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Impact of structural design criteria on the comfort assessment of tall buildings
Journal of Wind Engineering & Industrial Aerodynamics 180 (2018) 231–248
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Impact of structural design criteria on the comfort assessment of tall buildings author names and affiliations Ferrareto A. Johann * Escola Politecnica da Universidade de S~ ao Paulo, Department of Structural and Foundation Engineering, Avenida Professor Almeida Prado, trav. 2, 83, Cidade Universit aria, S~ ao Paulo, SP, 05508-900, Brazil
A R T I C L E I N F O
A B S T R A C T
Keywords: Tall buildings Structural analysis Dynamic analysis Comfort assessment Design criteria Wind loads Wind tunnel
Assessing tall building oscillation due to wind-induced motion is a multidisciplinary task that involves knowledge from several fields of study, including: structural engineering, wind engineering, reliability, and even human physiology. With the modern high strength structural materials and the latest tendencies in tall buildings construction, new structural systems have become slender and new buildings have reached greater heights as time passes. This context leads to a situation where these slender structures become sensitive to the dynamic effects of wind loads, case in which the human comfort is often the prevailing criterion for the structural design. This paper addresses criteria from finite element modelling, modal truncation, wind directionality, and comfort assessment applied to two building studies (buildings A and B) subjected to wind tunnel testing. Then, the impact of structural design criteria on many different disciplines is exposed, establishing a comparison between different criteria. This investigation intends to bring precision to the procedure, while creating a reliable set of criteria to perform an assessment of the dynamic response from the wind tunnel testing of tall buildings.
1. Context, introduction and reasons for the study 1.1. Context In today's context of big cities, the category of tall building construction has quickly gained ground due to environmental and economic issues (Ali and Moon, 2007; Drew et al., 2014). These new constructions require extensive and multidisciplinary knowledge to make them feasible, leaving a great deal of responsibility to a multidisciplinary group of areas of study: structural engineering, wind engineering and comfort assessment. This paper is focused on the understanding of the set of criteria of each discipline, on the use of these data to perform a tall building's motion assessment, and on the impact of each criterion on the final motion assessment. Latest advances in structural materials, including 65psi (450MPa) high strength steel, high strength concrete, and new composite structures allow for a great reduction in the use of material in tall buildings (Rosa et al., 2012; Sarkisian, 2012). These improvements enable both slender structures and slender structural systems, which lead to an overall reduction of the building stiffness. These slender structural systems are commonly used in tall building design and often present fundamental modes of vibration with a behavior very similar to a cantilever beam (Wu
et al., 2007; Sarkisian, 2012). Moreover, these structural systems often present important torsional modes of vibration and a greater number of natural frequencies under 1:0Hz, making them more susceptible to dynamic effects of wind loads (Rosa et al., 2012). These circumstances emphasize the importance of service limit state (SLS) studies on tall buildings for comfort assessment when compared to ultimate limit state (ULS), due to: higher modal contribution, torsional acceleration and cantilever behavior of the structural system (Hansen et al., 1973; ISO10137, 2007; Kim et al., 2009; Rosa et al., 2012). 1.2. Introduction: structural data, wind tunnel testing and comfort assessment The structural data have a clear importance in the assessment of the response of wind-induced motions in tall buildings. For a specific approach to structures of multi-story tall buildings subjected to wind tunnel testing (WTT), these data can be summarized as: natural frequencies; mode shapes or mode deflection shapes; mass matrix; and damping of the system. Finite-element (FE) models are not always as precise as they might look when it comes to finding out the natural frequencies of a building.
* Tel.: +55 27 99237 8696. E-mail address: [email protected]. https://doi.org/10.1016/j.jweia.2018.07.006 Received 14 February 2018; Received in revised form 16 May 2018; Accepted 6 July 2018 0167-6105/© 2018 Elsevier Ltd. All rights reserved.
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Journal of Wind Engineering & Industrial Aerodynamics 180 (2018) 231–248
Kim et al. (2009) performed field measurements in three buildings to acquire the first three natural frequencies of each building, and found discrepancies of up to 33% between the measured values and the results of the finite element model. The results showed a great underestimation of the natural frequencies for the FE models, where the authors investigated the phenomena through several axes of investigation, among which the most relevant ones for this paper were the flexural stiffness of floor slabs and the increase in the modulus of elasticity of structural members due to concrete ageing. Structural data are gathered and analyzed for both buildings (A and B) for different FE models and for different sets of criteria, concrete ageing, and floor slab modelling. Then, dynamic responses are analyzed for the different models created. The increased modulus of elasticity is the Young's modulus for “t → ∞” in eq. (1) of the Brazilian concrete code NBR6118-2014. This equation shows the increase in the elasticity modulus with the increase of the concrete age “t”: n nh ioo0:5 ECi;∞ ¼ limECi;28 exp s 1 ð28=tÞ0:5 ¼ ECi;28 expðs=2Þ t→∞
1:00% for building B, which is consistent with the results obtained by Wu et al. (2007) for the overall damping during SLS winds, and with the Brazilian wind code NBR6123, 1988. The WTT of both buildings used the high frequency pressure integration (HFPI) method. Along with the building's structural data, this test can evaluate overall forces at the base (background and resonant), and modal loads acting on each mode of vibration. In addition, due to the assessment of precise loads over the building's height, this test allows for a better evaluation of higher modal loads, i.e., for modes of vibration after each fundamental sway/torsional mode (Irwin et al., 2013). Moreover, this test provides a detailed time history of loads distribution on the building's façade, enabling a precise time domain analysis. These features make the HFPI a powerful tool to evaluate the responses of tall buildings to wind-induced loads. Finally, the users’ comfort during motion in this paper was evaluated by the acceleration at the floor of interest (in the case studies it was the highest occupied floor). Lateral drift, angular velocity, angular acceleration (yaw), derivative of acceleration (jerk), and frequency of movement are important parameters, as well as age, body posture, and quality of insulation, among other physiological and psychological features. These parameters and features were extensively discussed by Ferrareto et al. (2015), from where we gathered the compilation of comfort criteria used in this paper for the current approach to human comfort. This compilation represents the current and most frequently used assessment criteria, according to several national/international standards.
(1)
where: ECi;28 is the Young's Modulus of the concrete after 28 days, according to NBR6118-2014; s is a coefficient depending on the category of cement: in the tall buildings analyzed in this paper, this coefficient has the value of 0:25; ECi;∞ stands for the Young's Modulus of the matured concrete, referred to here as probable E.
1.3. Reasons for the study
The schematics of the categories of concrete strength for each structural element are given in Fig. 1 for both buildings (buildings A and B). The studies of Kim et al. (2009) showed a sensitive increase in the natural frequencies of buildings due to concrete ageing (up to 12%), which lead to an important effect in the final acceleration assessed on the top of the building. Intended for the scope of wind effects on tall buildings, a lumped mass system approach was used to model the dynamic behavior of the structure (NBR6123, 1988; Rosa et al., 2012). Based on the rigid floor diaphragm hypothesis, this approach neglected in-plane floor deformations and the restricted motion of each floor to three degrees of freedom (DOF): translations on x and y-axes and rotation around the z-axis of the building (Rosa et al., 2012). As for the damping ratio, there are several types of damping that might contribute to the control of a tall building's motion, including: structural damping “ζs ”; damping ratios “ζd ” originated by dampers; and aerodynamic damping “ζa .” In the case studies conducted in this paper, the overall damping value will be equal to 1:25% for building A and
Nowadays, most of the responsibility for the post-treatment of WTT's results lies mainly on the hands of the wind tunnel facility, with the exception of structural data. With the set of criteria studied in this paper, WTT's results may achieve more accurate results and so may structural engineers. As a final point, this paper brings knowledge about the impact of structural design throughout different disciplines and intends to bring better understanding and verification tools for the whole procedure to all fields of study that take part in the WTT. This paper provides tools to enable control and responsibility increasing the role of the structural engineer during the WTT's analysis of results. 2. Case study and methodology The choice of the tall buildings studied in this chapter is justified by their representative features when it comes to their technical context and location. Together, the buildings represent two of the most used
Fig. 1. Concrete strength for each building: A (left) and B (right). 232
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Fig. 2. Building's structure: a) blueprint; b) construction photo; c) 3D model.
2.3. FE modelling
structural materials/systems currently used in Brazil (and very often used worldwide): composite structure with concrete core (building A) and concrete structure with concrete core (building B). Both have absolute heights and/or relative heights when compared with their surroundings to be considered as a tall building, and therefore require a WTT (Irwin et al., 2013). Building B was designed to be the tallest building in S~ao Paulo when its construction started. Both buildings have office use on the typical floors.
FE models were made using a Brazilian commercial structural analysis software: TQS™. These models were later validated by Robot™ and Strap™ models. For each building presented (A and B), two different structural models were made, generating four structural models: A1, A2, B1, and B2. The first structural model for building A (model A1) incorporates usual criteria for FE modelling for tall building's structures, while the
2.1. General information on building A The building is 137:30m high, with five basement levels, which results in a structure 157:50m high. The building has 29 typical floors, with a floor-to-floor height of 4.28 m each, and two technical levels on the top, including a heliport. The total number of structural levels of this tall building is 40. The structural design of the building is based on gravity columns near its façade, with a stiff concrete core in the center (see Fig. 2). This concrete core works for both for vertical loads and horizontal loads (wind loads). The structure supporting the floor slab is a composite structure with a steel deck and built-up steel sections with a 8:0cm concrete screed. The live loads acting on the typical floors is 5:0kN=m2 .
2.2. General information on building B Building B (see Fig. 3) is 178:00m high, with seven basement levels, which results in a structure with a height of 203:60m. The building has 35 typical floors, with a floor-to-floor height of 4:00m 5:00m, and four technical levels on the top, including a heliport. The whole extent of structural levels of this tall building is 51. This building structural design is quite similar to that of building A, based on gravity columns near its façade, with a stiff concrete core in the center. The main difference lies on the material used, which in this building is reinforced concrete, instead of the composite structure of building A.
Fig. 3. Studied building (render). 233
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qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi γ 2 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi g ¼ 2lnðνðnÞ TÞ þ p 2 2lnðνðnÞ TÞ
second model (model A2) incorporates the structural modelling criteria presented in chapter one, which includes the probable modulus of elasticity due to concrete ageing, and floor slab modelling. The organization of building B's models is analogous to that of building A (models B1 and B2). This part of the methodology aims at more accurate FE models for the subsequent dynamic analysis. The contribution of non-structural walls (NSW) was not included in this study, since none of the studied buildings present in-filled frames with NSW that could work in strut models, as presented by Cavaleri and Papia (2003), nor were the NSWs continuously placed on all building stories. The floor slabs were modelled with shell elements in order to provide the coupling between two shear walls and between shear walls and the external columns, discretized by a 50cm 50cm mesh of rod elements to simulate a grid.
where “γ” stands for the Euler's constant, equal to 0:5772, “T” stands for the duration of the event; and:
ν
ðnÞ
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi R ∞ 2ðnþ1Þ f Sz ðfÞdf 2 R0 ∞ 2ðnÞ ¼ f Sz ðfÞdf 0
(3c)
where “f” stands for the frequency of motion, and the value of “n” refers to the derivative of the displacement related to time: “n ¼ 0” for displacement; “n ¼ 1” for velocity; “n ¼ 2” for acceleration. Finally, when all components of acceleration (“ax ”, “ay ”, and “aθ R”) are correctly evaluated, the resultant peak acceleration “aPeak ” is calculated using the maximum value between “aPeak;x ”, “aPeak;y ” and “aPeak;xþy ”, from eq. (4a), (4b) and (4c), respectively (Chen and Huang, 2009).
2.4. BLWT loads, duration of numerical simulations and domain of dynamic analyses The BLWT data for building A correspond to a time-history of 222 pressure taps over 4920s of duration for each azimuth multiple of 10 , starting from the north. Building B has a time history of 363 pressure taps during 13894s, also for each azimuth multiple of 10 . The angle gaps chosen for this study follow the same interval as the BLWT's studies, since a tall building's response can greatly vary between two 10 azimuths (Irwin et al., 2005). The overall duration of each of the WTT was reduced to smaller durations “T” and analyzed separately. Each duration “T” was reduced to increase the precision for the Fourier transform, achieving lower values for the harmonic frequencies. However, this period was high enough for both buildings to allow the ergodic hypothesis used for the frequency domain analysis. The overall damping ratio is 1:25% for building A, and the first natural frequency for the first structural model (A1) is 0:2957Hz. For model B1, these values are 1:00% and 0:2060Hz, respectively. The first structural model was used to define the minimum period of integration, since it is the least stiff one. Considering the given natural frequencies “f”, overall damping ratios “ζ”, and the constants related to time “τ ¼ 1=2πfζ” (Jeary, 2003), the minimum time span for the
aPeak;x ¼
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 ðax Þ2 þ aθ ey 2 ey ax aθ ρaxθ
(4a)
aPeak;y ¼
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 ay þ ðaθ ex Þ2 þ 2 ex ay aθ ρayθ
(4b)
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 ffi aPeak;xþy ¼ 0:8 ðax Þ2 þ ay; þ ðaθ RÞ2 þ 2 ex ay aθ ρayθ ey ax aθ ρaxθ
0;5
hold the relation “ðe2x þ e2y Þ ¼ R”. The time domain analysis was performed using a simple 4th order Runge-Kutta (Chapra and Canale, 2008). For the time domain analysis, once the three accelerations components (“ax ”, “ay ” and “aθ R”) are assessed for each time step, the vectorial sum was made more elaborated in order to compose the complex movement. At each time-step, the acceleration was calculated at eight different locations of the building floor (see Fig. 4). The final acceleration for each time-step was calculated according to eq. (5). ! j! a Peak j ¼ ! axþ! ayþ ! aθ R
(2)
j¼1
where “Φðx;y;θÞ ” stands for the “jth ” mode shape at the “ℓth ” floor for the chosen direction (x and y translations or rotation θ), and “n” is the overall number of modes of vibration used in the analysis. Some standards allow the direct use of rms acceleration for comfort assessment (ISO6897, 1984), while others require the peak acceleration (ISO10137, 2007). In order to transform the rms “σðx;y;θÞ ” into peak acceleration “aðx;y;θÞmax ”, a peak factor “g” was applied: aðx;y;θÞmax ¼ gσðx;y;θÞ
(5)
The acceleration is calculated at the eight locations of the floor, retaining the highest value of these locations. This criterion will be discussed with more detailing in section 3.3.2. Since the length of time for each test (converted to real scale) was much higher than 889s, several samples were analyzed for each azimuth. The peak results obtained from each sample were gathered and final
obtained through a Fourier analysis of each modal load, where each acceleration component was calculated by: n X 2 Φðx;y;θÞ;ℓj σY;j €
(4c)
where “ρaxθ ” and “ρayθ ” are the correlation coefficients between translational components and the torsional component, adapting Chen and Huang's (2009) approach to a greater amount of modes of vibration (see section 2.5). The terms “ex ” and “ey ” stand for the eccentricities of the user's location regarding the axis of reference for the project and they
Fourier transform is 215s for building A and 434s for building B (considering a total duration of 5 constants). A 889s period was used for both analyses, covering both requirements. The differences between buildings A and B can be explained by the height difference and structural materials used in their constructions. The 889s period allowed a precision of 0:0011Hz for the frequency step in the Fourier transform, where 3186 harmonics were obtained to perform the posterior frequency domain analysis. Frequency domain results for rms modal accelerations “σY;j € ” were
σ2ðx;y;θÞ ¼
(3b)
(3a) Fig. 4. Locations for resultant acceleration assessment. 234
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Journal of Wind Engineering & Industrial Aerodynamics 180 (2018) 231–248
acceleration level for the sought return period. Finally, a sector-by-sector method (Simiu and Filliben, 2005) is carried to provide comparison with the up-crossing method. The sectors method chosen is the Multi-sector method (Holmes and Bekele, 2015) with a sector size of 22:5 , following the available meteorological data.
results calculated using their average. 2.5. Higher modal contribution For tall building designs, the usual number of modes of vibration used in a dynamic analysis is 3 (two sway modes and one torsional mode). However, current investigations indicate non-negligible differences if higher modal contributions are taken into consideration (Huang and Chen, 2007; Rosa et al., 2012; Ferrareto et al., 2014). The overall building peak acceleration might increase up to 10%, according to Ferrareto et al. (2014), while the torsional acceleration showed an increase of 36%, according to Huang and Chen (2007). It is important to state that the increase in the resultant acceleration for the user's comfort is relevant for the final assessment. The motion perception by the user, including higher modes and the shape of movements, will be discussed in section 3.2, along with the results of such increase.
3. Results and discussion 3.1. Structural modelling criteria 3.1.1. Natural frequencies Building A's natural frequencies of vibration showed a significant increase due to the structural modelling criteria (see Table 1). The modelling of the floor slab and concrete ageing generated the structural model A2. In the research by Kim et al. (2009), these were steps two and four and, when combined, represented an overall increase between 10% and 23% in the natural frequencies of the translational natural modes of vibration. For the torsional mode, it represented an overall increase between 16% and 23% in the natural frequency. For model A2, the translational modes presented an increase between 9:63% (2nd mode) and 15:21% (4th mode, also a torsional mode). For this same building, the torsional modes presented an increase of 16:98% on average. This result is consistent with the third building in the research of Kim et al. (2009), which presents a structural system that is similar to that of building A, studied in this paper. There is a significant increase in the natural frequencies of torsional modes when compared with the translational ones. According to Kim et al. (2009), the warping rigidity of the diaphragm is related to its out-of-plane rigidity, and the floor slab modelling (which generated building A2) presents an important increase in the stiffness of the vertical direction of the floor slab. This feature (floor slab modelling) is responsible for the higher average increase in natural frequencies of torsional modes for building A2. Together, the criteria presented in section 2.3 indicated overall increases in the natural frequencies of building A, varying from 9:63% to 19:66%. Different modelling criteria allowed for the assessment of natural frequencies for model B2 (see Table 2). The overall increase in the natural frequencies varied between 4% and 7%. The results were slightly
2.6. Wind climate modelling Initially, the worst-case method was used to calculate the final responses. This approach allows for one to properly observe the directional dependency of the building's response and compare the three different structural models for each building. For the worst-case method, the pressure taps data were normalized by the dynamic pressure of the wind tunnel at “1:52m” for building A. In order to find the pressure in the real scale, the final recorded value from each tap needed to be multiplied by the dynamic pressure of the wind speed at a height of “1:52m 400 ¼ 608m” (since the scale model is 1:400). This pressure must also take into consideration the “fetch” of the approaching terrain roughness for each azimuth. For building B, the reference dynamic pressure is at 500m for the standard open exposure. The methodology described by Irwin et al. (2005) is used in the up-crossing analysis. Differently from the sector methods, which attribute a different response to each direction, the up-crossing method looks for the asked magnitude of the response, regardless of the direction. To develop a better understanding of the procedure, one might observe the wind speed associated with a given building's response magnitude (for example, a 5:0milli g overall acceleration) for each sector of the compass. This curve is denominated “response boundary,” which is assessed for several required pressures, corresponding to several wind speeds. Then, rate “R” at which the magnitude of the response will happen is: vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u 2 k 1 2 N X 1 _ u Ai ki V i CV ki jα_ j dVi R¼ e i V i t1 þ i2 2 Ci Ci V_ dα i¼1
Table 1 Comparison of natural frequencies for structural models A1 and A2. Mode
(6) 1 2 3 4 5 6
i
where “Vi ” is the wind speed, “α” is the azimuth, and “Ai ;”. “Ci ;” and “ki ,” are parameters of the Weibull distribution of wind speeds for each sector “i”. Parameters “jα_ j” and “V_ ” can be calculated through empirical ex-
fn (Hz)
Type
A1
A2
i1-2
0.2957 0.3032 0.4282 0.9409 1.0920 1.2470
0.3262 0.3324 0.5124 1.0840 1.2250 1.4850
þ þ þ þ þ þ
10.31% 9.63% 19.66% 15.21% 12.18% 19.09%
Translational Translational Torsional Translational with torsional components
pressions as functions of wind speed “V”, and are suitable for extratropical winds (Irwin et al., 2005): V_ ¼ 0:065V þ 0:5e0:252V
(7a)
jα_ j ¼ 6:5 1 þ 3:3e0:252V
(7b)
Table 2 Comparison of natural frequencies for structural models B1 and B2. Mode
The return period “m,” associated with the magnitude of the chosen response is calculated by (Irwin et al., 2005): m¼
1 8760R
1 2 3 4 5 6 7 8 9
(8)
Several pairs of acceleration “am ” vs. return period “m” are obtained in a tabular form and plotted into a chart, where a regression curve takes place to interpolate these values and provide the final resultant 235
fn
Type
(Hz)
B1
B2
i1-2
0.2060 0.2187 0.3012 0.5821 0.6812 0.7380 1.0581 1.2327 1.2737
0.2207 0.2274 0.3186 0.6072 0.7199 0.7698 1.0971 1.2547 1.3197
þ þ þ þ þ þ þ þ þ
7.13% 3.99% 5.77% 4.31% 5.69% 4.31% 3.69% 1.78% 3.61%
Translational y dir. Translational x dir. Torsional Torsional Tors. with transl. in y dir. Tors. with transl. in x dir. Torsional Translational x dir. Tors. with transl. in y dir.
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Journal of Wind Engineering & Industrial Aerodynamics 180 (2018) 231–248
B2). The mode deflection shapes for models A1 are presented in Appendix A: Figure A.1. In Fig. 6, it is possible to verify that the sway component of the mode deflection shapes for the first two natural modes of vibration have a considerable difference. The increase in the natural frequencies of model A2 and the change in its mode shapes for the sway modes can be explained by two main effects (Kim et al., 2009): Transfer of axial forces from the exterior frame, generating a resistant moment on the core walls in an effect analogous to an outrigger system (Choi et al., 2012), but considerably less substantial than the actual system; Increased coupling between the shear walls through the floor slab (Kim et al., 2009). Both effects tend to approximate the mode deformation shapes of the structure to the ones of a moment resisting frame (shown with more details in Appendix B). Only the sway components of the mode deflection shapes for the two first modes of vibration are presented in Fig. 6. Torsional components of these modes are very similar when we compare models A1 and A2. The remaining mode deflection shapes are either purely torsional (3rd mode) or very much stiffer than the first two modes (4th to 6th modes), with a natural frequency ratio higher than 3:1 between the 4th mode and the 1st mode, and up to 4:55 between the 6th mode and the 1st mode. The stiffer modes are much less sensitive to smaller stiffness increases, such as the outrigger effect or the shear wall coupling, and do not present any significant changes in the mode deflection shapes, neither for the x axis nor the y axis. These modes (3rd to 6th), however, are purely or highly torsional and very sensitive to the warping rigidity increase and present minor changes in the torsional components. These changes in the mode shapes are responsible for a change in the modal loads, while the changes in the natural frequencies bring the resonant response to different values of the PSD of the wind loads. When combined, these features change the modal responses and their sensitivity concerning the azimuth, and even change the critical direction of
Fig. 5. Building B floor plan.
reduced when compared with building A. This is due to two main factors: first, the building structural system is composed of moment frames in both orthogonal directions (see Fig. 5); second, the “stiffness increase divided by the mass” ratio is considerably smaller for this building when compared with building A (as the average density is nearly 56% higher for building B due to its structural material). The “moment frame” and/or “coupled shear walls” structural systems in both directions lead to a reduced participation of the floor slab as a structural element, as previously discussed in the first building's case study and showed in the study of Kim et al. (2009). 3.1.2. Mode deflection shapes The structural systems (moment frames and coupled shear walls) in both directions for building B led to well-behaved mode deflection shapes in well-defined directions (see Figure A.2, in the Appendix, where translations in the x and y axes have little or no torsional components) and no differences between these shapes for the assessed models (B1, and
Fig. 6. Translational mode shapes for models A1 and A2 (modes 1 and 2). 236
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sixth mode compared to the fifth mode of vibration for this azimuth is 0:36%. The PSD was normalized with the variance of the respective component acceleration “σR ” using all modes of vibration available (6 for building A and 9 for building B). This azimuth was chosen for being the most critical regarding higher modal contribution, as it will be discussed later in this chapter. These results support the justification to study higher modal truncation in the fifth mode of vibration in the current case study of building A. However, studies carried out with other tall buildings might need even higher modal truncation to provide reliable results. This is the case of building B, which required an analysis with three extra modes (up to the ninth mode) and results with higher modal truncation for the seventh mode, as shown in Fig. 9. For building B, the incremental variation in the resultant acceleration originated from using modes fourth to sixth compared to the use of the first three fundamental modes of vibration is 25:2%, whilst the use of the seventh mode increases the previous response in 3:91% and the use of the eighth and ninth modes represented increases of less than 0:01%. The 10 azimuth was chosen for being one of the most critical regarding higher modal contributions for building B. The rms of the time domain response is lower and very close to the rms of frequency domain response for nearly all azimuths (building A, model A2). This behavior corroborates the steady-state theory (Jeary, 2003), as it was also observed in the results found by Wu et al. (2007). The final accelerations calculated in both time and frequency domains for all azimuths for building A2 are given in Fig. 10, where it can be observed that some of the azimuths present responses that are bigger for the time domain, when compared with the frequency domain (300 , 320 and 70 ). The correlation factor between the modes in this study is nearly 0:20 between the two first natural modes of vibration, and 0:00 for all other combinations of modes of vibration for all azimuths. Huang and Chen's (2007) results for their second situation of study have a similar behavior between different modes of vibration, and present joint-action factors around 0:88. Fig. 11 presents higher modal contribution to the overall acceleration for building A (model A2). The higher modal contribution presented the following increases in the maximum value for each acceleration component:
the building's response. These changes will be presented in section 3.1.3, and their impacts in the wind climate modelling are shown in section 3.3.1. 3.1.3. Results from structural modelling criteria Resultant accelerations using the presented methodology for the frequency domain analysis are given for all azimuths and two structural models per building (A1 vs. A2, and B1 vs. B2) in Fig. 7. The rms results were obtained through eq. (2) and the modal combination was made using the square route of sum squares (SRSS) rule. As expected, pattern “A1>A2” is respected for most of the azimuths, including the maximum acceleration. The critical direction for building A1 is 220 , where the peak acceleration on the floor of interest is 1:61mili g. For building A2, these results are 130 and 1:36mili g. The way in which the wind climate will be introduced to the procedure will define how this change in the critical direction can impact the final acceleration assessment. For the worst-case method, the results are given and a reduction of 11:4% is observed in the results, due to the use of the structural modelling criteria presented in this paper. These and other features of the wind climate associated with the structural modelling criteria are explored in section 3.3.1. This is an evidence of how the structural modelling criteria can influence the Davenport's chain of wind loading. Resultant accelerations using the same methodology as those used for building A were calculated for building B using a 1-year return period (BLWT-normalized wind pressures for 26m=s wind speed at 500m of altitude), and a total of three modes of vibration. The modal truncation criteria for this building will be discussed in section 3.2. As previously observed in Table 2, the structural modelling criteria play a minor role in building B when compared with building A. Differently from building A, there is no change in the critical direction for building B, as there is no change in the mode deflection shapes due to different modelling criteria. 3.2. Dynamic analysis criteria The normalized PSD for the components and for the resultant accelerations for the 300 azimuth are given in Fig. 8, from which it is plausible to infer that the sixth mode already has very little participation when compared with the fifth mode. The incremental variation of the
Fig. 7. Resultant accelerations for models A1, A2, B1, and B2. 237
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Fig. 8. Normalized PSD of the components and of the resultant accelerations for the 300 azimuth (Building A).
X axis component (210 and along-wind direction for this sector): 1:86%; Y axis component (300 and cross-wind direction for this sector): 32:6%; Torsional component: 1:05%.
frequencies under 1:00Hz and the seventh mode with nearly 1:00Hz. Leading to several modes of vibration (seven at the total) with natural frequencies highly sensitive to dynamic effects from wind loads, from which only three were initially used in the WTT. Resultant acceleration presented an overall increase of 26% as a result of contributions from modes 4 7 (from 25milli g in sector 350 to 31:7milli g in sector 10 ). This increase is quite significant for the user comfort, just as the 9:47% increase for building A. However, assembling seven different oscillations (or five, in case of building A) makes room for doubt regarding the user's perception of such a movement. In order to verify the perception, the shape of the movement is presented in Fig. 13, where the highest values of displacement where highlighted in black for the most critical acceleration/displacement time lapse. It is important to note that the movement is nearly oval with a very elongated shape, which means that despite the complex combination of five modes of vibration, the user will perceive an uniaxial movement (Tamura et al., 2006).
The overall resultant acceleration presented an increase of 9:47% in the maximum value, mainly due to a higher modal contribution from Y axis for the 300 azimuth. This result can also be observed in the PSD presented in Fig. 8, where modes 4 and 5 contribute with a significant part of the final response of the building for this azimuth. Results of higher modal contribution are presented for building B (model B2) in Fig. 12, where a noticeable increase in the maximum peak resultant acceleration can be observed. The most perceptible increase of 47% occurs in the 10 sector. In that sector, components x, y, and torsional presented results of 19%, 23%, and higher than 50%, respectively, due to the contribution of modes 4 7. In this case study, the contribution of higher modes was equally important for both along-wind and cross-wind loads, while the torsional component showed to be far more relevant than both translational components. A closer look into the PSD of the response of 10 azimuth shows significant contribution from these modes. The explanation of such importance to higher modes is the slenderness of Brazilian buildings. This slenderness is a direct result of no significant seismic activity and quite low wind speeds (30–40 m/s) in the country, leading to lower natural frequencies of its buildings. This is clear in Table 2, where a 178:00m high building has six modes with natural
3.2.1. Results from dynamic analysis criteria The resultant acceleration for each model from building A, using the main dynamic analysis criteria, is presented in Fig. 14, where the worstcase method was applied and the results for 10 and 50-year return periods were obtained. This figure shows that the most severe acceleration occurs in model A1 in the frequency domain, which happens to be the most common criteria used by BLWT and structural engineers around the world. A reasonable reduction was obtained by improving the structural models.
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Fig. 9. Normalized PSD of the components and of the resultant accelerations for the 10 azimuth (Building B).
Fig. 10. Final acceleration results (Model A2, 5 modes of vibration).
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Fig. 13. Shape of movement (model A2, time domain, five modes).
Fig. 11. Higher modal contribution (Model A2, 3 and 5 modes of vibration).
Fig. 14. Worst case method resultant peak accelerations vs. return period (Building A).
Fig. 12. Higher time domain).
modal
contribution,
peak
acceleration
(model
case, the time domain analysis with a higher modal contribution for model A2 presented resultant accelerations higher than the resultant accelerations in the frequency domain for the same model. The worstcase method was used in this analysis and generated the results presented in Fig. 14. However, different results are expected with the use of not only the most severe acceleration, but also the contribution from each sector to the final response. The results of the up-crossing method will be presented in section 3.3.1. Analogously, for building B, the same set of criteria is presented in Fig. 15. In this figure, structural modelling criteria show a reduction of 3:6%. Higher modal contribution (model B2, time domain, seven modes), on the other hand, presented an increase of nearly 15:8%, leading to an overall increase in the resultant acceleration of 8.5%, when compared with model B1 in the frequency domain for three modes. The dispersion of results is clearly great for this type of analysis and, therefore, consolidating criteria between structural engineers and WTT facilities should be a priority when it comes to structural modelling and
B2,
The three-mode analysis in the time domain showed one of the highest levels of reduction. However, higher modal contribution showed to be quite relevant in these resultant accelerations, and neglecting it would lead to less reliable results. The most precise set of criteria did not present lower results. In this
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domain (5:92milli g, 1-year return period) for five modes of vibration. However, for the up-crossing method, the acceleration response of building A2 is quite close to those of model A1. This means that the decrease in the overall acceleration response from model A2 (37%) is lower than that of model A1 (42%) when the up-crossing method is applied. The explanation for this behavior is that model A2 has a critical direction equal to the critical direction of the wind climate, while these directions are different for model A1 (see Fig. 17). Fig. 17 shows the probability of exceedance of the wind speed for Congonhas Airport, in S~ao Paulo (Brazil). The curves from the most central to the most external positions represent the probabilities of exceeding that velocity (these probabilities are, respectively, 0:001%, 0:010%, 0:100%, and 1:000%). In this figure, we can also read the resultant acceleration response for building A1 in the frequency domain, and for building A2 in the time domain for five modes of vibration. By overlapping these curves, we can verify that the stronger contributions of model A2 to the final response are in azimuths 40 , 190 , and 290 , where the wind speed of the probability curves reaches its maximum values (or where they are closer to their maximum values). In contrast, the stronger contribution of building A1 to the final response is between azimuths 210 260 , where the wind speed of these curves has its minimum values. Hence, the contribution of model A1's responses between azimuths 130 190 (one of the critical azimuth gaps for wind climate) are much smaller than building A2's contribution. This is one of the results of the change in the modal deflection shapes discussed in section 3.1.2. The change in the modal-deflection-shape led to a change in the critical direction of the building and in the building's response distribution over the different sectors, which, in turn, led to different results in the application of the up-crossing method. Building B's responses are given in Fig. 18, where the application of the up-crossing method presented the same decrease for models B1 and B2 (45%). A similar impact from the up-crossing method on the resultant acceleration was expected for this building, as there was no significant change in mode deflection shapes or in the natural frequencies due to the structural modelling criteria, leading to no difference in the critical direction of the building. Finally, a closer look at figures Figs. 16 and 18 allows for comparison with the Up-crossing method and the Sector-by-sector method. Results
Fig. 15. Worst case method resultant peak accelerations vs. return period (Building B).
dynamic analysis. Structural modelling criteria, along with dynamic analysis criteria, may represent a noticeable increase or decrease in the building's final response, and should be taken into consideration for greater precision in the assessment of building motion using WTT data.
3.3. Wind and comfort 3.3.1. Up-crossing method Previous results of the resultant acceleration were presented using non-directional wind climate for both buildings, so as to analyze structural and dynamic analysis criteria purely, with no interference from other disciplines. In this section, the wind climate modelling is introduced to evaluate its impact on the final response from buildings A and B. The results from models A1 and A2, for both frequency and time domain, are presented in Fig. 16. For the worst-case method, there is a significantly smaller result (nearly 7% smaller) for model A2 in the time domain (5:52milli g, 1year return period), when compared with model A1 in the frequency
Fig. 16. Up-crossing, Sector-by-sector and Worst case methods (Building A).
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Fig. 17. Critical directions (Building A): wind climate and building's responses.
Fig. 18. Up-crossing, Sector-by-sector and Worst case methods results (Building B).
method) are compared with the most precise set of criteria, including wind modelling (models A2 and B2, time domain, higher modal contribution, up-crossing method). Looking at this figure, it is important to restate the small consistency of comfort criteria around the world. This lack of consistency can still be justified by the different tolerance to motion in different countries. The user of a building in Chicago, traditionally a very windy city of high-rises, may have more tolerance to motion than the user of a building in S~ao Paulo, a city with a recent culture of high-rises and with much lower wind speeds in design. Therefore, the comfort thresholds in the building codes of these two cities/countries could be different as well.
show consistency with the case study presented by Burton et al. (2015), where an example is shown with a directional building in a directional wind climate, prevailing the same critical direction both for the wind and for the building's response. In this case, the Sector-by-sector method is more conservative than the up-crossing method, as shown in Fig. 19 for 1-year return period. 3.3.2. Comfort assessment The peak acceleration analysis for time domain is presented in Fig. 20, where the most simple and conservative set of criteria (models A1 and B1, frequency domain, 3 modes of vibration, and worst case
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Fig. 19. Up-crossing, Sector-by-sector and Worst case methods results (Buildings A and B).
Fig. 20. Peak acceleration analysis (Buildings A and B).
Fig. 21. Peak and rms responses at different floor locations (300 sector).
recent and precise thresholds, as well as dynamic analysis criteria. Thus, it is reasonable to pursue comfort through thresholds closer to perception of motion until this practice is better developed in Brazil. The most severe peak acceleration of the floor will be used, based on the location of the building (Brazil) and on the type of assessment (perception).
ISO10137 (2007) and NBR6123, 1988 are related to perception, while the criteria of NBCC (1990) and CTBUH are related to comfort. The verification of comfort in tall buildings in Brazil should more focused on the perception thresholds for the next years, due to its recent history with high-rises. NBR6123, 1988 is currently under revision to integrate more
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The inconsistency in the overall criteria, conversely, is more concerning. Both buildings A and B, in the most conservative set of criteria, do not pass the comfort verification using the threshold defined in NBR6123, 1988. On the other hand, using more precise parameters, and comparing them with codes with higher thresholds, like the NBCC (1990), the resultant accelerations achieve a ratio where they are only 29% to 64% of the comfort threshold for the same return period (10 years). Hence, all sets of criteria pass in the comfort verification for a smaller return period (1 year), with the exception of the worst-case method for model B1, which passes the comfort verification (Sarkisian, 2012), but doesn't pass the SLS verification based on perception (ISO10137, 2007). Comparing three modal responses with time domain (model A2) and frequency domain (model A1), the time domain response is even lower and should lead to a more economic design (allowing further structural optimization). However, considering higher modal contributions, the final acceleration for model A2 in the time domain is quite similar to the responses for model A1 in the frequency domain. This means that this could be the case where “two wrongs made a right,” and the different response behavior throughout the azimuths and higher modal contributions (which lead to higher responses) balanced the reduced response with the use of structural modelling criteria and time domain analysis (which lead to lower responses). Fig. 20 shows the worst peak resultant acceleration, considering the most critical location of the user on the highest occupied floor. The subsequent analysis will explore the aspect of this location in order to evaluate the human comfort during wind-induced motions. The other peak and rms accelerations for the other top occupied floor positions are shown in Fig. 21. In this figure, we can observe that the rms accelerations do not present a significant variation over the floor positions, while the peak accelerations do. The rms accelerations adopt an almost constant value, with an average of 1:03milli g throughout the positions, while the peak accelerations vary between 3:49milli g and 5:52milli g. This variation occurs as a result of the torsional components of both torsional and translational modes of vibration, which is particularly significant in this project. The constructive interference between the translational and the torsional components in one position of the floor is a destructive interference in the opposite direction, generating these discrepancies. As a result, the peak factors for this floor also vary greatly. The peak factor presented for sector 300 (critical sector in the final analysis of building A2) in the previous sections is 5:34 and corresponds to the highest peak acceleration, while the average peak factor for this floor is 4:31. To correctly evaluate the comfort level of the user, one must define whether the perception of movement or the annoyance levels will be assessed. If the annoyance levels are chosen, the average value and probably the rms acceleration should be used. However, if the perception of movement is chosen, then there is a chance that the occupants in the region with the most severe result will perceive the motion and alarm the other occupants on the floor. In this case, the peak acceleration is probably the most suitable way to evaluate comfort.
Table 3 Summary of results of each set of criteria for buildings A and B. Building
Structural modelling
Higher modal contribution
Wind climate modelling
Comfort criteria
Total
A B
11.4% 3.6%
6.4% 15.8%
39.8% 44.7%
36.9% 36.9%
¡66.9% ¡62.1%
generating relevant deviations in the probabilistic wind climate analysis. Time domain analyses present several paybacks when compared with the frequency domain analyses. The assessment of complex motion is one of them, where one can precisely calculate the exact vector acceleration at any location on the floor for all time steps. This feature allows for a precise modal combination (including higher modes) and peak responses, without the need for any modal combination rule or statistical peak factors, and also allows for the assessment of the exact values through the rms acceleration. Higher modes presented an important contribution to the final acceleration (up to 15:8%). Part of this increase in response, however, is largely compensated by a decrease in other criteria, as it can be observed in Table 3. The wind climate criteria presented the most relevant impact in the final response, decreasing the overall response by nearly 37 45%. Different mode shapes that result from structural modelling criteria also contributed to the wind climate analyses, since these mode shapes changed the critical direction of the building. Table 3 shows the summary of variation results for each set of criteria studied in this paper through an exhaustive analysis of Figs. 10, 14, 15 and 20. Structural modelling criteria were evaluated by a comparison of the results of models A1 vs. A2, and B1 vs. B2 in the frequency domain for three modes of vibration (worst-case method). Higher modal contribution is evaluated by comparison of the results from building A2 (B2) for three and five (seven) modes in the time domain (worst case method). Wind modelling criteria could be evaluated through the variation of the results of model A2 (B2) for the worst-case method and for the upcrossing method. The comfort criteria were evaluated using the ratios of a specific set of criteria (A2/B2, 5/7 modes, time domain, up-crossing method) and two comfort thresholds: ISO 10137 (2007) and Sarkisian's (2012) for offices. For building A, these ratios were, respectively: 3:53=8:20 ¼ 0:43, and 3:53=13:0 ¼ 0:27, and its variation was 36:9%. This calculation works analogously for building B. This result shows that the impact of design criteria may represent response reductions up to 66:9% (for building A) when compared with the results obtained from a conservative analysis and a conservative threshold. A reduction through different sets of criteria lead to more efficient designs, which, in turn, lead to the reduced use of material, lower costs, and lower embodied energy of the structure. Acknowledgements
4. Conclusions
A special thanks to the following companies and universities, without which the results obtained in this paper wouldn't be possible: Escola Politecnica da Universidade de S~ ao Paulo, Alan G. Davenport Wind Engineering Group, França & Associados Projetos Estruturais, Rowan Williams Davies and Irwin Inc.
First, the modelling criteria are very relevant for comfort and for the SLS analysis. They represent a substantial increase in the building's natural frequencies (up to 19:66%, as observed in building A). In addition, there were visible changes in mode deflection shapes,
Appendix A. Supplementary data Supplementary data related to this article can be found at https://doi.org/10.1016/j.jweia.2018.07.006.
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Appendix A. Mode deflection shapes
Fig. A.1. Mode shapes for structural model A1. 245
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Fig. A.2. Mode shapes for structural models B1 and B2.
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Appendix B. mode deflection shapes and Building A's critical wind direction As explained in section 3.1 and presented in Fig. 6, the FE models A1 and A2, generated from building A, presented many different structural features. Undeniably, mode deflection shapes from both models present important differences due to the modelling of the floor slab criterion. These differences led to the results shown in Fig. 7, where it can be observed a sensitive difference of behavior or response pattern in a few sectors (mostly around azimuths 160 , 200 and 260 , in order of significance).
Fig. B.1. Building A floor slab.
To give a better overview of the impact of structural modelling in the mode deflection shapes, one can observe Figure B.1, featuring the mode deflection shape of the second mode of vibration, which is the mode of vibration more susceptible to benefit from frame behavior of the floor slab. In this figure, it is possible to observe: 1) Floor slab deflection pattern following shear-wall connections in a straight line; 2) Cross section of the modelled floor slab, which for composite floors presents high stiffness due to the presence of the steel section. 3) Clamped portion of the floor slab to the external columns. The frame behavior observed in FE model A2 is not present in model A1 and despite the very low values of bending moment acting on these floor slabs, the cumulative effect on every building floor is very expressive and, for this building, it generates the differences in the mode deflection shapes and in the natural frequencies presented respectively in Fig. 6 and in Table 1.
Ferrareto, J.A., França, R.L.S., Mazzilli, C.E.N., 2014. The impact of comfort assessment criteria on building design. In: Proceedings of Council of Tall Buildings and Urban Habitat (CTBUH) – Future Cities, towards Sustained Vertical Urbanism. Shanghai, pp. 722–730. Ferrareto, J.A., França, R.L.S., Mazzilli, C.E.N., 2015. Wind-induced motion on tall buildings: a comfort criteria overview. J. Wind Eng. Ind. Aerod. 142, 26–42. Hansen, R.J., Reed, J.W., Vanmarcke, E.H., 1973. Human response to wind-induced motion of buildings. J. Struct. Div., ASCE 99 (7), 1589–1605. Holmes, J.D., Bekele, S.A., 2015. Directionality and wind-induced response – calculation by sector methods. In: XIV International Conference on Wind Engineering (ICWE), Porto Alegre. Huang, G., Chen, X., 2007. Wind load effects and equivalent static wind loads of tall buildings based on synchronous pressure measurements. Eng. Struct. 29, 2641–2653. Irwin, P., Denoon, R., Scott, D., 2013. Wind Tunnel Testing of High-rise Buildings: an Output of the CTBUH Wind Engineering Working Group. Council of Tall Buildings and Urban Habitat, Chicago. Irwin, P., Garber, J., Ho, E., 2005. Integration of wind tunnel data with full scale wind climate. In: Proceedings of the 10th Americas Conference on Wind Engineering. Baton Rouge, LA.
References Ali, M.M., Moon, K.S., 2007. Structural developments in tall buildings: current trends and future prospects. Architect. Sci. Rev. 50 (3), 205–223. Burton, M., Li, Y.F., Cammelli, S., 2015. Wind directionality effects: revisiting an old conundrum. In: XIV International Conference on Wind Engineering (ICWE), Porto Alegre. Cavaleri, L., Papia, M., 2003. A new dynamic identification technique: application to the evaluation of the equivalent strut for infilled frames. Eng. Struct. 25, 889–901. Chapra, S.C., Canale, R.P., 2008. Metodos Numericos para Engenharia, fifth ed. McGrawHill Interamericana do Brasil. Chen, X., Huang, G., 2009. Evaluation of peak resultant response for wind-excited tall buildings. Eng. Struct. 31, 858–868. Choi, H.S., Goman, H., Joseph, L., Mathias, N., 2012. Outrigger Design for High-rise Building: an Output of the CTBUH Outrigger Working. Group Council of Tall Buildings and Urban Habitat, Chicago. Drew, C., Fernandez, K., Fanning, K., 2014. The Environmental Impact of Tall vs. Small: a comparative study. In: Proceedings of Council of Tall Buildings and Urban Habitat (CTBUH) – Future Cities. Towards Sustained Vertical Urbanism. Shanghai, pp. 418–424.
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Journal of Wind Engineering & Industrial Aerodynamics 180 (2018) 231–248 NBR6123, 1988. Forças Devidas Ao Vento Em Edificaç~ oes. Associaç~ao Brasileira de Normas Tecnicas, Rio de Janeiro, Brasil. Rosa, L., Tomasini, G., Zasso, A., Aly, A.M., 2012. Wind-induced dynamics and loads in a prismatic slender building: a modal approach based on unsteady pressure measurements. J. Wind Eng. Ind. Aerod. 107–108, 118–130. Sarkisian, M.P., 2012. Designing Tall Buildings Structure as Architecture. Routledge, New York. Simiu, E., Filliben, J.J., 2005. Wind tunnel testing and the sector-by-sector approach to wind directionality effect. J. Struct. Eng., ASCE 131 (7), 1143–1145. Tamura, Y., Kawana, S., Nakamura, O., Kanda, J., Nakada, S., 2006. Evaluation perception of wind-induced vibration in buildings. Proc. Inst. Civ. Eng. Struct. Build. 159 (SB5), 283–293. Wu, J.R., Liu, P.F., Li, Q.S., 2007. Effects of amplitude-dependent damping and time constant on wind-induced responses of super tall building. Comput. Struct. 85, 1165–1176.
ISO6897, 1984. Guidelines for the Evaluation of the Response of Occupants of Fixed Structures, Especially Buildings and Offshore Structures, to Low-frequency Horizontal Motion (0.063 to 1 Hz). International Organization for Standardization, Geneva. ISO10137, 2007. Bases for Design of Structures – Serviceability of Buildings and Walkways against Vibrations. International Organization for Standardization, Geneva. Jeary, A.P., 2003. The effect of time-constants on the response of very large structures. In: Eleventh International Conference on Wind Engineering. Kim, Y.J., Yu, E., Kim, Y.D., Kim, S., 2009. Calibration of analytical models to assess windinduced acceleration responses of tall buildings in serviceability level. Eng. Struct. 31, 2086–2096. NBCC, 1990. National Building Code of Canada. Part 4 Structural Design (Chapter 4) Commentaries on Part 4 of the National Building Code. NBR6118, 2014. Projeto de estruturas de concreto – Procedimento. Associaç~ao Brasileira de Normas T ecnicas, Rio de Janeiro, Brasil.
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Impact of structural design criteria on the comfort assessment of tall buildings author names and affiliations Ferrareto A. Johann * Escola Politecnica da Universidade de S~ ao Paulo, Department of Structural and Foundation Engineering, Avenida Professor Almeida Prado, trav. 2, 83, Cidade Universit aria, S~ ao Paulo, SP, 05508-900, Brazil
A R T I C L E I N F O
A B S T R A C T
Keywords: Tall buildings Structural analysis Dynamic analysis Comfort assessment Design criteria Wind loads Wind tunnel
Assessing tall building oscillation due to wind-induced motion is a multidisciplinary task that involves knowledge from several fields of study, including: structural engineering, wind engineering, reliability, and even human physiology. With the modern high strength structural materials and the latest tendencies in tall buildings construction, new structural systems have become slender and new buildings have reached greater heights as time passes. This context leads to a situation where these slender structures become sensitive to the dynamic effects of wind loads, case in which the human comfort is often the prevailing criterion for the structural design. This paper addresses criteria from finite element modelling, modal truncation, wind directionality, and comfort assessment applied to two building studies (buildings A and B) subjected to wind tunnel testing. Then, the impact of structural design criteria on many different disciplines is exposed, establishing a comparison between different criteria. This investigation intends to bring precision to the procedure, while creating a reliable set of criteria to perform an assessment of the dynamic response from the wind tunnel testing of tall buildings.
1. Context, introduction and reasons for the study 1.1. Context In today's context of big cities, the category of tall building construction has quickly gained ground due to environmental and economic issues (Ali and Moon, 2007; Drew et al., 2014). These new constructions require extensive and multidisciplinary knowledge to make them feasible, leaving a great deal of responsibility to a multidisciplinary group of areas of study: structural engineering, wind engineering and comfort assessment. This paper is focused on the understanding of the set of criteria of each discipline, on the use of these data to perform a tall building's motion assessment, and on the impact of each criterion on the final motion assessment. Latest advances in structural materials, including 65psi (450MPa) high strength steel, high strength concrete, and new composite structures allow for a great reduction in the use of material in tall buildings (Rosa et al., 2012; Sarkisian, 2012). These improvements enable both slender structures and slender structural systems, which lead to an overall reduction of the building stiffness. These slender structural systems are commonly used in tall building design and often present fundamental modes of vibration with a behavior very similar to a cantilever beam (Wu
et al., 2007; Sarkisian, 2012). Moreover, these structural systems often present important torsional modes of vibration and a greater number of natural frequencies under 1:0Hz, making them more susceptible to dynamic effects of wind loads (Rosa et al., 2012). These circumstances emphasize the importance of service limit state (SLS) studies on tall buildings for comfort assessment when compared to ultimate limit state (ULS), due to: higher modal contribution, torsional acceleration and cantilever behavior of the structural system (Hansen et al., 1973; ISO10137, 2007; Kim et al., 2009; Rosa et al., 2012). 1.2. Introduction: structural data, wind tunnel testing and comfort assessment The structural data have a clear importance in the assessment of the response of wind-induced motions in tall buildings. For a specific approach to structures of multi-story tall buildings subjected to wind tunnel testing (WTT), these data can be summarized as: natural frequencies; mode shapes or mode deflection shapes; mass matrix; and damping of the system. Finite-element (FE) models are not always as precise as they might look when it comes to finding out the natural frequencies of a building.
* Tel.: +55 27 99237 8696. E-mail address: [email protected]. https://doi.org/10.1016/j.jweia.2018.07.006 Received 14 February 2018; Received in revised form 16 May 2018; Accepted 6 July 2018 0167-6105/© 2018 Elsevier Ltd. All rights reserved.
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Kim et al. (2009) performed field measurements in three buildings to acquire the first three natural frequencies of each building, and found discrepancies of up to 33% between the measured values and the results of the finite element model. The results showed a great underestimation of the natural frequencies for the FE models, where the authors investigated the phenomena through several axes of investigation, among which the most relevant ones for this paper were the flexural stiffness of floor slabs and the increase in the modulus of elasticity of structural members due to concrete ageing. Structural data are gathered and analyzed for both buildings (A and B) for different FE models and for different sets of criteria, concrete ageing, and floor slab modelling. Then, dynamic responses are analyzed for the different models created. The increased modulus of elasticity is the Young's modulus for “t → ∞” in eq. (1) of the Brazilian concrete code NBR6118-2014. This equation shows the increase in the elasticity modulus with the increase of the concrete age “t”: n nh ioo0:5 ECi;∞ ¼ limECi;28 exp s 1 ð28=tÞ0:5 ¼ ECi;28 expðs=2Þ t→∞
1:00% for building B, which is consistent with the results obtained by Wu et al. (2007) for the overall damping during SLS winds, and with the Brazilian wind code NBR6123, 1988. The WTT of both buildings used the high frequency pressure integration (HFPI) method. Along with the building's structural data, this test can evaluate overall forces at the base (background and resonant), and modal loads acting on each mode of vibration. In addition, due to the assessment of precise loads over the building's height, this test allows for a better evaluation of higher modal loads, i.e., for modes of vibration after each fundamental sway/torsional mode (Irwin et al., 2013). Moreover, this test provides a detailed time history of loads distribution on the building's façade, enabling a precise time domain analysis. These features make the HFPI a powerful tool to evaluate the responses of tall buildings to wind-induced loads. Finally, the users’ comfort during motion in this paper was evaluated by the acceleration at the floor of interest (in the case studies it was the highest occupied floor). Lateral drift, angular velocity, angular acceleration (yaw), derivative of acceleration (jerk), and frequency of movement are important parameters, as well as age, body posture, and quality of insulation, among other physiological and psychological features. These parameters and features were extensively discussed by Ferrareto et al. (2015), from where we gathered the compilation of comfort criteria used in this paper for the current approach to human comfort. This compilation represents the current and most frequently used assessment criteria, according to several national/international standards.
(1)
where: ECi;28 is the Young's Modulus of the concrete after 28 days, according to NBR6118-2014; s is a coefficient depending on the category of cement: in the tall buildings analyzed in this paper, this coefficient has the value of 0:25; ECi;∞ stands for the Young's Modulus of the matured concrete, referred to here as probable E.
1.3. Reasons for the study
The schematics of the categories of concrete strength for each structural element are given in Fig. 1 for both buildings (buildings A and B). The studies of Kim et al. (2009) showed a sensitive increase in the natural frequencies of buildings due to concrete ageing (up to 12%), which lead to an important effect in the final acceleration assessed on the top of the building. Intended for the scope of wind effects on tall buildings, a lumped mass system approach was used to model the dynamic behavior of the structure (NBR6123, 1988; Rosa et al., 2012). Based on the rigid floor diaphragm hypothesis, this approach neglected in-plane floor deformations and the restricted motion of each floor to three degrees of freedom (DOF): translations on x and y-axes and rotation around the z-axis of the building (Rosa et al., 2012). As for the damping ratio, there are several types of damping that might contribute to the control of a tall building's motion, including: structural damping “ζs ”; damping ratios “ζd ” originated by dampers; and aerodynamic damping “ζa .” In the case studies conducted in this paper, the overall damping value will be equal to 1:25% for building A and
Nowadays, most of the responsibility for the post-treatment of WTT's results lies mainly on the hands of the wind tunnel facility, with the exception of structural data. With the set of criteria studied in this paper, WTT's results may achieve more accurate results and so may structural engineers. As a final point, this paper brings knowledge about the impact of structural design throughout different disciplines and intends to bring better understanding and verification tools for the whole procedure to all fields of study that take part in the WTT. This paper provides tools to enable control and responsibility increasing the role of the structural engineer during the WTT's analysis of results. 2. Case study and methodology The choice of the tall buildings studied in this chapter is justified by their representative features when it comes to their technical context and location. Together, the buildings represent two of the most used
Fig. 1. Concrete strength for each building: A (left) and B (right). 232
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Fig. 2. Building's structure: a) blueprint; b) construction photo; c) 3D model.
2.3. FE modelling
structural materials/systems currently used in Brazil (and very often used worldwide): composite structure with concrete core (building A) and concrete structure with concrete core (building B). Both have absolute heights and/or relative heights when compared with their surroundings to be considered as a tall building, and therefore require a WTT (Irwin et al., 2013). Building B was designed to be the tallest building in S~ao Paulo when its construction started. Both buildings have office use on the typical floors.
FE models were made using a Brazilian commercial structural analysis software: TQS™. These models were later validated by Robot™ and Strap™ models. For each building presented (A and B), two different structural models were made, generating four structural models: A1, A2, B1, and B2. The first structural model for building A (model A1) incorporates usual criteria for FE modelling for tall building's structures, while the
2.1. General information on building A The building is 137:30m high, with five basement levels, which results in a structure 157:50m high. The building has 29 typical floors, with a floor-to-floor height of 4.28 m each, and two technical levels on the top, including a heliport. The total number of structural levels of this tall building is 40. The structural design of the building is based on gravity columns near its façade, with a stiff concrete core in the center (see Fig. 2). This concrete core works for both for vertical loads and horizontal loads (wind loads). The structure supporting the floor slab is a composite structure with a steel deck and built-up steel sections with a 8:0cm concrete screed. The live loads acting on the typical floors is 5:0kN=m2 .
2.2. General information on building B Building B (see Fig. 3) is 178:00m high, with seven basement levels, which results in a structure with a height of 203:60m. The building has 35 typical floors, with a floor-to-floor height of 4:00m 5:00m, and four technical levels on the top, including a heliport. The whole extent of structural levels of this tall building is 51. This building structural design is quite similar to that of building A, based on gravity columns near its façade, with a stiff concrete core in the center. The main difference lies on the material used, which in this building is reinforced concrete, instead of the composite structure of building A.
Fig. 3. Studied building (render). 233
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qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi γ 2 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi g ¼ 2lnðνðnÞ TÞ þ p 2 2lnðνðnÞ TÞ
second model (model A2) incorporates the structural modelling criteria presented in chapter one, which includes the probable modulus of elasticity due to concrete ageing, and floor slab modelling. The organization of building B's models is analogous to that of building A (models B1 and B2). This part of the methodology aims at more accurate FE models for the subsequent dynamic analysis. The contribution of non-structural walls (NSW) was not included in this study, since none of the studied buildings present in-filled frames with NSW that could work in strut models, as presented by Cavaleri and Papia (2003), nor were the NSWs continuously placed on all building stories. The floor slabs were modelled with shell elements in order to provide the coupling between two shear walls and between shear walls and the external columns, discretized by a 50cm 50cm mesh of rod elements to simulate a grid.
where “γ” stands for the Euler's constant, equal to 0:5772, “T” stands for the duration of the event; and:
ν
ðnÞ
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi R ∞ 2ðnþ1Þ f Sz ðfÞdf 2 R0 ∞ 2ðnÞ ¼ f Sz ðfÞdf 0
(3c)
where “f” stands for the frequency of motion, and the value of “n” refers to the derivative of the displacement related to time: “n ¼ 0” for displacement; “n ¼ 1” for velocity; “n ¼ 2” for acceleration. Finally, when all components of acceleration (“ax ”, “ay ”, and “aθ R”) are correctly evaluated, the resultant peak acceleration “aPeak ” is calculated using the maximum value between “aPeak;x ”, “aPeak;y ” and “aPeak;xþy ”, from eq. (4a), (4b) and (4c), respectively (Chen and Huang, 2009).
2.4. BLWT loads, duration of numerical simulations and domain of dynamic analyses The BLWT data for building A correspond to a time-history of 222 pressure taps over 4920s of duration for each azimuth multiple of 10 , starting from the north. Building B has a time history of 363 pressure taps during 13894s, also for each azimuth multiple of 10 . The angle gaps chosen for this study follow the same interval as the BLWT's studies, since a tall building's response can greatly vary between two 10 azimuths (Irwin et al., 2005). The overall duration of each of the WTT was reduced to smaller durations “T” and analyzed separately. Each duration “T” was reduced to increase the precision for the Fourier transform, achieving lower values for the harmonic frequencies. However, this period was high enough for both buildings to allow the ergodic hypothesis used for the frequency domain analysis. The overall damping ratio is 1:25% for building A, and the first natural frequency for the first structural model (A1) is 0:2957Hz. For model B1, these values are 1:00% and 0:2060Hz, respectively. The first structural model was used to define the minimum period of integration, since it is the least stiff one. Considering the given natural frequencies “f”, overall damping ratios “ζ”, and the constants related to time “τ ¼ 1=2πfζ” (Jeary, 2003), the minimum time span for the
aPeak;x ¼
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 ðax Þ2 þ aθ ey 2 ey ax aθ ρaxθ
(4a)
aPeak;y ¼
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 ay þ ðaθ ex Þ2 þ 2 ex ay aθ ρayθ
(4b)
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 ffi aPeak;xþy ¼ 0:8 ðax Þ2 þ ay; þ ðaθ RÞ2 þ 2 ex ay aθ ρayθ ey ax aθ ρaxθ
0;5
hold the relation “ðe2x þ e2y Þ ¼ R”. The time domain analysis was performed using a simple 4th order Runge-Kutta (Chapra and Canale, 2008). For the time domain analysis, once the three accelerations components (“ax ”, “ay ” and “aθ R”) are assessed for each time step, the vectorial sum was made more elaborated in order to compose the complex movement. At each time-step, the acceleration was calculated at eight different locations of the building floor (see Fig. 4). The final acceleration for each time-step was calculated according to eq. (5). ! j! a Peak j ¼ ! axþ! ayþ ! aθ R
(2)
j¼1
where “Φðx;y;θÞ ” stands for the “jth ” mode shape at the “ℓth ” floor for the chosen direction (x and y translations or rotation θ), and “n” is the overall number of modes of vibration used in the analysis. Some standards allow the direct use of rms acceleration for comfort assessment (ISO6897, 1984), while others require the peak acceleration (ISO10137, 2007). In order to transform the rms “σðx;y;θÞ ” into peak acceleration “aðx;y;θÞmax ”, a peak factor “g” was applied: aðx;y;θÞmax ¼ gσðx;y;θÞ
(5)
The acceleration is calculated at the eight locations of the floor, retaining the highest value of these locations. This criterion will be discussed with more detailing in section 3.3.2. Since the length of time for each test (converted to real scale) was much higher than 889s, several samples were analyzed for each azimuth. The peak results obtained from each sample were gathered and final
obtained through a Fourier analysis of each modal load, where each acceleration component was calculated by: n X 2 Φðx;y;θÞ;ℓj σY;j €
(4c)
where “ρaxθ ” and “ρayθ ” are the correlation coefficients between translational components and the torsional component, adapting Chen and Huang's (2009) approach to a greater amount of modes of vibration (see section 2.5). The terms “ex ” and “ey ” stand for the eccentricities of the user's location regarding the axis of reference for the project and they
Fourier transform is 215s for building A and 434s for building B (considering a total duration of 5 constants). A 889s period was used for both analyses, covering both requirements. The differences between buildings A and B can be explained by the height difference and structural materials used in their constructions. The 889s period allowed a precision of 0:0011Hz for the frequency step in the Fourier transform, where 3186 harmonics were obtained to perform the posterior frequency domain analysis. Frequency domain results for rms modal accelerations “σY;j € ” were
σ2ðx;y;θÞ ¼
(3b)
(3a) Fig. 4. Locations for resultant acceleration assessment. 234
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acceleration level for the sought return period. Finally, a sector-by-sector method (Simiu and Filliben, 2005) is carried to provide comparison with the up-crossing method. The sectors method chosen is the Multi-sector method (Holmes and Bekele, 2015) with a sector size of 22:5 , following the available meteorological data.
results calculated using their average. 2.5. Higher modal contribution For tall building designs, the usual number of modes of vibration used in a dynamic analysis is 3 (two sway modes and one torsional mode). However, current investigations indicate non-negligible differences if higher modal contributions are taken into consideration (Huang and Chen, 2007; Rosa et al., 2012; Ferrareto et al., 2014). The overall building peak acceleration might increase up to 10%, according to Ferrareto et al. (2014), while the torsional acceleration showed an increase of 36%, according to Huang and Chen (2007). It is important to state that the increase in the resultant acceleration for the user's comfort is relevant for the final assessment. The motion perception by the user, including higher modes and the shape of movements, will be discussed in section 3.2, along with the results of such increase.
3. Results and discussion 3.1. Structural modelling criteria 3.1.1. Natural frequencies Building A's natural frequencies of vibration showed a significant increase due to the structural modelling criteria (see Table 1). The modelling of the floor slab and concrete ageing generated the structural model A2. In the research by Kim et al. (2009), these were steps two and four and, when combined, represented an overall increase between 10% and 23% in the natural frequencies of the translational natural modes of vibration. For the torsional mode, it represented an overall increase between 16% and 23% in the natural frequency. For model A2, the translational modes presented an increase between 9:63% (2nd mode) and 15:21% (4th mode, also a torsional mode). For this same building, the torsional modes presented an increase of 16:98% on average. This result is consistent with the third building in the research of Kim et al. (2009), which presents a structural system that is similar to that of building A, studied in this paper. There is a significant increase in the natural frequencies of torsional modes when compared with the translational ones. According to Kim et al. (2009), the warping rigidity of the diaphragm is related to its out-of-plane rigidity, and the floor slab modelling (which generated building A2) presents an important increase in the stiffness of the vertical direction of the floor slab. This feature (floor slab modelling) is responsible for the higher average increase in natural frequencies of torsional modes for building A2. Together, the criteria presented in section 2.3 indicated overall increases in the natural frequencies of building A, varying from 9:63% to 19:66%. Different modelling criteria allowed for the assessment of natural frequencies for model B2 (see Table 2). The overall increase in the natural frequencies varied between 4% and 7%. The results were slightly
2.6. Wind climate modelling Initially, the worst-case method was used to calculate the final responses. This approach allows for one to properly observe the directional dependency of the building's response and compare the three different structural models for each building. For the worst-case method, the pressure taps data were normalized by the dynamic pressure of the wind tunnel at “1:52m” for building A. In order to find the pressure in the real scale, the final recorded value from each tap needed to be multiplied by the dynamic pressure of the wind speed at a height of “1:52m 400 ¼ 608m” (since the scale model is 1:400). This pressure must also take into consideration the “fetch” of the approaching terrain roughness for each azimuth. For building B, the reference dynamic pressure is at 500m for the standard open exposure. The methodology described by Irwin et al. (2005) is used in the up-crossing analysis. Differently from the sector methods, which attribute a different response to each direction, the up-crossing method looks for the asked magnitude of the response, regardless of the direction. To develop a better understanding of the procedure, one might observe the wind speed associated with a given building's response magnitude (for example, a 5:0milli g overall acceleration) for each sector of the compass. This curve is denominated “response boundary,” which is assessed for several required pressures, corresponding to several wind speeds. Then, rate “R” at which the magnitude of the response will happen is: vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u 2 k 1 2 N X 1 _ u Ai ki V i CV ki jα_ j dVi R¼ e i V i t1 þ i2 2 Ci Ci V_ dα i¼1
Table 1 Comparison of natural frequencies for structural models A1 and A2. Mode
(6) 1 2 3 4 5 6
i
where “Vi ” is the wind speed, “α” is the azimuth, and “Ai ;”. “Ci ;” and “ki ,” are parameters of the Weibull distribution of wind speeds for each sector “i”. Parameters “jα_ j” and “V_ ” can be calculated through empirical ex-
fn (Hz)
Type
A1
A2
i1-2
0.2957 0.3032 0.4282 0.9409 1.0920 1.2470
0.3262 0.3324 0.5124 1.0840 1.2250 1.4850
þ þ þ þ þ þ
10.31% 9.63% 19.66% 15.21% 12.18% 19.09%
Translational Translational Torsional Translational with torsional components
pressions as functions of wind speed “V”, and are suitable for extratropical winds (Irwin et al., 2005): V_ ¼ 0:065V þ 0:5e0:252V
(7a)
jα_ j ¼ 6:5 1 þ 3:3e0:252V
(7b)
Table 2 Comparison of natural frequencies for structural models B1 and B2. Mode
The return period “m,” associated with the magnitude of the chosen response is calculated by (Irwin et al., 2005): m¼
1 8760R
1 2 3 4 5 6 7 8 9
(8)
Several pairs of acceleration “am ” vs. return period “m” are obtained in a tabular form and plotted into a chart, where a regression curve takes place to interpolate these values and provide the final resultant 235
fn
Type
(Hz)
B1
B2
i1-2
0.2060 0.2187 0.3012 0.5821 0.6812 0.7380 1.0581 1.2327 1.2737
0.2207 0.2274 0.3186 0.6072 0.7199 0.7698 1.0971 1.2547 1.3197
þ þ þ þ þ þ þ þ þ
7.13% 3.99% 5.77% 4.31% 5.69% 4.31% 3.69% 1.78% 3.61%
Translational y dir. Translational x dir. Torsional Torsional Tors. with transl. in y dir. Tors. with transl. in x dir. Torsional Translational x dir. Tors. with transl. in y dir.
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B2). The mode deflection shapes for models A1 are presented in Appendix A: Figure A.1. In Fig. 6, it is possible to verify that the sway component of the mode deflection shapes for the first two natural modes of vibration have a considerable difference. The increase in the natural frequencies of model A2 and the change in its mode shapes for the sway modes can be explained by two main effects (Kim et al., 2009): Transfer of axial forces from the exterior frame, generating a resistant moment on the core walls in an effect analogous to an outrigger system (Choi et al., 2012), but considerably less substantial than the actual system; Increased coupling between the shear walls through the floor slab (Kim et al., 2009). Both effects tend to approximate the mode deformation shapes of the structure to the ones of a moment resisting frame (shown with more details in Appendix B). Only the sway components of the mode deflection shapes for the two first modes of vibration are presented in Fig. 6. Torsional components of these modes are very similar when we compare models A1 and A2. The remaining mode deflection shapes are either purely torsional (3rd mode) or very much stiffer than the first two modes (4th to 6th modes), with a natural frequency ratio higher than 3:1 between the 4th mode and the 1st mode, and up to 4:55 between the 6th mode and the 1st mode. The stiffer modes are much less sensitive to smaller stiffness increases, such as the outrigger effect or the shear wall coupling, and do not present any significant changes in the mode deflection shapes, neither for the x axis nor the y axis. These modes (3rd to 6th), however, are purely or highly torsional and very sensitive to the warping rigidity increase and present minor changes in the torsional components. These changes in the mode shapes are responsible for a change in the modal loads, while the changes in the natural frequencies bring the resonant response to different values of the PSD of the wind loads. When combined, these features change the modal responses and their sensitivity concerning the azimuth, and even change the critical direction of
Fig. 5. Building B floor plan.
reduced when compared with building A. This is due to two main factors: first, the building structural system is composed of moment frames in both orthogonal directions (see Fig. 5); second, the “stiffness increase divided by the mass” ratio is considerably smaller for this building when compared with building A (as the average density is nearly 56% higher for building B due to its structural material). The “moment frame” and/or “coupled shear walls” structural systems in both directions lead to a reduced participation of the floor slab as a structural element, as previously discussed in the first building's case study and showed in the study of Kim et al. (2009). 3.1.2. Mode deflection shapes The structural systems (moment frames and coupled shear walls) in both directions for building B led to well-behaved mode deflection shapes in well-defined directions (see Figure A.2, in the Appendix, where translations in the x and y axes have little or no torsional components) and no differences between these shapes for the assessed models (B1, and
Fig. 6. Translational mode shapes for models A1 and A2 (modes 1 and 2). 236
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sixth mode compared to the fifth mode of vibration for this azimuth is 0:36%. The PSD was normalized with the variance of the respective component acceleration “σR ” using all modes of vibration available (6 for building A and 9 for building B). This azimuth was chosen for being the most critical regarding higher modal contribution, as it will be discussed later in this chapter. These results support the justification to study higher modal truncation in the fifth mode of vibration in the current case study of building A. However, studies carried out with other tall buildings might need even higher modal truncation to provide reliable results. This is the case of building B, which required an analysis with three extra modes (up to the ninth mode) and results with higher modal truncation for the seventh mode, as shown in Fig. 9. For building B, the incremental variation in the resultant acceleration originated from using modes fourth to sixth compared to the use of the first three fundamental modes of vibration is 25:2%, whilst the use of the seventh mode increases the previous response in 3:91% and the use of the eighth and ninth modes represented increases of less than 0:01%. The 10 azimuth was chosen for being one of the most critical regarding higher modal contributions for building B. The rms of the time domain response is lower and very close to the rms of frequency domain response for nearly all azimuths (building A, model A2). This behavior corroborates the steady-state theory (Jeary, 2003), as it was also observed in the results found by Wu et al. (2007). The final accelerations calculated in both time and frequency domains for all azimuths for building A2 are given in Fig. 10, where it can be observed that some of the azimuths present responses that are bigger for the time domain, when compared with the frequency domain (300 , 320 and 70 ). The correlation factor between the modes in this study is nearly 0:20 between the two first natural modes of vibration, and 0:00 for all other combinations of modes of vibration for all azimuths. Huang and Chen's (2007) results for their second situation of study have a similar behavior between different modes of vibration, and present joint-action factors around 0:88. Fig. 11 presents higher modal contribution to the overall acceleration for building A (model A2). The higher modal contribution presented the following increases in the maximum value for each acceleration component:
the building's response. These changes will be presented in section 3.1.3, and their impacts in the wind climate modelling are shown in section 3.3.1. 3.1.3. Results from structural modelling criteria Resultant accelerations using the presented methodology for the frequency domain analysis are given for all azimuths and two structural models per building (A1 vs. A2, and B1 vs. B2) in Fig. 7. The rms results were obtained through eq. (2) and the modal combination was made using the square route of sum squares (SRSS) rule. As expected, pattern “A1>A2” is respected for most of the azimuths, including the maximum acceleration. The critical direction for building A1 is 220 , where the peak acceleration on the floor of interest is 1:61mili g. For building A2, these results are 130 and 1:36mili g. The way in which the wind climate will be introduced to the procedure will define how this change in the critical direction can impact the final acceleration assessment. For the worst-case method, the results are given and a reduction of 11:4% is observed in the results, due to the use of the structural modelling criteria presented in this paper. These and other features of the wind climate associated with the structural modelling criteria are explored in section 3.3.1. This is an evidence of how the structural modelling criteria can influence the Davenport's chain of wind loading. Resultant accelerations using the same methodology as those used for building A were calculated for building B using a 1-year return period (BLWT-normalized wind pressures for 26m=s wind speed at 500m of altitude), and a total of three modes of vibration. The modal truncation criteria for this building will be discussed in section 3.2. As previously observed in Table 2, the structural modelling criteria play a minor role in building B when compared with building A. Differently from building A, there is no change in the critical direction for building B, as there is no change in the mode deflection shapes due to different modelling criteria. 3.2. Dynamic analysis criteria The normalized PSD for the components and for the resultant accelerations for the 300 azimuth are given in Fig. 8, from which it is plausible to infer that the sixth mode already has very little participation when compared with the fifth mode. The incremental variation of the
Fig. 7. Resultant accelerations for models A1, A2, B1, and B2. 237
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Fig. 8. Normalized PSD of the components and of the resultant accelerations for the 300 azimuth (Building A).
X axis component (210 and along-wind direction for this sector): 1:86%; Y axis component (300 and cross-wind direction for this sector): 32:6%; Torsional component: 1:05%.
frequencies under 1:00Hz and the seventh mode with nearly 1:00Hz. Leading to several modes of vibration (seven at the total) with natural frequencies highly sensitive to dynamic effects from wind loads, from which only three were initially used in the WTT. Resultant acceleration presented an overall increase of 26% as a result of contributions from modes 4 7 (from 25milli g in sector 350 to 31:7milli g in sector 10 ). This increase is quite significant for the user comfort, just as the 9:47% increase for building A. However, assembling seven different oscillations (or five, in case of building A) makes room for doubt regarding the user's perception of such a movement. In order to verify the perception, the shape of the movement is presented in Fig. 13, where the highest values of displacement where highlighted in black for the most critical acceleration/displacement time lapse. It is important to note that the movement is nearly oval with a very elongated shape, which means that despite the complex combination of five modes of vibration, the user will perceive an uniaxial movement (Tamura et al., 2006).
The overall resultant acceleration presented an increase of 9:47% in the maximum value, mainly due to a higher modal contribution from Y axis for the 300 azimuth. This result can also be observed in the PSD presented in Fig. 8, where modes 4 and 5 contribute with a significant part of the final response of the building for this azimuth. Results of higher modal contribution are presented for building B (model B2) in Fig. 12, where a noticeable increase in the maximum peak resultant acceleration can be observed. The most perceptible increase of 47% occurs in the 10 sector. In that sector, components x, y, and torsional presented results of 19%, 23%, and higher than 50%, respectively, due to the contribution of modes 4 7. In this case study, the contribution of higher modes was equally important for both along-wind and cross-wind loads, while the torsional component showed to be far more relevant than both translational components. A closer look into the PSD of the response of 10 azimuth shows significant contribution from these modes. The explanation of such importance to higher modes is the slenderness of Brazilian buildings. This slenderness is a direct result of no significant seismic activity and quite low wind speeds (30–40 m/s) in the country, leading to lower natural frequencies of its buildings. This is clear in Table 2, where a 178:00m high building has six modes with natural
3.2.1. Results from dynamic analysis criteria The resultant acceleration for each model from building A, using the main dynamic analysis criteria, is presented in Fig. 14, where the worstcase method was applied and the results for 10 and 50-year return periods were obtained. This figure shows that the most severe acceleration occurs in model A1 in the frequency domain, which happens to be the most common criteria used by BLWT and structural engineers around the world. A reasonable reduction was obtained by improving the structural models.
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Fig. 9. Normalized PSD of the components and of the resultant accelerations for the 10 azimuth (Building B).
Fig. 10. Final acceleration results (Model A2, 5 modes of vibration).
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Fig. 13. Shape of movement (model A2, time domain, five modes).
Fig. 11. Higher modal contribution (Model A2, 3 and 5 modes of vibration).
Fig. 14. Worst case method resultant peak accelerations vs. return period (Building A).
Fig. 12. Higher time domain).
modal
contribution,
peak
acceleration
(model
case, the time domain analysis with a higher modal contribution for model A2 presented resultant accelerations higher than the resultant accelerations in the frequency domain for the same model. The worstcase method was used in this analysis and generated the results presented in Fig. 14. However, different results are expected with the use of not only the most severe acceleration, but also the contribution from each sector to the final response. The results of the up-crossing method will be presented in section 3.3.1. Analogously, for building B, the same set of criteria is presented in Fig. 15. In this figure, structural modelling criteria show a reduction of 3:6%. Higher modal contribution (model B2, time domain, seven modes), on the other hand, presented an increase of nearly 15:8%, leading to an overall increase in the resultant acceleration of 8.5%, when compared with model B1 in the frequency domain for three modes. The dispersion of results is clearly great for this type of analysis and, therefore, consolidating criteria between structural engineers and WTT facilities should be a priority when it comes to structural modelling and
B2,
The three-mode analysis in the time domain showed one of the highest levels of reduction. However, higher modal contribution showed to be quite relevant in these resultant accelerations, and neglecting it would lead to less reliable results. The most precise set of criteria did not present lower results. In this
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domain (5:92milli g, 1-year return period) for five modes of vibration. However, for the up-crossing method, the acceleration response of building A2 is quite close to those of model A1. This means that the decrease in the overall acceleration response from model A2 (37%) is lower than that of model A1 (42%) when the up-crossing method is applied. The explanation for this behavior is that model A2 has a critical direction equal to the critical direction of the wind climate, while these directions are different for model A1 (see Fig. 17). Fig. 17 shows the probability of exceedance of the wind speed for Congonhas Airport, in S~ao Paulo (Brazil). The curves from the most central to the most external positions represent the probabilities of exceeding that velocity (these probabilities are, respectively, 0:001%, 0:010%, 0:100%, and 1:000%). In this figure, we can also read the resultant acceleration response for building A1 in the frequency domain, and for building A2 in the time domain for five modes of vibration. By overlapping these curves, we can verify that the stronger contributions of model A2 to the final response are in azimuths 40 , 190 , and 290 , where the wind speed of the probability curves reaches its maximum values (or where they are closer to their maximum values). In contrast, the stronger contribution of building A1 to the final response is between azimuths 210 260 , where the wind speed of these curves has its minimum values. Hence, the contribution of model A1's responses between azimuths 130 190 (one of the critical azimuth gaps for wind climate) are much smaller than building A2's contribution. This is one of the results of the change in the modal deflection shapes discussed in section 3.1.2. The change in the modal-deflection-shape led to a change in the critical direction of the building and in the building's response distribution over the different sectors, which, in turn, led to different results in the application of the up-crossing method. Building B's responses are given in Fig. 18, where the application of the up-crossing method presented the same decrease for models B1 and B2 (45%). A similar impact from the up-crossing method on the resultant acceleration was expected for this building, as there was no significant change in mode deflection shapes or in the natural frequencies due to the structural modelling criteria, leading to no difference in the critical direction of the building. Finally, a closer look at figures Figs. 16 and 18 allows for comparison with the Up-crossing method and the Sector-by-sector method. Results
Fig. 15. Worst case method resultant peak accelerations vs. return period (Building B).
dynamic analysis. Structural modelling criteria, along with dynamic analysis criteria, may represent a noticeable increase or decrease in the building's final response, and should be taken into consideration for greater precision in the assessment of building motion using WTT data.
3.3. Wind and comfort 3.3.1. Up-crossing method Previous results of the resultant acceleration were presented using non-directional wind climate for both buildings, so as to analyze structural and dynamic analysis criteria purely, with no interference from other disciplines. In this section, the wind climate modelling is introduced to evaluate its impact on the final response from buildings A and B. The results from models A1 and A2, for both frequency and time domain, are presented in Fig. 16. For the worst-case method, there is a significantly smaller result (nearly 7% smaller) for model A2 in the time domain (5:52milli g, 1year return period), when compared with model A1 in the frequency
Fig. 16. Up-crossing, Sector-by-sector and Worst case methods (Building A).
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Fig. 17. Critical directions (Building A): wind climate and building's responses.
Fig. 18. Up-crossing, Sector-by-sector and Worst case methods results (Building B).
method) are compared with the most precise set of criteria, including wind modelling (models A2 and B2, time domain, higher modal contribution, up-crossing method). Looking at this figure, it is important to restate the small consistency of comfort criteria around the world. This lack of consistency can still be justified by the different tolerance to motion in different countries. The user of a building in Chicago, traditionally a very windy city of high-rises, may have more tolerance to motion than the user of a building in S~ao Paulo, a city with a recent culture of high-rises and with much lower wind speeds in design. Therefore, the comfort thresholds in the building codes of these two cities/countries could be different as well.
show consistency with the case study presented by Burton et al. (2015), where an example is shown with a directional building in a directional wind climate, prevailing the same critical direction both for the wind and for the building's response. In this case, the Sector-by-sector method is more conservative than the up-crossing method, as shown in Fig. 19 for 1-year return period. 3.3.2. Comfort assessment The peak acceleration analysis for time domain is presented in Fig. 20, where the most simple and conservative set of criteria (models A1 and B1, frequency domain, 3 modes of vibration, and worst case
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Fig. 19. Up-crossing, Sector-by-sector and Worst case methods results (Buildings A and B).
Fig. 20. Peak acceleration analysis (Buildings A and B).
Fig. 21. Peak and rms responses at different floor locations (300 sector).
recent and precise thresholds, as well as dynamic analysis criteria. Thus, it is reasonable to pursue comfort through thresholds closer to perception of motion until this practice is better developed in Brazil. The most severe peak acceleration of the floor will be used, based on the location of the building (Brazil) and on the type of assessment (perception).
ISO10137 (2007) and NBR6123, 1988 are related to perception, while the criteria of NBCC (1990) and CTBUH are related to comfort. The verification of comfort in tall buildings in Brazil should more focused on the perception thresholds for the next years, due to its recent history with high-rises. NBR6123, 1988 is currently under revision to integrate more
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The inconsistency in the overall criteria, conversely, is more concerning. Both buildings A and B, in the most conservative set of criteria, do not pass the comfort verification using the threshold defined in NBR6123, 1988. On the other hand, using more precise parameters, and comparing them with codes with higher thresholds, like the NBCC (1990), the resultant accelerations achieve a ratio where they are only 29% to 64% of the comfort threshold for the same return period (10 years). Hence, all sets of criteria pass in the comfort verification for a smaller return period (1 year), with the exception of the worst-case method for model B1, which passes the comfort verification (Sarkisian, 2012), but doesn't pass the SLS verification based on perception (ISO10137, 2007). Comparing three modal responses with time domain (model A2) and frequency domain (model A1), the time domain response is even lower and should lead to a more economic design (allowing further structural optimization). However, considering higher modal contributions, the final acceleration for model A2 in the time domain is quite similar to the responses for model A1 in the frequency domain. This means that this could be the case where “two wrongs made a right,” and the different response behavior throughout the azimuths and higher modal contributions (which lead to higher responses) balanced the reduced response with the use of structural modelling criteria and time domain analysis (which lead to lower responses). Fig. 20 shows the worst peak resultant acceleration, considering the most critical location of the user on the highest occupied floor. The subsequent analysis will explore the aspect of this location in order to evaluate the human comfort during wind-induced motions. The other peak and rms accelerations for the other top occupied floor positions are shown in Fig. 21. In this figure, we can observe that the rms accelerations do not present a significant variation over the floor positions, while the peak accelerations do. The rms accelerations adopt an almost constant value, with an average of 1:03milli g throughout the positions, while the peak accelerations vary between 3:49milli g and 5:52milli g. This variation occurs as a result of the torsional components of both torsional and translational modes of vibration, which is particularly significant in this project. The constructive interference between the translational and the torsional components in one position of the floor is a destructive interference in the opposite direction, generating these discrepancies. As a result, the peak factors for this floor also vary greatly. The peak factor presented for sector 300 (critical sector in the final analysis of building A2) in the previous sections is 5:34 and corresponds to the highest peak acceleration, while the average peak factor for this floor is 4:31. To correctly evaluate the comfort level of the user, one must define whether the perception of movement or the annoyance levels will be assessed. If the annoyance levels are chosen, the average value and probably the rms acceleration should be used. However, if the perception of movement is chosen, then there is a chance that the occupants in the region with the most severe result will perceive the motion and alarm the other occupants on the floor. In this case, the peak acceleration is probably the most suitable way to evaluate comfort.
Table 3 Summary of results of each set of criteria for buildings A and B. Building
Structural modelling
Higher modal contribution
Wind climate modelling
Comfort criteria
Total
A B
11.4% 3.6%
6.4% 15.8%
39.8% 44.7%
36.9% 36.9%
¡66.9% ¡62.1%
generating relevant deviations in the probabilistic wind climate analysis. Time domain analyses present several paybacks when compared with the frequency domain analyses. The assessment of complex motion is one of them, where one can precisely calculate the exact vector acceleration at any location on the floor for all time steps. This feature allows for a precise modal combination (including higher modes) and peak responses, without the need for any modal combination rule or statistical peak factors, and also allows for the assessment of the exact values through the rms acceleration. Higher modes presented an important contribution to the final acceleration (up to 15:8%). Part of this increase in response, however, is largely compensated by a decrease in other criteria, as it can be observed in Table 3. The wind climate criteria presented the most relevant impact in the final response, decreasing the overall response by nearly 37 45%. Different mode shapes that result from structural modelling criteria also contributed to the wind climate analyses, since these mode shapes changed the critical direction of the building. Table 3 shows the summary of variation results for each set of criteria studied in this paper through an exhaustive analysis of Figs. 10, 14, 15 and 20. Structural modelling criteria were evaluated by a comparison of the results of models A1 vs. A2, and B1 vs. B2 in the frequency domain for three modes of vibration (worst-case method). Higher modal contribution is evaluated by comparison of the results from building A2 (B2) for three and five (seven) modes in the time domain (worst case method). Wind modelling criteria could be evaluated through the variation of the results of model A2 (B2) for the worst-case method and for the upcrossing method. The comfort criteria were evaluated using the ratios of a specific set of criteria (A2/B2, 5/7 modes, time domain, up-crossing method) and two comfort thresholds: ISO 10137 (2007) and Sarkisian's (2012) for offices. For building A, these ratios were, respectively: 3:53=8:20 ¼ 0:43, and 3:53=13:0 ¼ 0:27, and its variation was 36:9%. This calculation works analogously for building B. This result shows that the impact of design criteria may represent response reductions up to 66:9% (for building A) when compared with the results obtained from a conservative analysis and a conservative threshold. A reduction through different sets of criteria lead to more efficient designs, which, in turn, lead to the reduced use of material, lower costs, and lower embodied energy of the structure. Acknowledgements
4. Conclusions
A special thanks to the following companies and universities, without which the results obtained in this paper wouldn't be possible: Escola Politecnica da Universidade de S~ ao Paulo, Alan G. Davenport Wind Engineering Group, França & Associados Projetos Estruturais, Rowan Williams Davies and Irwin Inc.
First, the modelling criteria are very relevant for comfort and for the SLS analysis. They represent a substantial increase in the building's natural frequencies (up to 19:66%, as observed in building A). In addition, there were visible changes in mode deflection shapes,
Appendix A. Supplementary data Supplementary data related to this article can be found at https://doi.org/10.1016/j.jweia.2018.07.006.
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Appendix A. Mode deflection shapes
Fig. A.1. Mode shapes for structural model A1. 245
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Fig. A.2. Mode shapes for structural models B1 and B2.
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Appendix B. mode deflection shapes and Building A's critical wind direction As explained in section 3.1 and presented in Fig. 6, the FE models A1 and A2, generated from building A, presented many different structural features. Undeniably, mode deflection shapes from both models present important differences due to the modelling of the floor slab criterion. These differences led to the results shown in Fig. 7, where it can be observed a sensitive difference of behavior or response pattern in a few sectors (mostly around azimuths 160 , 200 and 260 , in order of significance).
Fig. B.1. Building A floor slab.
To give a better overview of the impact of structural modelling in the mode deflection shapes, one can observe Figure B.1, featuring the mode deflection shape of the second mode of vibration, which is the mode of vibration more susceptible to benefit from frame behavior of the floor slab. In this figure, it is possible to observe: 1) Floor slab deflection pattern following shear-wall connections in a straight line; 2) Cross section of the modelled floor slab, which for composite floors presents high stiffness due to the presence of the steel section. 3) Clamped portion of the floor slab to the external columns. The frame behavior observed in FE model A2 is not present in model A1 and despite the very low values of bending moment acting on these floor slabs, the cumulative effect on every building floor is very expressive and, for this building, it generates the differences in the mode deflection shapes and in the natural frequencies presented respectively in Fig. 6 and in Table 1.
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