considered for the damper may range from annual low and high temperatures. It is suggested that the damper manufacturer is consulted when determining these factors. For a better understanding, a practical example is presented (NEHRP, 2015), illustrating the property variation factors for a nonlinear viscous damper with nominal properties C 5 128 kips:s=in and α 5 0:38. Fig. 5.19 shows the nominal force
velocity plot (filled curve) and the data (red points) obtained from a prototype test including: (1) ten full cycles performed at various amplitudes and constant temperature (21.1 C) and (2) three reversible cycles under various velocities and temperatures 4.4 C, 21.1 C, and 37.8 F. The maximum and minimum property variation factors can be estimated, respectively, in Eqs. (5.4) and (5.5) that give λmax 5 1:2 and λmin 5 0:8. Subsequently, the maximum and minimum

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CHAPTER 5 Design procedures for tall buildings

500 400

Nominal –10%

300

+10% –20%

200

+20% Test data

Force (kips)

316

100 0 –100 –200 –300 –400 –500 –20

–15

–10

–5

0

5

10

15

20

Velocity (in/s)

FIGURE 5.19 Force
velocity relationship for a nonlinear viscous damper (NEHRP, 2015).

damping coefficients that must be considered from Eqs. (5.6) and (5.7) are Cmax 5 128 3 1:2 5 153:6 kips:s=in and Cmin 5 128 3 0:8 5 102:4 kips:s=in. This variation can be seen in Fig. 5.19 where it is shown the force
velocity relationship associated with 220% and 120% tolerance. The analysis of the building structure with dampers may be conducted separately, using Cmax and Cmin where the velocity exponent is fixed to 0.38. In this case, the first analysis may lead to larger damper forces and the second one results in less energy dissipation and larger drifts.

5.2.1.8.4 Load combinations The effects on the dynamic modification system and its components due to gravity loads and seismic/wind forces can be combined as shown from Eqs. (5.37)
(5.40) (Section 5.2.1.1.4). In the seismic load combinations, the horizontal seismic force, EL ; in the damping system shall be determined for the ELF or response-spectrum procedures as the maximum between the following three different stages (ASCE, 2017a): •

Maximum displacement rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi XNm E L 5 Ω0 ðFmSFRS Þ2 6 FDSD m

(5.103)

5.2 Passive Damping Systems

•

Maximum velocity rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi XNm ðFmDSV Þ2 m

(5.104)

rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi XNm ðFCmFD Ω0 FmSFRS 1FCmFV FmDSV Þ2 6 FDSD m

(5.105)

EL 5

•

Maximum acceleration EL 5

• •

•

•

where: Ω0 is the overstrength factor based on the lateral force
resisting system chosen as given in Table 5.16 (Step 2, Section 5.2.1.2). FmSFRS is the force in an element of the damping system equal to the design seismic force for the mth mode. The definition of design force in the modal form Fim expressed in Eq. (5.55) is equal to FmSFRS . FDSD is the force in an element of the damping system necessary to resist maximum design seismic forces of displacement-dependent dampers, determined at displacements up to the design story drift, ΔiD , of the structure (refer to Step 5, Section 5.2.1.5). Note that FmSFRS and FDSD may differ depending upon the considered damper level. FmDSV is the force in the damping system required to resist design seismic forces for velocity-dependent dampers. For viscous dampers reads:    α FmDSV 5 max Fd;m 5 cdj ðGah Þj ri;mD

(5.106)

For viscoelastic dampers, this modal force can be expressed by:     FmDSV 5 kdj ðGah Þj Δi;mD 1cdj ðGah Þj ri;mD

•

(5.107)

where ri;mD is the interstory velocity for the ith story and the mth mode, at the design displacement. FC mFD and FC mFV are the force coefficient determined as follows:
Fundamental mode. The coefficients FC 1FD and FC 1FV are specified from Tables 5.21 and 5.22 using the velocity exponent, α, of viscous dampers, and damping is equal to the total damping minus the hysteretic one (see Step 4, Section 5.2.1.4).
Higher modes. The coefficients FC mFD and FC mFV can be specified from Tables 5.21 and 5.22 using the velocity exponent α 5 1, and total damping is determined for the displacement ductility, μ, in Step 4 (Section 5.2.1.4).

The coefficients CmFD and CmFV shall be taken as 1 for viscoelastic dampers, unless proved by test data or analysis. For intermediate values of α and μ interpolation is allowed for the values given in Tables 5.21 and 5.22.

5.2.1.9 Step 9: Check response acceptability The results from the RHA under wind/earthquake design, using a model consisting of both the structural and the damping systems, must be applied to recheck all the

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Table 5.21 Force Coefficient, FCmFD (ASCE 7-16 (ASCE, 2017a)) μ,1 Total Damping

α # 0:25

α 5 0:5

α 5 0:75

α $ 1:0

CmFD 5 1a

, 0.05 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 .1.0

1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00

1.00 1.00 0.95 0.92 0.88 0.84 0.79 0.75 0.70 0.66 0.62

1.00 1.00 0.94 0.88 0.81 0.73 0.64 0.55 0.50 0.50 0.50

1.00 1.00 0.93 0.86 0.78 0.71 0.64 0.58 0.53 0.50 0.50

μ $1 μ $1 μ $ 1:1 μ $ 1:2 μ $ 1:3 μ $ 1:4 μ $ 1:6 μ $ 1:7 μ $ 1:9 μ $ 2:1 μ $ 2:2

CmFD shall be taken as one for μ greater than the values shown.

a

Table 5.22 Force Coefficient, FC mFV (ASCE 7-16 (ASCE, 2017a)) Total Damping

α # 0:25

α 5 0:25

α 5 0:75

α $ 1:0

, 0.05 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 .1.0

1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00

0.35 0.44 0.56 0.64 0.70 0.75 0.80 0.83 0.90 1.00 1.00

0.20 0.31 0.46 0.58 0.69 0.77 0.84 0.90 0.94 1.00 1.00

0.10 0.20 0.37 0.51 0.62 0.71 0.77 0.81 0.90 1.00 1.00

elements of the structure. Any unacceptable response may include a dynamic instability, a nonconvergent analysis, a response that exceeds the allowable range of a deformation-controlled member, or the average strength of a critical force-controlled component (NEHRP, 2015). It is important to understand that this procedure may be iterative. Therefore, it might require an update of the damper parameters (i.e., going back to Step 5 (Section 5.2.1.5) and properties in Step 7 (Section 5.2.1.7)) in order to satisfy the criterion of the structural system and dampers. In particular, based on the appropriate load combination, as shown in Step 1.4 (Section 5.2.1.1.4), the following section briefly reviews the criteria for the structural design that shall be taken into consideration.

5.2 Passive Damping Systems

Table 5.23 Allowable Story Drift, Δa (ASCE, 2017a) Risk Category Structure

I or II

III

IV

Structure 4 stories or less (no masonry) with nonstructural elements detailed to accommodate story drifts Masonry cantilever shear wall structures Other masonry shear wall structures All other structures

0.025

0.020

0.015

0.010 0.007 0.020

0.010 0.007 0.015

0.010 0.007 0.010

5.2.1.9.1 Structural system For the structure-including dampers, the strength requirements should be satisfied using the demands obtained from the analysis with DE (NEHRP, 2015). The seismic force-resisting system needs to be designed for a strength that is not less than 75% of the strength without damping system (as already discussed in Step 4.1 (Section 5.2.1.4.1)). Further, considerations about member design of the main lateral force
resisting system, as well as the gravity system, are outside the scope of this book. Interested readers should refer to the relevant code on the subject (e.g., concrete (ACI, 2014) and steel (AISC, 2016a)).

5.2.1.9.2 Drift criteria According to design standards (e.g., ASCE (2017a)), the design story drift, ΔiD , (i.e., the drift under design ground motions) for any story i obtained from the time-history analysis (or RSA) of the structural system supported by dampers should satisfy the following criterion (ASCE, 2017a): ΔiD #

R Δa Cd

(5.108)

where R and Cd are listed, for the present structural system, in Table 5.16 and the allowable story drift Δa can be chosen from Table 5.23 with regard to the type of structure and risk category determined based on the occupancy of tall buildings (ASCE, 2017a). Furthermore, it is stated (NEHRP, 2015) that the peak story drift under MCER ground motion, ΔiM , may be checked with the use of the following criterion and drift limits specified in Table 5.23:  R ΔiM # min 0:03; 1:5 Δa ; 1:9Δa Cd

(5.109)

5.2.1.9.3 Acceleration criteria In order to be within acceptable limits with regard to human response to rather ordinary motions of buildings, horizontal accelerations of building with a specific

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return period (e.g., 1 or 10 years) are applied to the evaluation of habitability (e.g., ISO 10137 (2007)). In Chapter 3 (Section 3.4.2), different code requirements and relative perception thresholds were discussed in detail and the building response should follow these requirements. The peak accelerations of the target floor, computed from the history dynamic analysis, should not exceed the basic evaluation curve shown in Chapter 3, Fig. 3.24 (and relative Table 3.3) for the respective occupancy and the relevant code. It is important to note that the torsion acceleration should be verified also. This refers to the equivalent translational acceleration defined as the multiplication of the distance ðrt Þ from the center of torsion to the objective point and the angular acceleration, aθ ðtÞ, of the torsional vibration, that is, rt 3 aθ ðtÞ.

5.2.1.9.4 Damper criteria The following criteria shall be satisfied by the damping system: •

•

•

•

•

The dampers and their connections should resist the forces, displacements, and velocities from the MCER ground motions remaining in their elastic state (NEHRP, 2015). The hardware of all dampers (e.g., the cylinder of a piston-type device) and the connections between the devices and the structure must remain elastic under MCER. The damper components should be assessed with respect to their nominal strength in order to resist the seismic forces obtained from the nonlinear history procedure using the load combinations for the strength design, expressed in Eqs. (5.37) and (5.38). In case fewer than four energy dissipation devices per direction (or two on each side of the center of rigidity) are used, the maximum calculated displacement and velocity, under MCER, shall be increased by 130% (NEHRP, 2015). Damping device elements that cannot take any inelastic deformation capacity (force-controlled elements (NEHRP, 2015)) shall be designed for an increase of 20% of the MCER actions.

The forces and deformations provided from this analysis shall be given to the manufactures that will design accordingly the mechanical part of the damper device being utilized. Elements of the dampers are allowed to exceed strength limits under design loads if it is indicated by test or analysis where: • •

Inelastic responses do not adversely affect damper function. The design forces (QE ) in damper elements, computed by Eqs. (5.103)
(5.105) using Ω0 5 1, do not exceed the strength required to satisfy the load combinations expressed in Eq. (5.37).

5.2 Passive Damping Systems

A design review of the damping systems and relevant testing programs. After completion of the design calculations, a design review is recommended with the aid of an independent team of experts and experienced people in seismic analysis and passive energy dissipating systems. This step may require the review of the following (ASCE, 2017a; NERHP, 2015): • • •

Seismic criteria of the site comprising, for example, the development of site spectra and ground motion histories The preliminary design of the structural system and damping system, as well as design parameters of dampers The final design and all the analyses of the structural system and damping system

5.2.1.10 Step 10: Quality control, maintenance, and inspection requirements After the design of the building and damping components a quality control plan shall be written by the design professional to verify the following items (NEHRP, 2015): • • • •

Manufacturing process Preinstallation tests (e.g., prototype and production tests) to validate the designed damping properties and force
velocity
displacement relationships. Commissioning and system tuning Inspection/maintenance procedures A more detailed discussion on these aspects is given in Chapter 7.

5.2.2 STEP-BY-STEP PROCEDURE FOR MASS DAMPERS In Chapter 4 (Section 4.1.2), the essentials of mass damping systems, TMD, TLD, and TLCD were introduced. The same general step-by-step procedures shown in Fig. 5.8 have been utilized for this device category. In the following sections, first, some design considerations are reviewed and then the proposed step-by-step procedure for the design of mass dampers is reviewed in detail.

5.2.2.1 General design considerations 5.2.2.1.1 Tuned mass dampers The effectiveness of a TMD is determined by its basic design parameters: mass ratio (the ratio of TMD mass to the generalized mass of the building in its target mode of vibration) and TMD mass displacement. Depending on the target performance and the space constraints, a mass ratio in the range of 0.5%
2.0% is generally specified. Mass ratios higher than 2% can be used for cases where predicted wind-induced responses (i.e., accelerations) are significantly high and larger reductions of accelerations are required to bring them down to

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acceptable levels for occupant comfort. However, mass ratio increase has its own limits, which are driven by the limited gains in the TMD efficiency and the increased demand for its envelope space. Typically, a 30%
40% reduction in wind-induced acceleration responses of tall buildings can be achieved through the implementation of TMDs. Reductions as high as 50% can be practically achieved by high-efficiency TMDs which can generate a total equivalent damping ratio of 5%. Determining the size of the TMD mass and the space required for the entire TMD system is the first step of the TMD implementation. A close coordination with the design team is required at this stage to also determine the optimal location of the TMD room. Typically the modal height associated with the tuning frequency is the optimal location, which does not correspond to the top of the building. The top is just convenient from an architectural and coordination perspective. The mass is then computed based on the predicted accelerations at the uppermost occupied floor of the building for service-level winds and the dynamic properties of the building provided by the structural engineer (i.e., frequencies, mode shapes, mass distribution along the height of the building, and inherent structural damping ratio), to achieve the desired serviceability performance can be determined. Once the TMD mass is established, its anticipated peak displacement for design wind events is evaluated. This information is used as a basis to determine the envelope space requirements and develop the general arrangement. In general, several options are available to optimize the cost of the TMD mass, like choosing between different ballasts weight, such as steel, lead, concrete, and depleted uranium. Once the TMD concept has been developed and its envelope space requirements are fully coordinated with the architectural and structural design of the building, the performance of the TMD system must be evaluated through detailed time-domain wind and seismic response analysis for a wide range of wind speeds and directions, as well as earthquake intensities. The results of these analyses are used as a basis to determine the wind and seismic loads required for strength design and fatigue checks of the TMD components. Also, the results of the detailed performance analysis are used as a basis to determine the TMD
structure interface loads required for the structural design of the TMD supporting structure and additional supplementary damping devices if present.

5.2.2.1.2 Tuned liquid dampers The first step of the TLD sizing is to establish a suitable tank location and dimensions, through coordination with the design team. In situations where it is not possible to achieve the desired TLD mass with a single tank, multiple tanks can be employed by either stacking the tanks or locating them elsewhere on the floor plate. In these cases, superior TLD system performance can often be achieved by having each tank tuned to a slightly different frequency. The dimensions of the TLD must be determined from the natural frequency of the structural mode(s) to be controlled. The dimensions must be selected such that the TLD will function

5.2 Passive Damping Systems

satisfactorily over the expected range of as-built frequencies and return period wind events. The TLD must therefore have adjustable tuning and damping to enable device optimization after the final as-built frequencies are determined. This optimization must consider the variation in structural accelerations that will occur at different structural frequencies. Nonlinear phenomena, including liquid “spring-hardening,” and the incorporation of obstructions for the creation of liquid damping may alter the frequency of the tanks, should be taken into consideration as well. TLDs can often accommodate unusual tank geometries and remain effective when a building’s floor plan is not conducive to rectangular tank geometries. As the design develops, the performance of TLD systems must be validated through either nonlinear simulations that represent the nonlinear effects or scalemodel testing. Ultimate wind and seismic loads must be determined at the ultimate mean recurrence interval as dictated by the applicable building code. Due to the nonlinear behavior of TLDs, it is ill advised to apply factors to scale servicelevel loads up to ultimate loads. Since the TLD loads are oscillatory, it is necessary that all components are designed to resist fatigue loads that are expected at an acceptable mean recurrence interval. TLD tanks are generally constructed out of concrete and must be able to resist the peak dynamic pressures predicted under ultimate loading. The structural engineer is typically responsible for designing the concrete tank to resist the loads specified by the TLD designer. Careful attention must be paid to waterproofing, which is generally done using tank linings and/or concrete admixtures. If permitted by the applicable code, TLD tanks may serve the dual function as water storage for fire suppression. Implementation of the TLD requires careful coordination with the mechanical, electrical, and plumbing engineer to ensure provisions are made for water conditioning to prevent freezing and microbial growth. Drainage and fill provisions and interior tank access (for periodic inspection and maintenance) must also be coordinated. TLD installation is typically conducted by the general contractor with input from other trades as necessary. As construction approaches the floor that will house the TLD, the TLD designer should conduct frequency measurements on the partially completed building. Through coordination with the structural engineer, the measured frequencies are used to forecast the final as-built frequencies. By completing these measurements prior to the tanks being poured, it is possible to modify the TLD design if the forecasted frequencies are outside of the TLD tuning range, or finalize the tank dimensions for bidirectional systems. After the building is fully complete, the TLD designer must conduct final tuning and commissioning, in which the water depths and damping devices are finalized.

5.2.2.1.3 Tuned liquid column damper The first step of the TLCD design is the early coordination with the design team to find a geometry that will suit the design requirements. As a rule of thumb, TLCD generally requires that the long side of the tank stretches completely across the floor plan dimension, in the direction of the motion to be controlled. If more

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CHAPTER 5 Design procedures for tall buildings

than one building vibration mode is to be controlled, additional tanks may be used, often arranged perpendicular to each other if necessary. The vessel can be narrower along its width, because it does not play any part in the determination of TLCD natural resonant frequency, since it cannot be bituned. Furthermore, upturned column dimensions need to be defined based on the column of water that they contain to correctly tune the TLCD to the as-built building structural properties. Therefore, the designer must anticipate some of the uncertainty inherent in estimating as-built structural frequencies, and have adjustable elements and/or a construction schedule that allows geometry adjustment in time for installation/pouring of the tank. Energy dissipation in a TLCD is generally provided through turbulenceinducing devices (i.e., screens) that induce nonlinear behavior to this type of liquid damper. Careful attention must be given during the design stage to ensure that sufficient adjustability is designed into the dissipation mechanism. This will permit optimal behavior to be realized when matching the as-built conditions of the building. The damping should be tested with a scale model early in the design stage to be certain of successful implementation. With sufficient design preparation, this dissipation can also be tested at full scale during the commissioning of the TLCD within the completed structure. The uncertainty of the as-built building frequencies, and fine-tuning of internal dissipation, can lead to a wide range of TLCD behaviors in very strong wind or seismic events. These ultimately mean that recurrence level events will cause fluid motion that exceeds the responses expected during less severe winds associated with serviceability performance. It is critical to evaluate the worst-case scenario of water column movement and the loads and pressures exerted by the moving water on its containment walls. These loads are calculated by the TLCD designer and are then typically given to the structural engineer to design the tank walls (and columns and ceiling). If chosen with care, the waterproofing system should last for decades. A costsaving decision to buy an inferior waterproofing system has repeatedly been seen to cause early problems, necessitating complete removal and replacement in only a few years. However, if chosen well, the level of maintenance required thereafter is little more than ensuring that the water level is kept at the proper depth. Microbial growth within the dark tank interior is only minor, and the MEP (mechanical, electric, plumbing) engineer should specify any necessary treatment, along with measures to prevent freezing. Fill and drain provisions, along with the access for periodic interior inspection, round out the list of other necessary considerations.

5.2.2.1.4 Available procedures for mass dampers The available design procedures for mass damping systems are listed in Table 5.24. While there is a wide literature on the subject, it is worth noticing that no particular design recommendations, in international standard codes, are available.

5.2 Passive Damping Systems

Table 5.24 Mass Damper: Available Design Procedures Available Methods TMD

TLD

TLCD

Soong and Dargush (1997) Rana and Soong (1998) Sadek et al. (1997) Chang and Qu (1998) Chang (1999) Chen and Wu (2001)

Fujino et al. (1992) Sun et al. (1995)

Sadek et al. (1998) Chang and Qu (1998) Chang (1999) Wu et al. (2005) Taflanidis et al. (2005) Wu and Chang (2006) Farshidianfar and Oliazadeh (2009) Shum (2009) Lee et al. (2011)

Connor (2003) Rasouli and Yahyahi (2002) Li and Liu (2002) Bakre and Jangid (2004) Miranda (2005) Gerges and Vickery (2005) Christopoulos and Filiatrault (2006) Kim et al. (2008) Ueng et al. (2008) Hoang et al. (2008) Ok et al. (2009) Moon (2010) Lu and Chen (2011a, 2011b) Aly (2012) Farghaly and Ahmed (2012) Moutinho (2012) De Angelis et al. (2012) Anh and Nguyen (2013) Özsarıyıldız and Bozer (2014) Elias and Matsagar (2014) Tuan and Shang (2014) Marian and Giaralis (2014)

Chang and Qu (1998) Yu et al. (1999) Banerji et al. (2000) Olson and Reed (2001) Tait et al. (2004) Tait (2008) Halabian and Torki (2011) Lee et al. (2011) Love and Tait (2012) Min et al. (2014) Chang (2015) Ruiz et al. (2016)

Quaranta et al. (2011) Di Matteo et al. (2014) Min et al. (2014)

The above-listed approaches could be generally applicable for building structures under both wind and seismic excitations. Many of these methods propose simplified relations to determine the optimal properties of dampers (e.g., mass, stiffness, and damping for TMDs; tank dimensions for TLDs; and tube characteristics for TLCDs). These are frequently established based on harmonic forces,

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harmonic ground motions, and white-noise ground accelerations of wind/seismic type. When the structure is subjected to more realistic excitations (wind events and earthquake ground motions), more complicated approaches (e.g., optimization algorithms) are required to optimize the damper properties. These methods, which are not treated in this book, include genetic algorithm (GA) (Hadi and Arfiadi, 1998; Singh et al., 2002; Marano et al., 2010; Mohebbi and Joghataie, 2011; Huo et al., 2013; Herve´ Poh’sie´ et al., 2015), bionic algorithm (Steinbuch, 2011), particle swarm optimization (Leung and Zhang, 2009), harmony search method (Bekdas and Nigdeli, 2011, 2013), ant colony optimization (Farshidianfar and Soheili, 2013), evolutionary operation (Islam and Ahsan, 2012), and charged system search (Kaveh et al., 2015). The majority of the present references do not offer step-by-step, yet simple, procedures, for the design of mass damping systems. Therefore, the design procedure presented in this section relies on different methods found in the literature (e.g., Soong and Dargush (1997); McNamara et al. (1999); Banerji et al. (2000); Connor (2003); Tait (2008); Christopoulos and Filiatrault (2006); Min et al. (2014); Tuan and Shang (2014); Chang (2015)). In the proposed step-by-step procedure, the estimation of optimal properties of damping devices is addressed mainly under harmonic forces, base harmonic accelerations, and artificial excitations (e.g., white-noise time histories of type wind and earthquake types). Hence, the procedure can be more accurately checked in the final phase using explicit modeling and more realistic load conditions (e.g., real ground motion accelerations). For this aim, commercial software packages (e.g., SAP2000 (CSI, 2016a); ETABS (CSI, 2016b)) can be used to easily simulate TMDs. For the case of TLDs/TLCDs, due to the nonlinear behavior of the liquid, it is more complicated to build a model using such a software; thus, one simplified choice is to model an equivalent TMD in lieu of TLDs or TLCDs with equivalent properties. It is important to note that the proposed design approach is potentially iterative, since the response criteria may be not satisfied during the first round of the design.

5.2.2.2 Step 1: Building and site categorization This step is identical to the one conducted for distributed dampers as described in Section 5.2.1.1.

5.2.2.3 Step 2: Select force-resisting system The second step of this method is to choose the appropriate lateral load
resisting structural systems for the tall building under study. Refer Section 5.2.1.2 for an in-depth review of the possible lateral force
resisting system.

5.2.2.4 Step 3: Building fundamental properties and preliminary structural analyses After the determination of the main structural system, modal properties, including frequencies, fm , mode shapes, φm , generalized mass, generalized stiffness, and

5.2 Passive Damping Systems

modal participation factors, should be estimated. For this aim, a numerical (linear) modal analysis with the use of available commercial software could help designers to compute these parameters. Enough modal periods and mode shapes should be calculated to obtain at least 90% mass participation of the actual mass in each horizontal direction of the building, as recommended by ASCE 7-16 (ASCE, 2017a). It should be noted that the effective stiffness for RC structural elements should be taken into account in the model in order to more accurately calculate the modal parameters (more details are provided in Section 5.1.3). Subsequently, the designer should analyze and design the bare structural system based on code requirements (ASCE, 2017a). From this analysis, the designer understand if the bare structural system can resist the lateral loads without requiring excessive structural members sizes and detailing in order to satisfy strength, drift, and code acceleration requirements. Moreover, for seismic loading, inelastic behavior is expected and this would induce damage to the structure causing reliability and economical concern as already explained in Chapter 3. Based on these analyses, the designer would understand the benefit of a dynamic modification system to be added to the main structural system selected in Step 2 (Section 5.2.2.3). In the following steps, the required procedure for the design of structures with mass damping technologies is reviewed in detail.

5.2.2.5 Step 4: Select a suitable analyses procedure As already discussed in Section 5.2.2.1.4, there are no codes available that regulate the design of this category of dynamic modification devices. Therefore, the only permitted analysis procedure (by ASCE (2017a)), for this category of devices, is NLTHA. The basics of this procedure were already discussed in Section 5.2.1.4.2 for distributed dampers and the same recommendations are to mass damper, as well.

5.2.2.6 Step 5: Select total target damping In this step, the inherent damping of the main structural and additional damping due to the isolated damping systems should be selected. For the inherent damping, a small value (usually less than 3%) should be chosen for all the modes, as recommended by ASCE (2017a) and NEHRP (2015). The designer should refer to Section 3.2 for an extensive discussion on the inherent damping and its selection. The total damping, ζ T , required for design purposes can be selected with respect to the dominant (wind-based or seismic-based) design type. For the windbased design, a wind-tunnel test can be adopted to estimate the required damping ratio, as recommended by McNamara et al. (1997). For this aim, with regard to a desirable response reduction percentage (e.g., roof lateral acceleration), the structural responses generated using the tunnel test, for various levels of damping, can be utilized to choose an appropriate effective damping. If the seismic-based design is of interest, response spectra can be used appropriately. In this case, the method proposed by Soong and Dargush (1997) and Christopoulos and Filiatrault

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CHAPTER 5 Design procedures for tall buildings

(2006) is available for determining the effective damping ratio in the first mode by satisfying the following criteria: 8   < Γ1 SD ω1 ; ζ T # uN ðmaxÞ or  : Γ1 SA ω1 ; ζ T # u€ N ðmaxÞ

(5.110)

where Γ1 is the fundamental mode modal participation factor; ω1 is the fundamental mode natural frequency; ζ T , is the total effective damping associated with the fundamental mode; SD and SA are the design displacement and acceleration spectra, respectively; and uN ðmaxÞ and u€ N ðmaxÞ are the target (allowable) peak relative displacement and peak absolute acceleration at the roof level of the building, respectively. These thresholds are those which will be used in the final step to check the acceptability of the more accurate model results. More discussion on the selection of the total damping based on code requirements was given in Step 5 of the distributed damper procedures (Section 5.2.1.5).

5.2.2.7 Step 6: Damper type, configuration, and distribution 5.2.2.7.1 Step 6.1: Selection of the damper type In this section, the designer should decide which kind of mass damping systems (TMD, TLD, and TLCD) is most appropriate for the building design at hand. Several considerations need to be taken into account and some of them are the following: 1. Total cost of dampers. Several factors are contributed to the total cost of mass damper systems. In general, TMDs are slightly more expensive than liquid dampers because of their large mass (Wang et al., 2016). Moreover, the TLDs/TLCDs water tank can be useful for other emergencies, for example, fire-extinguishing water storage. Alternatively, the combination of tuned mass and liquid dampers is also proposed (e.g., Xu et al., 1992; Jae-Sung Heo et al., 2009; Wang et al., 2016) to utilize the economic advantages of TLCDs and the effectiveness of TMDs. 2. Directional control of response. It is easier to control the vibrations and responses in two directions, simultaneously, using TLDs (Sadek et al., 1998). 3. Required space to place dampers. Sloshing dampers usually requires less space than TMD because they do not require space for accommodating the stroke length (Sadek et al., 1998). 4. Type of dominant excitation force. The efficiency of mass damping systems in mitigating wind-induced response is extensively verified (see Chapter 4 for a detailed discussion). Matta (2013) reported that the effectiveness of TMDs decreases as the input duration shortens (e.g., pulse-like ground motions). An example of this could be for buildings located at near-field sites in the presence of ground motions with forward directivity or fling-step effects. Instead, sloshing liquid dampers, if appropriately designed, can be very

5.2 Passive Damping Systems

effective in controlling overall force, floor acceleration, and deformation responses of multistory building structures for broadband earthquake-type base excitations (Samanta and Banerji, 2012). 5. Modeling simplicity. It is well known that with the use of TMDs, the designer deals with physical properties (mass, stiffness, and damping) and it is an easy task to model these parameters explicitly. On the contrary, modeling of both TLDs and TLCDs is more complicated due to the nonlinear behavior of water (see Chapter 4 and Appendix A for a detailed discussion).

5.2.2.7.2 Step 6.2: Damper distribution Mass damping systems can be categorized with regard to the number of devices utilized in a building, such as single-tuned dampers (conventional devices) and multiple-tuned dampers (e.g., Iwanami and Seto (1984); Yamaguchi and Harnpornchai (1993); Fujino and Sun (1993); Abe and Fujino (1994); Kareem and Kline (1995); Sadek et al. (1998); Chang et al. (1998); Yalla and Kareem (2000); Li (2000), (2002); Min et al. (2005); Kim et al. (2006); Ashasi-Sorkhabi et al. (2014)). Single (conventional) mass damper. One of the advantages of conventional TMDs is related to its established technology as well as successful implementations in several tall buildings: for example, Taipei 101 (Section 8.2.3) (Soto and Adeli, 2013) (see Chapter 8 for several case studies). However, conventional TMDs can be tuned only for a certain structural frequency and this may be subject to uncertainties and to variations during strong motions. Furthermore, higher mode response control becomes a reliability problem since single TMD can control only the fundamental mode of vibration (Moon, 2010). Another main concern is the relatively high maintenance costs of such devices as they require special floor and various mechanical elements like springs, viscous dampers, and activation mechanisms. Similar considerations can be drawn for liquid mass dampers (see Chapter 4 and Appendix A for more details). Multiple mass dampers. Multiple-tuned mass dampers (MTMDs) can have two different distributions: horizontal distribution in one floor (usually the building top) (Elias and Matsagar, 2014) and vertical distribution along the height (Moon, 2010). The designer may eventually choose which kind of TMD configuration is appropriate based on the following considerations: •

Horizontal distribution. Superior reliability may be achieved by distributing MTMDs horizontally. Indeed, the system could work even if some of the devices are out of service or there are tuning errors (Moon, 2010). Kareem and Kline (1995) concluded that the MTMDs were most effective in controlling the motion of the primary system under random loading. In addition, they reported that the individual damping devices of MTMDs need less space than a massive single TMD, improving their constructability and maintenance. The essential characteristics of horizontally distributed MTMDs were investigated by some researchers (e.g., Yamaguchi and Harnpornchai

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CHAPTER 5 Design procedures for tall buildings

•

(1993); Abe and Fujino (1994)), emphasizing their effectiveness and robustness for harmonically forced structural oscillations in comparison with an optimum single TMD. Vertical distribution. The designer usually chooses vertical distributed TMD since their efficiency is higher than single TMDs (Iwanami and Seto, 1984; Bergman et al., 1989; Xu and Igusa, 1992; Abe and Fujino, 1994; Moon, 2010). Jangid (1999) investigated the optimum parameters of MTMDs for an undamped main system. Results showed that the optimum damping ratio of the MTMDs decreases by increasing the number of TMDs and that the damping increases with the increase in the mass ratio. Moreover, the optimum bandwidth of an MTMD system increases with the increase in both mass and number of MTMDs. The most important studies carried out on this regards are the following:
Chen and Wu (2001) reported that the application of MTMDs installed at lower floors is more effective than upper floors for mitigating acceleration responses under seismic forces and that a single TMD is less effective. For displacement suppression, instead, the MTMDs almost behave identically to single TMDs.
Li (2002) emphasized the superior performance and robustness of optimum MTMDs against single TMDs.
Bakre and Jangid (2004) investigated the optimum parameters of MTMDs for suppressing the dynamic response of a base-excited damped main system using a numerical searching technique.
Lin et al. (2010) emphasized that the optimum MTMDs were not only effective in controlling the building responses but also successful in suppressing its stroke.
Moon (2010) concluded that using vertical distribution of MTMDs based on mode shapes can be advantageous in controlling not only the firstmode response but also those of higher modes. Moreover, this has a high potential of practical applications for tall building motion control. The zones to be considered with the vertically distributed TMDs for each mode of interest of the building can be specified based upon its mode shape (see Fig. 5.20 for the vertical distribution of TMDs for the first two modes (with the second one nonlinear) of a tall building (Moon, 2010)).

Regarding liquid dampers (TLDs and TLCDs), similar configurations to TMD can be utilized and, in literature, several studies have been conducted trying to look at the efficiency of multiple liquid dampers. A brief summary of the most important studies is the following: •

Sadek et al. (1998) reported that, although multi-TLDs (MTLDs) are not necessarily superior to single TLCDs, however, they are more robust regarding errors in the approximation of the structural parameters (Fujino and Sun, 1993; Gao et al., 1999).

5.2 Passive Damping Systems

FIGURE 5.20 Example of vertically distributed MTMDs based on mode shapes in a 60-story building. Adapted from Moon, K.S., 2010. Vertically distributed multiple tuned mass dampers in tall buildings: performance analysis and preliminary design. Struct. Design Tall Spec. Build. 19 (3), 347
366.

•

•

•

•

Gao et al. (2005) showed that a greater number of TLCDs in multi-TLCD systems enhances the efficiency of the system, but no significant enhancement is observed when the number of TLCD becomes more than five. Mint et al. (2004) demonstrated that the efficiency of MTLCDs is almost similar to that of the single TLCDs when there is no uncertainty in stiffness. MTLCDs show superior performance once stiffness uncertainty exists. Chang (2015) showed that if the required response reduction is less than 60%, then the single TLDs may be appropriate; in any other case MTLDs seem to be more robust. Mohebbi et al. (2015) proposed to utilize MTLCDs with different dynamic characteristics that can be located all in one floor or vertically distributed similarly to MTMDs (as discussed earlier).

5.2.2.8 Step 7: Damping system preliminary design In this step, the major parameters utilized for the design of mass damping systems are reviewed in detail. First the mass ratio between the damper and the structure is computed and then various optimal parameters per each device type are discussed in detail.

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5.2.2.8.1 Step 7.1: Mass ratio One of the most important design parameters for mass damping systems is the mass ratio, μ, which is defined as the ratio between the damper mass and the generalized mass of the main structure for the mode being suppressed. Depending on the type of mass damping systems (TMDs, TLDs, and TLCDs), different procedures can be utilized as explained in the following sections. TMD mass ratio. The general formulas were already reviewed in Chapter 4 for single (Eq. 4.23) and multiple (Eq. 4.125) TMDs. The main factor that influences the selection of the mass ratio is the required supplemental damping ratio. Indeed, using larger μ (i.e., large TMD mass) leads to a higher damping ratio (Bekdas and Nigdeli, 2013). However, this causes an increase in building weight; thus, the seismic forces could be amplified and excessive axial forces could occur in columns. Luft (1979) proposed the following simplified formulation based on the total and inherent damping, which was updated by Soong and Dargush (1997) and Chritopulos and Filiatrault (2006):  2 μ 5 16 ζ T 20:8ζ i

(5.111)

where ζ i and ζ T are the inherent and total damping, respectively, selected in Step 5 (Section 5.2.2.6). Further insights in the selection of the mass ratio can be found in the literature. Marano and Chiaia (2010) reported that TMD with a small mass ratio controls the response via resonance, leading to a rather large movement in relation to the main structure. The control mechanism differs for large TMD mass ratio. Indeed, Bekdas and Nigdeli (2013) recommended to have a minimum mass ratio for high-rise buildings. Moreover, the designer should take into consideration physical limitations, for example, available space at the floor of interest in preselecting the mass ratio. McNamara et al. (1997) stated that the mass ratio can be selected from the available charts of mass ratio versus the equivalent damping ratio, ζ T . According to this reference, μ approximately equals 2% for the first mode. Besides, Connor (2003) reported that for most applications, the mass ratio should be less than 5%. Therefore, based on these studies, as a general rule of thumb, the mass of a TMD can be selected around 0.25%
1.0% of the fundamental modal mass of the building (Chey, 2007). TLD mass ratio. The TMD mass ratio is defined as the ratio between the damper and the structural mass (Chapter 4 (Section 4.1.2.2)) (Tait et al., 2004a,b; Tait, 2008). Banerji et al. (2000) have shown that if the mass ratio is less than 1% and the inherent damping of the main system is greater than 2%, then the TLD is not going to be effective as a control device. TLCD mass ratio. The mass ratio for TLCDs can be computed as shown in Chapter 4 in Eq. (4.28) and (4.29) for single and multiple TLCDs, respectively. Sadek et al. (1998) state that the mass ratio, μ, should be selected based on the tradeoff between the response reduction, cost, space, and weight of the TMDs. Based on these aspects they recommended that the practical range of μ is from 0.5% to 4%. Similarly, Shum (2009) recommended a range between 0.5% and 5%.

5.2 Passive Damping Systems

5.2.2.8.2 Step 7.2: Determination of TMD design parameters Optimal tuning frequency and damping ratio. Generally speaking, the design of TMDs involves the selection of three parameters: mass, damping, and stiffness. The ideal values of these parameters depend on the optimal properties of TMDs: mass ratio, μ, frequency ratio, f d;opt , and damping ratio, ζ d;opt . These properties may be identified with respect to four criteria: the damping existence in the main structure; the type of excitation force (i.e., harmonic or random); the location of the excitation (i.e., directly on the primary structure or on at its base); and the type of control criteria (e.g., displacement or acceleration). Simplified relationships can be utilized based on two categories: (1) undamped and (2) damped systems. 1. Simplified relations for undamped systems with single TMD. In the existing literature, there are available several relationships for undamped structures (i.e., negligible inherent damping). Table A.1 (Appendix A) lists the available relations with regard to the type and position of the excitation, and also on the control criteria to optimize. 2. Simplified relations for damped systems with single TMD. Similar to the simplified relations defined before for undamped systems in the case of damped structures, Table A.2 (Appendix A) shows a list of available relations with regard to the type and position of the excitation, and also on the control criteria to optimize. In alternative to the relations presented in Table A.2 (Appendix A), design charts are available (e.g., Connor (2003) numerically developed the curves (see Figs. 4.A12 and 4.A.13 (Appendix A) (Connor, 2003)). Determination of mass, stiffness, and damping coefficients of TMDs. With regard to the choice of single or multiple TMDs for controlling the building response, the mechanical properties of TMD systems can be correspondingly determined. •

•

Single (conventional) TMDs. After determining the optimal tuning frequency, f d;opt , and damping ratio, ζ d;opt , of the single TMD, given the mass ratio from Step 7.1 (Section 5.2.2.8.1), the physical mass, md , stiffness, kd , and damping constant, cd , of the TMD can be calculated as follows: md 5 μmm

(5.112)

2 kd 5 f d;opt ω2m

(5.113)

cd 5 2ζ d;opt f d;opt ωm

(5.114)

where m denotes the mode of vibration of the primary system for which the TMD is tuned. In this stage, the mechanical parameters of the TMD determined may be checked by the device manufacturer. MTMDs. Manufacturing of MTMDs with uniform stiffness is simpler than those with varying stiffnesses (Xu and Igusa, 1992; Elias and Matsagar, 2014).

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Based on this assumption, the stiffness of TMDs can defined as (Bakre and Jangid, 2004): kd;1 5kd;2 5    kd;Nd 5kd

(5.115)

Therefore, according to the assumptions and the formulations proposed by Bakre and Jangid (2004), the mass of jth TMD can be expressed by: md;j 5

md;1 ω21 ωd;j 2

(5.116)

where md;1 5

μm 11

ω21 ω22

1  1

ω21 ωNm 2

(5.117)

and    Nd 1 1 ω d;opt ; ωd;j 5 f d;opt ωm 1 1 j 2 2 Nd 2 1

j 5 1; :::; Nd

(5.118)

where f d;opt and ω d;opt are presented in Table A.3 (Appendix A). Thus the identical stiffness for every TMD is given by: kd;j 5md;j ω2d;j 5kd

(5.119)

Instead, the optimal damping coefficient of jth TMD can then be determined as: cd;j 5 2md;j ζ d;opt ωd;j

(5.120)

where ζ d;opt is the damping ratio that is kept constant for all the MTMDs (see Table A.3 (Appendix A)). In case the stiffness and mass of each TMD are different, Elias and Matsgar (2014) proposed to use the following relationships: kd;j 5  1 ω2d;1

μ 1

PNm m51 1 ω2d;2

mm

;

1...1 md;j 5

j 5 1; . . .; m

(5.121)

1 ω2d;n

kd;j ω2d;j

(5.122)

where mm is the generalized modal mass of the building for the mth mode. The damping coefficient can then be estimated with Eq. (5.120).

5.2.2.8.3 Step 7.3: Determination of design parameters of TLD Optimal tuning frequency and damping ratio. To get the optimal performance, one can select the ωd equal to the dominant frequency of the main structure, ω, leading to the tuning ratio to be unity, that is, f d;opt 5 1 (Banerji et al., 2000). The

5.2 Passive Damping Systems

other approach to get the optimal tuning frequency, while the main system is undamped, is to use (Warburton, 1982a,b; Tait and Deng, 2010): pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 1 μ=2 f d;opt 5 11μ

(5.123)

In this case, the effective optimum damping ratio of the structure-TLD system can be estimated as follows (Tait, 2008; Tait and Deng, 2010): 1 ζ d;opt 5 4

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi μ 1 μ2 1 1 3μ=4

(5.124)

TLD tank dimensions. Based on the geometrical shape of TLD tank (e.g., rectangular, circular; see Chapter 4 for a deeper discussion on which geometry is more efficient), the various design dimensions can be calculated as follows:   • Liquid depth ratio rTL 5 dTL =LTL . This parameter denotes the ratio between the still water depth in the tank and the tank length. The practical value for the liquid depth ratio may be selected as close to the shallow water depth limit, that is, 0:15 (Banerji et al., 2000) (see Chapter 4, Section 4.1.2.2, for a detailed discussion on the water level in a TLD tank). The robustness of a TLD can be improved by selecting smaller liquid depth ratios (Tait, 2008; Tait and Deng, 2010). • Tank length ðLTL Þ. Given the liquid depth ratio, using the definition of linear water sloshing frequency (Banerji et al., 2000; Tait, 2008), the following expression gives the tank length in the direction of the sloshing motion: g

LTL 5

2

4πf d;opt fx2

tanhðπrTL Þ

(5.125)

where g is the gravitational acceleration and fx is the fundamental mode frequency of the structure in the x-direction. Note that the use of damping screens inside the tank guarantees the validity of this expression over a larger range of input excitation amplitudes (Tait, 2004). The other main direction length, bTL , can be determined similarly as follows: bTL 5

• •

g 2

4πf d;opt fy2

tanhðπrTL Þ

(5.126)

Note that bTL 5 LTL if the fundamental mode frequency of building is identical in two orthogonal directions. Water depth ðdTL Þ. After determining the tank length ðLTL Þ, the still water length can be easily calculated by dTL 5 rTL LTL . Number of tanks ðNd Þ. Having determined the nominal dimensions of the TLD tank, it is now possible to estimate the required number of tanks (Banerji et al., 2000): Nd 5

μm LTL  bTL  dTL  ρF

(5.127)

where m is the mass of primary structure and μ is the selected mass ratio.

335

336

CHAPTER 5 Design procedures for tall buildings

Equivalent mechanical properties of TLD. It may be possible to model the behavior of TLD systems with an equivalent TMD system; otherwise, complex fluid nonlinear analyses are required (see Section 4.1.2.2.2 (Chapter 4) and Appendix A.6). In the past decades, several simplified approaches have been proposed, as follows: •

•

•

•

•

•

Sun et al. (1995) proposed equivalent mass, stiffness, and damping of the TLD using an SDOF-TMD analogy and the experimental results are measured for rectangular, circular, and annular tanks, subject to harmonic base excitation. Yu et al. (1997) modeled TLD as an equivalent TMD with nonlinear stiffness and damping. The model described the behavior of TLD under a wide range of excitation amplitude. Empirical expressions were developed (Yu et al., 1999; Olson and Reed, 2001) for determining the properties of an equivalent nonlinear TMD model that captures the behavior of a TLD system under a variety of loading conditions. The properties of an equivalent amplitude-dependent TMD, with equal energy dissipation as a TLD equipped with damping screens, were evaluated experimentally using shake table tests (Tait et al., 2004a) and the performance of this semiempirical amplitude-dependent model was verified as well (Tait et al., 2004b). An equivalent mechanical linearized structure-TLD system with equivalent mass, stiffness, and damping was developed by Tait (2008) for both sinusoidal and random excitations; and was validated using experimental tests. Ruiz et al. (2016) proposed a TLD with a floating roof (TLD-FR), consisting of a traditional TLD with the addition of a floating roof. For this kind of isolated damper, a dynamic behavior based on linear TMD can be better captured.

In the following, several studies are reviewed for estimating the equivalent properties for rectangular and circular tanks. Rectangular tanks Tait (2008) provided the expressions for the equivalent mass and stiffness, corresponding to the fundamental sloshing mode of the TLD system with a rectangular tank as follows: 8ρF bTL LTL tanhðπrTL Þ π3

(5.128)

8ρF bTL LTL g tanh2 ðπrTL Þ π2

(5.129)

md;eq 5 kd;eq 5

The damping coefficient can be estimated for random and sinusoidal excitation as shown in the following (Tait, 2008): •

Random excitation for a given value of an equivalent response motion, σr , (Tait, 2008): cd;eq 5 Cl

16ρF bTL LTL π3

rffiffiffiffiffi 32 tanh3 ðπrTL Þδn Ξdm ωdm σr π3

(5.130)

5.2 Passive Damping Systems

100

Cd CI

Cd, Cl

10

Modified Cd

1

Modified CI 0.1 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

S

FIGURE 5.21 Drag coefficient values for slat screens (Tait et al., 2005).

where Cl is the loss coefficient of the screens inside the tank; this parameter can be estimated from Fig. 5.21. In the figure, the solidity parameter, STL , is defined as (Tait, 2008): STL 5

ATL bTL dTL

(5.131)

where ATL is the area of the (submerged) screen normal to the flow. Note that for solidity ratios less than 0.3, the modified curves (dashed lines) shown in Fig. 5.21 should be used (Baines and Peterson, 1951). The frequency of the mth mode of the sloshing water is expressed by (Tait, 2008): ωd;m 5

rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi mπg tanhðmπrTL Þ LTL

(5.132)

The parameter δn (damping due to the screen-induced losses related to the horizontal component of flow) in the mth mode of the sloshing water can be obtained as (Tait, 2008): δm 5

1 1 1 3 sinh2 ðmπrTL Þ3

(5.133)

The damping due to screen locations in the tank, Ξd;m , can be calculated for the mth mode of the sloshing water by (Tait, 2008): Ξd;m 5

Ns X j51

 mπxj 3 sin LTL

(5.134)

337

CHAPTER 5 Design procedures for tall buildings

where xj is the location of the jth screen from the left-hand side edge of the tank and Ns is the number of screens that should be selected by the designer. The parameter σr , root mean square (RMS) relative response motion of the equivalent mechanical linear model is given by (Tait, 2008): sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 11μ σr 5 σs 2μ 1 3μ2 =2

•

(5.135)

where σs is the target structural response level that can be estimated from Fig. 5.22 with the use of optimum effective damping ratio ζ d;opt expressed in Eq. (5.124). In the figure the value of σs;target is the structural response amplitude resulting in the highest level of effective damping for the structure-TLD system. The equivalent damping coefficient for the sinusoidal excitation is given by (Tait, 2008): cd;eq 5 Cl

256ρF bTL LTL tanh3 ðπrTL Þδm Ξd;m ωd;m xr 3π5

(5.136)

where xr is the displacement variable associated with the equivalent linearized mechanical model of the TLD system.

4.0

3.0

ζeff (%)

338

2.0

1.0 Analytical Experimental 0.0 0.0

0.5

1.0 σs/σs,target

1.5

2.0

FIGURE 5.22 Measured and predicted effective damping versus normalized target structural response level (Tait, 2008).

5.2 Passive Damping Systems

Alternatively, Chang and Qu (1998) proposed to calculate the equivalent mass, stiffness, and damping of the rectangular TLD as follows: mdeq 5 ρF bTL LTL dTL 8ρF bTL LTL g tanh2 ðπrTL Þ π2 rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi g tanhðπrTL Þ cdeq 5 2ζ d;opt ρF bTL LTL dTL π LTL kdeq 5

(5.137) (5.138) (5.139)

Circular tank For circular TLD systems, the following relationship can be utilized (Chang and Qu, 1998) for determining the main parameters: md;eq 5 ρF πL2TL dTL

(5.140)

kd;eq 5 0:419ρF gπL2TL tanh2 ð1:84rTL Þ

(5.141)

rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi g tanhð1:84rTL Þ cd;eq 5 2πζ d;opt ρF L2TL dTL 1:84 LTL

(5.142)

5.2.2.8.4 Step 7.4: Determination of TLCD design parameters Optimum tuning frequency and damping ratio. The design parameters of single TLCDs, that is, tuning ratio and head loss coefficient, and of multiple TLCDs (MTLCDs), that is, central tuning ratio, tuning bandwidth, and number of damper groups, can be selected based on the following theory. •

Single TLCDs Tuning frequency (f d;opt ). Under white-noise base-acceleration ground motions, the optimum tuning frequency can be calculated as (Sadek et al., 1998): pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 2 μ=2 f d;opt 5 11μ

(5.143)

Instead, in the case of earthquake excitation, the optimum tuning frequency can be estimated as follows (Chang, 1999): pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 1 μ 2 3ΨTLCD =2 f d;opt 5 11μ

(5.144)

 2 where ΨTLCD 5 μ bTLCD =LTLCD is called the efficiency index that is proportional to the ratio between the width, bTLCD , and total length, LTLCD , of the TLCD tube. Chang (1999) suggested the values of ΨTLCD 5 0:6μ, ΨTLCD 5 0:8μ, and ΨTLCD 5 1:0μ. Similarly, Sadek et al. (1998) recommended a value of ΨTLCD 5 0:8μ. Subsequently, the relative optimum damping ratio may be estimated as follows (Chang, 1999): 1 ζ d;opt 5 2

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi   ffi μ 1 1 μ 2 5ΨTLCD =4   ð1 1 μÞ 1 1 μ 2 3ΨTLCD =2

(5.145)

339

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CHAPTER 5 Design procedures for tall buildings

Note that the inherent damping of the main systems is neglected; if the main system is damped, the optimum relations proposed for TMDs in Table A.2 (Appendix A) can be used depending on the type of excitation and its position. For wind loading excitation, the optimum tuning frequency may be expressed by (Chang, 1999): f d;opt 5

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 1 μ 2 ΨTLCD =2 11μ

(5.146)

Based on the latter equation, Shum (2009) proposed a similar expression, while the multiplier of ΨTLCD is unity in lieu of 1/2. Subsequently, the relative optimum supplemental damping ratio can be expressed by: 1 ζ d;opt 5 2

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi   ΨTLCD 1 1 μ 2 ΨTLCD =4   ð1 1 μÞ 1 1 μ 2 ΨTLCD =2

(5.147)

Head loss coefficient ðηd;opt Þ. The other design parameter of TLCDs is the head loss coefficient which depends on the expected ground acceleration and the orifice opening ratio (area of opening to cross-sectional area of tube) (Sadek et al., 1998). Note that the head loss coefficient is used to select the orifice opening of the TLCD. For ηd 5 0; the orifice is fully open and for ηd 5 N, the orifice is closed. The value of ηd can be defined in terms of orifice opening ratio, as explained by Blevins (1984), or it can be determined from experiments for specific orifice shapes and sizes. Therefore, the head loss coefficient can be expressed by (Sadek et al., 1998): ηd;opt 5

3:58μ a=u€ g;max

(5.148)

The practical ranges of the mass and inherent damping ratio are: ratio is 0:05 # μ # 0:04 and 0:02 # ζ i # 0:05, respectively; u€ g;max denotes the maximum ground acceleration, as a multiplier of gravity acceleration, g. The range of this parameter may be assumed as 0:05g # u€ g;max # 1g. Wu et al. (2005, 2009) proposed design tables for TLCD parameters including the values of optimum design parameters (tuning frequency, head loss coefficient, and effective supplemental damping ratio). These values are extracted for both harmonic and white-noise excitations, based on various primary mass inherent damping ratio, ζ i , mass ratio, μ, and ratio of the horizontal length to total length of the liquid column of TLCD, rTLCD . Table 5.25 lists the optimal values for harmonic loading for inherent damping of the main mass 1%. Similarly, Table 5.26 gives the corresponding numbers for white-noise loading cases. Similarly, Shum (2009) presented design tables for designers in order to estimate the optimum values of tuning frequency and head loss coefficient.

5.2 Passive Damping Systems

Table 5.25 Harmonic Loading and Inherent Damping (Wu et al., 2009, 2009) ζ i 5 0:01 ηd;opt ð1022 Þ μ

r TLCD

f d;opt

95%a

100%b

95%c

ζ d;opt

0.01

0.5 0.6 0.7 0.8 0.9 0.5 0.6 0.7 0.8 0.9 0.5 0.6 0.7 0.8 0.9 0.5 0.6 0.7 0.8 0.9 0.5 0.6 0.7 0.8 0.9

0.9930 0.9923 0.9915 0.9906 0.9897 0.9866 0.9854 0.9839 0.9822 0.9804 0.9805 0.9786 0.9765 0.9741 0.9714 0.9744 0.9721 0.9693 0.9661 0.9626 0.9685 0.9656 0.9623 0.9584 0.9541

6.073 6.898 7.722 8.535 9.365 15.465 17.773 20.052 22.494 24.873 26.998 31.289 35.596 39.966 44.378 40.181 46.835 53.524 60.220 67.114 54.867 64.132 130.509 83.069 92.721

9.519 10.687 11.841 12.849 14.023 23.523 26.563 29.275 33.127 36.385 40.511 46.472 52.253 58.169 64.132 59.503 68.936 78.000 86.624 96.218 81.047 93.760 106.811 119.471 132.435

12.543 13.765 15.031 16.320 17.632 30.091 33.740 37.467 41.220 45.016 51.051 57.869 64.770 71.748 78.790 74.714 85.288 95.976 106.753 117.689 100.689 115.500 73.576 145.660 161.011

2.64 2.99 3.34 3.69 4.05 3.35 3.85 4.34 4.84 5.34 3.89 4.49 5.10 5.71 6.33 4.34 5.03 5.74 6.44 7.15 4.72 5.50 6.29 7.08 7.87

0.02

0.03

0.04

0.05

a

5% degradation (from the left) from the optimal head loss coefficient on each side. The case related to the optimal head loss coefficient. c 5% degradation (from the right) from the optimal head loss coefficient on each side. b

•

MTLCDs Optimum parameters of MTLCDs are conceptually similar to MTMDs, where the important design parameters are the frequency range of the devices and their damping ratio (Yamaguchi and Harnpornchai, 1993; Kareem and Kline, 1995). Three parameters can be proposed to characterize an MTLCD system: central tuning ratio, fd;0 , tuning bandwidth, Δfd , and the number of TLCD groups, Nd (Sadek et al., 1998). The central tuning ratio can be computed as follows: fd;0 5

fd;Nd 1 fd;1 2

(5.149)

341

342

CHAPTER 5 Design procedures for tall buildings

Table 5.26 White-Noise Loading and Inherent Damping (Wu et al., 2005, 2009) ζ i 5 0:01 ηd;opt ð1022 Þ μ

r TL

f d;opt

95%a

100%b

95%a

ζ d;opt

0.01

0.5 0.6 0.7 0.8 0.9 0.5 0.6 0.7 0.8 0.9 0.5 0.6 0.7 0.8 0.9 0.5 0.6 0.7 0.8 0.9 0.5 0.6 0.7 0.8 0.9

0.9942 0.9939 0.9935 0.9931 0.9926 0.9886 0.9880 0.9873 0.9865 0.9856 0.9831 0.9823 0.9812 0.9800 0.9788 0.9778 0.9766 0.9753 0.9738 0.9721 0.9725 0.9711 0.9695 0.9676 0.9655

1.702 1.853 1.987 2.110 2.225 3.983 4.323 4.632 4.917 5.183 6.528 7.083 7.589 8.055 8.490 9.261 10.048 10.765 11.426 12.040 12.141 13.172 14.110 14.975 15.776

3.474 3.623 3.771 3.918 4.063 7.545 7.955 8.351 8.731 9.096 11.979 12.697 13.383 14.030 14.648 16.677 17.735 18.734 19.675 20.564 21.586 23.006 24.337 25.586 26.760

7.445 7.369 7.398 7.482 7.597 14.769 15.033 15.396 15.805 16.234 22.557 23.246 24.017 24.814 25.614 30.701 31.872 33.097 34.325 35.526 39.134 40.827 42.541 44.224 45.851

2.04 2.29 2.53 2.78 3.03 2.55 2.90 3.25 3.60 3.95 2.94 3.38 3.80 4.24 3.475 3.28 3.77 4.27 4.78 5.29 3.57 4.13 4.69 5.26 5.81

0.02

0.03

0.04

0.05

a

The case related to the 5% degradation (vicinity) from the optimal head loss coefficient on each side. The case related to the optimal head loss coefficient.

b

where fd;1 and fd;N refer to the tuning frequency of the first and Nd th group of TLCDs, respectively. An important assumption  of thisdefinition is that the difference between adjacent tuning ratios, fd;j11 2 fd;j , are assumed to be constant. Sadek et al. (1998) reported that for the best efficiency in response reduction, the central tuning ratio, fd;0 , of an MTLCD system should be tuned to the (dominant) natural frequency of the main structure. The tuning bandwidth frequency is defined by: Δfd 5

fd;Nd 2 fd;1 fd;0

(5.150)

5.2 Passive Damping Systems

Sadek et al. (1998) recommended that Δfd should be 0.125, 0.1, 0.05, and 0.025 for mass ratios 0.04, 0.02, 0.01, and 0.005, respectively. Given the value of fd;0 and Δfd from Eqs. (5.149) and (5.150), respectively, the tuning ratios, fd;j , associated with jth group of TLCDs is calculated by: fd;j 5 fd;1 1 ði 2 1Þ

where

fd;Nd 2 f1 Nd 2 1

8 0 1 > > Δf > d > @ A > < fd;1 5 fd;0 1 2 2 > fd;0 > > f 5 ð2 1 Δfd Þ > > : d;Nd 2

(5.151)

(5.152)

Tube dimensions. In this section, the geometrical parameters (i.e., liquid column length, cross-sectional area of the tube, tube width to liquid length ratio, and tube width) of single TLCDs and of MTLCDs can be determined by the designer (Sadek et al., 1998). •

Single TLCDs Liquid column length ðLTLCD Þ. Given the optimum tuning frequency, f d;opt , from Eqs. (5.143), (5.144), or (5.146), the liquid column length, LTLCD , can be determined by the following (Sadek et al., 1998): LTLCD 5

2g 2 ω2 fd;opt

(5.153)

where ω is the natural frequency of the main mass. Cross-sectional area of the tube ðATLCD Þ. Given the mass ratio from Step 7.1 (Section 5.2.2.8.1) and the liquid length, LTLCD , the cross-sectional area of the tube of TLCDs can be easily obtained as: ATLCD 5

μm ρF LTLCD

(5.154)

  Tube width to liquid length ratio rTLCD 5 bTLCD =LTLCD . For this design parameter a range from 0.1 to 0.9 is suggested by Sadek et al. (1998) that the larger the ratio the larger the response reduction. Moreover, Sadek et al. (1998) suggest an optimal value of 0.80 for practical design. Alternatively, Shum (2009) proposed values between 0.7 and 0.9 for an economical design. However, it is important to remember that Sun et al. (1995) reported that increasing this parameter enlarges the RMS displacement of the structure. To get the best performance of TLCDs, it is better to have the crosssectional area of the horizontal segment of the U-tube to be much larger than the vertical segments. Hence, more energy is dissipated by the movement of

343

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CHAPTER 5 Design procedures for tall buildings

the liquid in the horizontal segment and the vertical segments perform as a reservoir for the moving liquid (Sadek et al., 1998). Tube width ðbTLCD Þ. Given the tube width to liquid length ratio, rTLCD , and the liquid length, LTLCD , the tube width can be determined as: bTLCD 5 LTLCD rTLCD

•

(5.155)

MTLCDs   Liquid column length of each group LTLCD;j . Once the tuning frequency, fd;j , is determined from Eq. (5.151) for each group of MTLCDs, the liquid length, LTLDC;j , for ith group can be computed by: 2g 2 ω2 fd;j

(5.156)

μm PNd ρF j51 LTLCD;j

(5.157)

LTLCD;j 5

  Cross-sectional area of the tube ATLCD;j . Considering the same tube cross-sectional area, ATLCD;j 5 ATLCD , for each group of TLCDs, given the total mass ratio, μ (Step 7.1, Section 5.2.2.8.1) and liquid length, LTLCD;i , the following relation gives: ATLCD 5

  Tube width bLTCD;j . Considering rTLCD as the practical tube width to liquid length ratio, identical for all the groups of TLCDs, the tube width, bLTCD;j , associated with jth group can be determined as: bLTCD;j 5 LTLCD;j rTLCD

(5.158)

TLCD equivalent mechanical properties. Given the dimension of the TLCD tube, it is possible to determine the relative equivalent TMD mechanical properties (mass (md;eq ), stiffness (kd;eq ), and damping coefficient (cd;eq )). Simplified expressions are proposed by Chang and Qu (1998) and Chang et al. (1998) as follows: md;eq 5 ρF ATLCD LTLCD

(5.159)

kd;eq 5 2ρF ATLCD g

(5.160)

cd;eq 5

1 ρ ATLCD LTLCD ηd ju_ F j 2 F

(5.161)

where ηd is the head loss coefficient and u_ F is the liquid level velocity, which depends on the loading intensity. For a given loading intensity, iteration is necessary to define the velocity of the building
TLCD system (Chang and Qu, 1998).

5.2.2.9 Step 8: Update building model and perform analyses Given all the structural and damping properties of the building structure and mass damper, the designer is able to, first, update the mathematical model of the structure built in Step 3 (Section 5.2.2.4) and, then, explicitly model the damping

5.2 Passive Damping Systems

system with the use of commercial software packages. In this step, the hysteretic properties of structural elements may be accounted in the model. Depending on the type of the damping system chosen (TMD, TLD, TLCD), the corresponding mechanical parameters determined in Step 7 (Section 5.2.2.8) can be adopted. Eventually, the designer should conduct a time-history dynamic analysis, under wind or earthquake excitations, of the combined system of building structure and mass damper to evaluate the effectiveness of the damping system in mitigating vibrations and reducing desirable responses of the building (Tuan and Shang, 2014). The responses of interest, for example, lateral displacement, acceleration, and base shear, may be extracted from the history analysis. Note: it is recommended to use wind tunnel test results and/or computational fluid dynamics simulation to determine the wind loads acting on the building structure (Lee and Ng, 2010; Tuan and Shang, 2014). In the following, some recommendations for the modeling of the mass damping devices are given. •

•

•

TMD modeling The model can be built as a 3D structure, while the TMDs, depending on the installation position (e.g., top), can be modeled using link elements for springs and dampers (Farghaly and Ahmed, 2012). The mass, stiffness, and damping properties obtained in Step 7.2 (Section 5.2.2.8.2) can all be assigned to the link elements. According to CSI Knowledge Base (CSI, 2017), a TMD may be modeled using a spring
mass system with damping in SAP2000 (CSI, 2016b) or ETABS (CSI, 2016b). In this case, some useful guidelines are provided as follows:
Spring: Modeling a linear two-joint link with an assigned stiffness, kd , (spring) property in which one joint is attached to the structure, and the other one is free. The kd is obtained in Step 7.2 (Section 5.2.2.8.2)
Mass: Assigning TMD mass (md ) from in Step 7.2 (Section 5.2.2.8.2) to the free joint.
Damping: If SAP2000 (CSI, 2016b) is used, linear damping is included directly in the linear link property, while nonlinear damping is modeled using a viscous damping link object in parallel with the linear link. Using ETABS (CSI, 2016a), whether the system is linear or not, the damping objects are modeled in parallel. For the damping of TMD the value of cd , calculated in Step 7.2 (Section 5.2.2.8.2), should be used. TLD modeling In order to model a liquid damper because of the nonlinear behavior of the liquid, the TMD analogy according to the instructions given in the previous section can be utilized. The equivalent mass, stiffness, and damping coefficient of TLD systems are previously determined in Step 7.3 (Section 5.2.2.8.3). TLCD modeling Similar to the TLD modeling, the same approach can be used to model TLCD systems using the equivalent mass, stiffness, and damping obtained in

345

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CHAPTER 5 Design procedures for tall buildings

Step 7.4 (Section 5.2.2.8.4). Sadek et al. (1998) state that the analysis results for SDOF systems equipped with TMDs and TLCDs give similar reductions in their responses for identical mass ratios. Therefore, TLCDs may be modeled as equivalent TMDs using commercial software. Lee et al. (2012) used the TMD analogy by involving equivalent supplemental viscous damping of the inherent nonlinear supplemental damping term of a TLCD.

5.2.2.10 Step 9: Check response acceptability The results obtained from the time-history analysis under design wind/earthquakes for the explicit model considered should be used to check all elements of the structure. For structures equipped with mass damping systems, strength requirements should be satisfied using the demands obtained from the nonlinear RHA under the DE (ASCE, 2017a; NEHRP, 2015). In addition, the following criteria should be satisfied: • •

•

Drift criteria. The same consideration for distributed dampers applied for this device category. Refer to Section 5.2.1.9.2 for further details. Acceleration criteria. Acceleration is considered the governing factor for human discomfort (see Chapter 3 for more details). For TMDs such as those in the John Hancock Tower in Boston or the Citicorp Center in New York, whenever the horizontal acceleration exceeds 0.003 g for two consecutive cycles, the system is automatically activated (Moon, 2010). Refer to Section 5.2.1.9.3 for further details. Damper criteria. The mass damping system response shall satisfy all design requirements defined during the procedure. Moreover, the demand in the system shall be sent to the mass damper consultants for the mechanical verification of the system. Regarding code requirements, the general consideration provided by NEHRP (2015) (for distributed dampers, Section 5.2.1.9.4) can be applied for this device category as well.

Note that in case the response results obtained in Step 8 (Section 5.2.2.9) may not satisfy the design criteria, the present design procedure is potentially iterative. In this case, the designer must refer back to Step 5 (Section 5.2.2.6) in order to reselect a new effective total damping and repeat subsequent steps anew. This may lead to an update of the damper parameters such that the considered criteria are satisfied.

5.2.2.11 Step 10: Quality assurance and experimental evaluation After the design of the building and relative damping components a quality control plan shall be written by the design professional to verify the following items (NEHRP, 2015): • •

Manufacturing process Preinstallation tests (e.g., prototype and production tests) to validate the design mass damping properties and force
velocity
displacement relationships

5.3 Isolation Systems

• •

Commissioning and system tuning Inspection/maintenance procedures A detailed discussion on all these aspects is given in Chapter 7.

5.3 ISOLATION SYSTEMS 5.3.1 STEP-BY-STEP PROCEDURE FOR BASE ISOLATION The basic idea of seismic isolation is that the superstructure (that is above the isolation system) is decoupled from the horizontal earthquake ground movement (Section 4.2 (Chapter 4)). This is achieved by having a stiff superstructure and a flexible isolation interface. In this way, most of the deformation demand tends to concentrate on the isolation system and therefore the superstructure tends to behave as an SDOF system (mass of the superstructure and stiffness of the isolation system). This behavior produces less overturning moments, less accelerations demand (with less content damages and less earthquake perception), less interstory drifts (with less structural and nonstructural damages), but greater deformation demand, which is mostly concentrated at the isolation interface. This greater deformation level produces two undesired effects: first, it requires a gap at the perimeter in order to avoid collision with the adjacent structures (as well as for incoming building utilities) and second, it lowers the compression capacity of the isolators due to P-delta effects. Therefore, the increase in displacement needs to be controlled and for this scope, adding supplemental damping to the isolation system could be a solution. The addition of damping will lower the isolation system’ displacement demand and the amount of energy that excites the superstructure by further improving the efficiency of the isolation system (see Figs. 3.26 and 3.27 (Chapter 3)).

5.3.1.1 Design procedures literature review The procedures for design of base-isolated structures under seismic excitations are mainly developed based on the provisions and methods addressed in Section 5.1.1. ASCE 7-16 (ASCE, 2017a) and FEMA P-1050-1 (NEHRP, 2015) provide a design approach for new seismically isolated structures in which structural and isolation systems are designed according to the MCER demand. They allow the adoption of the equivalent linear analysis (not permitted for tall buildings), RSA or NLTHAs. Similarly, for the retrofit of existing structures, ASCE 41-13 (ASCE, 2013) provides recommendations as shown in Section 5.5. Similar to US design codes for the design of base-isolated structures, Eurocode 8 (CEN, 2004) allows the use of equivalent linear analysis, RSA, or NLTHAs. The Italian code (NTC, 2008), based on the Eurocode 8 (Cen, 2004), introduces a collapse limit (MCER-type earthquake) for designing isolators in parallel to a DE level for designing the superstructure. The Chinese code GB 50011 (GB50011, 2010) also

347

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CHAPTER 5 Design procedures for tall buildings

addresses the design of multistory (RC) structures with isolation stories, in which the structure is modeled as shear-type system to be analyzed using time-history analysis. The Japanese code (JSSI Design Guideline and Manual (JSSI, 2010)) gives the basic principles of designing seismically isolated buildings by using time-history analysis to examine their safety under earthquake excitation. The design of both new and retrofitted buildings is in the scope of Japanese code. Among all the available procedures in most of the cases, equivalent linear analysis techniques have been used for the simplified design of base-isolated buildings. This has been proposed by both codes (e.g., FEMA (1997); ICBO (1997); NEHRP (1997); AASHTO (2002); ICC (2003); FEMA (2003); CEN (2004); ASCE (2005); NTC (2008); AASHTO (2010); ASCE (2010); ASCE (2013); ASCE (2017a)) and researchers (e.g., Hwang and Chiou (1996); Kwan and Billington (2003); Blandon and Priestley (2005); Jara and Casas (2006); Dicleli and Buddaram (2007); Jara et al. (2012); Liu et al. (2014)). Several research works discuss procedures based on standard design codes, which are briefly revised as follows: •

•

•

•

•

•

Naeim and Kelly (1999) presented a step-by-step procedure for base isolation design, which is compliant with requirements of UBC (1997). This procedure consisted of a preliminary and a final design phase that include the steps for analyses and verifications of the base isolation system. A detailed example using the proposed procedure was provided. Higashino and Okamoto (2006) in their textbook presented a design flowchart based on the Japanese JSSI Design Guideline and Manual (JSSI, 2000). The design example of a 10-story RC structure with the use of this step-by-step procedure was presented. Christopoulos and Filiatrault (2006) proposed two types of design methods for base isolation systems of buildings: static and dynamic analyses. The methods were mostly based on those provided in ICC (2003) and FEMA (2003). Wen and Baifeng (2008) proposed a two-step design method based on Chinese code (GB50011, 2010). The first step was devoted to the estimation of isolation layer from few basic structural data. The second step was adopted to address a detailed design of superstructure, foundation, and base isolation devices. Kani et al. (2010) represented a design flowchart by following the approach presented in MRIT (2000), with equivalent linear and time-history analysis methods. They outlined that isolated buildings higher than 60 m should be designed using time-history analysis method. A 7-story base-isolated RC building was designed using the proposed design procedure. Feng et al. (2012) proposed a preliminary two-stage design procedure, called CW2012, for seismically isolated buildings, based on international seismic isolation codes (MRIT (2000); ASCE (2005); NTC (2008); ICC (2009); GB50011 (2010)). This procedure was mainly based on Japanese 2000 code (MRIT (2000)) and recommends a time-history analysis method, proposed by

5.3 Isolation Systems

•

JSSI (2010). It also addresses the use of the equivalent linear analysis method with highlighted limitations. Becker et al. (2015) reported that Japanese design code (e.g., SSI, 2000) has clearly outlined the procedures for designing isolated high-rise buildings. Using isolation systems in high-rise buildings in Japan could demonstrate that is practical also under US code (ASCE, 2010). However, US requirements are considerably more stringent than the Japanese ones (JSSI, 2000).

In addition to code prescriptive design procedures, several researches have proposed alternative ones. A brief review of the most important is the following: •

•

•

•

Shinozaki et al. (2004) addressed useful design issues of tall building equipped with base isolation systems. They reported the high seismic performance in the design of two built base-isolated tall buildings (over 60 m high). Pan et al. (2005) presented basic design procedures based on common Japanese design practice. In addition, some design issues of base-isolated buildings are reviewed: variation in base isolation material properties, how to apply for high-rise buildings, influences of vertical ground motions, and response under near-fault ground motions. Lee and Liang (2012) proposed a comprehensive review of seismic isolation design principles in their textbook chapter based on SDOF and MDOF models. Islam et al. (2011, 2012) developed a simplified step-by-step design procedure. This method was separately proposed for two isolator materials: lead
rubber bearings (LRBs) and high-damping rubber bearings (HDRBs). The proposed design procedures were proposed to be included in Bangladesh National Building Code (BNBC, 1993).

5.3.1.2 Step 1: Building and site categorization In the first step, tall building categorization (e.g., the building risk category and relative occupancy importance factor) and relative site categorization (e.g., spectral response acceleration and response spectrum) should be specified. For more details about above-mentioned information, the reader is encouraged to refer to Step 1 of Section 5.2.1.1. However, for seismically isolated structures, the seismic importance factor shall be taken as 1.0 regardless of risk category assignment.

5.3.1.3 Step 2: Select the structural system(s) A proper selection of a seismic load-resisting structural system(s) is desired. To this end, Section 5.2.1.2 provides adequate details for designers based on ASCE 7-16 (ASCE, 2017a). Structural system should minimize the axial loads induced by the overturning moment to avoid tension/uplift or excessive compression forces on the isolators, especially on taller buildings. This is more easily achieved

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CHAPTER 5 Design procedures for tall buildings

with structural systems based on moment frames rather than core wall because they typically have a greater level arm. Avoiding tension forces (or uplifts) on the isolators’ units usually determines the limit of whether or not seismically isolating a tall building is feasible. In addition, the aspect ratio H/L (i.e., the ratio between height H and width L of the building) has several limitations as it can be found in the literature (Li and Wu, 2006): •

Site soil condition. Hard sites permit higher aspect ratio limits than softer sites under every seismic intensity (Fig. 5.23). Hence, base-isolated tall buildings (as well as not isolated ones) are preferred to be built on hard sites, and it is dangerous to build them on soft sites with potential strong ground motions.

(A) 18 16 Hard site

Limit ratio of H/B

14 12 10 8 6

Medium site

4

Soft site

2 0 0.2

0.3

0.7 0.6 0.4 0.5 Peak acceleration of ground (g)

0.8

(B) 18 16

Hard site

14 Limit ratio of H/B

350

12 10 8 6 Medium site

4

Soft site 2 0

1

1.2

1.4 1.6 1.8 2 Period of isolated structure (s)

2.2

2.4

FIGURE 5.23 Aspect ratio estimated limits in rubber-type base-isolated buildings against (A) peak ground acceleration and (B) period of isolated structure (Li and Wu, 2006).

5.3 Isolation Systems

• •

Ground motion intensity. Higher ground acceleration generally leads to a decrease in the aspect ratio of isolated buildings (Fig. 5.23A). Period of isolated system. Isolated buildings with longer (fundamental) periods may exhibit higher aspect ratio limits (see Fig. 5.23B); this relationship is more dominant when the site is harder.

5.3.1.4 Step 3: Target vibration period and total damping ratio selection The appropriate selection of the target vibration period TM for MCER is based on the achievement of a desired level of acceleration and displacements based on spectrum demand. Based on the target vibration period and the mass m of the superstructure, the target global stiffness of the isolation system can be preliminary estimated based on the equations for an SDOF system: KM 5 4π2

m 2 TM

(5.162)

Note that this estimation will be more accurate if the superstructure is very stiff, which cannot be the case in taller buildings. The target total damping ratio (ζ TM ) of the isolated building should be selected by the designer, so that a desired reduction in a target response (e.g., base shear, superstructure accelerations or isolation system displacement demand) can be achieved. Usually based on the selected base isolation system (Step 4, Section 5.3.1.5) the relative added damping can be estimated according to experimental tests or known information. For example, for isolators with high-damping rubber material Naeim and Kelly (1999) suggested to using a 10
12% damping ratio. According to ASCE 41-13 (ASCE, 2013), the effective damping created by elastomeric isolators is typically less than 7% for shear strains in the range of 0
2, while with LRBs and frictional devices damping ratios larger than 15% can be usually be obtained.

5.3.1.5 Step 4: Isolation type and distribution In this stage, it is useful to decide which kind of isolation (bearing) systems is suitable for the building under study to achieve the desired target vibration period and damping ratio. According to NEHRP (2009) an acceptable isolation system should have the following characteristics: • • • • •

Stable for maximum earthquake displacements Increasing resistance with increasing displacement Limited degradation under repeated cycles of earthquake load Minimum restoring force requirement Well-established and repeatable engineering properties (effective stiffness and damping).

5.3.1.5.1 Determine type of isolation system The most common type of seismic isolation systems used in US and Japanese buildings are (Higashino and Okamoto, 2006): HDRB, LRB, sliding bearing

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systems, such as the friction pendulum system, or some combination of elastomeric and sliding isolators. If several types of isolators are combined, one type should be dominant (Pan et al., 2005). NRB and LRB were often used because of the lower cost compared to HDRB types and the difficulty of achieving large isolated periods due to the increased lateral stiffness of HDRBs. The sliding bearings are frequently used in combination with NRB, LRB, or HDRB to decrease the stiffness of the isolation layer for the large displacement domain (Pan et al., 2005) and be able to achieve large target vibration periods. See Chapter 4 (Section 4.2) for a detailed discussion on base isolation devices. Seismic base isolation solutions become usually less effective for high-rise buildings due to long periods of the fixed-base structure configuration and also because wind forces may govern the design of these types of structures and isolation systems are generally not activated under wind loads. Therefore, it may be recommended to incorporate energy dissipation devices (e.g., viscous dampers) at the isolation layer in such buildings (Pan et al., 2005; Becker et al., 2015). This is so called hybrid isolation system. The advantages of using dampers in conjunction with isolators could be: • • •

Reduction in relative displacement demand in isolation layer (Hall and Ryan, 2000; Pan et al., 2005; Wolff et al., 2014) Reduction in story drifts (or even floor acceleration) when viscous dampers are used (Hall and Ryan, 2000) Reducing impact of near-fault ground motion (Ariga et al., 2006; Providakis, 2008)

However, using such dampers, with too high damping, may be detrimental when the isolated building is excited by far-field earthquakes (Hall and Ryan, 2000; Providakis, 2008; Wolff et al., 2014). In Japan, the most common hybrid isolation solutions utilized for high-rise building are (Pan et al., 2005): • • • •

NRBs combined with lead dampers NRBs combined with steel coiled dampers LRBs combined with steel, lead, or oil dampers HDRBs combined with steel, lead, or oil dampers

Applications of hysteretic dampers (at the isolation level) were carried out by Okamoto et al. (2002) and Pan et al. (2005) that recommended to adopt a total yield force of hysteretic-type dampers (e.g., steel or lead dampers) between about 3% and 5% of the total weight of superstructure. An additional study carried out by Takewaki (2008) showed the influence of viscous (from viscous dampers) and friction (from friction-type bearing) damping in dissipating energy (to attain a given target drift in base isolation) for different building heights. It was demonstrated that for taller base-isolated buildings (40-story), the role of friction damping (i.e., friction-type isolator) is predominant than in lower rise isolated buildings; moreover, the overall damping ratio is less. Despite these studies an

5.3 Isolation Systems

alternative solution was proposed by Komuro et al. (2005) that introduce the hybrid TAISEI Shake Suppression system in which only a combination of sliding and rubber bearings are utilized without requiring additional dampers. Komuro et al. (2005) demonstrated that this system can lead to similar strong seismic performance for high-rise buildings of a base isolation that has additional dampers (such as steel or lead dampers) without a large increase in the construction costs as in the case of the utilization of additional dampers. Similarly in the United States, the following typical combinations are utilized (Wolff et al., 2014): • • • •

Elastomeric bearings with nonlinear viscous dampers HDRBs combined with nonlinear viscous dampers Single friction pendulum bearings with nonlinear viscous dampers Triple/quintuple friction pendulum bearings with linear viscous dampers

5.3.1.5.2 Determine location and distribution of isolation system Having defined the type of isolation devices, target period (and therefore isolation system stiffness) and target damping, the next step is to determine the distribution of the isolators in the building. Isolation systems do not necessarily need to be at the base of a structure. They can be at any level; however, only the elements above the isolation system are decoupled from the horizontal earthquake ground movement and are therefore seismically protected by the isolation system. For this reason, codes require that structures below the isolation level are designed for the elastic seismic demand, which in some cases produces substructure elements larger in size than usual. Another important aspect is that vertical circulation systems need to be detailed to accommodate movement at the isolation interface (see Chapter 6 for further details). In general, isolators are located in plan based on the vertical load paths. Usually, there is a need for at least one isolator under each column and at least two under each wall (depending on wall length). Transfer systems may be used with caution in order to decrease the number of isolator required and therefore achieve the target vibration period defined in Step 3 (Section 5.3.1.4) more easily. Moreover, friction bearing-type isolators should have larger tributary loads to activate the system; this is why they are preferably placed in interior locations. The isolator stiffness distribution is chosen in order to minimize eccentricity with superstructure mass. Moreover, isolators that provide higher dissipation are usually located on the perimeter of the plan to increase energy dissipation and to improve torsional stiffness (see Fig. 5.24 for an isolator plan distribution example for Nunoa Capital Building in Chile and relative case study in Section 8.3.1 (Chapter 8)). Note: it is worth mentioning that the isolated plane should have a robust and relatively stiff diaphragm to transmit the lateral loads in a relatively uniform fashion.

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FIGURE 5.24 Plan distribution example for Nunoa Capital Building, Santiago de Chile. Courtesy of Rene Lagos Engineers.

5.3.1.6 Step 5: Preliminary structural analysis Preliminary structural analysis should be performed in order to obtain an estimation of the isolation system displacement and force demand for the MCER, so that a preliminary design of the isolators can be made. According to US design codes, ASCE 7-16 (ASCE, 2017a), ASCE 41-17 (ASCE, 2017b), and FEMA P-1050-1 (NEHRP, 2015), seismically isolated structures shall be designed using dynamic procedures (response spectrum and response history). ELF procedure is also allowed only when the following requirements are met: • • • • • •

For building in site classes A, B, C, and D. Period of isolated structure at maximum displacement less than or equal to 5.0 second and greater than 3 times the period of the fixed base structure Height of structural above isolation system less than 19.8 m. Effective damping of isolation system at maximum displacement is less than 30%. No structural irregularity of the building above the isolation level. The isolation system shall meet the following requirements: • The effective stiffness at maximum displacement is greater than one-third of the effective stiffness at 20% of the maximum displacement. • Have restoring force. • The isolation system does not limit the maximum earthquake displacement.

5.3 Isolation Systems

Despite the fact that it is not allowed for all types of buildings, the ELF method provides a good starting point for preliminary isolation system demand estimation (displacements and forces) since both dynamic procedures (response spectrum and nonlinear time history) require minimum displacement and shear demands based on the results of the ELF procedure. Furthermore, ELF allows a better understanding of the force flow as the CQC and SRSS methods use square root of squared results. For these reasons, in the following, the basic principles of ELF are briefly reviewed. The first step consists in calculating the maximum displacement demand and corresponding effective vibration period as follows: •

Maximum displacement: DM 5

•

gSM1 TM 4π2 Bζ;TM

(5.163)

Effective period at maximum displacement: sffiffiffiffiffiffiffiffi W TM 5 2π kM g

(5.164)

where Bζ;TM is the coefficient related to the total effective damping (isolation plus intrinsic) at maximum displacement (ζ TM ) for the isolated modes, per Table 5.18. According to ASCE 7-16 (ASCE, 2017a) the damping contribution from the isolator is computed based on the upper- and lower-bound force
deflection behavior of individual isolator units, as follows: P

ζ dM 5

EM 2πkM D2M

(5.165)

P where EM is the total energy dissipated in the isolation system during a full cycle response at maximum displacement. kM is the effective stiffness of the isolation system as selected in Step 4 (Section 5.3.1.5). According to ASCE 7-16 (ASCE, 2017a) the effective stiffness shall be based on the upperand lower-bound force
deflection behavior of individual isolator units, as follows: kM 5

P 

 P  2 1 F  FM 1 M 2DM

(5.166)

P  1  P  2  where FM and FM are the sum of the force absolute values for all isolators at positive and negative maximum displacements, respectively. The total displacement of the elements in the isolation system needs to take into consideration the actual and accidental torsion, based on the spatial stiffness distribution and the critical location of the eccentric mass. The maximum total

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displacements for uniform spatial distribution of lateral stiffness should be calculated using the following equation:   y 12e $ 1:15DM DTM 5 DM 1 1 2 2 PT L1 1 L22

(5.167)

where y is the distance between the center of rigidity of the isolation system and of the element under consideration, measured perpendicular to the loading direction; e is the eccentricity, measured as the distance between the center of mass of the structure above the isolation interface and the isolation system itself. Additionally, an accidental eccentricity of 5% of the longest plan dimension, measured perpendicular to the loading direction, shall be included; L1 is the structure’s longest plan dimension; L2 is the structure’s shortest plan dimension, measured perpendicular to L1 ; and PT is the ratio of translation to torsional period of the isolation system as determined from dynamic analysis or from the following equation (ASCE, 2017a): 1 PT 5 rl

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi PNd  2 2 i51 xi 1 yi $1 Nd

(5.168)

where xi and yi are the two horizontal axes distances of each isolator unit i from the center of mass; Nd is the number of isolator units; rl is the radius of gyration qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  ffi of the isolation system as L21 1 L22 =12. The second step consists in calculating the minimum design lateral forces for the elements above and below the isolation system. For all the structural elements below the isolation system, the maximum lateral force (VMb ) can be determined as follows: VMb 5 kM DM

(5.169)

For the structural elements above the isolation system, the design shear force, VMa , shall be calculated as follows: VMa 5

Vst RI

(5.170)

where RI is a factor equal to three-eighths the response modification factor of the structural system above isolation (as per Table 5.16) with a value between 1 and 2 and Vst is the total unreduced seismic design force for the elements above the isolation level, determined as follows:  ð122:5ζ TM Þ Ws Vst 5 VMb W

(5.171)

5.3 Isolation Systems

where W and Ws are the effective seismic weights of the structure above the isolation level with and without the effective weight of the base level. In case the distance between the top of the isolator and the underside of the base level floor 0.9 m the two values are equal. Note the exponential term is greater than  1 2 2:5ζ TM shall be replaced by 1 2 3:5ζ TM in case the isolation system hysteretic behavior has an abrupt transition from the preyield and postyield (or preslip to postslip) behavior. ASCE (2017a) provides three limits on the value of the shear force above the isolation level as follows: •

• •

Lateral shear force required by code for a fixed-based structure (Eq. 5.44) of the same seismic weight Ws and isolated period TM using upper-bound properties of the isolation system Factored design wind load base shear (Section 5.2.1.1.4) Vst calculated as per Eq. (5.171) with VMb set as the force to fully activate the isolation system using the greatest between the upper bound properties, or: • 1.5 times the nominal properties for the yield level of a softening system • The ultimate capacity of a sacrificial wind-restraint system • The breakaway frictional force of a sliding system • The force at zero displacement for the sliding system following a complete cycle of motion at DM .

Subsequently, the shear force above the isolation level should be distributed vertically as follows (ASCE, 2017a): VMa wx hkx fx 5 Pn k i52 wi hi

(5.172)

where fx portion of VMa that is assigned to level x; wx portion of W that is located at or assigned to level x; hx height above the base of level x; and k 5 14ζ MT TMb , where TMa is the period of the structure above the isolation level computed assumed a fixed-based system. Having determined the distributed forces in the structure above the isolation level, the axial forces on each isolator due to both static loads and seismic overturning moments should be estimated.

5.3.1.7 Step 6: Isolation system preliminary design The design of the isolation system is an iterative process. For example, leadplug and friction pendulum isolation bearings can be generally modeled using a bilinear hysteretic model (see Section 4.2.1 (Chapter 4) and Naeim and Kelly (1999)). Three main parameters are utilized to describe this behavior: elastic stiffness, k0 ; postyield stiffness, k0p ; and characteristic strength f0 . Herein, k0 is estimated from test data for elastomeric bearing or as a multiple of k0p for

357

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CHAPTER 5 Design procedures for tall buildings

lead-plug and friction pendulum bearings. The characteristic strength for a lead-plug bearing is a function of the yield stress, whereas for a friction pendulum bearing, it is a function of the friction coefficient and the vertical load. These values are calculated for the (effective) target vibration periods ((for each isolator unit) TM ) of Step 3 (Section 5.3.1.4), displacement demands (DM ) of Step 5 (Section 5.3.1.6), (effective) target stiffnesses (kM ) of Step 3 (Section 5.3.1.4), and (effective) target total damping (ζ TM ) of Step 3 (Section 5.3.1.4). Based on these parameters, the characteristic strength can be initially estimated by neglecting the yield displacement (Dy 5 0) (Naeim and Kelly, 1999): f0M 5

EDM π 5 kM DM ζ TM 2 4DM

(5.173)

where the index M stands for MCER demand and EDM is the area under the hysteresis loop, computed as: WDM 5 2πkM D2M ζ TM

(5.174)

The postyield stiffness can then be derived from the following expression: k0pM 5 k0M 2 f0M =DM

(5.175)

The elastic stiffness can be assumed as a function of the postyield stiffness and the bearing type. For example, Naeim and Kelly (1999) proposed the following relationships: k0M 5 10k0pM for lead-plug bearing K1M 5 100k0pM for friction pendulum bearing

(5.176)

Having determined the elastic and the postyield stiffnesses the first estimation of the yield displacement can be obtained from the following expression (Naeim and Kelly, 1999): DyM 5

f0M k0M 2 k0pM

(5.177)

Afterward the characteristics strength can be updated based on the yield displacement as follows: 2 2π Wg T2πM D2M ζ TM   f0M 5 4 DM 2 DyM

(5.178)

Finally, the postyield stiffness can be updated as well using Eq. (5.175). It is worth mentioning that the value of k0M may vary over a wide range and while it has no influence on the effective stiffness, it significantly influences the supplemental damping (Naeim and Kelly, 1999).

5.3 Isolation Systems

For the specific case of friction pendulum bearings, simple expressions to predetermine design parameters (radius of concave plate r, friction coefficient rμ , and the initial stiffness k0 ) are listed, respectively, as (Naeim and Kelly, 1999): rM 5

2 gTM ð2πÞ2

 πζ TM DM  rM 2 2 πζ TM  rμM 1 k0M 5 W 1 DM rM

rμM 5 

(5.179) (5.180)

(5.181)

Generally speaking, the size of a bearing depends upon the amount of vertical load that should be sustained by it, the target stiffness/damping, and the maximum amount of lateral earthquake displacement that must be accommodated (FEMA 751 (NEHRP, 2012)).

5.3.1.8 Step 7: Update building model and final analyses After the preliminary design of the isolators is completed, the model must be updated and dynamic analysis should be performed. ASCE (2017a) requires to utilize a mathematical model that includes the isolation system, the seismic forceresisting system, and all the other structural elements that influence the dynamic behavior of the structure. The design of both isolation system and structure above shall be performed separately for upper- and lower-bound properties of the isolation system. The structure above the isolation system is permitted to be modeled as a linearly elastic if the seismic force-resisting system is essentially elastic under a lateral force not less than 100% VMa (from Eq. 5.170). Two alternatives dynamic analysis methods are allowed by ASCE (2017a): RSA and NLTHA. Each of them has its own advantages and disadvantages. RSA could be more suitable to design the structure, but it considers the response reduction due to additional damping indirectly by dividing the spectrum demand by the Bζ factor (Section 5.2.1.4.1) and may not be suitable for friction-based devices. Instead, in NLTHA the energy dissipation is directly modeled through hysteretic behavior. Regardless of the dynamic analysis procedure chosen, according to ASCE 716 (ASCE, 2017a), the elements above the isolation level shall be designed according to the requirements for no-isolated structure with a seismic force computed as per Eq. (5.170). Additional requirements depending on the analysis carried out are the following: • •

For RSA the lateral force for the structural elements above the isolation system shall not be less than VMa (from Eq. 5.170) For RHA of regular structures, the design lateral force, for the structural elements above the isolation system, VMa (from Eq. 5.170) shall not be taken as less than 80% of the VMb (from Eq. 5.169) computed from an ELF analysis.

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•

Moreover, the limits on the base shear, VMa , as specified in Step 5 (Section 5.3.1.6) for ELF analysis shall be verified. For RHA of irregular structures, the design lateral force, for the structural elements above the isolation system, VMa (from Eq. 5.170) shall not be taken as less than 100% of the VMb (from Eq. 5.169) computed from an ELF analysis. Moreover, the limits on the base shear, VMa as specified in Step 5 (Section 5.3.1.6) for ELF analysis shall be verified.

5.3.1.8.1 Response-spectrum analysis For RSA the modal damping, for the fundamental mode in the main direction, shall be not greater than the isolation system effective damping 30% of critical. Instead, for higher modes, appropriate damping values shall be selected for the structure assuming a fixed base. To determine the total maximum displacement (under MCER), simultaneous excitation forces should be considered with 100% of the ground motion in the desired direction and 30% of the ground motion in the perpendicular direction (ASCE, 2017a). The total displacement is then calculated as the vector sum of the two orthogonal displacements.

5.3.1.8.2 Nonlinear time-history analysis For nonlinear time history a set of not less than seven pairs of horizontal acceleration components shall be considered with characteristics similar to those of the control MCER (ASCE, 2017a; PEER, 2017). Amplitude and spectral matching is allowed to scale the ground motion (see Section 5.2.1.4.2 for more details). Each pair of ground motion shall be applied simultaneously to the model considering the most disadvantageous condition of eccentric mass (in addition to an accidental mass eccentricity equal to 5% of the diaphragm dimension). The maximum displacement of the isolation system shall be calculated as the vector sum of the two orthogonal directions per each time step and the average of each response parameter shall be used for design.

5.3.1.8.3 Isolation system modeling The isolation system shall be modeled in order to accurately represent its behavior. The isolators are modeled with their nonlinear force
deflection characteristics obtained from Step 6 (Section 5.3.1.7). The characteristics of the isolation system must be justified through testing (Section 7.2.3 (Chapter 7)) and must consider the nonlinear properties of the system itself. In literature, the following recommendations for isolator modeling can be found: •

Single concave friction pendulum. FEMA 751 (NEHRP, 2012) recommends modeling this category of devices with a nonlinear model. This model usually requires the user to input the initial stiffness (effective stiffness before the slider displaces on the concave plate), the friction coefficient, and the radius

5.3 Isolation Systems

•

•

•

•

of the concave plate (Eqs. 5.179
5.181). Furthermore, it also requires the input of three additional sliding friction parameters (NEHRP, 2012): 1. “Fast speed” sliding coefficient of friction. This value represents velocities more than approximately 2.5
5.1 cm/s. Typically, during strong ground motions, sliding velocities are well in excess of 5.1 cm/s and isolation system response is dominated by “fast speed” sliding friction properties. 2. “Slow speed” sliding coefficient of friction. 3. “Rate” parameter that essentially governs the transition between slow and fast speed properties (e.g., when the bearing reaches peak displacement and reverses direction of travel). Double/triple/quintuple friction pendulum. It requires more sophisticated software (e.g., 3D-BASIS (Nagarajaiah et al., 1991; Reinhorn et al., 1994; Tsopelas et al., 1994a,b; SAP2000 (CSI, 2016b)). Indeed, different friction coefficients for all the surfaces of top and bottom concave plates need to be defined. The different modeling possibilities for multiple friction pendulum are discussed in detail by Lee and Constantinou (2015). The isolation system should be modeled to account for the spatial distribution of isolator units which is determined in Step 4 (Section 5.3.1.5) (ASCE, 2017a). The effects of vertical load, bilateral load, and/or the variability of isolation system properties (e.g., due to rate of loading) on the force
deflection characteristics of the isolation system must be accounted for in the modeling (ASCE, 2017a). Avoid damping leakage (Sarlis and Constantinou, 2010) that is described as “the undesirable scenario where the user-assigned modal damping in an isolated model is effectual for the modes corresponding to the isolation system, thus ‘leaking’ into the isolation system and ultimately resulting in underestimation of the actual response. This phenomenon can be easily controlled in the FNA because the method gives the capability to the user to assign global values of damping for all the modes (e.g., by Rayleigh, constant, and linear damping) while at the same time damping values can be manually overridden for a number of modes, a feature that is not available in the nonlinear DI time-history analysis method” (Oikonomou et al., 2016).

It is important to understand that variabilities in isolation properties may occur due to several factors, such as manufacturing tolerances, effects of heating during cyclic motion, effects of aging, contamination, ambient temperature, and history of loading. To take into consideration these variabilities, modification factors are utilized (Table 5.27 (NEHRP, 2015)). These factors multiplied by the nominal properties (as shown in Section 5.1.3.3.3) produce upper and lower bound force
deflection loops of the isolation system, as per Eqs. (5.4) and (5.5). Then, dynamic analyses are performed and the resulting demands are enveloped for design purposes. It is worth mentioning that the most preferred method to establish property modification factors is to utilize rigorous qualification testing of

361

Table 5.27 Default Upper and Lower Bound Multipliers for Isolation Bearings (NEHRP, 2015) Variable Aging and Environmental Factors and Testing Factors

Sliding Bearing Unlubricated Interfaces μa or Qd b

Sliding Bearing Lubricated (liquid) Interfaces μa or Qd b

Plain Low Damping Elastomeric k

LRBc kd

LRB Qd

HDRBd kd

HDRB Qd

Aging λa Contamination λc Example upper bound λae;max Example lower bound λae;min All cyclic effects, upper All cyclic effects, lower Example upper bound λtest;max Example lower bound λtest;min λPM;max (1 1 (0.75 ( λae;max 21))  λtest;max λPM;min (1- (0.75 (1
λae;min ))  λtest;min Lambda factor for spec. tolerance λspec;max Lambda factor for spec. tolerance λspec;min Upper bound design property multiplier Lower bound design property multiplier Default upper bound design property multiplier Default lower bound design property multiplier

1.3 1.2 1.56 1 1.3 0.7 1.3 0.7 1.85

1.8 1.4 2.52 1 1.3 0.7 1.3 0.7 2.78

1.3 1 1.3 1 1.3 0.9 1.3 0.9 1.59

1.3 1 1.3 1 1.3 0.9 1.3 0.9 1.59

1 1 1 1 1.6 0.9 1.6 0.9 1.6

1.4 1 1.4 1 1.5 0.9 1.5 0.9 1.95

1.3 1 1.3 1 1.3 0.9 1.3 0.9 1.59

0.7

0.7

0.9

0.9

0.9

0.9

0.9

1.15

1.15

1.15

1.15

1.15

1.15

1.15

0.85

0.85

0.85

0.85

0.85

0.85

0.85

2.12

3.2

1.83

1.83

1.84

2.24

1.83

0.6

0.6

0.77

0.77

0.77

0.77

0.77

2.1

3.2

1.8

1.8

1.8

2.2

1.8

0.6

0.6

0.8

0.8

0.8

0.8

0.8

a

Friction coefficient in sliding bearings. Characteristic strength in sliding bearings. c Lead
rubber bearing. d High-damping rubber. b

5.3 Isolation Systems

materials and manufacturing methods by a qualified manufacturer (see Chapter 7 for more details about testing). In general, for most isolation systems, no modification factors for ambient temperature effects are considered, if they are located in a conditioned space, where the anticipated temperature varies between 21 C and 38 C (NEHRP, 2015). Moreover, thermal effects can be important for sliding bearings and lead
rubber bearings, while no consideration is needed for elastomeric bearings of either low or high-damping rubber (Constantinou et al., 2007). In addition to the specific recommendation for the modeling of isolation devices, the following considerations, for the analysis of structures equipped with isolation devices, are important: •

•

•

•

•

The P-delta effects which can be quite significant on the isolation system and adjacent elements of the structure shall be considered in modeling (NEHRP, 2012). The maximum displacement of the isolation system shall be calculated from the vectorial sum of the two orthogonal displacements computed at each time step. Appropriate selection and scaling of ground motions should be done by a ground motion expert having experienced with earthquake hazard conditions of the region, considering site conditions, earthquake magnitudes, fault distances, and source mechanisms that influence ground motion hazard at the building site (NEHRP, 2012). To account for the seismic load effects, the load combinations recommended in Section 5.2.1.1.4 can be considered for isolated structures (ASCE, 2017a; NEHRP, 2015). A nonlinear static analysis for an MCER displacement of the entire structural system, including the isolation system, is also allowed to demonstrate the isolation system stability and showing that the lateral and vertical stabilities are maintained (ASCE, 2013; NEHRP, 2015).

Lateral displacement due to wind loads over the depth of the isolation system should be limited to a value similar to that required for other stories of the superstructure.

5.3.1.8.4 Usual practice The usual practice is to perform only nonlinear time history, or nonlinear time history for isolation and global performance followed by ELF distribution of resulting story shear distribution. From the NLTHA, the following values are obtained: •

Maximum isolation system demands • Maximum displacements (DM , DTM ) • Maximum axial loads on isolators

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•

•

Effective properties • Effective stiffness of isolation system (kM ) • Effective vibration periods of the structure (TM ) POs • Maximum floor accelerations • Maximum interstory drifts

These values can be used to validate the preliminary base isolation design carried out with ELF. Uplifts on isolators should be avoided and maximum compression should be feasible to be applied in a laboratory test. Also, the gap between isolated and nonisolated structure must be greater than DTM (Fig. 5.25). Moreover, the response acceptance criteria in terms of admissible accelerations and interstory drifts should be met.

5.3.1.9 Step 8: Quality assurance An independent engineering team, with one or more individuals with a minimum of one registered design professional, should conduct a design review of the isolation system and related test programs. The review shall include at least the following criteria (ASCE, 2017a): • •

Site-specific spectra and ground motion histories Isolation preliminary design: device selection and determination of force and displacement levels

FIGURE 5.25 Gap (red perimeter) between isolated (light gray) and nonisolated (dark gray) structures. Courtesy of Rene Lagos Engineers.

5.4 Active, Semiactive, and Hybrid Systems

• • • •

Appropriate selection of property modification factors Prototype testing program Design of isolation units and structure Production testing program

Quality assurance programs are defined by the structural engineer, while prototype tests (Chapter 7) for each type of isolator must be performed by the isolator suppliers in order to confirm the effective stiffness and damping ratios assumed in the design as assumed in the previous steps. For further details, refer to Chapter 7 (Section 7.2.3).

5.4 ACTIVE, SEMIACTIVE, AND HYBRID SYSTEMS 5.4.1 LITERATURE REVIEW In Chapter 4 (Section 4.3), the main principles of active, semiactive, and hybrid damping systems were introduced. In the present section, the design procedures for buildings with the most common types for this category of dynamic modification device are reviewed. It is worth mentioning that no standard code is available for the design of active, semiactive, and hybrid control systems. Thus, the proposed design procedure is essentially based on the existing research works available in the literature. These methods (that are mainly for active-tuned mass damper (ATMD) and magnetorheological (MR) dampers) are briefly reviewed in the following: •

•

•

•

Chang et al. (1988) developed the theoretical design aspects of a controlled SDOF system with an active damper. The active damper utilized is made of prestressing tendons connected to an actuator. An optimal closed-loop control scheme using a quadratic performance index (PI) was applied to reduce the response of a structure under seismic excitation. Kobori et al. (1991a,b) presented a design method for an active mass driver (AMD) system, including the installation location, the capacity, and the stability of the system. The numerical example of an actual 10-story office building using the proposed method was shown. Chang et al. (1995) studied some design issues for buildings modeled as a SDOF system controlled by an ATMD. A closed-loop complete-feedback control algorithm was used for optimization aims. Some optimal relations for the estimation of mechanical properties of active dampers were proposed, in analogy with the classical TMDs. The ATMD design in a 10-story building frame was presented using the proposed approach. Ankireddi and Yang (1996) proposed a simplified method for the design of the ATMD based on an SDOF study of tall buildings under wind load. The procedure starts with obtaining the optimal frequency ratio and damping ratio for an equivalent TMD using analytical expressions. Subsequently, the optimal

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•

•

•

•

•

•

•

•

controller feedback gains (optimal control forces) were derived with closedform analytical expressions for the corresponding ATMD. The proposed design technique was examined for two tall buildings and analysis results show that it is accurate enough and facilitates a simple and practical design procedure. Xu (1996) introduced a method for selecting design parameters of AMDs, using a parametric study for wind-excited tall buildings. He examined the efficiency of the method with a 184-m-tall building. Yan et al. (1999) verified the analytical relations proposed by Ankireddi and Yang (1996), using some optimum algorithms for both along-wind and acrosswind excitations. They reported that the expression for the damper frequency ratio should be modified for the case of across-wind excitation. Nagashima (2001) developed an optimal displacement feedback control law, using the linear quadratic regulator (LQR), for the control of an SDOF system with an ATMD. For design purposes, the expressions of control gains were presented analytically with the help of the solution of the Riccati’s equation (that is the first-order differential equation for motion control). Moreover, analytical relations of optimal equivalent damping due to ATMDs were proposed depending on the excitation type (wind or earthquake). Ribakov et al. (2001) introduced a procedure (non-step-by-step type) for the design of building structures with active viscous damping system (AVDS) applicable to new or existing buildings. They used an active control theory (ACT) to achieve the control forces at each time step during an external excitation. The efficiency of the proposed control system was demonstrated using the numerical simulation of a 7-story building subjected to earthquakes. Cao and Li (2004) proposed control strategies for the design of ATMDs under harmonic and random forces (i.e., wind and earthquakes), leading to a simplified design method. A simple relation for the estimation of equivalent damping ratio induced by an ATMD was developed. This is very useful in the system design process. The application of the procedure to some tall building examples showed close results to those obtained from the LQR method and a better reduction on acceleration response. Du et al. (2006) developed, using a reduced-order model of a 20-story tall building, a controller design of an active mass damper to mitigate excessive vibrations induced by seismic excitation. Preumont and Seto (2008) extensively presented, in their textbook, the conceptual design of active, semiactive, and hybrid damping systems, for example, AMDs and isolated systems, using different control strategies. Various numerical examples (e.g., shear frame under seismic force) in civil structures (tall buildings) under wind and earthquake excitations could be found in the book. Ou and Li (2009) proposed a general step-by-step procedure (based on LQR control force strategy) for the optimal design of active and semiactive damping systems, for example, fluid viscous dampers, variable friction

5.4 Active, Semiactive, and Hybrid Systems

•

•

•

•

•

dampers, and MR fluid dampers. The proposed method had three general steps and it assumes identical performance for both active and semiactive control devices. Two numerical examples (20- and 76-story buildings) were analyzed. Chey et al. (2010) proposed a step-by-step design procedure of semiactivetuned mass dampers. Therein, the TMD was the entire upper portion of the building which is isolated and protected by a resettable device as the semiactive controlling system. Preumont (2011) wrote a comprehensive textbook on active control of structures. In this document, various steps for the design of active systems were briefly introduced. Xu et al. (2012) presented a detailed design process of MR dampers including the material selection, geometry design, and magnetic circuit design. The experimental tests of such dampers were performed to investigate its mechanical behavior and energy dissipation performance. Consequently, it was established that the proposed design approach is reliable for designing and optimizing MR dampers. Yang et al. (2014) proposed a simplified design method of shear-valve MR dampers considering the magnetic circuit optimization. They developed a damping force prediction model of the MR dampers and demonstrated that the simplified design procedure proposed is simple, effective, and reliable. Hazaveh et al. (2016) developed a code-based (simplified) stepwise procedures (force-based and displacement-based) for design of semiactive viscous dampers, in which the building is modeled as an SDOF system. In this procedure, the modified relations for damping reduction factor proposed by Eurocode 8 (CEN, 2004) were utilized.

5.4.2 STEP-BY-STEP PROCEDURE A simplified step-by-step design procedure, which is applicable for both active, and hybrid semiactive control of structures, is presented in this section (see Fig. 5.26). This is similar to the general procedure proposed for passive dampers shown in Fig. 5.8. Given that no code-based method is available, the main steps of the proposed procedure are based on Preumont (2011) and Ou and Li (2009). Meanwhile, some other relevant works on active control-based damping systems are reviewed within the procedure to provide a more detailed design process. Concerning the step related to the design of active control system, according to the literature, the simplest and most popular active control strategy is to use the LQR algorithm. This method needs to solve the Riccati’s equation to find the optimal gain parameters of the active (semiactive) control system. In order to solve the Riccati’s equation, users have to employ numerical software, for example, MATLAB (MathWorks Inc., 2016) or MATHEMATICA (Wolfram Research Inc., 2016). Therefore, to tackle the complexity of the use of optimization algorithms, some relations developed in the literature, for the simple (optimal) design

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FIGURE 5.26 Step-by-step procedure for active, semiactive, and hybrid damping systems.

of active and semiactive controlling systems, are applied in the present procedure. For instance, simplified expressions are proposed by the following: •

AMD. The analytical solutions of Riccati’s equation proposed by Nagashima (2001) to obtain optimal gain parameters instead of using complicated algorithms. Moreover, additional simplified expressions were provided by Ankireddi and Yang (1996), Yan et al. (1999), and Cao and Li (2004).

5.4 Active, Semiactive, and Hybrid Systems

• •

Active system. In lieu of using the LQR approach simplified design method was proposed by Cao and Li (2004). Semiactive systems. For MR fluid dampers, simplified design expressions were proposed by Yang et al. (2014). Moreover, simplified design process for a semiactive viscous damper was introduced by Hazaveh et al. (2016) and for a semiactive-tuned mass damper (SATMD) by Chey et al. (2010).

Most of these simplified procedures are based on the construction of an equivalent SDOF. This is important because, when dealing with the MDOF systems constructing the structural matrices (M,C,K) can be difficult if the structural system is complex. Therefore, idealization of the structure as an SDOF system, based on the fundamental mode, is carried out in the proposed procedure.

5.4.2.1 Step 1: Building and site categorization In the first step, the tall building categorization (e.g., the building risk category and relative occupancy importance factor) and relative site categorization (e.g., spectral response acceleration and response spectrum) should be specified. For more details about above-mentioned information, the reader is encouraged to refer to Section 5.2.1.1.

5.4.2.2 Step 2: Select the structural system(s) Being the tall building to be designed a new structure, the proper selection of a seismic load-resisting structural system(s) is desired. To this end, Section 5.2.1.2 provides adequate details for designers based on ASCE 7-16 (ASCE, 2017a).

5.4.2.3 Step 3: Building fundamental properties and preliminary structural analyses After the definition of the main structural system, modal properties, including frequencies, fm , mode shapes, φm , generalized mass, generalized stiffness, and modal participation factors, should be estimated. For this aim, a numerical (linear) modal analysis with the use of available commercial software could help designers to compute these parameters. The required number of modal periods and mode shapes should be defined to reach at least 90% mass participation of the actual mass in each horizontal direction of the building, as recommended by ASCE 7-16 (ASCE, 2017a). It should be noted that the effective stiffness for RC structural elements should be considered in the model in order to more accurately calculate the modal parameters (see Section 5.1.3). Subsequently, the designer should analyze and design the bare structural system based on code requirements (ASCE, 2017a). From this analysis, the designer would understand if the bare structural system can resist the lateral loads without requiring excessive structural member sizes and detailing to satisfy strength, drift, and acceleration requirements. Moreover, for seismic loading inelastic behavior is expected, and this would induce damage to the structure causing reliability and economical concern as already explained in Chapter 3.

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Based on these analyses, the designer would understand the necessity to add dynamic modification system to the main structural system selected in Step 2 (Section 5.4.2.2). In the following steps, the required procedures for the design of structures will be active, semiactive, and hybrid damping technologies that will be reviewed in detail.

5.4.2.4 Step 4: Selection of performance objective In this step, the appropriate PO for the control strategy is selected. The objective may differ depending if the main is to mitigate identified deficiencies (for existing buildings) or structural response. The selection of the appropriate PO is essential for the design and evaluation of the active, semiactive, and hybrid damping system. A possible objective could be to reach a target total damping ratio and as such the optimum gain parameter(s) or control force(s) can be defined based on the analysis relations as shown in Step 8 (Section 5.4.2.8).

5.4.2.5 Step 5: Specification of the bandwidth of active and semiactive systems In this step, depending on the dominant disturbance-type exciting the structure (as determined in Step 1, Section 5.4.2.1), it is appropriate to specify the effective bandwidth for the controller system, ωb . This can be determined as the frequency range in which the amplitude of the Fourier transform of the excitation is more dominant (Preumont and Seto, 2008). For a better understanding Fig. 5.27 shows the effective excitation (harmonic) bandwidth for a typical system. It can be seen that when the excitation has a limited bandwidth, for ω , ωb , the contribution of higher order frequency modes in the overall response, and consequently in the controller system, becomes insignificant. Therefore, the knowledge about the effective bandwidth can help the designer in choosing which vibration modes to control; this is useful when dealing with model reduction in the full structure.

5.4.2.6 Step 6: Damper type, configuration, and distribution of sensors and actuators 5.4.2.6.1 Device type The choice of type of active control systems depends upon several factors, for example, the PO, excitation type, and structural configuration. As discussed in detail in Section 4.3 (Chapter 4) the designer can choose between several different devices, for example, AMD, AVDS, and semiactive base-isolated systems. The designer choice is based on the most suitable system to achieve the desired structural performance. One of the major criteria for the selection of active-based controller devices is the type and level of excitation, for example, wind excitation and small/largescale earthquakes. Preumont and Seto (2008) reported that AMD and hybrid mass damper (HMD) are useful when dealing with wind excitation or small scale of earthquake. Using active- and hybrid-controlled bridge between two buildings is

5.4 Active, Semiactive, and Hybrid Systems

FIGURE 5.27 (A) Fourier spectrum of the excitation F with a limited frequency content ω , ωb . (B) Dynamic amplification of mode m such that ωm , ωb and ωk cωb . Adapted from Preumont, A., Seto, K., 2008. Active Control of Structures. John Wiley & Sons. Ltd, Chichester, UK.

effective, when the structure is excited by small/large-scale earthquakes. Also, semiactive brace-damper and semiactive base-isolated systems (e.g., adjustable oil damper and MR damper) can be reliable under large-scale earthquakes.

5.4.2.6.2 Device location Since active/semiactive control system contains sensors (for monitoring the structural response) and actuators (for controlling the structural response), their location is the most important factor influencing the performance of the control system. The actuators are suggested to be placed where their ability to control the modes is the largest (Preumont, 2011). A control system where actuator and sensor are attached to the same DOF is called a collocated control system (Preumont and Seto, 2008; Preumont, 2011). In this case, actuator and sensor should also be dual, that is, the actuator force must be associated with a translation sensor (e.g., measuring displacement, velocity, or

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acceleration). Therefore, the product of the actuator signal and the sensor signal represents the energy (power) exchanged between the structure and the control system. The location of actuators may also depend upon the type of control system to be designed. For instance, single AMD which is usually installed at the top of buildings requires actuators/sensors at the same level (Abdullah et al., 2001). Also, active tendon mechanisms can be easily installed at discrete locations on civil engineering structures (Abdullah et al., 2001). The optimum placement of sensors and control systems, such that their efficiency can be maximized, was studied by Brown et al. (1999) for shear frames subjected to earthquake and wind excitations. Using a multiobjective linear quadratic Gaussian methodology based on Pareto optimal controllers, they concluded that: • • •

The use of many actuators is preferable. The actuator placement is much more important than sensor placement. The number and location of actuators depend on the properties and configurations of the structure.

Abdullah et al. (2001) suggested the simultaneous placement of sensor/actuators to obtain a more economical and desirable design. For an accurate placement of sensors and actuators in tall buildings, there are various methods such as GAs (Liu et al., 2003, Tan et al., 2005; Cha et al., 2012) and artificial neural networks (Amini and Tavassoli, 2005). It is worth noting that the review of these more complicated techniques is beyond the scope of this book. Therefore, in the following step, a simplified model is described.

5.4.2.7 Step 7: Build simplified and reduced model To build the simplified model, the first phase is to compute the modal properties (i.e., natural frequencies (periods) and mode shapes) through a linear modal analysis as done in Step 3 (Section 5.4.2.3). If the actuators are considered in the frequency band of interest, their effects can be neglected temporarily in the model and taken into consideration on the system performance control after the design is completed. Otherwise, they should be considered in the model before the design of controller (Preumont, 2011).

5.4.2.7.1 Model reduction In general, structures are distributed systems by nature, and design of a controller system may be complicated for such structures. In contrary, a reduced-order model based on lumped parameter systems is more suitable for the design of a controlling system in a physical state space, since the number of modes is reduced (Seto et al., 1998). One of the major issues of utilizing such an approach is the elimination of the spillover phenomenon, that is, the interference of higher modes on the controlled ones (Balas, 1978). This can be achieved by allocating actuators or sensors in correspondence with neglected higher mode nodes (further discussion will be given in the following sections).

5.4 Active, Semiactive, and Hybrid Systems

To obtain a reduced-order model the first stage is to determine the number and positions of modeling points (i.e., locations of lumped masses). The choice of these points is based on the strategy utilized in such a way that the main structure is observable (using sensors) and controllable (using actuators), to have a meaningful controller design (Preumont and Seto, 2008). Assuming that a tall building may be seen as a continuum (beam-like) cantilever system, the modeling points can be determined using the first four mode shapes of the structure (Fig. 5.28 (Preumont and Seto, 2008)). In Fig. 5.28, φqi and φri are the ith mode shape components at the location of control (actuator-induced) force (i.e., point q) and sensor (i.e., point r), respectively. If control force and sensor points are zeros, the system is uncontrollable and unobservable; while if not zeros, the system is controllable and observable. Accordingly, if the control force (actuator) is applied to a modal node (i.e., where the mode shape value is zero, φ 5 0) than this mode is uncontrollable. Moreover, if a sensor is mounted to a modal node that mode is then unobservable (Preumont and Seto, 2008). As it can be observed from Fig. 5.28, the first and second modes are both controllable and observable since the control force and sensor are located at nonzero nodes of the corresponding modes. In contrary, the third mode is observable but uncontrollable, because the control force (point q) is placed at a zero value of the mode while the sensor (point r) is not. Inversely, the fourth mode is controllable but unobservable due to the location of the actuator at nonzero node and the sensor at zero node of the fourth mode. Based on these considerations, a general method to reduce the full model to a simplified one can be summarized here as follows: • • • •

Analysis and determination of the mode shapes of the reference structure that will be controlled (e.g., first two modes) Selection of the zero nodes of the lowest order mode that is not controlled (e.g., third mode) Placement of the lumped masses at the select nodes (at zero nodes of the lowest order mode), resulting in an n-DOF system Determination of the mass and stiffness constants through sensitivity analysis

Thus, it can be concluded that if the objective is to just control the first two modes, two modeling points (i.e., the points that are both controllable and observable) are required. These points can be located at the zero nodes of the third mode, and in this way the actuator and sensor can be placed confidently. Note that in doing this the third mode becomes uncontrollable and unobservable.

5.4.2.7.2 Modeling the SDOF system To control tower-like structures, the behavior can be simplified with an SDOF model (Preumont and Seto, 2008). In this case, design of active dynamic absorbers, such as AMDs, becomes easier. For constructing an SDOF system, controlling the first two modes, it is necessary to understand the relationship between modeling points and the corresponding SDOF systems. There are two possible modeling

373

FIGURE 5.28 Relationship between controllability/observability and locations of sensors and actuators. Adapted from Preumont, A., Seto, K., 2008. Active Control of Structures. John Wiley & Sons. Ltd, Chichester, UK.

5.4 Active, Semiactive, and Hybrid Systems

(A)

Modeling points

(B)

u1 m1 u2 m2 k1 k2

FIGURE 5.29 SDOF model for tower-like structures. Adapted from Preumont, A., Seto, K., 2008. Active Control of Structures. John Wiley & Sons. Ltd, Chichester, UK.

approaches as shown in Fig. 5.29. In Fig. 5.29A, the modeling point is at the top. In this case, locating the actuator (control force) and sensor at this point leads to a controllable and observable controlling system for the first mode. Moreover, this modeling point is not coincident with the zero node of the second mode leading to effectively control it. Instead in Fig. 5.29B, the selected modeling point is located at the zero node of the second mode. Hence, application of the control force and sensor at this point does not let to control the second mode, but it is still useful in controlling the first mode. Therefore, the choice of the modeling point (position of the lumped mass) depends upon the designer’s need to control either modes or only the first mode. In Fig. 5.29, m1 , m2 , and k1 , k2 are the masses and stiffnesses estimated at two types of modeling points, respectively. These values can be easily achieved using the mass response method (Seto et al., 1987). It is useful to know that if the modeling point is selected at the top structure (Fig. 5.29A), smaller mass and stiffness are obtained (Preumont and Seto, 2008). Hence, the best mounting location of the AMD or HMD controller is at the top of the structure for controlling the first vibration mode (Preumont and Seto, 2008).

5.4.2.7.3 Higher order DOF systems In addition to the SDOF system, it is also possible to reduce the full structure as an equivalent system with two, three, and four lumped masses: •

Two-DOF system (Seto et al., 1995) is useful to consider the behavior of the first two bending modes of the structure.

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• •

Three-DOF model (Kar et al., 2000) is applied for a broad building structure, accounting for twisting modes in addition to bending ones. Four-DOF model (Preumont and Seto, 2008) can be used for bridge tower structures to control the first four vibration modes, two bending and two twisting ones.

5.4.2.7.4 Spillover phenomenon In ACT, when dealing with a reduced model of a structure, a problem called spillover may occur. This problem is due to the interference between the controlled modes and uncontrolled ones (higher modes). In other words, when applying the control force into the controlled modes, the actuator may also excite the higher modes that are not included in the reduced model. Similarly, sensors can have spillover problems since they may not only capture the information related to the controlled modes, but also that of the uncontrolled modes. The spillover may be a dangerous phenomenon, leading to local damages. Therefore, avoiding or suppressing spillover is a very important task for a successful control. There are different ways to reduce/avoid spillover problem, such as: •

•

•

•

Modal filtering. It is essentially based on the separation of the information for the controlled modes from uncontrolled ones. This approach needs the same number of sensors and actuators as that of the controlled modes (Balas, 1982). Direct feedback. It requires the placement of sensors and actuators at the same locations (i.e., collocation). Significant control effects could not be anticipated with this method, but the stability of this control system is guaranteed (Balas, 1979). Low-pass filtering. It is based on cutting off either the captured sensor signals or the control (actuator) forces to reduce the effects of higher uncontrolled modes. This method is simple but has often failed in controlling multiple modes (Hori and Seto, 2000). Robust control. Filtered LQR and H-infinity (based on minimizing two weighting functions (Preumount and Seto, 2008)) state feedback controls are some robust control methods used to mitigate the effects of uncontrolled higher modes (Hori and Seto, 2000; Preumount and Seto, 2008).

It is worth noticing that, in the following procedure, the SDOF reduced modeling approach is selected. This will simplify the design of the controlling system as shown in the subsequent step.

5.4.2.8 Step 8: Design of the controller system In this step, several simplified design approaches depending on the type of controller system (e.g., ATMDs, MR dampers, and semiactive dampers) are presented. For ATMDs, which are most commonly used by active controlling devices in tall buildings, three approaches are represented. Moreover, a simplified approach for design of MR dampers, which are widely used as semiactive control devices, is provided. Lastly, simplified design guidelines for semiactive viscous

5.4 Active, Semiactive, and Hybrid Systems

dampers and TMDs are addressed. All the approaches contain several substeps addressing simplified relations for which the design parameters can be determined.

5.4.2.8.1 Design of ATMD For ATMD system, there are several works that address simplified design relations to obtain optimal control gains without dealing with complex optimization algorithms. Three simplified approaches are reviewed in this section: Approach 1 (based on Ankireddi and Yang (1996) and Yan et al. (1999)); Approach 2 (based on Nagashima (2001)); Approach 3 (based on Cao and Li (2004)). Approach 1 (Ankireddi and Yang, 1996). In this approach, the building is modeled as an SDOF system, dominated by the first-mode response. The approach is composed of two stages in which, first, the optimal characteristics of a passive TMD is predetermined; then, the active control system is designed accordingly. This method is applicable for buildings under wind loads and is developed based on the complete-feedback (namely, feedback of displacement, velocity, and acceleration) control of the system. Note that the main structure is assumed undamped (i.e., negligible inherent damping). The sequence of parameters to define is the following: •

•

Selection of a mass ratio μ In this step, a trial mass ratio, μ, as the ratio between the auxiliary mass and main system mass (generalized mass associated with the suppressed mode of the building) can be selected. For a proper selection of this parameter, one can refer to Step 7 of the mass damping procedure (Section 5.2.2.8.1). Specification of optimal frequency ratio fopt and supplemental damping ratio ζ d;opt In this stage, using the selected mass ratio and assuming a negligible inherent damping, the following relations, proposed by Ankireddi and Yang (1996), can be utilized to determine the ATMD optimal values of frequency and damping ratio (for a deeper discussion refer to Step 7, Section 5.2.2.8.2). For buildings under along-wind excitation: sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 21μ μð4 1 3μÞ ;ζ d;opt 5 fopt 5 8ð1 1 μÞð2 1 μÞ 2ð11μÞ2

(5.182)

These relations are also verified by Yan et al. (1999). For buildings under across-wind excitation, the following expression is suggested for the optimal frequency by Yan et al. (1999) to achieve more accurate results:   fopt 5 134:6f12 2 87:74f1 1 11:9 μ2   2 26:82f12 2 17:71f1 1 3:359 μ   2 0:029f12 2 0:019f1 1 0:996

Here, f1 is the fundamental frequency of building.

(5.183)

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•

•

Determination of mechanical properties of auxiliary mass Having determined the optimal frequency ratio and damping ratio (Eqs. 5.182 and 5.183), the stiffness, kd , and damping constants, cd , of the auxiliary mass should be specified as: kd 5 md ω2d

(5.184)

cd 5 2ζ d;opt md ωd

(5.185)

where md and ωd are generalized mass and frequency of the auxiliary mass, respectively. After determination of optimal properties of a passive mass damper, the next phase of the design should be based on calculating active controlling features. Selection of acceleration feedback gain ratio μg In this step, a parameter, called acceleration feedback gain ratio, μg , should be selected. This parameter controls the ratio between the gain of acceleration feedback, mg , adopted for the active control and the generalized main mass, m1 : μg 5

mg m1

(5.186)

A selection criteria (effective range), such that the ATMD system function is stable, was proposed by Ankireddi and Yang (1996) as: 2

•

μd , μg # 0 11μd

which means that μg has a negative value. Calculation of the optimal controller velocity and displacement feedback gain coefficients εg;opt and ψg;opt The optimal values of velocity feedback gain, εg;opt , and displacement feedback, ψg;opt , as proposed by Ankireddi and Yang (1996) and Yan et al. (1999) can be calculated as follows: cd 1 cg εg;opt 5 5 m1 ω 1 ψg;opt 5

•

(5.187)

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi μg μ2 ð413μÞμ3 1 2 ð11μÞ 4ð11μÞ3

μ2 1 2μ 1 2μg 1 2μg μ kd 1 kg 5 2 m1 ω1 2ð11μÞ2

(5.188)

(5.189)

Determination of optimal gains of velocity and displacement feedback Having determined the velocity and displacement feedback coefficients in the previous step, the optimal control gains can be derived from the following set of equations:   cg 5 εgopt 2 2ζ s;opt fopt μ m1 ω1

2 μ m1 ω21 kg 5 ψgopt 2 fopt

(5.190) (5.191)

5.4 Active, Semiactive, and Hybrid Systems

•

Determination of optimum control force An optimum active control force, uopt , is desired, because an increase in this force does not necessarily mean an increase in ATMD effectiveness: uopt 5 2mg x€ d 2cg x_ d 2kg xd

(5.192)

where xd is the relative displacement of the active mass damper. Approach 2 (Nagashima, 2001). For a structure controlled by an ATMD system, the active control law (LQR method) can be simplified to be composed of two different feedback gains: one for the structure displacement and one for the auxiliary mass velocity (Nagashima, 2001). This is considered as “optimal displacement feedback control” that may be useful for design of ATMD systems. Hence, using the simplified expressions developed by Nagashima (2001), the damping design parameters of the ATMD system can be proposed in closed-form solution for an undamped SDOF structure controlled with an ATMD. The sequence of parameters to define is the following: • •

•

•

Selection of a mass ratio μ The mass ratio is selected in the same way as shown in Approach 1. Selection of a target supplemental damping ratio A target supplemental damping, ζ d , can be selected based on the recommendations given for the step-by-step procedure for mass damping systems (Step 5, Section 5.2.2.6). It is worth mentioning that a desirable damping ratio may be more easily specified using the analytical expressions of the optimal damping ratio for TMDs in undamped SDOF systems (refer to Table A.1 (Appendix A)). Calculation of auxiliary mass md Based on the mass ratio, μ, selected, the auxiliary mass, md , can be computed similarly to what was shown in Eq. (5.112). Estimation of the proposed displacement feedback gain (G1 ) In this step, based on the simplified relations developed by Nagashima (2001), an active control parameter called displacement feedback gain (G1 ) can be determined for both wind and earthquake excitations:
Wind excitation  4ζ 2 G1 5 1 2 d md ω21 μ




(5.193)

where ω1 is the frequency of fundamental mode, and 0 # G1 # md ω21 . Note that for G1 . md ω21 the added damping ratio expected by the active system is negligible, that is, ζ d 5 0. Earthquake excitation  G1 5 m ω2

1 4ζ 2 2 d md ω21 μ 11μ m ω2

(5.194)

d 1 d 1 where 0 # G1 # 1 1 μ. But, for G1 . 1 1 μ the damping ratio expected by the active system is negligible, that is, ζ d 5 0.

379

380

CHAPTER 5 Design procedures for tall buildings

•

Calculation of the proposed velocity feedback gain (G4 ) of auxiliary mass stroke Similar to the control gain determined in the previous step, Nagashima (2001) proposed an active control parameter called velocity feedback gain (G4 ) that can be estimated as follows: sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  2 ω2 G4 5 2ζ d ωd md 2 2μ d2 G1 1 2ζ d ωd md ω1

•

where G1 $ 0 and ωd is the frequency of the auxiliary mass. Feedback control low Having calculated the control gain, it is possible to compute the feedback control law, u, as a function of time as follows: uðtÞ 5 G4 x_ d 1 G2 x1

•

(5.195)

(5.196)

Here, x_ d and x1 are, respectively, the velocity of auxiliary mass stroke and displacement of the main mass (SDOF) system. Determination of frequency of auxiliary mass ωd According to Nagashima (2001), two PIs are used for the optimization of feedback gains: displacement performance index (DPI) and velocity performance index (VPI). Therefore, the optimal frequency, ωd , of the ATMD for both of these indices can be determined as follows:
Optimization based on DPI ωd 5

ω1 11μ

(5.197)

where this tuning frequency coincides with the well-known optimal tuning condition for a passive TMD developed by, for example, Den Hartog (1956), Warburton (1982a,b), and Chritopulos and Filiatrault (2006) (refer to Chapter 4, Section 4.1.2.1).
Optimization based on VPI ω1 ωd 5 pffiffiffiffiffiffiffiffiffiffiffi 11μ

•

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi μ G4 11 2 md ω21

(5.198)

Determination of mechanical properties of auxiliary mass Having determined the amount of auxiliary mass (md ) and frequency (ωd ), the stiffness and damping constants of the ATMD systems are given, respectively, in Eqs. (5.184) and (5.185). Nagashima (2001) emphasized that the optimization based on the DPI is practical and the ATMD performance is improved as the displacement feedback gain G4 increases. However, the system performance using the VPIbased optimization is limited (increase in the stiffness of the auxiliary mass with G4 and not improving control performance even for large G4 ), leading to an inappropriate control strategy.

5.4 Active, Semiactive, and Hybrid Systems

Approach 3 (Cao and Li, 2004). Cao and Li (2004) developed a simplified approach for the design of control strategy, based on LQR technique, which accounts for the inherent damping of the main system. The sequence of parameters to define is the following: • •

Selection of a mass ratio μ The mass ratio is selected in the same way as shown in Approach 1. Determination of optimal frequency ratio and damping ratio In order to be able to determine the optimal gains for control feedbacks, based on the mass ratio and inherent damping, the optimal values of frequency ratio, fd;opt , and supplemental damping ratio, ζ d;opt , can be calculated using expressions, described in Table A.2 (Appendix A), depending upon the type and position of the external excitation applied on the primary (SDOF) system. Alternatively, Li et al. (1999) proposed to utilize the following simplified relationship: pffiffiffi ζ d;opt 5 0:5 μ

•

Calculation of expected frequency and added damping of ATMD Given the optimal frequency ratio and added damping ratio from the previous step, the frequency, ωd , and added damping, ζ d , due to the passive damping system can be simply calculated as: ωd 5fd;opt ω1 ;

•

(5.199)

ζ d 5 ζ d;opt

(5.200)

Note that, alternatively, the damping factor can be selected based on a certain level of reduction in a desired response. Determination of optimal control gains The expressions developed for the optimal gains usually depend on the excitation type. Here, the relations for harmonic excitations (with frequency ω and angle phase θ) and random forces (white-noise) are presented.
Harmonic excitations (xðtÞ 5 Xsinωt) (Cao and Li, 2004) 1. Displacement feedback (G3 5 G4 5 G5 5 G6 5 0; G1 ; G2 6¼ 0)   μ 2ζ s ωd ωB 2 ω 2 Asinðθ2 2 θ1 Þ ω21

(5.201)

ω2 ω 1 2ζ s cosðθ2 2 θ1 Þ 2 1 ωd ω21

(5.202)

G1 5 G2 5

2. Velocity feedback (G1 5 G2 5 G5 5 G6 5 0; G3 ; G4 6¼ 0)   ω2 Acosðθ2 2 θ1 Þ 1 ω2 2 ω2d B 2ζ 1 ω1 ωAsinðθ1 2 θ2 Þ  2  2 ω A 1 ω 2 ω2d Bcosðθ2 2 θ1 Þ 21 G4 5 2ζ s ωd ωBsinðθ1 2 θ2 Þ G3 5 μ

3. Acceleration feedback (G1 5 G2 5 G3 5 G4 5 0; G5 ; G6 6¼ 0)

(5.203) (5.204)

381

382

CHAPTER 5 Design procedures for tall buildings   2ζ s ωd ωB G5 5 μ 21 Aωsinðθ2 2 θ1 Þ G6 5

where

ω2d ωd 2 2ζ s cosðθ2 2 θ1 Þ 2 1 ω2 ω

Λ21 v20 1 μ2 ω4 B2 2 A02 θ2 5 cos 2 2Λ1 v0 μω2 B  2 μω B 2ζ 1 ω1 ω sinθ2 1 tan21 2 θ1 5 sin21 A0 ω1 2 ð1 1 μÞω2 21

with

(5.205) (5.206)



qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  2  2 0 A 5 A ω21 2 ð11μÞω2 1 2ζ 1 ω1 ω

(5.207) (5.208)

(5.209)

Here, v0 is the harmonic force amplitude; A and B are positive (static) displacement amplitudes of main structure (SDOF) and ATMD system, respectively. Cao and Li (2004) suggested to use arbitrary values for parameter A (e.g., A 5 0.8, 1, 1.2) and determine the parameter B by satisfying the following limiting conditions:   Λ1 v0 2 μω2 B # A

Pn

(5.210) (5.211)

Si φ2i1

where Λ1 5 , in which i denotes the number of story; n is the m1 number of building floors; Si is the static amplitude of wind load at ith floor; φi1 is the modal value associated with the first mode and ith floor. Random excitation (Cao and Li, 2004) When the structure is excited by a random force, for example, whitenoise, the optimal control gains (G1 to G6 ) can be extracted from the optimization of displacement responses variant by solving the following set of linear equations (for further explanation about this set of equations interested, readers should refer to the publication by Cao and Li (2004)): i51




  Λ1 v0 2 A0  # μω2 B

8 @A4 @B4 > > B4 2 A4 50 > > > @G @G 1 1 > > > > > @A4 @B4 > > 2 A4 50 > B4 > > @G @G 2 2 > > > > > @A4 @B4 > > 2 A4 50 B > > < 4 @G3 @G3 @A4 @B4 > > B4 2 A4 50 > > > @G @G 4 4 > > > > > @A4 @B4 > > B 2 A4 50 > > > 4 @G5 @G5 > > > > > @A4 @B4 > > B 2 A4 50 > > : 4 @G6 @G6

(5.212)

5.4 Active, Semiactive, and Hybrid Systems

The fundamental parameters required for the derivation of optimal gains are:   A4 5 a0 2 a4 a21 1 a1 a2 a3 2 a0 a23

(5.213)

B4 5 a4 ½b0 ða3 a2 2 a4 a1 Þ 1 a0 ða3 b1 1 a1 b2 Þ

(5.214)

where

8 > > > > <

a0 5 ð1 1 G2 Þω21 ω2d a1 5 2ð1 1 G4 Þω21 ζ s ωd 1 2ð1 1 G2 Þω2d ζ 1 ω1 a2 5 ð1 2 G1 1 G6 Þω21 1 4ð1 1 G4 Þζ s ωd ζ 1 ω1 1 ð1 1 μÞð1 1 G2 Þω2d > > > a3 5 2ð1 2 G3 1 G6 Þζ 1 ω1 1 2ð1 1 μÞð1 1 G4 Þζ s ωd > : a4 5 1 2 G5 1 ð1 1 μÞG6 8 > b0 5 Λ1 2 ð11G2 Þ2 ω4d > < 2 b1 5 2 2Λ1 ð1 1 G2 Þð1 1 G6 Þω2d 1 4Λ1 2 ð11G4 Þ2 ω2d ζ s 2 > b2 5 Λ1 2 ð11G6 Þ2 > : b3 5 0

•

(5.215)

(5.216)

Determination of supplemental damping ratio due to the active controller The supplemental damping ratio due to the active control system can be estimated using the simplified relation proposed by Cao and Li (2004) as follows: ζd 5

a4 Λ21 A4 2ω31 B4

(5.217)

The active control added damping ratio, ζ d , shall be checked against the added damping ratio, ζ d , as follows: ζ d $ ζd

•

(5.218)

If the above inequality is not satisfied or ζ d is significantly larger than ζ d , the designer can change the controlling parameters A4 or B4 by changing the mass ratio, μ, supplemental damping ratio, ζ d , or frequency, ωd , of the ATMD system. Specification of mass, stiffness, and damping of ATMD Having obtained the mass ratio (μd ) and frequency (ωd ), the mass, stiffness, and damping constants of the ATMD system are calculated as shown in Eqs. (5.112), (5.184), and (5.185), respectively.

5.4.2.8.2 Design of semiactive systems Concerning semiactive controlling systems, Ou and Li (2009) reported that various semiactive dampers (e.g., MR dampers and variable friction dampers) can be designed in the same manner as the active dampers of the same type. This assumes that the response of a building controlled with active control systems can be considered to be the same as that with semiactive devices. First the design strategy, proposed by Ou and Li (2009), considers to determine active control

383

384

CHAPTER 5 Design procedures for tall buildings

forces using the LQR algorithm, according to the expected reduction in a response; then, replaces the active devices by semiactive ones by taking the following assumptions: • •

The maximum output force of the semiactive device is identical to that of the active control systems. The response of the structure with the semiactive systems is the same as that with active devices.

As mentioned earlier, for the determination of active control forces, it is required to employ complicated algorithms (e.g., LQR), and this results in a timeconsuming and complex design. Therefore, more simplified design procedures are presented in this section for the most practical semiactive systems: MR fluid dampers, viscous dampers, and TMDs. Design of MR dampers. In general, the working mode of MR dampers can be categorized as follows: shear, valve, extrusion, and shear-valve modes. Among these, the shear-valve mode has been extensively employed in the design of MR dampers for civil engineering structures because of its efficiency and geometry simplicity (Yang et al., 2014). The MR damper design process generally consists of the following phases: material selection, geometry, and magnetic circuit design. All these aspects are addressed in the following based on the recommendations of Yang et al. (2014). •

•

Material selection Suitable materials for MR dampers are generally based on two objectives (Xu et al., 2012):
Selection of a type of MR fluid with low apparent viscosity and proper magnetic saturation yield strength
Selection of cylinder and piston materials in such a way that the saturation induction density is higher than the magnetic field intensity when MR fluid reaches magnetic saturation yield strength As an example, fluid MRFXZD08-01 which has antisettlement properties and low apparent viscosity in low-frequency vibration has been utilized in the past (Xu et al., 2012). Moreover, the DT4 electrical pure iron and No. 45 steel have been adopted for manufacturing the piston and the cylinder, respectively (Xu et al., 2012). Another practical MR device utilizes carbon steel for piston and cylinder and MRF-J01 fluid (Yang et al., 2014). Geometric and properties selection/design The main geometric parameters that define MR dampers can be computed as follows (Fig. 5.30):
Total effective length of the damper is expressed as follows (Yang et al., 2014): L5

2nr 2 B1 pffiffiffiqffiffiffiffiffiffiffih 2 2rB 1 3 2B μ I Bd 0

(5.219)

FIGURE 5.30 Schematic diagram of a shear-valve MR damper. Adapted from Yang, D., Lu, Z., Zhu, H., Li, Z., 2014. Simplified design method for shear-valve magnetorheological dampers. Earthquake Eng. Eng. Vib. 13, 637
652.

386

CHAPTER 5 Design procedures for tall buildings

where n is the number of piston sections; B1 is the saturation value of magnetic induction of the magnetic core (1.5 for carbon steel; Yang et al. (2014)); B2 is the saturation value of magnetic induction of MR fluids (1 for fluid MRFXZD08-01 (Xu e al., 2012) and 0.6 for fluid MRF-J01 (Yang et al., 2014)); I is the maximum value of current input; μ0 is the permeability of air; d is the diameter of electromagnetic coils; h is the width of damping path; and r is the radius of magnetic core. Note that the resulting L is a function of h and r at this stage (i.e., h and r are unknown at this level).
Average circumference of the damping path is estimated as follows (Yang et al., 2014): sffiffiffiffiffiffiffiffiffiffi pffiffiffi 2B2 h D 5 2r 1 h 1 3 d μ0 I 0

(5.220)

0




Here, D is a function of h and r. Effective cross-sectional area of the piston is estimated as follows (Yang et al., 2014): !2 pffiffiffi sffiffiffiffiffiffiffiffiffiffi 3 2B2 h Ap 5 π d1r 2 πr02 μ0 I 2

(5.221)

where Ap is a function of h and r. Moreover, r0 is the radius of piston plate, which is estimated as follows: r0 $




rffiffiffiffiffiffi F πσ

where σ is the yielding stress of material of the piston shafts. Depth of groove accommodating the electromagnetic coil is estimated as follows (Yang et al., 2014): pffiffiffi sffiffiffiffiffiffiffiffiffiffi 3 2B2 h h1 5 d 2 μ0 I




(5.223)

Damping path effective length, L1, and width of the groove, L2, accommodating the electromagnetic coils are estimated is as follows (Yang et al., 2014): L1 5

r 2 B1 2ðr 1 h1 ÞB2

L2 5 2h1




(5.222)

(5.224) (5.225)

Thickness of the cylindrical housing estimated is as follows (Yang et al., 2014): t5

rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi B2 2ðr 1 h1 ÞL1 1 ðr1h1h1 Þ2 2 r 2 h 2 h1 B2

(5.226)

5.4 Active, Semiactive, and Hybrid Systems

To control the performance requirements of the MR damper, two additional parameters need to be defined: dynamic range, β, and controllable force, F. The dynamic range is the adjustment factor of damping force which equals to the ratio of its maximum to its minimum (that should be as large as possible (Xu et al., 2012; Kasemi et al., 2011)). The controllable force usually consists of two components: valve and shear (Yang et al., 2014). The appropriate choice of these parameters is subject to iteration since they are functions of several parameters, which are as follows: 8 12ηLA2p 3Lτ y > > > Ap F5 u1 > < πD0 h3 h > > > > :

•

β5

πD0 τ y h2 4ηAp u

(5.227)

where τ y and η are the shear yield stress and viscosity of MR fluid, respectively; and u_ is the relative velocity between piston and cylindrical housing (Xu et al. (2012) proposed the velocity of 100 mm/s and Yang et al. (2014) used 80 mm/s). At the beginning an initial guess should be tried, and in literature several recommendations can be found, such as:
Yan et al. (2014) suggest that β values range between 7.7 and 22 are based on experimental testing for civil applications.
Yang et al. (2000, 2001, 2002a,b) and Fujitani et al. (2002) designed and fabricated a full-scale MR damper with a maximum damping force of F 5 200 kN.
Xu et al. (2012) developed the design of an MR damper system for mitigation of earthquake in civil engineering for F 5 200 kN and β . 15 Magnetic circuit design The objective of magnetic circuit design is to determine the number of electromagnetic coils, N, so that the magnetic induction density in the damping path, generated by magnetic circuit, is more than the magnetic field intensity (Xu et al., 2012). This number can be estimated by (Yang et al., 2014): N5

2B2 h μ0 I

(5.228)

It can be seen that N is only dependent on h and independent on the other geometric parameters. Design of semiactive viscous dampers. In this section, the design of a semiactive viscous damper (Fig. 5.31) is presented as proposed by Hazaveh et al. (2016). The orifices existing in the device may be opened or closed depending on the direction of velocity and displacement at each time step (sensors are installed in the structure to record these responses). Correspondingly, the minimum and maximum damping can be achieved when the orifices are closed or opened, respectively.

387

388

CHAPTER 5 Design procedures for tall buildings

FIGURE 5.31 Schematic representation of semiactive devices attached to an SDOF system. Adapted from Rodgers, G.W., Mander, J.B., Chase, J.G., Mulligan, K.J., Deam, B.L., Carr, A., 2007. Reshaping hysteretic behaviour—spectral analysis and design equations for semi-active structures. Earthquake Eng. Struct. Dyn. 36 (1), 77
100.

FIGURE 5.32 Schematic hysteresis for (A) 1-4 device, (B) 1-3 device, and (C) 2-4 device. Adapted from Hazaveh, N.K., Pampanin, S., Rodgers, G.W., Chase, J.G., 2014. Novel semi-active viscous damping device for reshaping structural response. In: Conference: 6WCSCM (Sixth World Conference of the International Association for Structural Control and Monitoring).

Based on such a device, three different device control laws (called 1-4 device, 1-3 device, and 2-4 device) can be presented (see the corresponding hysteretic loops in Fig. 5.32 (Hazaveh et al., 2014)). The 1-4 law provides damping in all four quadrants recreating a response similar to passive viscous dampers (Fig. 5.32A). The 1-3 law provides damping only in the first and third quadrants, resisting away from

5.4 Active, Semiactive, and Hybrid Systems

equilibrium (Fig. 5.32B). The 2-4 law provides damping only in the second and fourth quadrants, resisting only toward equilibrium (Fig. 5.32C). The simplified design herein is mainly based on the 2-4 device (Fig. 5.32C) which is simultaneously effective in reducing displacement and base-shear demands. Note that the main structure is idealized as an SDOF system. •

•

Selection of supplemental damping ζ d The supplemental damping of semiactive device, ζ d , can be selected. The effective damping of the device 2-4 that it is added to structure is different from the nominal damping capacity of the device, determined as shown in the next step. Estimation of nominal damping ζ dn The nominal supplemental damping for 2-4 devices can be determined given through one of the following methods (Hazaveh et al., 2016) (based on interpretation of numerical results):
Linear approximation method 8 > <

!2

0:048T ζ dn 5 Bζ 20:910:15T 2 0:05 for T1 # 2:7 s >  pffiffiffiffiffi : ζ dn 5 0:07 2 0:02 Bζ Bζ ð24:54Þ for 2:7 , T1 # 5 s




where Bζ is the damping reduction factor (as discussed in Section 5.2.1.4.1) and T1 is the SDOF fundamental period. Eurocode 8 (EC8, 2004) as modified by Priestley et al. (2005, 2007) The following relation (Hazaveh et al., 2016) is proposed to straightforwardly estimate the total nominal damping of devices based on the effective damping: ζ dn 5 4:93ζ d 2 0:078

•

(5.229)

(5.230)

Note that if the ζ dn resulted from two above equations are different, an average of two values can be considered as the design damping (Hazaveh et al., 2016). Determination of damping coefficient C From Fig. 5.33 it can be seen that the hysteretic loop of the 2-4 semiactive viscous dampers (Fig. 5.33A) is half of the area associated with one to four

FIGURE 5.33 Hysteretic loops of (A) 2-4 device and (B) 1-4 device. Adapted from Hazaveh, N.K., Rodgers, G.W., Pampanin, S., Chase, J.G., 2016. Damping reduction factors and code-based design equation for structures using semi-active viscous dampers. Earthquake Eng. Struct. Dyn.

389

390

CHAPTER 5 Design procedures for tall buildings

device (Fig. 5.33B). Accordingly, the relationship between supplemental equivalent damping ratios is determined as follows (based on Eq. (3.60) (Chapter 3)):  1 1 Ed ζ d;224 5 ζ d;124 5 2 2 4πEs

(5.231)

Assuming a harmonic motion (Ed 5 πcωU02 and Es 5 k0 U02 =2, where k0 is the structural stiffness of the SDOF system (main structure) and U0 is the amplitude of harmonic motion) and considering the same damping constant for both systems (1-4 and 2-4 device), after some manipulations, the following expression can be obtained: ζ d;224 5

 1 Tc 2 4πm

(5.232)

Here, T and m are, respectively, the natural period and mass of SDOF system. Consequently, considering ζ d;224 5 ζ d , the equivalent damping constant is given by: C5

•

8πm ζ T d;224

(5.233)

Determination of nominal damping coefficient The choice of device configuration and distribution is basically similar to the case of passive (viscous) dampers (Section 5.2.1.6). Considering a uniform distribution of devices along the building height the nominal damping coefficient associated with a single damper is simply calculated by: c5

c N

(5.234)

Therefore, based on the performance function of 2-4 semiactive viscous dampers, the damping force in such devices is expressed by:  FD 5

•

cu_ d 0

for sgnðud Þ 6¼ sgnðu_ d Þ for sgnðud Þ 5 sgnðu_ d Þ

(5.235)

Determination of physical dimensions The fundamental design parameters of such a semiactive system are piston diameter, D, individual chamber length, L0 , and maximum piston displacement, δ, as shown in Fig. 5.34. Mulligan (2007) states that the piston displacement should be less than chamber length (i.e., δ # L0 Þ. The use of these parameters is helpful in controlling the stiffness of the device, Kd . The verification of such parameters should be conducted using experimental tests as shown in Step 9, in Section 5.4.2.9. The piston diameter can be approximated using the expression proposed by Mulligan (2007), as follows: sffiffiffiffiffiffiffiffiffiffiffiffiffi 2L0 Kd D5 πγP0

(5.236)

5.4 Active, Semiactive, and Hybrid Systems

FIGURE 5.34 Design parameters of 2-4 semiactive damper. Adapted from Mulligan, K.J., 2007. Experimental and analytical studies of semi-active and passive structural control of buildings. Ph.D. Thesis, Department of Mechanical Engineering, University of Canterbury, Christchurch, New Zealand.

where γ is the ratio of specific heats (1.4 for air) and P0 is the initial chamber pressure (typically atmospheric pressure). The chamber length, L0 , is typically constrained by the application and it is determined by the stroke required during large structural response (a maximum length of 30 cm is recommended (Mulligan, 2007)). Moreover, Mulligan (2007) recommended a piston diameter smaller than 20 cm, that is, D # 20 cm. An empirical relation to approximate the required damper stiffness was proposed by Rodgers et al. (2007), as follows: kd 5 6:29

ζd k

(5.237)

where k denotes the structural stiffness of SDOF system. Fig. 5.35 shows several curves for selection of piston diameter and chamber length, each one is associated with different device effective stiffnesses (Chase et al., 2006). The range of practical values of these parameters is also indicated as black rectangle in the figure. Hence, appropriate values can be selected with the use of estimated stiffness. More realistic experiments may be required for manufacturing these devices for application in real structures (see Step 9, Section 5.4.2.9). Design of semiactive-tuned mass dampers. This system is developed based on the conventional TMD system in such a way the tuned mass is an upper part of building itself (see Fig. 5.36A). To avoid excessive lateral stroke of the tuned mass (upper portion of building), the isolators (e.g., rubber or elastomeric bearings) are combined with a viscous damper (to get a passive TMD) or a resettable device (to get the SATMD), similar to what is shown in Fig. 5.36. Such a controlled building is idealized with an equivalent SDOF system (i.e., the lower part of building isolated by dampers from the upper portion) equipped with SA TMD (see Fig. 5.36B), generally resulting in a 2-DOF system. The overall effectiveness of such a system is based on the amount of seismic-induced energy transferred to the upper part (i.e., tuned mass), the size of the tuned mass,

391

CHAPTER 5 Design procedures for tall buildings

0.700

250 kN/m

0.600 0.500 Diameter (m)

392

125 kN/m

0.400 50 kN/m

0.300

25 kN/m 0.200 0.100 0.000 0.000

0.100

0.200 L0 (m)

0.300

0.400

FIGURE 5.35 Curves relating chamber length L0 to diameter D for different device nominal stiffness values. The black box indicates the range of possible design (Chase et al., 2006).

FIGURE 5.36 (A) Schematic of SATMD model using a resettable device and (B) idealized SDOF system with an SATMD. PTMD, Passive TMD. Adapted from Chey, M.-H., Chase, J.G., Mander, J.B., Carr, A.J., 2010. Semi-active tuned mass damper building systems: design. Earthquake Eng. Struct. Dynam. 39, 119
139.

5.4 Active, Semiactive, and Hybrid Systems

and the capability of resettable device in dissipating that energy. The sequence of parameters to define is as follows: •

•

•

•

Selection of a mass ratio μ The mass ratio is the ratio between the total mass of the isolated stories and the total mass of lower stories (stories located under the semiactive damper level). A large mass ratio can be selected (e.g., μ 5 0:5 (Chey et al., 2010)). Calculation of optimal frequency ratio and damping ratio of TMD The optimal tuning frequency, fopt , and supplemental damping ratio, ζ d;opt , can be calculated using expressions described in Appendix A (Tables A.1 and A.2), depending upon the type and position of the external excitation applied on the primary (SDOF) system. Calculation of optimal stiffness and damping Having determined the optimal frequency ratio and damping ratio, the optimal stiffness, kd , and damping, cd , coefficients associated with the TMD can be calculated as shown in Eqs. (5.113) and (5.114). Note that the calculated kd and cd are assigned, respectively, to rubber bearing and viscous damper, if a passive TMD is employed at interface of tuned mass and main mass. Since the scope of this procedure is to design the SA TMD, the kd should be considered as the sum of stiffness of semiactive (resettable) device (kdðresÞ ) and rubber bearings (kdðRBÞ ) (see Fig. 5.36B). Perform a time-history analysis Chey et al. (2010) suggest to model the 2-DOF system (Fig. 5.36B) and the spring member, kd 5 kdðRBÞ 1 kdðresÞ , using adequate software. For an effective controller evaluation, it is recommended (Chey et al., 2010) to perform history analysis using 30 earthquake time histories having multilevel hazard intensities (50% in 50 years (low intensity), 10% in 50 years (medium intensity), and 2% in 50 years (high intensity)); each of these three intensity levels may contain 10 pairs of earthquake records. Semiactive resettable devices can be simulated with Ruaumoko (Carr, 2007), where two types of relevant hysteretic loops are shown in Fig. 5.37 with (Fig. 5.37A) and without saturation (Fig. 5.37B). In the first type, the force in the device is proportional to the displacement until it reaches yield forces of the resettable device (i.e., saturation force); see Fy1 and Fy2 in Fig. 5.37. After it yields, the system behavior is perfectly plastic. For the type without saturation (Fig. 5.37B), the force is always proportional to the displacement with the device stiffness, and the system behavior can be defined with an idealized Bouc
Wen model (Wen, 1976) (see Chapter 4, Section 4.1.1.2.1, for more details about this model). In both types, the device is resetting once the force automatically drops to zero (at maximum and minimum displacements). It is recommended to set a maximum force of device equivalent to 13.8% of total structural weight multiplied by mass ratio (Hunt, 2002; Chey et al., 2010).

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CHAPTER 5 Design procedures for tall buildings

FIGURE 5.37 Hysteresis behavior of semiactive resettable device: (A) with saturation and (B) without saturation (Chey et al., 2010).

•

Note that in this design procedure of SATMDs, the main focus is on the stiffness of the device to be compared with passive TMD approaches. For the accurate modeling of dynamic characteristics (hysteretic loops) of such devices, experimental investigations are required as discussed in Chapter 7. Statistical assessment Having analyzed (in the previous step) the 2-DOF system with a suite of random seismic excitation, a statistical assessment of maximum structural responses (response spectra) can be carried out in this step. To this end, the use of lognormal statistics is recommended (Chey et al., 2010). Hence, the results obtained from the analysis of each earthquake suite (the set of 10 recorded histories) can be combined using two statistical parameters (median x^ and dispersion factor β) for each response (e.g., peak interstory drift, peak displacement, or peak acceleration) (Rodgers et al., 2007): ! n 1X x^ 5 exp lnðxi Þ n i51 sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi n   2 1 X β5 ln xi =x^ n 2 1 i51

(5.238)

(5.239)

where n is the number of samples (depending on the number of earthquake records) and xi is the maximum (spectral) response (displacement or acceleration) associated with ith sample (earthquake record).

5.4.2.9 Step 9: Verification analyses and quality control After designing the damping systems, it is important to check if the system satisfies the selected PO. In case this is not verified the device design parameters should be revised to improve the system performance. The explicit modeling of

5.4 Active, Semiactive, and Hybrid Systems

active-based damping systems is a difficult task and the detailed review of this is outside the scope of this publication. Thus, analytical expressions (models) and experimental tests are usually proposed for the response analysis of such systems (see Chapter 7, Section 7.2.2).

5.4.2.9.1 Active tuned mass dampers In this section, the controlled structural responses obtained on the basis of design approaches (Section 5.4.2.8.1) (Approaches 1
3) are presented. Consequently, the designer can compare the controlled and uncontrolled responses in order to assess the performance of active controlling system designed. Approach 1. Determination of the standard deviation of roof displacement. Since the PI of this design approach was based on the roof displacement, in this step, the relative standard deviation, σs , is given by (Ankireddi and Yang, 1996): ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi s ffi πSb N σ s 5 φ1 ð H Þ m21 D

(5.240)

where N5

 2    B0 ðA2 A3 2 A1 A4 Þ 1 A3 B21 2 2B0 B2 1 A1 B22 A0   D 5 A1 ðA2 A3 2 A1 A4 Þ 2 A0 A23

(5.241) (5.242)

with B2 5 μ 1 μg ;B1 5 εgopt ;B0 5 ψgopt

8 > > < A4 5 μ 1 μ g 1 μμg ;A3 5 ð1 1 μÞεgopt 1 2ζ 1 ω1 μ 1 μg A2 5 μ 1 μg ω21 1 ð1 1 μÞψgopt 1 2ζ 1 ω1 εgopt > > : A1 5 ω21 εgopt 1 2ζ 1 ω1 ;A0 5 ω21

(5.243)

(5.244)

In Eq. (5.240), Sb is the uniform power spectral density of the stationary white-noise disturbance of wind type. This parameter can be simply calculated for the existing excitation using available routines in MATLAB software (Samui et al., 2016). Alternatively, for wind excitation, the nondimensional power spectral density can be given by (Balendra et al., 1995; Yan et al., 1998): 2

Sb 5

4k0 F Φ ωω1

(5.245)

where ω is the frequency of the harmonic excitation, and:

!αp 8 2 U r π4 Ψω1 U10 > > z > Φ5 h ; Uz 5 U10 10 i5=6 ; U r 5 > > Uz < 21 ðπ3 Ψω1 Þ2 > > ω1 lx F0 π4 > > Ψ5 4 ; F 5 2 ; F0 5 ρ0 A0 C0 Uz2 > : 2π U10 ω 1 m1

(5.246)

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CHAPTER 5 Design procedures for tall buildings

where k0 is the ground surface drag coefficient; lx is the wave length; z is the height of structure; U10 is the mean wind speed at the reference height of 10 m; αp is the power law exponent; ρ0 is the air density; A0 is the structure frontal area; C0 is the drag coefficient; and Uz is the mean wind speed at the height z. Interested readers should refer to Choi and Kanda (1993) for the across-wind formulation of the nondimensional spectra of the wind force. It is worth mentioning that since the device stroke is dominated by the damper mass, the use of active control would increase the stroke. Hence, the device stroke should be checked to be in a reasonable range (Yan et al., 1999). Approach 2. Determination of mean-square responses. Given that the DPI case represented in Approach 2 is more practical than the VPI one, the normalized mean-square response of displacement and velocity of the main mass ; x_1 ) and  22  (x  122 22 _ _ , E x , E x auxiliary mass (x ; x ), respectively, indicated by E x d d 1 d , and 1   E x_ 22 , for both wind and earthquake excitations, can be computed as follows d (Nagashima, 2001): •

For wind excitation pffiffiffi pffiffiffiffiffiffi m ω2 ðμ 1 4ζ 2 Þ G1 1 d 1 3μ s  22  3 2ω1 md qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi E x1 5 pffiffiffi 4 μð1 1 μÞ G 1 m ω2 ð11μÞ21  G 1 2ζ 2 m ω2 μ21 1 d 1 1 d 1 s

E



x_ 22 1



pffiffiffi pffiffiffiffiffiffi 2  m ω2 ½4ð1 1 μÞζ 2 1 ðμ3 1 3μ2 1 μÞ G1 1 d 1 μð1 1 μÞðsμ2 1 2μ 1 3Þ 2ω1 md μ 1 2μ 1 3 5 pffiffiffi  qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 4 μð11μÞ2 G1 1 md ω21 ð11μÞ21 G1 1 2ζ s 2 md ω21 μ21

E



x22 d



md ω21 md 2 ω41 pffiffiffi 2 2ð11μÞ3 G1 1 μð1 1 μÞ G1 1 μð11μÞ2 5 3 3=2 pffiffiffi qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi μ 4ω1 ma G 1 2ζ 2 m ω2 μ21 1

  5 E x_ 22 d

d

s

d

(5.248)

(5.249)

1

pffiffiffi 2ð1 1 μÞ G1 1 md ω21 ffi pffiffiffiffiffiffi 3=2 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 4ω1 md μ G 1 2ζ 2 m ω2 μ21 1

•

s

(5.247)

(5.250)

1

For earthquake excitation pffiffiffi m ω2 ½4ð1 1 μÞζ 2 1 μ pffiffiffiffiffiffi G1 1 d 1 3μð1 1 μÞs  22  3 2ω1 ð1 1 μÞ md E x1 5 pffiffiffi  qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 4 μ G1 1 md ω21 ð11μÞ21 G1 1 2ζ s 2 md ω21 μ21

(5.251)

pffiffiffi pffiffiffiffiffiffi m ω2 ½4ð1 1 μÞζ 2 1 μ G1 1 d 1 3μð1 1 μÞs  22  3 2ω1 md E x_ 1 5 pffiffiffi  qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 4 μ G2 1 md ω21 ð11μÞ21 G1 1 2ζ s 2 md ω21 μ21

(5.252)

5.4 Active, Semiactive, and Hybrid Systems

  5 E x22 d

E



x_ 22 d



h ih i md ω21 md ω21 pffiffiffi G1 1 1 1 μ 2ð11μÞ5 G1 1 μ pffiffiffi qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 4ω31 ma 3=2 μ G1 1 2ζ s 2 md ω21 μ21

(5.253)

pffiffiffi md ω21 G1 1 1 1 2ð11μÞ3 μ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 5 pffiffiffiffiffiffi 4ω1 ma μ3=2 G 1 2ζ 2 m ω2 μ21 1

s

d

(5.254)

1

The above expressions give the controlled responses in case the displacement feedback parameter G1 is already known. For evaluation purposes, if G1 5 0 is substituted into the above equations, the passive-controlled responses are comparable to those obtained from the active-controlled system. Approach 3. Determination of responses. Regarding Approach 3, the expressions of response analysis are represented for the system under both harmonic and random excitations, as follows: •

For harmonic excitation The displacements of main structure and ATMD are expressed, respectively, by: y1 ðtÞ 5 Aeiðωt2θ1 Þ xd ðtÞ 5 Be

(5.255)

iðωt2θ2 Þ

(5.256)

where θ1 , θ2, A, and B are given in Section 5.4.2.8.1. Consequently, the control force is given by:  uðtÞ 5 2md

•

G1 2 G3 G5 ω y1 1 G2 ω2d xd 1 2 ζ 1 ω1 y_ 1 1 2G4 ζ s ωd x_ d 1 y€ 1 G6 x€ d μ 1 μ μ 1

(5.257)

For random excitation Based on the proposed approach, the standard deviation of structural displacement, controlled by the ATMD, can be calculated by: rffiffiffiffiffiffiffiffiffiffi B4 π σs 5 a4 A4

(5.258)

where A4 and B4 are determined in Section 5.4.2.8.1. σs can be compared with the uncontrolled (inactive or passive) responses in order to check the system performance; for this purpose, the gain parameters G1
G6 must be set to zero in the definitions of A4 and B4 (Eqs. 5.213 and 5.214).

5.4.2.9.2 Semiactive (magnetorheological) dampers In order to evaluate the properties of a manufactured MR damper, conducting performance tests (magnetic field tests and dynamic tests) is appropriate (Xu et al., 2012) (see Chapter 7, Section 7.2.2.3 for more details). Moreover, the accuracy of

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CHAPTER 5 Design procedures for tall buildings

FIGURE 5.38 Bouc
Wen model of the MR damper.

the designed parameters of the device can be examined by conducting a finite element simulation on the magnetic circuit (Yang et al., 2014). Simpler dynamic models of MR dampers are proposed for the simulation of damper behavior and structural vibration control (Gamato and Filiskom, 1991; Spencer et al., 1997; Wereley et al., 1998; Yang et al., 2004). Based on the test data, Spencer et al. (1997) proposed to use a Bouc
Wen model (Wen, 1976) for MR dampers (Fig. 5.38, see Chapter 4, Section 4.1.1.2.1, for more details about this model). The force in the model is provided by the following relationship: F 5 c0 x_ 1 k0 ðx 2 x0 Þ 1 αz

(5.259)

where c0 is the damping coefficient; k0 is the linear spring coefficient; x and x_ are the absolute displacement, α is the postyield ratio and velocity; z is the evolutionary variable governed by: z_ 5 2 γ jx_ jzjzjn21 2 β x_ jzjn 1 Ax_

(5.260)

The parameters, γ, β, n, and A, are dimensionless quantities controlling the hysteretic behavior of the model and they should be identified by experimental tests for the designed MR device (Wen, 1976). Another model (see Fig. 5.39) was developed by Yang et al. (2004) in which the fluid inertial effect is represented by an equivalent mass, m; the accumulator spring stiffness, k; frictional force due to the damper seals, f0 ; and the postyield _ This velocity-dependent damping can be plastic damping coefficient, cðxÞ. expressed as follows: _ 5 a1 e2ða2 jx_ jÞ cðxÞ

p

(5.261)

which is defined as a mono-decreasing function with respect to the absolute _ The coefficients a1 , a2 , and p are positive and can be estimated using velocity x. experimental results (Yang et al., 2004).

5.4 Active, Semiactive, and Hybrid Systems

FIGURE 5.39 Proposed mechanical model of MR dampers.

Subsequently, the damper force can be estimated with the following relationship: f 5 mx€ 1 cðx_ Þx_ 1 kx 1 αz 1 f0

(5.262)

with the evolutionary variable z determined as shown in Eq. (5.260).

5.4.2.9.3 Semiactive viscous dampers For the verification of designed semiactive viscous damper, experimental tests should be conducted in order to establish the dynamic characteristics under various inputs. Moreover, the efficiency of the control law and hysteretic loop of device in adding supplemental damping can be investigated (Franco-Anaya et al., 2007). Furthermore, with respect to the size and force capacity of these devices, they are appropriate for conducting large-scale structural experimental testing such that results can be applicable for real structures. It is suggested to consulate the manufacturer of the prototype devices during the design process (e.g., hardware selection and piston and cylinder sizes) and relative tests (Mulligan, 2007). For more details, it is encouraged to refer to the experimental parts of research works by Mulligan (2007) and Mulligan et al. (2009) and also to Chapter 7, Section 7.2.2.3.

5.4.2.9.4 Semiactive-tuned mass dampers In this step, two sets of verifications are conducted on the SATMD. The first case is to verify the results of statistical assessment (Section 5.4.2.8.2), which is based

399

400

CHAPTER 5 Design procedures for tall buildings

on the analysis of 2-DOF system, using corresponding results computed by nonlinear analysis of a full model (MDOF system) of building structure and explicit modeling of SATMD (Chey et al., 2010). For this aim, Ruaumoko (2004) can be employed. In parallel to this, the experimental validation of semiactive device can be performed using devices testing (Mulligan, 2007; Mulligan et al., 2009) and reduced-scale test of structure equipped with semiactive device. The concept of experimental tests for such resettable devices is similar to those explained in the previous section (see Chapter 7, Section 7.2.2.3, for more details).

5.5 RETROFIT OF EXISTING BUILDINGS “Retrofit” means to improve structural capabilities (e.g., strength, stiffness, ductility, regularity in height/plan, structural integrity, and stability) of a building that shows deficiency, based usually on code requirements. Nevertheless, “seismic retrofit” or “seismic rehabilitation” can be defined as the design of measures to enhance the seismic performance of structural or nonstructural components of a building by refining deficiencies identified with a seismic evaluation in proportion to a selected PO (ASCE, 2017a). Similarly, wind retrofit means to enhance the building performance from a wind deficiency point of view. Retrofit code requirements are mainly focused on the seismic aspects and for this reason seismic provisions are mainly reviewed in the following section.

5.5.1 CODE REQUIREMENTS Few standards are available worldwide for building retrofit as shown in Section 5.1.1. In the following, the history of the development of the US standards is briefly reviewed since, based on the authors knowledge, it is considered the most comprehensive standard available. Other provisions (e.g., Japanese and Chinese) are briefly reviewed as well: •

United States: one of the first codes, which explicitly addressed the seismic evaluation methodology of existing buildings, was ATC-14 (ATC, 1987). This standard presented a method to guide practitioners in assessing existing buildings to identify potential seismic deficiencies and vulnerabilities. Moreover, recommendations for upgrading buildings to achieve the minimum life-safety PO were given. The procedures suggested in ATC-14 (ATC, 1987) are the extended version of analysis methods and evaluation concepts developed in ATC-3 (ATC, 1978) and ATC-6-2 (ATC, 1983). ATC-14 (ATC, 1987), a handbook for the seismic evaluation of existing buildings, was developed by FEMA (1992a). This standard, called FEMA-178 (FEMA, 1992a), sets a series of evaluation statements for zones with high seismicity. Moreover, FEMA-172 (FEMA, 1992b) developed further information on techniques to lessen seismic deficiencies for various construction types.

5.5 Retrofit of Existing Buildings

•

•

Subsequently, FEMA 310 (FEMA, 1998a,b), later published as ASCE 31-03 (ASCE, 2003), provided a procedure with tiers for seismic evaluation of existing buildings in view of multiple levels of seismicity and two POs (life safety and immediate occupancy). In parallel, Vision 2000 (SEAOC, 1995) was developed to be used for the evaluation and upgrade of existing buildings. This was the first document that fully summarized performance-based methodologies considering seismic hazard, performance levels, and building use. Moreover, FEMA 273 (FEMA, 1997) Guidelines for the Seismic Rehabilitation of Buildings was developed as a base for future development of performance-based building codes. Some features such as simplified and systematic rehabilitation methods and the procedures for incorporating new technologies into rehabilitated structures were discussed. The evolution of this code was realized with FEMA 356 (ASCE, 2000). This standard was then published as ASCE 41-06 (ASCE, 2007), demonstrating the procedures to rehabilitate existing building based on achieving different performance levels. Combining the standards ASCE 31-03 (ASCE, 2003) and ASCE 41-06 (ASCE, 2007), a most updated version, ASCE 41-13 (ASCE, 2013), was developed for the seismic evaluation and retrofit of existing buildings (that was recently updated with the 2017 version (ASCE, 2017b)). ASCE 41-13 (ASCE, 2013) introduces an approach including three-tier evaluation steps for existing building and the relative retrofit strategies. Japan: The Japanese Building Disaster Prevention Association (TJBDPA, 2005) provides a technical manual for the seismic evaluation and retrofit of existing RC buildings. Takewaki et al. (2013a,b) state that also the document released by the Japanese Government (MLIT, 2011) proposed provision for the retrofit of existing high-rise buildings in Japan based on a set of simulated long-period ground motions. China: The Chinese code (GB50223, 2008) proposed four protection categories to improve seismic protection requirements: moderate, standard, emphasized, and particular protection. Correspondingly, different design schemes are adopted for each of these categories.

In alternative to code prescriptive procedures, in literature there are available several nonprescriptive procedures, such as: •

•

•

Martinez-Rodrigo and Romero (2003) proposed a numerical scheme for evaluation and retrofit of multistory building using linear and nonlinear viscous dampers. Accordingly, a 6-story steel frame was investigated to find the optimum retrofit scheme. Weng et al. (2012) developed a simplified (step-by-step) design procedure for seismic retrofit of RC buildings using viscous dampers and proved its effectiveness as seismic retrofit design for earthquake-damaged frames structures. Li et al. (2015) developed a step-by-step procedure for design and retrofit of buildings equipped with metallic structural fuses using damage-reduction spectrum method. They assessed the performance procedure for a 5-story frame using the buckling restrained bracings (BRBs) as the structural fuse.

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CHAPTER 5 Design procedures for tall buildings

Having briefly discussed the major procedures for the retrofit of existing buildings with dynamic modification devices, in the following the proposed design procedure, mainly based on US standards, is reviewed.

5.5.2 EVALUATION PROCEDURES BASED ON ASCE 41-13 (ASCE, 2013) The building evaluation process is the first step for defining what is the required (if any) seismic retrofit procedure of a building. In ASCE 41-13 (ASCE, 2013), three evaluation procedures are generally proposed: Tier 1, Tier 2, and Tier 3, which are briefly described in following: •

•

Tier 1 (screening procedure) Tier 1 refers to an evaluation report checklist that allows to identify potential defects in a building based upon performance of similar buildings in past earthquakes. This method gives the opportunity to exert a quick evaluation of the building elements (structural, nonstructural, and foundation), geologic hazard, and site conditions. Two structural performance levels are allowed: immediate occupancy and life safety. While for the nonstructural elements the following are permitted: position retention and life safety. After performing Tier 1 checklist, if any defect is identified, then the designer may proceed to a more detailed evaluation method (Tier 2). Tier 2 (deficiency-based procedure) This method is applicable for certain building types and POs. It allows to establish if evaluated potential deficiencies (e.g., identified using Tier 1 method) need mitigation. In most of the cases, it might not be required to analyze the response of the entire structure. Therefore, for obtaining the building properties, it is permitted to use destructive and nondestructive examinations. The scope of this approach is to identify the cause and the extent of the deficiencies. Tier 2 evaluation procedure involves conducting simplified linear analyses (i.e., linear static and linear dynamic procedures) of the building in view of the potential defects identified in Tier 1. This tier is suitable for small, rather simple, buildings (e.g., those with not complex structural systems) and for buildings without a need to advance analytical approaches (e.g., those based upon nonlinear analysis techniques). This is because the common defects are almost well understood and the mitigation approaches are straightforwardly attainable. The structural performance levels (immediate occupancy and life safety) and nonstructural performance levels (position maintenance and life safety) are accepted for Tier 2 procedure. In case partial retrofit is necessary (e.g., due to limited funding or being done while the building is occupied), using Tier 2 procedure retrofitting should be adopted in a priority order, that is, the more critical ones at first. In alternative, the designer can proceed with Tier 3 for a more comprehensive evaluation. Indeed, Tier 2 procedures may produce more conservative results compared to those of Tier 3 because of a diversity of simplifying assumptions (ASCE, 2013).

5.5 Retrofit of Existing Buildings

•

Tier 3 (systematic procedure) Tier 3 is an evaluation procedure in which the response analysis of the building is fully performed under seismic hazards. This systematic evaluation procedure may be applied at any time (e.g., at the beginning of evaluation process) or may be used to further evaluate the potential deficiencies identified in Tier 1 or Tier 2 procedures. This kind of evaluation is more suitable for complex structures (e.g., tall buildings) and it requires to focus on the nonlinear structural response. Nonlinear analysis procedures may be employed in preliminary evaluations without testing given that the required testing is conducted before the retrofit. Albeit Tier 3 procedure is complicated and expensive to carry out, it frequently leads to construction savings. Starting the evaluation immediately with Tier 3 procedure is often suitable when the building has significant seismic defects regarding the selected PO (ASCE, 2013).

In the case of tall buildings, Lai et al. (2015) state that Tier 1 is not applicable, and Tier 3 is automatically required. According to ASCE 41-13 (ASCE, 2013), seismic isolations or damping systems are considered as possible retrofit technique and their analysis and design are included in Tier 3 procedure. Readers should refer to ASCE 41-13 (ASCE, 2013) (and the most updated version of ASCE 41-17 (ASCE, 2017b)) for more details about the limitations of using Tier 1 and Tier 2 based on the building type (load-resisting structural system) and number of stories.

5.5.3 STEP-BY-STEP PROCEDURE Based on the literature review presented in the previous sections, a step-by-step procedure for the seismic retrofit process of tall buildings is presented (see Fig. 5.40). This is mainly based on the requirements of ASCE 41-13 (ASCE, 2013) and the main focus is on supplementary damping (and isolation) systems as retrofit strategy, while other retrofit strategies useful to tall buildings are just addressed.

5.5.3.1 Step 1. Initial considerations The first important step involves a building evaluation to determine if the existing structure has acceptable performance capacity and to identify eventual deficiencies. According to ASCE 41-13 (ASCE, 2013), initial considerations may include: •

•

Structural characteristics of the building. The structural characteristics including the type of structural systems, type of material, and geometrical dimensions should be analyzed before starting retrofit design. Seismic hazards at the site. Seismic hazards other than ground shaking may exist at the building site. The risk and possible damage from geologic site

403

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CHAPTER 5 Design procedures for tall buildings

FIGURE 5.40 Step-by-step procedure for retrofit process of existing buildings.

• •

hazards should be considered. In some cases, it may be more feasible to mitigate the site hazard than retrofit the building. Results of prior seismic evaluations. If there is any seismic evaluation, performed previously, it could be considered before the current retrofit process. Building use and occupancy requirements. To estimate the significance of potential temporary or permanent disruptions associated with various

5.5 Retrofit of Existing Buildings

•

• •

•

risk-mitigation schemes, the use of the building must be considered. Regarding vulnerable buildings, the occupancy can be reduced; moreover, redundant facilities can be provided, and nonhistoric buildings can be demolished and replaced. Historic status of the building. The historic status of the building should be determined if it is at least 50 years old. This should be made as early as possible, since it could influence the choices of retrofit strategy. Economic considerations. The range of costs and impacts of retrofit (e.g., the variation associated with different POs) should be considered. Societal issues. Since existing buildings have been built with the use of earlier standards and often are occupied, several issues may arise, such as distribution impacts on various parts of the community, reduced business interruption, occupancy dislocation and the loss of housing, the treatment of historic properties, and methods for financing seismic rehabilitation (FEMA 275 (FEMA, 1998a,b)). Local jurisdictional requirements. Particular local jurisdiction requirements shall be carefully evaluated since they could be more stringent than the main standard.

5.5.3.2 Step 2. Performance objectives and hazard levels After the first step of initial evaluation, it is important to define the target PO as described by ASCE 41-13 (ASCE, 2013). A PO may consist of one or more combinations of selected “seismic hazard levels,” with a target “structural performance level” and a target “nonstructural performance level.” Performances can be defined qualitatively based on different aspects, such as safety of building occupants during and after the event (earthquake); cost and possibility of reverting the building to its preevent condition; period required for the building to be converted from service to effect repairs; and influences of economical, architectural, or historical problems on the larger community. These features are directly related to the level of damage that the building and its consisting systems would withstand during an event (ASCE, 2013). In other words, the PO, selected as a basis for design, specifies the cost and practicality of a project, and the achieved advantages in terms of enhanced safety, decrease in damage, and interruption of use in case of future earthquakes. To select the appropriate level, Table 5.28 lists the POs for a typical building. Based on the code recommendations three different levels of POs can be selected: • • •

Basic POs for existing building (BPOE) Enhanced PO Limited PO To reach each PO the following objectives need to be reached:

•

BPOE:
g and i

405

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CHAPTER 5 Design procedures for tall buildings

Table 5.28 Performance Objectives (ASCE, 2013) Target Building Performance Levels

Seismic Hazard Level 50%/50 years BSE-1E (20%/ 50 years) BSE-2E (5%/ 50 years) BSE-2N (ASCE 7-16 (ASCE, 2017a) MCER)

•

•

Operational Performance Level (1-A)

Immediate Occupancy Performance Level (1-B)

Life Safety Performance Level (3-C)

Collapse Prevention Performance Level (5-D)

a e

b f

c g

d h

i

j

k

l

m

n

o

p

Enhanced POs:
g and i, j, m, n, o, or p
l and e or f
g and l and a, or b
k, m, n, or o alone Limited POs:
g alone
l alone
c, d, e, or f

To use this table, two factors should be defined: seismic hazard level (Section 5.5.3.2.1) and target building performance level (Section 5.5.3.2.2). Note that another PO, called basic PO equivalent to new building standards (BPON), is defined in ASCE 41-13 (ASCE, 2013). The scope of this objective is to retrofit the building such that it reaches the same performance level of a new structure based on the new building standard requirements.

5.5.3.2.1 Seismic hazard level Seismic hazard due to ground shaking can be defined as acceleration response spectra or ground motion acceleration histories specified based upon a probabilistic or a deterministic analysis (ASCE, 2013). This hazard may depend upon the location of the building with respect to faults, the regional and site-specific geologic and geotechnical features, and the specified seismic hazard levels. Different seismic hazard level can be defined (ASCE, 2013) and relative 5% damped acceleration response spectrum for short period (Ts 5 0:2 second), SS , and long period

5.5 Retrofit of Existing Buildings

(T1 5 1 second), S1 , in the maximum direction of horizontal response, can be determined as follows: •

•

•

•

Basic safety earthquake-2 (BSE-2N). It is equivalent to MCER to be used for the BPON standards. Therefore, it is computed using values of SS and S1 taken from the MCER spectral response acceleration contour maps (ASCE, 2017a). Basic safety earthquake-1 (BSE-1N). Defined as two-thirds of the BSE-2N useful for the BPON standards. Therefore, it is estimated using two-thirds of the SS and S1 values obtained for the BSE-2N seismic hazard level. Basic safety earthquake-1 (BSE-1E). It is equivalent to a seismic hazard with a 20% probability of exceedance in 50 years (lower than the BSE-1N). It is computed using values from approved 20%/50-year maximum-direction spectral response acceleration contour maps (SS and S1 ). Values for BSE-1E are not required to be greater than those achieved for BSE-1N. Basic safety earthquake-2 (BSE-2E). It is considered as a seismic hazard with a 5% probability of exceedance in 50 years (lower than the BSE-2N). It is computed using values from approved 5%/50-year maximum-direction spectral response acceleration contour maps (SS and S1 ). Values for BSE-2E are not required to be greater than those obtained for BSE-2N.

In addition to the above-mentioned procedures, it is also possible to specify the acceleration response spectra with the use of site-specific procedure. This is based on the geologic, seismologic, and soil characteristics associated with the building site. Reader may refer to Section 2.4.2 of ASCE 41-13 (ASCE, 2013) and also Section 5.2.1.1 for more details. Independent ground motion acceleration histories with magnitude, fault distances, and source mechanisms can be chosen for the BSE-1N, BSE-2N, BSE-1E, or BSE-2E seismic hazard levels. At least three data sets of ground motion acceleration, for site seismic hazard, should be used for the RHA, where each one includes two horizontal components. In case the vertical motion is important, two horizontal components and one vertical component of at least three records should be selected and scaled. It is recommended to refer to Section 2.4.2.2 of ASCE 4113 (ASCE, 2013) or to Section 16.2 of FEMA P-1050 (FEMA, 2015) for a more detailed discussion (as well as Section 5.2.1.1). The required number of ground motion pairs (N) is listed in Table 5.29 depending on the building site distance from the active fault. These limiting numbers are for POs of existing buildings (e.g., BPOE).

5.5.3.2.2 Target building performance level A target building performance level may be composed by structural and nonstructural target performance levels. Fig. 5.41 illustrates estimated target performance levels and ranges in buildings (ASCE, 2013). With regard to structural and

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Table 5.29 Required Number of Ground Motion Acceleration Records and Method of Response Analysis (ASCE, 2013) Building Site Distance From Active Fault (km)

Method of Calculating Responses

Limiting Number of Earthquake Record Pairs (N)

.5 .5 #5 #5

Average Maximum Average Maximum

N $ 10 3#N#9 N $ 10 3#N#9

FIGURE 5.41 Target building performance levels and ranges. Adapted from ASCE, 2013. ASCE41-13: Seismic Evaluation and Retrofit of Existing Buildings. American Society of Civil Engineers, Reston, VA.

nonstructural performance levels, the damage patterns of structural systems and elements can be found in Section 2.3 of ASCE 41-13 (ASCE, 2013). The basic POs for existing buildings depend upon the risk category defined in ASCE 41-13 (ASCE, 2013), as given in Table 5.30, given the risk category, hazard level, and the evaluation procedures (Tiers 1
3).

5.5 Retrofit of Existing Buildings

Table 5.30 Basic POs for Existing Buildings (ASCE, 2013) Evaluation Procedure

Tier 3

Hazard Level Risk Category I and II

III

IV

BSE-1E LS structural performance LS nonstructural performance (3-C) DC structural performance PR nonstructural performance (2-B) IO structural performance PR nonstructural performance (1-B)

BSE-2E CP structural performance Nonstructural performance not considered (5-D) LS structural performance Nonstructural performance not considered (4-D) LS structural performance LS nonstructural performance not considered (3-D)

Note: LS, life safety; LS, limited safety; IO, immediate occupancy; CP, collapse prevention; DC, damage control; PR, position retention.

Enhanced PO can be achieved if one of the following options or a combination of them is considered: • • •

Target building performance levels are higher than those of BPOE. Seismic hazard levels are higher than those of BPOE. Risk categories are higher than those of BPOE.

Accordingly, some possible enhanced POs can be the following, as recommended by ASCE (2013): •

• •

For a certain risk category, target structural or nonstructural performance levels which are higher than those of the BPOE at the hazard level of BSE1E, or BSE-2E, or both of them. For a certain risk category, target structural or nonstructural performance levels of the BPOE at a hazard level higher than BSE-1E, or BSE-2E, or both of them. Target building performance levels of the BPOE using a risk category higher than the one of the building.

If a PO is less than that of the BPOE, then a limited PO is obtained. This may be achieved by using a reduced PO or a partial retrofit objective. The reduced objective is defined when a lower seismic hazard level or a lower target building performance level than that of the BPOE is applied. The partial objective refers to the retrofit of parts of the building without the complete rehabilitation of the resisting system. It is worth mentioning that the use of a limited PO should satisfy the following requirements (ASCE, 2013): •

It should not lead to any reduction in the structural or nonstructural performance levels of the existing building for the same seismic hazard level.

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• •

It should not result in a new structural irregularity or in more severe structural irregularity. It should not lead to an amplification of the seismic forces in any component which is potentially incapable of resisting such forces.

5.5.3.3 Step 3. Evaluation of existing building Before starting the retrofit process of a building, it is recommended to obtain its as-built information to evaluate any deficiency. All the components of the building should be evaluated and analyzed so that the selected PO is satisfied. An appropriate evaluation procedure can be selected depending on the selected PO, level of seismicity, and building type. Based on ASCE 41-13 (ASCE, 2013) requirements, Tier 3 procedure is selected for the evaluation of tall buildings. The required investigations/information to be collected on the building are as follows: •

•

• •

•

Building type. Determined based on the seismic load-resisting system and the diaphragm type (see Table 3-1 of ASCE 41-13 (ASCE, 2013)). If the structural system of the building along each direction is different, separate building types may be chosen. Building configuration. Related to the type and arrangement of existing structural components of the vertical and seismic force-resisting systems as well as of the nonstructural elements with effective stiffness/strength when bearing loads. Potential seismic deficiencies, for example, discontinuities in the load path, weak links, irregularities, and insufficient strength/deformation capability in components, may be identified with the use of building configuration information. Component properties. Needed to analyze the strength and deformation capacities of structural components (e.g., beams, columns, and diaphragms). Site and foundation information. Determined based on existing building documentation, visual site inspection, or an investigation program of sitespecific subsurface (in case of inadequate available data to compute foundation capacities or to realize the presence of geologic site hazards). Adjacent buildings’ information. These are important to understand some of the possible phenomenon:
Building pounding. It can change the basic response of the building to earthquake, imposing extra inertial loads and energy to the building from adjacent ones. For example, extreme local damage to structural elements at the zones of impact may occur, especially where the floor and roof levels of adjacent buildings are not aligned in height.
Shared element condition. Shared elements (e.g., party walls) between existing building and adjacent ones may create two problems depending on if the buildings move independently or as an integrated unit. In the first case, a partial collapse may occur at the position of shared element.

5.5 Retrofit of Existing Buildings




Concerning the second case, an extreme load may be imposed to the buildings due to the presence of additional mass and inertial forces. Hazards from adjacent building due to potential falling debris, rooftop equipment, fire, and blast pressures. Refer to Section 3.2.5.3 of ASCE 4113 (ASCE, 2013) for further details.

Three levels of data collection knowledge are presented in ASCE 41-13 (ASCE, 2013): minimum data collection, usual data collection, and comprehensive data collection (Table 5.31). In this table, a knowledge factor, κ, is used to account for uncertainty in the collection of as-built data. This factor is used to express the confidence with which the properties of the building components are known, where calculating component capacities. It is worth mentioning that if the material testing is delayed up to retrofit construction, this may potentially lead to reevaluation or redesign of the retrofit due to differences between the assumed material properties and those determined by testing (ASCE, 2013). After performing the evaluation process, an evaluation report could be prepared accordingly. This report may contain, at the least, the following details (ASCE, 2013): • •

•

Scope and intent. The aim of the evaluation including a summary of the evaluation procedure(s) adopted and level of investigation applied. Site and building data. This might include: • General building description, including number of stories and dimensions, availability of original design, and construction documents • Structural system description, including material properties, load-resisting systems, floor diaphragms, basement, and foundation system • Nonstructural system description, including those affecting seismic performance of the building or being dangerous • Common building type and occupancy • Performance level • Level of seismicity • Soil type and conditions Findings. A list of seismic deficiencies identified could be prepared.

For example, a list of common seismic deficiencies identified in existing tall buildings previously built in Los Angeles, Oakland, and San Francisco are as follows (Lai et al., 2015): • • • • • • •

Low design base shear was considered at the design time. Small magnitude of drift limits were considered during the design. Simplified (static) analysis methods, which does not account for dynamic features, were used for the initial design. Vertical irregularities (especially close to the base of tall buildings) and plan irregularities. The case “strong-column-weak-beam” was not checked for member sizing. Beam and column joints and panel zones were not seismically designed. Column forces were not appropriately transferred to foundations.

411

Table 5.31 Data Collection Requirements (ASCE, 2013) Data Performance level Analysis procedures Testing

Level of Knowledge Minimum

Usual

Comprehensive

Life safety or lower

Life safety or lower

Greater than life safety

Linear static, linear dynamic

All types

All types

No tests

Usual testing

Comprehensive testing

Drawings

Design drawings or equivalent

No drawings

Design drawings or equivalent

Construction documents or equivalent

Condition assessment

Visual

Visual

Comprehensive

Visual

Comprehensive

Visual

Comprehensive

Material properties

From default values

From design drawings

From default values

From drawings and tests

From usual tests

From documents and tests

From comprehensive tests

Knowledge factor (κ)

0.75

0.9

0.75

1.00

1.00

1.00

1.00

5.5 Retrofit of Existing Buildings

5.5.3.4 Step 4: Model and analyze existing building In this step, the designer should model the building load-resisting structural system using appropriate software. At this level, all existing structural members effective on the response should be explicitly modeled (see Section 5.1.3.2.1). The following points are useful to be considered in modeling (ASCE, 2013): • •

•

• • • •

The load
displacement features of all components of building should be directly included in modeling. In case that the Ritz vector
based nonlinear response analysis is carried out using commercial software, the following three requirements shall be satisfied (see Section 5.1.3.2.3): • Sufficient modes should be included in the analysis so that at least 90% of mass participation is captured. • Time steps should be chosen as small as possible to confidently attain solution convergence. • Adequate vectors should be considered to accurately get local dynamic response of elements. For the analysis based on the 2D model, the deformations and forces in building elements should be evaluated under selected scaled ground motions. While for the 3D case, they should be assessed under a suite (series) of ground motions randomly oriented if the building is in a site at least 5 km far from an active fault. If the site distance from the fault is less than 5 km, the fault-normal components should be used for the analysis (ASCE, 2013). Inherent damping can be accounted using Rayleigh damping (ASCE, 2013; Lai et al., 2015) (see Section 3.3.1 (Chapter 3) for further details). P-Δ effects should be included in the mathematical model of building. SSI effects can be modeled explicitly if the spectral accelerations increase due to increase in fundamental period (ASCE, 2013). Uplift effects due to earthquake on the tension part of an element should be included in the analytical model as nonlinear DOFs (ASCE, 2013).

It is noted that nonlinear static (pushover) analysis, according to ASCE 41-13 (ASCE, 2013), is not allowed to be used for the analysis of tall buildings (since it neglects higher mode effects) (Lai et al., 2015). However, its uses may give basic information about postyield performance of the building. Having built the mathematical model of bare building, time-history analyses should be conducted for each pair of (horizontal) ground motion records (as determined in Step 2 (Section 5.5.3.2)). This is recommended by ASCE 41-13 (ASCE, 2013) to minimize or eliminate unnecessary seismic retrofits, since deformation and forces in building components can be determined more accurately. The following recommendations are given by ASCE 41-13 (ASCE, 2013) while conducting nonlinear analysis: •

The results obtained from nonlinear (dynamic) analysis can be straightforwardly compared with those achieved using tests to evaluate the performance of building components under a selected ground motion.

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•

•

For the structural component responses that are independent of the direction of loading (e.g., shear about the same axis in a beam/column/wall, plastic hinge rotation in walls, and building drifts), the maximum response (force or displacement) is computed as the maximum absolute responses obtained under each history analysis, and the average response should be calculated as the mean of the maximum values. For structural component responses that are dependent on the direction of loading (e.g., axial tension versus compression in a column and bending moment in an asymmetrical RC beam), the maximum response is specified independently for each loading direction as the maximum positive and minimum negative responses under each history analysis; the average response should be calculated independently for each loading direction as the mean of maximum values.

Based on the analyses results obtained in this step, there may be potential deficiencies with respect to some structural responses and the relative acceptance criteria can be checked in the next step.

5.5.3.5 Step 5. Acceptance criteria ASCE 41-13 (ASCE, 2013) divides the different components as primary and secondary to define their acceptability actions (i.e., forces and deformation). Primary are components of the lateral force
resisting system and secondary are not components of the lateral force
resisting system but they are affected by the structure lateral deformation. In any case, the components shall be able to carry gravity loads. Each action shall be classified (Fig. 5.42 and Table 5.32) as follows: •

Deformation controlled (ductile): Type 1 when d $ 2g, Type 2 when e $ 2g for primary components or f $ 2g for secondary component, Type 3 for secondary component if f $ 2g (Fig. 5.42). Expected material strength, QCE (mean value of the component resistance), shall be used to define the curves.

FIGURE 5.42 Component force
deformation curve. Adapted from ASCE, 2013. ASCE41-13: Seismic Evaluation and Retrofit of Existing Buildings. American Society of Civil Engineers, Reston, VA.

5.5 Retrofit of Existing Buildings

Table 5.32 Example of Components Force- and Deformation-Controlled Actions for Framing Systems (ASCE, 2013) Component

Deformation-Controlled Action

Force-Controlled Action

Moment (M)

M, V

Shear (V) Axial load (P), V Va P

P

V P, V, Mb M, Vc


P P P, M P, V, M P, V, M

Moment Frame Beam Columns Joint Shear walls Brace Frame Braces Beams Columns Shear link Connections Diaphragms a

V could be a deformation-controlled action in steel moment frame. P, V, and M actions could be deformation controlled for steel and wood constructions. c M and V are force controlled for diaphrams that carries lateral loads from vertical force-resisting elements above the diaphram level. b

•

Force controlled (nonductile): in all the other cases in which deformationcontrolled criteria are not verified. Lower bound material strength, QCL (mean value minus one standard deviation of the component resistance), shall be used to define the curves.

The strength Q is taken as the expected strength (QCE ) for deformationcontrolled action and the lower bound estimate (QCL , defined as the mean minus one standard deviation) for force-controlled actions, (ASCE, 2013). These values are defined for different structural materials in ASCE (2013). For deformation-controlled action ASCE 41-13 (ASCE, 2013) defines a generalized force
deformation curve (Fig. 5.43) for component modeling and acceptance criteria. The behavior can be divided as follows: • • • •

Linear from point A to B (that is the yield point) Strain hardening from point B to C Strength degradation from point C to D Reduced strength from point D to E

This curve can be given in terms of deformation (displacement, rotation) or deformation ratio as shown in Fig. 5.43A and B, respectively. Values for defining the modeling curve are given in the standard and their review is outside the scope of this publication. Similarly, ASCE 41-13 (ASCE, 2013) provides acceptance criteria limits for different building performance levels (Fig. 5.43C). In addition, ASCE 41-13 (ASCE, 2013) defines deformation nonlinear capacities for different

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FIGURE 5.43 Force
deformation modeling and acceptance criteria for deformation-controlled action as a function of (A) deformation, (B) deformation ratio, (C) and acceptance criteria. Adapted from ASCE, 2013. ASCE41-13: Seismic Evaluation and Retrofit of Existing Buildings. American Society of Civil Engineers, Reston, VA.

materials and structural components. Given the fact that nonlinear procedures shall be utilized (Section 5.5.3.4), the component capacity shall be calculated as given in Table 5.33.

5.5.3.5.1 Load combinations Different from new construction code requirements (Section 5.2.1.1.4 (ASCE, 2017a)), the load combinations for existing buildings are the following (ASCE, 2013): •

Linear procedures with deformation-controlled actions Seismic and gravity additive: 1:1ðD 1 L 1 SÞ 1 QE

(5.263)

Seismic and gravity counteracting: 0:9D 1 QE

•

(5.264)

Linear procedure with force-controlled actions Seismic and gravity additive: 1:1ðD 1 L 1 SÞ 1

QE C1 C2 J

(5.265)

5.5 Retrofit of Existing Buildings

Table 5.33 Nonlinear Procedure Component Capacity (ASCE, 2013) Parameter Deformation capacity (existing component) Deformation capacity (new component) Strength capacity (existing component) Strength capacity (new component)

Deformation-Controlled Action

Force-Controlled Action

κx Deformation limit




Deformation limit







κxQCL




QCL

κ is the knowledge factor as determined in Table 5.31.

Seismic and gravity counteracting: 0:9D 1

QE C1 C2 J

(5.266)

where J is the force reduction factor taken as the smallest demand capacity ratio for the component in the selected load path (greater than or equal to 1). In alternative, it can be assumed to be equal to 2.0, 1.5, and 1.0 for high, moderate, low level of seismicity, respectively. C1 is the modification factor to account for the maximum inelastic displacement in linear response and C2 is the factor to be taken into account the effect of the hysteresis loop (see ASCE (2013) for further consideration about these factors).

5.5.3.6 Step 6. Retrofit strategies After having identified the deficiencies in the existing building, selecting an appropriate retrofit strategy is required to achieve the target PO. The retrofit solution adopted should be considered in the building model (developed in Step 4, Section 5.5.3.4) through its effects on stiffness, strength, yield behavior, and deformability. Several retrofit strategies are prescribed in ASCE 41-13 (ASCE, 2013), such as: • • • • • •

Local modification of components Removal or reduction in existing irregularities Global structural stiffening Mass reduction Seismic isolation Supplementary energy dissipation

For large buildings (e.g., tall buildings), it is recommended to represent several retrofit strategies and compare alternative ways of removing deficiencies (ASCE, 2013). Note that using additional damping for retrofit purposes may be accompanied with the use of other retrofit strategies in order to further improve

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the building performance (Lai et al., 2015). Herein, retrofitting by means of dynamic modification devices is described.

5.5.3.6.1 Step 6.1: Selecting suitable type of dynamic modification devices In general, two types of dynamic modification devices (seismic isolation and distributed damping system, and no indication about mass damping system is given) have been used for retrofit aims (ASCE, 2013), which are as follows: •

•

Effectiveness of seismic isolation is higher for relatively stiff buildings with low profiles and large mass, and it is less effective for light and flexible structures. Guidelines about how to select an appropriate type of isolation system (bearing) are discussed in Section 5.3.1.5. Distributed damping system may be effective for the modification of defects of a building due to excessive deformations caused by insufficient global structural stiffness. Significant deformations (or strokes) are often required in dissipation devices to substantially dissipate energy. This is achievable where the structure experiences significant lateral displacements (i.e., relatively flexible structures with some inelastic deformation capacity). In general, the structural displacements are often reduced by the addition of damping systems, but the forces transferred to the structure may essentially be increased. See the step-by-step procedure for distributed dampers for a detailed discussion (Section 5.2.1). According to Lai et al. (2015), the common supplementary damping systems for retrofitting tall buildings in the United States are BRB, fluid viscous dampers, and viscous wall dampers. Based on some observations on postearthquake performances after major earthquakes (e.g., 2011 Tohoku of Japan and 2003 Colima of Mexico), it is concluded that supplementary viscous dampers in high-rise buildings satisfy the life-safety requirements; moreover, such devices are efficient in controlling damage level (EERI, 2012; Takewaki et al., 2013a,b).

5.5.3.6.2 Step 6.2: Determining appropriate configuration and distribution for dynamic modification system After selecting the type of dynamic modification system, the suitable configuration and distribution (in plan and in height) can be specified correspondingly. If the selected dissipating device is of distributed type, user is encouraged to refer to Section 5.2.1.6. For mass dissipating devices, user can refer to Section 5.2.2.7. Instead, for base isolation systems, one can refer to Section 5.3.1.5 for the choice of location and distribution of isolators.

5.5.3.6.3 Step 6.3: Select total target damping The inherent damping of existing building should be selected for all the modes, as recommended by ASCE 7-16 (ASCE, 2017a). The designer should refer to

5.5 Retrofit of Existing Buildings

Section 3.2 for further discussion on the choice of inherent damping. Moreover, a total damping required for the design purposes can be selected with respect to the dominant (wind-based or seismic-based) design type. Sections 5.2.1.5 (for distributed dampers), 5.2.2.6 (for mass dampers), and 5.3.1.4 (for base isolation systems) represent more details about the damping selection.

5.5.3.7 Step 7. Damping system preliminary design In this step, based upon the selected damping system and its distribution, a preliminary device design should be carried out. For distributed dampers (viscous, viscoelastic, friction, and hysteretic), Section 5.2.1.7 properly represents the preliminary determination of damping properties. When dealing with mass damping systems (TMD, TLD, and TLCD), Section 5.2.2.8 addresses the optimal characteristics and then mechanical properties of devices. Concerning the base isolation systems, Section 5.3.1.7 should be used for preliminary design. In the case of distributed dampers, the code requires that the device capacity is increased for the maximum values for design and rare earthquake occurrence, in order to sustain larger displacement and velocities, with the following details: •

•

When more than four energy dissipation devices per primary direction are utilized (with at least two located on each side of the center of stiffness), the devices should resist a demand greater than or equal to 130% and 200% of the maximum values for the rare earthquake and DE respectively. When less than four energy dissipation devices per primary direction are utilized (or fewer than two devices are located on each side of the center of stiffness), the devices should resist a demand greater than or equal to 200% of the maximum values for the rare earthquake.

The dissipation device’s nominal design properties shall be bounded based on lambda factors (λ), as shown in Section 5.1.3.3.3, which are related to the material property’s dependence on manufacturing tolerances, environmental effect, aging, etc.

5.5.3.8 Step 8. Update building model and perform analyses Having defined the retrofit strategy, the proposed design should be verified by analyzing the building with the adopted retrofit measures. To this end, first the mathematical model of bare building (constructed in Step 4, Section 5.5.3.4) can be updated by adding the explicit model of damping (or isolation) systems designed. For distributed dampers, the user can refer to Section 5.2.1.8, which shows explicit modeling of viscous, viscoelastic, and hysteretic dampers. In the case of isolated damping systems, Section 5.2.2.9 addresses the simulation approaches. Regarding base isolation systems, Section 5.3.1.8 introduces the modeling approach. For the analyses, both linear and nonlinear procedures can be utilized depending on different criteria. Linear analysis procedures can be utilized only when devices are present in all stories of the upgraded building, and both upper and

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lower bound property analyses should be performed. The criteria for the utilization of linear procedures are the following: essentially elastic behavior of the main structure; supplemental damping shall not exceed 30%; secant stiffness at maximum displacement of the dissipation devices shall be included in the model of the rehabilitate building; and dissipation devices shall be considered while evaluating building regularity. Both static and dynamic procedures are allowed. The static linear procedure can be utilized when the following requirements are satisfied: the ratio between the story resistance and demand shall range between 80% and 120% of the average ratio for all stories (to be satisfied by displacement-dependent devices only), with the resistance provided by the dissipation devices in a story required not to exceed 50% of the total story resistance. ASCE 41-13 (ASCE, 2013) requires the calculation of the design actions (for both upper and lower bound properties) at three distinct stages of deformation: (1) at maximum drift, (2) at maximum velocity and zero drift, and (3) at maximum floor acceleration. Dynamic linear procedure, such as response-spectrum procedure, can be utilized for both displacement- and velocity-dependent devices. Damping values shall be calculated independently for each mode of vibration and the demand calculated by dynamic analysis shall be more than 80% of the one calculated from static linear procedures. In case the linear procedures are not allowed, nonlinear procedures shall be utilized. Nonlinear procedures shall include the nonlinear force
displacement characteristics of the dynamic modification devices, as well as their dependency on excitation frequency, temperature, deformation, velocity, etc. Therefore, this requires multiple analyses with bounded properties’ values to consider these effects (Section 5.1.2.4). ASCE 41-13 (ASCE, 2013) also states the importance of taking accidental eccentric in dynamic analyses through multiple analyses with mass shifting or with amplification factors on forces, drifts, and deformations into consideration. From the analyses results, the desired structural responses of retrofitted building (e.g., story shear, story drift, additional equivalent damping ratio) can be obtained for checking acceptance criteria (see Section 5.5.3.5) or for comparison with those obtained from bare building analysis.

5.5.3.9 Step 9. Check retrofit response acceptability In this step, response of the bare building (Step 4, Section 5.5.3.4) can be compared with that obtained from the analysis of retrofitted building (Step 8, Section 5.5.3.8). This provides the opportunity to see the variation in the structural responses under different hazard levels and load combinations. For instance, Weng et al. (2012) recommended the comparison of story shear forces and story drifts between bare building and retrofitted building when viscous dampers are utilized for retrofitting framed buildings. In general, comparing various responses of bare-base and upgraded-base responses helps designer realize which response is mitigated and how much is the level of mitigation reached.

5.5 Retrofit of Existing Buildings

The selected retrofit measures (e.g., supplementary damping system) are satisfied if the acceptance criteria (Section 5.5.3.5) for the selected PO selected (Step 2, Section 5.5.3.2) are met for all the building’s element. In case this is not satisfied, the retrofit measures must be redesigned or an alternative retrofit strategy with a different PO may be employed. This may lead to an iterative design procedure, until the acceptance criteria for the selected PO are satisfied. The acceptance criteria for the different damping devices can be estimated based on the previous step-by-step procedures. Concerning the acceptance criteria for building components, for deformation-controlled actions (e.g., moment in beams, moment and shear in walls, axial force in braces), the expected deformation capacity (allowable inelastic deformation limits) of all components should not be less than maximum deformation demands calculated by the analysis. Concerning force-controlled actions (e.g., shear in beams, axial force in columns), the lower bound strengths (capacity) of all components should not be less than the maximum analysis forces (ASCE, 2013). Given that there are many conditional details about various types of building components (e.g., steel components and concrete components), the user is encouraged to directly refer to tables presented in the standard ASCE 41-13 (ASCE, 2013) for the different structural components. Note that it is important to understand the economic implication when checking the feasibility of the retrofit design. In case the retrofit strategy is not economical, there are three choices possible (ASCE, 2013): • • •

Considering more refinements in analysis Designing a different retrofit scheme Considering a different PO

ASCE (2013) defines different acceptance criteria depending on if the component is deformation (ductile) or force controlled (nonductile). The relative acceptance criteria were defined by looking at the force
deformation curve as shown in Fig. 5.42 (Step 5, Section 5.5.3.5). Component capacities are defined as given in Table 5.33, while the deformation capacity limits are defined for the structural materials in ASCE (2013).

5.5.3.10 Step 10. Quality control, maintenance, and inspection requirements After the retrofit design is completed, the construction documents including the requirements for construction quality assurance can be prepared. The quality of construction should be checked by the designer who is responsible for the seismic retrofit of a building. For this reason, the plan and requirements of the construction quality assurance are recommended in ASCE 41-13 (ASCE, 2013). The quality assurance plan (QAP) may recognize the work components which should be considered for quality assurance procedures; moreover, it may identify special inspection, testing, and observation requirements to confirm construction quality. The QAP may contain a plan to modify the retrofit design

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to take into consideration unexpected conditions found during the construction phase. Reader can refer to Section 1.5.10.1 of ASCE 41-13 (ASCE, 2013) for more details. In addition to the preparation of QAP, the designer will be responsible for conducting periodic structural observations of the retrofit work process at significant stages of construction (i.e., to visually observe the work in accordance with the construction documents and also to confirm the conditions considered during design). Moreover, an additional investigation, testing process, and reporting should be performed under responsibility of a special inspector (ASCE, 2013). For more details about testing requirements, see the different step-by-step procedures as previously revised as well as in Chapter 7.

5.5.4 CASE STUDY: RETROFITTING EXAMPLES OF HIGH-RISE BUILDING WITH DAMPING SYSTEMS 5.5.4.1 Retrofit strategies for a 35-story building in San Francisco with viscous dampers In 2015 the Pacific Earthquake Engineering Research Center published a project (Lai et al., 2015) on the retrofit of a 35-story steel-framed building. A two-stage retrofit strategy was explored to eliminate deficiencies, identified based on the Tier 3 method of ASCE 41-13 (ASCE, 2013), as follows: •

•

Retrofit stage 1. Replacing the heavy exterior cladding with a lightweight curtain wall system; retrofitting the column splices; and retrofitting the beamto-column connections Retrofit stage 2. Incorporating fluid viscous dampers utilizing a simplified optimization method to optimize damper properties, damper distributions, and damper placement configurations

Retrofit stage 1 had been demonstrated (Lai et al., 2015) to be sufficient for serviceability under BSE-1E hazard-level events, but was not insufficient under BSE2E events. Therefore, the retrofit stage 2 was selected as the most optimal solution. The authors selected an effective damping based on a spectrum modification method (developed by Rezaeian et al. (2012)) that lead to a total damping ratio of 10% and 15% for the X- and Y-direction, respectively, for the BSE-2E hazard level. To provide this level of supplemental damping, damper constants (for both linear and nonlinear ones) were determined based on strain energy method (see Chapter 4). For the nonlinear dampers, the velocity exponent 0.35 was first used, then further optimized based on a parametric study. The initial location of viscous dampers was based on storywise placement and three configurations were selected (Fig. 5.44). Based on preliminary analysis the authors (Lai et al., 2015) the building using uniform distribution (Scheme I) of dampers, but large devices were required at upper stories to large forces near the building base. Scheme II
retrofit resulted in damper dependent upon the ground motions analyzed. Scheme III (i.e., damping proportional to story stiffness) was

5.5 Retrofit of Existing Buildings

FIGURE 5.44 Three distribution schemes for damping constant along building height. Adapted from Lai, J.-W., Wang, S., Schoettler, M.J., Mahin, S.A., 2015. Seismic Evaluation and Retrofit of Existing Tall Buildings in California: Case Study of a 35-Story Steel Moment-Resisting Frame Building in San Francisco. PEER Report No. 2015/14. University of California, Berkeley.

the most effective in reducing story displacement, drift, peak floor acceleration, and beam-to-column connection failure. Additional consideration in damper placement was obtained from architectural constraints, since exterior frames are more suitable than interior ones that are usually adjacent to stairs and elevator boxes (Lai et al., 2015) (see also Section 5.2.1.6 for further considerations). Based on this preliminary study further refinement was conducted. Therefore, additional parametric studies demonstrated that lower stories were more effective for placing dampers compared to upper stories, due to larger deformations at these levels, as shown in Fig. 5.45. These refinements lead to a final total number of dampers of 172 (from a starting estimation of 272). Further optimization studies were conducted based on the reduced configuration of Fig. 5.46. This was based on the combination of PI and cost-related index (CI). The first one was defined as the linear combination of interstory drift ratio,

FIGURE 5.45 Plan and exterior frames equipped with viscous dampers. Adapted from Lai, J.-W., Wang, S., Schoettler, M.J., Mahin, S.A., 2015. Seismic Evaluation and Retrofit of Existing Tall Buildings in California: Case Study of a 35-Story Steel Moment-Resisting Frame Building in San Francisco. PEER Report No. 2015/14. University of California, Berkeley.

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FIGURE 5.46 Elevation of two damper distribution cases: (A) distributed in multiple bays and (B) distributed in corner bays. Adapted from Lai, J.-W., Wang, S., Schoettler, M.J., Mahin, S.A., 2015. Seismic Evaluation and Retrofit of Existing Tall Buildings in California: Case Study of a 35-Story Steel Moment-Resisting Frame Building in San Francisco. PEER Report No. 2015/14. University of California, Berkeley.

residual drift ratio, floor acceleration, and peak floor acceleration. Its value ranges from 0 to 1 where higher values means a better performance. Instead, the second index was estimated as a weight combination between the peak damper force and number of dampers. A smaller CI indicates a cheaper damper solution. To combine both effects a new index was defined subtracting PI and CI. This was identified per each story and the larger the index the more effective the dampers were. Additional parametric investigations were conducted, as follows: •

•

Nonlinear viscous damper velocity exponent. A study was conducted with four values of α (0.2, 0.5, 0.8, and 1) for a fixed damping constant and Scheme III distribution (Fig. 5.45). The results demonstrated that using α 5 1 (i.e., linear damper) is most efficient in reducing floor accelerations, while smaller α is more efficient in controlling story drift ratios. Furthermore, by investigating the effectiveness indices (i.e., PI and CI), it was reported that α in the range of 0.2
0.5 was more desirable in retrofit of such a high-rise building using fluid viscous dampers. Bracing stiffness. The bracings should be stiff enough to ensure that viscous dampers are out of phase with the structural response (Lai et al., 2015). A parametric study was adopted to select an optimal bracing stiffness based on a simplified SDOF model with a certain supplemental damping ratio. Several values of effective bracing stiffness (compared to story stiffness) were assessed, and a reasonable range of stiffness was chosen. Verification of the assumption was conducted through NLTHAs. It was reported (Lai et al., 2015) that where supplemental damping ratio was between 10% and 20%, the choice of a bracing stiffness equal to twice the story stiffness gives acceptable results.

5.5 Retrofit of Existing Buildings

•

Damper horizontal location. In order to ascertain the efficiency of dampers with respect to the plan location, a comparative study was carried out. To this end, two damper distribution cases were selected: distribution in multiple bays and distribution in single bay (see Fig. 5.46). Comparing peak story drift ratios obtained from two damper distributions (Lai et al., 2015) showed that the multiple-based distribution is more efficient in controlling the structural response but produces large forces. Note that concentrating damper along corner bays (Fig. 5.46B) led to larger axial forces (due to accumulation of damper forces) in columns adjacent to dampers. Therefore, the first damper distribution (Fig. 5.46A) was found more efficient.

5.5.4.2 Retrofit strategies for a 24-story building in Osaka (Japan) with oil dampers A 24-story building located in Osaka station was retrofitted using oil dampers. There are 26-m-long columns around the atrium and 10-m-long columns at sixth floor. For these reasons, the lateral stiffness of lower six stories was less than that of upper stories. Hence, it was decided to incorporate supplementary oil dampers in order to amend such a deficiency. A total of 48 oil dampers were adopted in the building with Chevron configuration spatially distributed. This type of damper was chosen based on the following reasons (Tanaka et al., 2003): • • •

No residual (permanent) displacement after damper functionality. Reduced required space for damper. Therefore, the use of displacementdependent dampers was not appropriate in this case. Smaller variations in initial (elastic) stiffness and natural period of building in comparison with metallic dampers.

The building was modeled with a lumped-mass scheme in which for the oil dampers the classical Maxwell model (a spring and a dashpot coupled in series, Section 5.2.1.8.1) was employed. Based on this model, for the design of oil dampers, first the total stiffness of supporting component (spring) was determined. Then, the damping constant and the peak force that can be sustained by damper was specified. The influence of variation in damper properties was also considered in the design process. For this aim, the minimum and maximum of (nominal) properties accounted for error in production and atmospheric temperature were considered, totally resulting in variations with 212% and 110%, respectively. Based on the time-history analysis, with several ground motion histories, the drift ratio acceptance criteria was met.

5.5.4.3 Retrofit strategies for a 30-story building in Osaka (Japan) with viscous dampers A 120-m high-rise building located in Osaka in Japan (Fig. 5.47), which is adjacent to an extension building of 70 m height, was retrofitted using viscous dampers connecting the main building to the extension one. The main structural

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FIGURE 5.47 Perspective of main and extension building (Matsumoto et al., 2012).

system is steel frame. The choice of such a connection is due to different dynamic characteristics (mass, stiffness, and natural period) of the two buildings. For the design of connecting viscous dampers, two investigations were conducted. In the first one, the influence of the damper floor location on seismic responses was studied. Hence, three models with different damper floor locations were investigated (Fig. 5.48A). In the second one, three models were considered (Fig. 5.49B) to analyze the influence of degree of distribution of dampers (with the same damping constant). The buildings were modeled using lumped-mass systems and connecting (linear) dampers by the Maxwell model (Section 5.2.1.8.1). A series of parametric analyses were conducted with variable damping constant and based on two seismic inputs in accordance with the Japanese code design spectrum. The results are shown in Fig. 5.49 as a function of the energy dissipation ratio (the ratio between energy dissipation of dampers and input energy due to seismic waves) for both cases. In the figure it can be seen that there is a local maximum ratio corresponding to an optimum damping coefficient. Moreover, locating dampers at upper floors dissipated more energy.

FIGURE 5.48 (A) Investigation 1 and (B) investigation 2. Adapted from Matsumoto, T., Akita, S., Amasaki, T., 2012. Seismic performance improvement of the existing high-rise building by connecting to its high-rise extension using viscous dampers. In: Proceedings of the 15th World Conference on Earthquake Engineering, Lisbon, Portugal.

FIGURE 5.49 Enerdy-dissipation ratio versus damping constant for models of (A) Investigation 1 and (B) investigation 2 (Matsumoto et al., 2012).

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FIGURE 5.50 (A) Plan view of installed connecting dampers and zoomed details and (B) Elevation view of frames connected by dampers. Adapted from Matsumoto, T., Akita, S., Amasaki, T., 2012. Seismic performance improvement of the existing high-rise building by connecting to its high-rise extension using viscous dampers. In: Proceedings of the 15th World Conference on Earthquake Engineering, Lisbon, Portugal.

Based on these studies, 12 dampers were installed at 14th and 15th floors (Fig. 5.50). The dampers were positioned at 45 degrees with respect to the principal axes of building in order to ensure identical performance in all directions.

5.5.4.4 Retrofit strategies for a 27-story building in Osaka (Japan) tuned mass damper A 130-m high-rise building with an isolating floor at third floor was retrofitted with two TMDs located at the top due to occupant comfort problems. The designed TMDs included: •

Ice thermal storage tank as the moving mass. The mass ratio obtained was 4.2% in Y-direction and 2.2% in torsional direction.

5.6 Dynamic Modification Devices Strategy Optimization

• • •

Flat steel bars as suspension system (to enable movement of mass from elastic deformation of bars and to get a frictionless system). Rotational slide bearing (to connect flat bars to frame and moving mass). Oil damper (which has the force proportional to square of stroke velocity in order to prevent excessive displacements). The designed TMDs were tested (on-site) as follows:

• •

Static loading test (by pushing the moving mass by oil jacks and determining the force
displacement loop). Free vibration test (by initially displacing one of TMDs and determining building top acceleration and TMDs displacement).

Using TMDs dynamic characteristics identified based upon on-site tests, structural analyses under strong winds were performed. Accordingly, the habitability PI (maximum horizontal acceleration) was determined against the frequency, leading to good performance (response reduction) in both Y- and torsional directions.

5.6 DYNAMIC MODIFICATION DEVICES STRATEGY OPTIMIZATION 5.6.1 INTRODUCTION The effectiveness of dynamic modification systems may differ depending on various parameters such as the type of damping system, damper configuration, damper distribution (location) in height/plan, and damper parameters. Concerning the selection of a suitable type of dampers, as well as the factors affecting how (configuration) and where (location) dynamic modification devices can be placed in buildings, some guidelines are presented in Section 5.2.1.6 for distributed-type dampers (viscous, viscoelastic, friction, and hysteretic), in Section 5.2.2.7 for mass-type dampers (TMD, TLD, and TLCD), and in Section 5.3.1.5.2 for baseisolation systems. Moreover, the dynamic modification parameters can be determined based upon initial requirements (e.g., supplemental damping ratio) that are selected by the designer; some iterations may be used for further refinement of structural response and of damper characteristics. Despite what already discussed in the previous sections and chapters, the dynamic modification device distribution (location) and dynamic modification device parameters may be further optimized with the help of more sophisticated optimization strategies such as various types of iterative algorithms or simpler (noniterative) means. Hence, in Section 5.6.2, the optimization algorithms available in literature, suitable for different kinds of dynamic modification systems, are addressed. Moreover, some more simplified strategies (Section 5.6.3) that are not based on complicated algorithms are briefly reviewed.

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5.6.2 ALGORITHM-BASED OPTIMIZATION PROCEDURES An extensive number of optimization methods based on algorithms have been presented in the literature to identify optimal parameter and placement of dynamic modification devices. In general, the most common ones can be categorized as gradient-based algorithms; GAs; control theory
based algorithms; and heuristic algorithms. The major applications of these optimization algorithms have been related to distributed-type damping systems, especially viscous dampers. In the following, the different procedures are briefly reviewed. Interested readers should refer to the references provided.

5.6.2.1 Gradient-based algorithms In order to determine the optimal device placement, a gradient-based optimization procedure based upon the optimality criteria and relevant performance sensitivities can be used (Takewaki et al., 2012). For a better understanding, various steps of this procedure are illustrated schematically in Fig. 5.51. In such a procedure, sensitivity analyses of the objective function should be usually performed with respect to the dampers’ damping coefficient to find the highest performance sensitivity. This method is subject to iterations (i.e., repeating the sensitivity analyses and finding the highest performance sensitivity) until the required total amount of supplemental damping is obtained. This category of algorithms usually requires programming. Typical gradient-based algorithms are often relative to linear structural behavior. Several studies have been conducted in the past for different device categories, such as: •

•

• • •

Viscous dampers (e.g., Balling and Pister, 1983; Takewaki, 1997, 1999, 2000; Singh and Moreschi, 2001; Mahendra and Moreschi, 2001; Uetani et al., 2003; Lee et al., 2004; Lavan and Levy, 2005, 2006; Attard, 2007; Aydin et al., 2007; Cimellaro, 2007; Viola and Guidi, 2009; Aydin, 2012; Adachi et al., 2013; Lavan, 2015) Viscoelastic dampers (Hwang et al., 1995; Singh and Moreschi, 2001; Mahendra and Moreschi, 2001; Lee et al., 2004; Park et al., 2004; Fujita et al., 2010) Hysteretic dampers (e.g., Uetani et al., 2003) TMDs (e.g., Zuo and Nyfeh, 2004; Wang et al., 2009; Salvi and Rizzi, 2014) TLCDs (Taflanidis et al., 2007)

5.6.2.2 Genetic algorithms GAs are usually efficient to identify the optimal location of dynamic modification devices in buildings and they do not restrict to have a linear behaving structure. Such methods are found more suitable for problems where the PI is not a continuous function of the design variables (e.g., damping constant) (Singh and Moreschi, 2002). One of the advantages of this approach is the possibility to set a

5.6 Dynamic Modification Devices Strategy Optimization

FIGURE 5.51 Representative schematic diagram of gradient-based optimization procedures. Adapted from Takewaki, I., 2009. Building Control with Passive Dampers: Optimal Performance-Based Design for Earthquakes. John Wiley & Sons (Asia), Singapore.

given dynamic modification device capacity, usually based on commercially available solutions. Consequently, the optimal location of a certain number of dynamic modification devices, with the fixed capacity selected, can be identified (Singh and Moreschi, 2002). As a shortcoming, these methods usually require long computational time demand (Singh and Moreschi, 2002). The GA-based optimization techniques have been employed for the identification of optimal placement of various dynamic modification devices, such as: •

Viscous dampers (e.g., Furuya et al., 1998; Singh and Moreschi, 2002; Wongprasert and Symans, 2004; Tan et al., 2005; Dargush and Sant, 2005; Silvestri and Trombetti, 2007; Lavan and Dargush, 2009; Kargahi and

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•

• • • • •

• •

Ekwueme, 2009; Shin, 2010; Apostolakis and Dargush, 2010; Hejazi et al., 2013; Greco et al., 2016) Viscoelastic dampers (e.g., Singh and Moreschi, 2002; Park and Koh, 2004; Dargush and Sant, 2005; Movaffaghi and Friberg, 2006; Shin, 2010; Qu and Li, 2012) Metallic dampers (Dargush and Sant, 2005; Shin, 2010) Hysteretic dampers (Moreschi and Singh, 2003; Ok et al., 2008) Friction dampers (Moreschi and Singh, 2003; Miguel et al., 2014) BRBs (Farhat et al., 2009) TMDs (e.g., Hadi and Arfiadi, 1998; Arfiadi and Hadi, 2011; Singh et al., 2002; Marano et al., 2010; Mohebbi and Joghataie, 2011; Fu et al., 2011; Huo et al., 2013; Herve´ Poh’sie´ et al., 2015; Venanzi, 2015; Greco et al., 2016) Tuned liquid dampers (Ahadi et al., 2012; Chakraborty and Debbarma, 2016) Isolation systems (Pourzeynali and Zarif, 2008; Charmpis et al., 2012; Xu et al., 2013)

5.6.2.3 Control theory
based algorithms Control theory
based algorithms are advantageous due to their capability in reducing the computational efforts because they do not require to compute the structural response using dynamic analyses. The simplified sequential search algorithm (Lopez-Garcia, 2001; Garcia and Soong, 2002) and analysis-redesign procedure (Levy and Lavan, 2006) are among the simplest examples of this kind of algorithms. As noted by Whittle et al. (2012), a disadvantage of such methods may be the lack of PBD criteria within the methods. The control theory
based algorithms have been frequently used for viscous dampers (Zhang and Soong, 1992; Gluck et al., 1996; Lopez-Garcia, 2001; Yang et al., 2002a,b; Ribakov and Reinhorn, 2003; Main and Krenk, 2005; Levy and Lavan, 2006; Cimellaro and Retamales, 2007; Aguirre et al., 2013) and viscoelastic dampers (Zhang and Soong, 1992; Loh et al., 2000; Lopez-Garcia, 2001).

5.6.2.4 Heuristic algorithms In addition to aforementioned algorithms, some other heuristic ones are applied in the literature for the purpose of optimizing dynamic modification systems, such as: •

• • •

Viscous dampers: performance-based heuristic approach (Liu et al., 2005) and artificial bee colony algorithm combined with a gradient-based algorithm (Snomez et al., 2013) Hysteretic dampers: adaptive smoothing algorithm (Murakami et al., 2013). Friction dampers: backtracking search optimization algorithm (Miguel et al., 2015). TMDs: bionic algorithm (Steinbuch, 2011), particle swarm optimization (Leung and Zhang, 2009), harmony search method (Bekdas and Nigdeli, 2011, 2013), ant colony optimization (Farshidianfar and Soheili, 2013), evolutionary operation (Islam and Ahsan, 2012), and charged system search (Kaveh et al., 2015)

5.6 Dynamic Modification Devices Strategy Optimization

5.6.3 NONALGORITHM-BASED OPTIMIZATION PROCEDURES Generally speaking, optimization techniques of dynamic modification systems based on algorithms can be time-consuming as well as complicated for structural engineers. Hence, simpler strategies could be alternatively utilized. Some possible strategies presented in the literature are listed below and are briefly explained: •

Optimality with maximization of supplemental damping ratio (viscous and hysteretic dampers). To locate viscous dampers at more suitable locations, several authors suggested to incorporate them such that the modes supplemental damping ratio, especially the fundamental one, are maximized (i.e., for the same damper properties the higher value of supplemental damping ratio is achieved). According to Ashour and Hanson (1987), such a maximum supplemental damping ratio was achieved once dampers were located in the first story, provided that the building is a shear-type one (e.g., concrete moment frame). Furthermore, to find the optimal placement, Liu et al. (2004) recommended to investigate the influence of various damper configurations on different PIs (e.g., story drift and cost of device) under earthquake. Hahn and Sathiavageeswaran (1992) suggested to place dampers within the lower half floors of shear buildings if story stiffnesses are uniform. For what regards hysteretic dampers in steel moment frames, Inoue and Kuwahara (1998) developed the optimal condition for the device strength and stiffness. The optimization was based on finding the optimal ratio (β, of damper shear strength to frame maximum resistance of the frame), to maximize equivalent viscous damping. This optimal ratio is a function of relative stiffness (k) between the damper and frame. Fig. 5.52 shows the

FIGURE 5.52 Optimum damper’s strength ratio (β opt ) and optimum trigger level coefficient (ψopt ) with respect to relative stiffness (k). Adapted from Inoue, K., Kuwahara, S., 1998. Optimum strength ratio of hysteretic damper. Earthquake Eng. Struct. Dyn. 27 (6), 577
588.

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•

•

•

•

proposed optimal curves for β and the trigger level coefficient (ψ, strength of the entire system (frame plus dampers) at initial yielding). Interstory drift proportional distribution (viscous dampers). Tsuji and Nakamura (1996) proposed some design guidelines for optimal placement of viscous dampers in shear buildings. They recommended to first place the dampers in half the stories in which interstory drifts are greater. Then, according to such a placement, the damping coefficient of dampers can be determined in proportion to the distribution shape of story drifts. Quasioptimal distribution. It is possible to first optimize the stiffness distribution along the building height; then, the damping distribution could be directly determined by considering that damping is proportional to stiffness (Connor and Klink, 1996; Connor et al., 1997). Optimal placement with controllability index (viscoelastic dampers). Shukla and Datta (1999) employed a controllability index (based on the root-meansquare value of interstory drifts) to find optimal locations of viscoelastic dampers in buildings. Accordingly, they stated that the optimal placement depends on the excitation process (e.g., narrowband or broadband excitations) and the modeling type of dampers (e.g., Kelvin model or Maxwell model). Mass-proportional damping (MPD) distribution. Viscous dampers can be placed in shear-type buildings by considering the mass proportionality of damping (see Fig. 5.53) (Trombetti and Silvestri, 2004, 2006; Silvestri and Trombetti, 2007). It was demonstrated by Trombetti and Silvetri (2004) that MPD provides higher value of the first modal damping ratio among Rayleightype damping systems and leads to more optimized solution when dealing with seismic design. The main disadvantage of such a damper distribution is

FIGURE 5.53 Various types of mass proportional damping systems. Adapted from Trombetti, T., Silvestri, S., 2004. Added viscous dampers in shear type structures: the effectiveness of mass proportional damping. J. Earthquake Eng. 8, 275
313.

5.6 Dynamic Modification Devices Strategy Optimization

•

that fixed points are required to install devices and this may not be always attainable in practice. The application of the MPD in a case study 18-story concrete-core and steel-frame building located in Italy is illustrated by Trombetti and Silvestri (2004). They proposed two solutions: 1. Using long BRBs to connect each story to the ground as shown in Fig. 5.53A. Such long systems may be constructed using unbonded braces (Clark et al., 1999a,b,c) or long prestressed steel cables coupled with silicon dampers. 2. Locating dampers between the structure and a very stiff vertical element adjacent to or inside the building; see Fig. 5.53B. Elevator/stairs concrete cores are a typical instance of such an element (Trombetti and Silvestri, 2004). Noniterative optimal design for brace-damper system. London˜o et al. (2012) developed a simple (noniterative) procedure for optimal design of viscous dampers (Maxwell-type model, Section 5.2.1.8.1) when installed in an SDOF system. They considered two criteria for sizing the damper and brace: optimum damper size (ODS) criterion and optimum brace stiffness (OBS) criterion. Having selected a target supplemental damping ratio (ζ s ) due to dampers, two controlling parameters (α 5 ratio between damper stiffness and SDOF stiffness and β 5 ratio between damping coefficient of damper and of SDOF system, multiplied by inherent damping ratio) can be determined using Fig. 5.54. The points associated with ODS and OBS are shown on the plot.

FIGURE 5.54 Added damping ratio map for a structure with 5% inherent damping (London˜o et al., 2012).

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•

•

•

Then, the damper and brace optimum size can be simply determined based on the values of α and β and given SDOF system parameters. Castaldo and De Iuliis (2014) proposed an optimal integrated cost-effective seismic design for viscous dampers supported by braces (Maxwell-type model, Section 5.2.1.8.1) in SDOF systems. The optimized objective function to be minimized was the cost index composed of the cost of SDOF system stiffness and of damper stiffness and damping. Optimality of TLCD parameters. Gao and Kwok (1997) stated that using larger ratio between vertical and horizontal cross-sectional areas in TLCDs can significantly decrease the length of damper; this is a benefit for the application of such devices in flexible structures. Explicit expressions were proposed for optimal parameters of TLCD (damping ratio, frequency ratio, and head loss coefficient) when the structure is undamped (Yalla and Kareem, 2000; Shum, 2015). For the damped case, numerical solutions were proposed by Yalla and Kareem (2000) and closed-form relations by Shum (2015). It was stated that for systems with light damping, the optimal damping ratio of TLCD does not depend on the inherent damping of main system under purely white-noise excitation (Yalla and Kareem, 2000). Ghosh and Basu (2007) developed an explicit relation to estimate the optimum tuning ratio of TLCDs, applicable for lightly to moderately damped structures under base earthquake excitations. The optimization was based upon the minimization of the peak transfer function of the displacement response of the structure. Optimality of TMD tuning ratio. Ghosh and Basu (2007) proposed a closedform expression to determine the optimal tuning ratio (frequency ratio) of TMD, when the main structure is damped. The base of this optimization was to minimize the peak displacement transfer function of the structure. Optimality of midstory isolation systems’ parameters. Zhou et al. (2016) developed an approach with the help of a simple two-DOF system as the equivalence of midstory isolated buildings. The analytical relations to estimate the optimal parameters and location of isolation system were derived based on the minimization of peak base-shear response under base excitations.