- Email: [email protected]
A review of vibration serviceability criteria for floor structures
Computers and Structures 83 (2005) 2488–2494 www.elsevier.com/locate/compstruc
A review of vibration serviceability criteria for floor structures Arya Ebrahimpour a
a,*
, Ronald L. Sack
b
College of Engineering, Idaho State University, Campus Box 8060, Pocatello, ID 83209, USA b Department of Civil and Environmental Engineering, University of Nevada Las Vegas, Las Vegas, NV 89154, USA Received 4 November 2003; accepted 17 March 2005 Available online 22 August 2005
Abstract This paper is a survey of the historical developments in modeling human dynamic loads, perception criteria used in structural floor vibrations, and the techniques used to mitigate the human-induced vibrations. Two of the techniques are explained in more detail, namely: semi-active control and passive control using advanced materials. Ó 2005 Elsevier Ltd. All rights reserved. Keywords: Dynamic loads; Vibrations; Floor systems; Perception criteria; Vibration control
1. Introduction Sports stadiums, discotheques, gymnasiums, aerobic dance studios, shopping malls, and airport terminal corridors are all subjected to significant dynamic loads produced by occupants either while remaining in one location or traversing the structure. Coherent crowd harmonic movements can produce resonant or near-resonant structural vibrations that are uncomfortable and intolerable for some occupants. Some structural failures, such as the Hyatt Regency Hotel in Kansas City [1], indicate that there can be many lives at stake when human loading is imposed. In addition, there have been serviceability problems that required costly remodeling or revision of building regulations.
At the present, US codes and standards are primarily concerned with avoiding structural failure (i.e., a strength requirement), and deal with excessive vibrations (i.e., a serviceability requirement) only to a limited degree [2,3]. Empirical serviceability requirements usually do not involve the frequency of the loading or the natural frequency of the structure. Many researchers believe these requirements are inadequate for controlling the human-induced vibrations. This paper provides a survey of the historical developments in modeling human dynamic loads, perception criteria used in structural vibrations, and various techniques that are used to mitigate the human-induced vibrations.
2. Human-induced dynamic loads * Corresponding author. Tel.: +1 208 282 4695; fax: +1 208 282 4538. E-mail address: [email protected] (A. Ebrahimpour).
Live loads are produced by the use and occupancy of a structure. Human loads comprise the large portion of the live loads in floors of offices and residential
0045-7949/$ - see front matter Ó 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.compstruc.2005.03.023
A. Ebrahimpour, R.L. Sack / Computers and Structures 83 (2005) 2488–2494
3. Human perception of structural vibrations The most frequently cited reference for human perception of vibration is by Reiher and Meister [13]. The Reiher–Meister scale is based on a displacement range of 0.01–10 mm and frequency range of 1–100 Hz. The modified Reiher–Meister scale was proposed by Lenzen [14] for vibrations due to walking impact. For floors with less than 5% critical damping, Lenzen suggested the original scale be applied if the displacement is increased by a factor of ten. Wiss and Parmelee [15] suggested that a constant product of frequency and displacement existed for a given combination of human response and damping. Allen and Rainer [16] developed vibration criteria in terms of acceleration and damping intended for quiet human occupancies such as residen-
tial buildings and offices. As damping increases, the steady-state response due to walking becomes a series of transient responses; resulting in a less significant response. Murray [17] suggested a human perception scale for required damping as a function of the product of initial displacement and frequency, which are the same parameters used in the Wiss–Parmelee scale. Allen et al. [18] suggested a design procedure for assembly floors subjected to rhythmic activities such as dancing and exercises. The International Standards Organization (ISO) [19] recommends vibration limits in terms of acceleration root-mean-squared (rms) and frequency. As shown in Fig. 1, a baseline curve is used by ISO and different multipliers are used for different occupancies. The vibration serviceability criteria for floors have been categorized into two broad categories. These are: criteria for steel beam and concrete slab construction, and wood/lightweight construction. The following sections describe the research in each category. 3.1. Criteria in steel beam and concrete slab construction Allen and Rainer [16] developed a vibration criterion for floors due to footstep loading which were based on tests on 42 long span floor systems. Ellingwood and Tallin [20] recommended a criterion for commercial floors. It is based upon a specified maximum deflection with a prescribed point load placed anywhere on the structure (i.e., a stiffness requirement). Updated guidelines for preventing annoying vibrations in steel framed floor systems are presented in a guide jointly published by the
25 Rhythmic Activities, Outdoor Footbridges
10 5
Peak Acceleration (%Gravity)
buildings. In assembly structures such as ballrooms, grandstands, health clubs, as well as pedestrian bridges, human-induced dynamic loads are the principal source of live loads. In general, the human live loads are classified into two broad categories: in situ and moving. Periodic jumping to music, sudden standing of a crowd, and random in-place movements are examples of in situ activities. Walking, marching, and running are examples of moving activities. Tilden [4] and Fuller [5] were among the first researchers to experimentally quantify the dynamic load effects of individuals and groups, respectively. Tilden considered both in situ and moving loads. Fuller attempted to experimentally quantify the crowd dynamic effect due to a group of people on a gymnasium balcony. Greimann and Klaiber [6] predicted the spectator dynamic loads on the Iowa Sate University stadium during a football game. Structural vibrations have been recorded as a result of spectator movements in rock concert in Canada [7]. Tuan and Saul [8] defined various types of in situ movements by measuring the load-time histories for individual subjects on a small piezoelectric force platform. Ebrahimpour and Sack [9] used a large instrumented force platform to measure in situ loads by individuals and groups of two and four people. In a subsequent study, Ebrahimpour and Sack [10] constructed a 3.7 m by 4.6 m floor system and measured forces of up to forty people performing in situ harmonic movements. They also recommended simple design values for coherent crowd harmonic movements. Only a very few studies of human moving loads have been reported. Canadian researchers measured dynamic forces of individuals and small groups of people [11]. Ebrahimpour et al. [12] measured the input forces imposed by moving groups of people using a set of instrumented platforms, mathematically modeled the loads, performed simulations, and suggested simple design loads for serviceability criteria.
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Indoor Footbridges, Shopping Malls, Dining & Dancing
2.5
1
Offices, Residences
0.5 0.25 ISO Baseline Curve For RMS Acceleration
0.1 0.05 1
3
4 5
8 10
25
40
Frequency, Hz Fig. 1. Peak accelerations for human comfort for vibrations due to human activities [19].
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American Institute of Steel Construction and the Canadian Institute of Steel Construction [21]. Criteria are provided both for walking and rhythmic excitations. In the walking criterion, the floor is acceptable if the peak acceleration, as determined by a simplified relation, does not exceed the ISO recommended acceleration limit. The rhythmic excitation design criterion is based on the natural frequency of the floor being larger than a minimum acceptable level. The minimum acceptable frequency level is a function of the ISO peak acceleration limit and the type of occupancy. 3.2. Criteria in wood/lightweight construction Research on human-induced vibration of lightweight wooden floors have been carried out by Smith and Chui [22], Ohlsson [23], Kalkert et al. [24], Foschi et al. [25], Dolan et al. [26], and Al-FoqahaÕa et al. [27]. Smith and Chui [22] developed methods for predicting dynamic behavior of lightweight wood floors. They recommended that root-mean-squared acceleration response of the floor under heel-drop impact be kept less than 0.45 m/ s2 and that floor natural frequency must be more than 8 Hz. The second requirement is to avoid the frequency band that humans are especially sensitive to (4–8 Hz). Ohlsson [23], presented a design approach for footstep loading in lightweight wood floors with frequencies higher than 8 Hz. For transient vibration, the method is based on determining the peak floor velocity response due to a unit impulse ((mm/s)/N s) and the product of damping coefficient and frequency. Both quantities are used to enter a vibration perception chart. Dolan et al. [26] proposed a stringent frequency requirement; they recommended that the floor fundamental frequency be greater than 15 Hz and 14 Hz for unoccupied and occupied floors, respectively.
4. Structural vibration control Vibration control may be achieved in several ways: passive, semi-active, and active. For a survey of structural control, with particular emphasis on mitigation of wind and seismic responses of buildings, see Housner et al. [28], Soong and Spencer [29], and Spencer and Nagarajaiaj [30]. The following sections describe vibration control, as applied to floor vibrations. 4.1. Tuned mass dampers A tuned mass damper (TMD) is one way of passively controlling the floor vibration. Lenzen [14] used a TMD to provide artificial damping in a floor to dampen the vibration in less than five cycles. The spring and dashpot unit had a frequency of about one cycle per second below the natural frequency of the floor and had a viscous
damping equivalent of 7.5%. Setareh and Hanson [31] provided both analytical study and experimental verification for selecting TMDs to decrease floor vibrations under rhythmic human activities. He presented a detail set of recommendations for design and placement of one or more TMDs. Several of these devices were installed in the balcony of a renovated historic theater in Detroit, Michigan. Several TMDs have been employed in BellagioÕs pedestrian bridges in Las Vegas [32]. It was anticipated that under certain conditions, such as festivals or large gatherings, excessive human-induced vibrations would be possible. Six TMDs, each weighing 1360 kg, were installed in each bridge. Tests on the bridges indicated that damping has been increased from 0.6% to more than 8%. Other successful applications of TMD systems have been recorded in real floors; for example, the cantilevered dance floors of the Terrace on the Park building in Flushing, NY [33,34]. TMD systems are typically effective over a narrow frequency band and must be tuned to a particular natural frequency. They are not effective if the structure has several closely spaced natural frequencies [34,35]. 4.2. Semi-active control During the 1980s, the auto industry researched, developed and tested various types of semi-active shock absorbers. That research produced a new type of control actuator that has applications in civil, mechanical, and aerospace engineering. These devices were developed in response to a need in the auto industry to provide improved ride comfort in vehicles. There are two broad classes of SA actuators: those that dissipate energy via damping and those that store energy by varying stiffness. There has also been an intensive effort since the mid 1980s to develop control systems for civil structures. The past effort has produced a range of designs that include fully active systems, entirely passive systems and designs that rely on a mix of those two (hybrid systems). Active control systems invariably require line power to achieve vibration mitigation. Passive designs require no power, and are usually less expensive than active designs, but are incapable of achieving the protection that an active system can provide. Spencer and Sain asserted that ‘‘Control strategies based on semi-active devices appear to combine the best features of both passive and active control systems and to offer the greatest likelihood for near-term acceptance of control technology as a viable means of protecting civil engineering structural systems. . .’’ [36]. Semi-active control systems provide a much needed technology between fully active structural control systems and passive designs. The term semi-active describes a system that consists of a variable actuator that requires very little power to operate. Both the semi-active (SA) hydraulic system and fully active (FA) hydraulic
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system designs include actuators, valving, etc. But the power required for the SA system is that necessary to modulate the valve position only. That power is typically many orders of magnitude less than that required to achieve a similar FA design. The utility of a SA design is realized when it is used to dissipate energy. Mitigating the motion of a structure during an earthquake, or attenuating the response of a beam due to dynamic loading are examples of applications where the motion of the structure can be harnessed to make a SA design functional. For these applications, analysis has shown that, if the hydraulic pump is removed from a FA hydraulic design, and the plumbing is altered, then the (now SA) system can provide attenuation that is equivalent to what would have been expected had the FA design been implemented. SA friction dampers, mounted as braces on a structure are examples of a SA control system. Hydraulic semi-active vibration dampers (SAHD), provide a combination of both damping and stiffness. Sack and Patten [37] conducted tests using a single-lane bridge 12.3 m in length that they subjected to vehicle loadings. They significantly reduced peak deflection by as much as 15% using feedback linearization to produce a suboptimal controller design. They also demonstrated the effectiveness of semi-active control on a full-scale experiment on an in-service bridge on interstate highway I-35 in Oklahoma. This application was the first full-scale implementation of semi-active control in the United States on a civil structure, and the results showed deflection reduction of more than 70% when compared to the vibration deflection of the bridge operated without dampers attached [38,39]. Setareh [40] and Koo et al. [41,42] proposed the use of a new class of semi-active tuned mass dampers, called ground-hook tuned mass dampers (GHTMD). Ground-hook control was initially introduced for vehicle application. Unlike the ‘‘skyhook’’ control that is designed to control the vibration of the sprung mass for the comfort of a rider, the ‘‘ground-hook’’ is intended to reduce the vibration of the unsprung mass (i.e., the tire and axle assembly). The ground-hook control is used for the stability of the vehicle. Because the structureÕs mass is similar to the unsprung mass of a vehicle, the ground-hook control is applicable in the control of structures attached to a TMD. Setareh obtained optimum design parameters for GHTMD in a floor structure, based on minimization of the acceleration response of the floor, mass ratios (damper to structure), and floor damping ratios. Koo et al. [42] suggested four control strategies for use in GHTMDs: two velocity-based and two displacement-based. In each case, two types of semi-active damping were considered: continuous and on-off. The study concluded that the on-off displacement-based control performs best in minimizing the structural vibrations.
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4.3. Active control Hanagan and Murray [33] and Hanagan et al. [43] developed an active electro-magnetic actuator that uses a piezoelectric velocity sensor and a feedback loop to generate control forces, thus adding damping to the supporting structure. Significant results were obtained on the office floor of a light manufacturing facility and a chemistry laboratory. High initial cost, maintenance, reliability, and the number of actuators needed to effectively reduce vibration levels were issues that were noted with this system. 4.4. Passive control using advanced materials 4.4.1. Damping in viscoelastic materials Ungar and Kerwin [44] and Ungar [45] used the concept of damping in viscoelastic materials in terms of strain energy and developed a model that expressed the overall damping in terms of the damping of individual layers. When viscoelastic material is added to a system, its influence on the overall system damping depends on how much strain energy is stored in the viscoelastic material under load. Therefore, the amount of damping material can be minimized by placing it where it will store the most strain energy [46]. Viscoelastic dampers have been used as vibration control to reduce wind-induced sway in tall buildings. They have been used in the World Trade Center Towers in New York City, Columbia SeaFirst building in Seattle, and Two Union Square building in Seattle, as documented by Mahmoodi and Keel [47] and Mahmoodi et al. [48]. Aiken et al. [49], Chang et al. [50], and Lai et al. [51] studied the feasibility of viscoelastic dampers in mitigating seismic responses of buildings. 4.4.2. Composites and viscoelastic materials The work in aerospace on dynamic behavior and damping in composite orthogrid and isogrid systems are closely related to the passive control of floor vibrations. Chen [52] and Chen and Gibson [53] investigated the damping properties of a composite isogrid panel with an embedded viscoelastic layer. Modal analysis showed that large shear deformation occurs in the region between the ribs and the face skin (i.e., the location of viscoelastic layer), which is caused by the mismatch in stiffness. Although not specifically used for vibration control, advanced composites such as carbon fiber reinforced polymer (CFRP) strips are used in civil engineering to strengthen existing structures [54]. These materials have high strength- and stiffness-to-weight ratios, are easily cut and fabricated on the job site, require no temporary bracings, and can conform to contours (even with obstacles present). Compared with steel, the installation and labor costs may offset the high material cost associated with advanced composites.
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Recently Ebrahimpour and Martell [55] retrofitted laboratory-constructed floors with laminates of carbon fiber reinforced polymer (CFRP) and constrained layers of viscoelastic material (see Fig. 2). The CFRP and viscoelastic retrofit uses high damping with some increase in stiffness to improve the vibration performance of the floor. In this study, the damping ratio of the floor increased from 2.4% to 11.7% (i.e., by 388%) with the addition of CFRP and viscoelastic layers. Fig. 3 shows a normalized deflection graph for the mass–drop test on an unmodified floor and a floor retrofitted with CFRP and viscoelastic materials (for comparison, maximum displacements are adjusted to one). Along with her experimental research, Martell [56] performed an analytical study of an indoor footbridge with a concrete deck and two steel beams. Fig. 4 shows the cross-section of the footbridge. The footbridge did not meet the recommended AISC vibration criterion [21]. A CFRP laminate (5 mm thick by 29 mm wide) and a constrained viscoelastic layer (7.6 mm thick by 29 mm wide) were attached to the bottom flange of each
Fig. 4. Footbridge cross-section.
Fig. 5. AISC recommended vibration criterion for the footbridge.
steel beam, along the entire span of the footbridge. As shown in Fig. 5, this retrofit decreased the peak acceleration and slightly increased the natural frequency of the structure, allowing it to meet the AISC recommended vibration serviceability criterion for an indoor footbridge. Fig. 2. Schematic of the experimental floor system and the data acquisition system.
Fig. 3. Laboratory floor mass–drop displacement responses.
5. Conclusions Coherent crowd harmonic movements may produce resonant or near-resonant structural vibrations that are uncomfortable and intolerable for some occupants. This paper presented a survey of the historical developments in modeling human dynamic loads, perception criteria used in structural floor vibrations, and the techniques used to mitigate the human-induced vibrations. Two of the techniques were explained in more detail, namely: semi-active control and passive control using advanced materials. Previous work on bridges establishes a reasonable basis by which a semi-active controller might be designed to provide vibration mitigation for vibration of building floor systems. The hardware, software, installation of the devices and selection of a controller design are dependent upon the structural system under consideration.
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Experience on full-scale bridges shows a deflection reduction of as much as 70% and significant acceleration reduction over the system with no controls. Passive control using CFRP laminate and constrained viscoelastic material seems appropriate for retrofitting floors with excessive vibrations. Laboratory and analytical results clearly indicate that occupantinduced vibration performance will be improved due to a significant increase in the overall structural damping and a slight increase in the stiffness.
[20] [21]
[22] [23]
[24]
References [25] [1] Pfrang EO, Marshall R. Collapse of the Kansas City Hyatt Regency walkways. Civ Eng, ASCE 1982;52(7):65–8. [2] International Building Code. International Code Council, Inc., Falls Church, Virginia, USA, 2003. [3] Structural Engineering Institute. Minimum design loads for buildings and other structures. SEI/ASCE 7-02, American Society of Civil Engineers, Reston, Virginia, 2002. [4] Tilden CJ. Kinetic effect of crowds. ASCE Proc 1913;34(3):325–40. [5] Fuller AH. Dynamic effects of moving floor loads—stresses measured in the floor and balcony of a college gymnasium. Am Arch Arch Rev 1924;126(11):455–6. [6] Greimann LF, Klaiber FW. Dynamic forces induced by spectators. J Struct Div, ASCE 1978;104(2):348–51. [7] Pernica G. Dynamic live loads at a rock concert. Can J Civ Eng 1983;10:185–91. [8] Tuan CY, Saul WE. Loads due to spectator movements. J Struct Eng, ASCE 1985;111(2):418–34. [9] Ebrahimpour A, Sack RL. Modeling dynamic occupant loads. J Struct Eng, ASCE 1989;115(6):1476–96. [10] Ebrahimpour A, Sack RL. Design live loads for coherent crowd harmonic movements. J Struct Eng, ASCE 1992;118(4):1121–36. [11] Pernica G. Dynamic load factors for pedestrian movements and rhythmic exercises. Can Acoust 1990;18(2). [12] Ebrahimpour A, Hamam A, Sack RL, Patten WN. Measuring and modeling dynamic loads imposed by moving crowds. J Struct Eng, ASCE 1996;122(12):1468–74. [13] Reiher H, Meister FJ. The effect of vibration on people. Forsch Gebeite Ingenieurwes 1931;2:381–6 [in German] English Translation: Report No. F-TS-616-RE, Headquarters Air Material Command, Wright Field, Ohio, 1946. [14] Lenzen KH. Vibration of steel joist-concrete slab floors. AISC Eng J 1966(3):133–6. [15] Wiss JF, Parmelee RA. Human perception of transient vibrations. J Struct Div, ASCE 1974;100(4):773–87. [16] Allen DE, Rainer JH. Vibration criteria for long-span floors. Can J Civ Eng 1976;3:165–73. [17] Murray TM. Acceptability criterion for occupant-induced floor vibrations. Sound Vib 1979:24–30. [18] Allen DE, Rainer JH, Pernica G. Vibration criteria for assembly occupancies. Can J Civ Eng 1985;12:617–23. [19] International Standard Organization. Evaluation of human exposure to whole body vibration—Part 2: human
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exposure to continuous and shock-induced vibrations in buildings (1 to 80 Hz). ISO 2631-2, 1989. Ellingwood B, Tallin A. Structural serviceability: floor vibrations. J Struct Eng, ASCE 1984;110(2):410–9. Murray TM, Allen DE, Ungar EE. Floor vibrations due to human activity. Steel design guide 11. American Institute of Steel Construction, 1997. Smith I, Chui YH. Design of lightweight wooden floors to avoid human discomfort. Can J Civ Eng 1988;15:254–62. Ohlsson SV. A design approach for foot-induced floor vibration. In: Proceedings of the International Conference on Timber Engineering, Seattle, Washington, USA, 1988. p. 722–9. Kalkert RE, Dolan JD, Woeste FE. Wood floor vibration design criteria. J Struct Eng, ASCE 1995;121(9):1294–7. Foschi RO, Neumann GA, Yao F, Folz B. Floor vibration due to occupants and reliability-based design guidelines. Can J Civ Eng 1995;2:471–9. Dolan JD, Murray TM, Johnson JR, Runte D, Shue BC. Preventing annoying wood floor vibrations. J Struct Eng, ASCE 1999;25(1):19–24. Al-FoqahaÕa AA, Cofer WF, Fridley KJ. Vibration design criterion for wood floors exposed to normal activities. J Struct Eng, ASCE 1999;125(12):1401–6. Housner GW, Bergman LA, Caughey TK, Chassiakos AG, Claus RO, Masri SF, et al. Structural control: past, present, and future. J Eng Mech, ASCE 1997;123(9):897–971. Soong TT, Spencer Jr BF. Supplemental energy dissipation: state of art and state of practice. Eng Struct 2002;24:243–59. Spencer Jr BF, Nagarajaiaj S. State of the art of structural control. J Struct Eng, ASCE 2003;129(7):845–56. Setareh M, Hanson RD. Tuned mass dampers for balcony vibration control. J Struct Eng, ASCE 1992;118:723–40. Breukelman B, Haskett T. Good vibrations. Civ Eng, ASCE 2001;71(12):55–9. Hanagan LM, Murray TM. Experimental implementation of active control to reduce annoying floor vibrations. AISC Eng J 1998;35(4):123–7. Webster AC, Vaicaitis R. Application of tuned mass dampers to control vibrations of composite floor systems. AISC Eng J 1992;3. Bachmann H, Ammann W. Vibration in structures induced by man and machines. Structural engineering documents. 3rd ed. International Association for Bridge and Structural Engineering; 1987. Spencer Jr BF, Sain MK. Controlling buildings: a new frontier in feedback. IEEE Control Syst 1997;17(6):19–35. Sack RL, Patten WN. Semiactive hydraulic structural control. In: Housner GW, Masri SF, editors. Proceedings International Workshop on Structural Control, Honolulu, Hawaii, August 1993. p. 417–31. Patten WN, Kuehn JL, Sun J, Song G, Sack RL. Impact vibration reduction via semiactive vibration absorbers (SAVA) for an interstate bridge. In: Proceedings, of 13th Annual International Bridge Conference, Pittsburgh, PA, June 3–5, 1996. Patten WN, Sack RL, He Q. Controlled semiactive hydraulic vibration absorber for bridges. J Struct Eng 1996;122(2):187–92.
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[40] Setareh M. Floor vibration control using semi-active tuned mass damper. Can J Civ Eng 2002;29:76–84. [41] Koo J-H, Ahmadian M, Setareh M. Experimental evaluation of magneto-rheological dampers for semiactive tuned vibration absorbers. In: Proceedings, SPIE— The International Society for Optical Engineering: Smart Structures and Materials 2003, Damping and Isolation, San Diego, CA, USA, vol. 5052, 2003. p. 83– 91. [42] Koo J-H, Ahmadian M, Setareh M, Murray TM. In search of suitable control methods for semi-active tuned vibration absorbers. J Vib Control 2004;10:163–74. [43] Hanagan LM, Murray TM, Premarante K. Controlling floor vibration with active and passive devices. Shock Vib Digest 2003;35(5). [44] Ungar EE, Kerwin Jr EM. Loss factors of viscoelastic systems in terms of strain energy. J Acoust Soc Am 1962;34(2):954–8. [45] Ungar EE. A guide to designing highly damped structures. Mach Des 1963;14:162–8. [46] Mantena PR, Gibson RF, Hwang SJ. Optimal constrained viscoelastic tape lengths for maximizing damping in laminated composites. AIAA J 1991;29(10):1678–85. [47] Mahmoodi P, Keel C. Performance of viscoelastic structural dampers for the Columbia center building. In: Proceedings of the Structures Congress. Seattle, WA: ASCE; 1986. p. 83–106. [48] Mahmoodi P, Robertson L, Yontar M, Moy C, Feld L. Performance of viscoelastic structural dampers in world trade center towers. In: Proceedings of the Structures Congress. Orlando, FL: ASCE; 1987.
[49] Aiken I, Kelly M, Mahmoodi P. The application of viscoelastic dampers to seismically resistant structures. In: Proceedings of the 4th US National Conference on Earthquake Engineering, Palm Springs, CA, vol. 3, 1990. p. 499–506. [50] Chang KC, Soong TT, Oh S-T, Lai ML. Effect of ambient temperature on viscoelastically damped structures. J Struct Eng, ASCE 1992;118(7):1955–73. [51] Lai ML, Chang KC, Soong TT, Hao DS, Yeh YC. Fullscale viscoelastically damped steel frames. J Struct Eng, ASCE 1995;121(10):1443–7. [52] Chen Y. Vibration characteristics and integral passive damping of composite isogrid structures. PhD dissertation, Wayne State University, 2000. [53] Chen Y, Gibson RF. Composite isogrid structures with integral passive damping. In: Proceedings Noise Control and Acoustics Division. ASME International Mechanical Engineering Congress and Exposition, Orlando, Florida, November 5–10, 2000, p. 425–33. [54] SIKA Systems, Strengthening of structures with carbon fiber reinforced polymer strips and steel plates. Sika Corporation, Lyndhurst, NJ, 1997. [55] Ebrahimpour A, Martell JL. Retrofitting floors with advanced materials to mitigate occupant-induced vibrations. In: Proceedings of the Structures Congress 2003. Seattle, Washington: ASCE; 2003. p. 29–31. [56] Martell JL. Experimental and analytical study on mitigating floor vibrations using advanced materials. Thesis presented to Idaho State University, Pocatello, ID, in partial fulfillment of the requirements for the degree of Master of Science, 2002.
A review of vibration serviceability criteria for floor structures Arya Ebrahimpour a
a,*
, Ronald L. Sack
b
College of Engineering, Idaho State University, Campus Box 8060, Pocatello, ID 83209, USA b Department of Civil and Environmental Engineering, University of Nevada Las Vegas, Las Vegas, NV 89154, USA Received 4 November 2003; accepted 17 March 2005 Available online 22 August 2005
Abstract This paper is a survey of the historical developments in modeling human dynamic loads, perception criteria used in structural floor vibrations, and the techniques used to mitigate the human-induced vibrations. Two of the techniques are explained in more detail, namely: semi-active control and passive control using advanced materials. Ó 2005 Elsevier Ltd. All rights reserved. Keywords: Dynamic loads; Vibrations; Floor systems; Perception criteria; Vibration control
1. Introduction Sports stadiums, discotheques, gymnasiums, aerobic dance studios, shopping malls, and airport terminal corridors are all subjected to significant dynamic loads produced by occupants either while remaining in one location or traversing the structure. Coherent crowd harmonic movements can produce resonant or near-resonant structural vibrations that are uncomfortable and intolerable for some occupants. Some structural failures, such as the Hyatt Regency Hotel in Kansas City [1], indicate that there can be many lives at stake when human loading is imposed. In addition, there have been serviceability problems that required costly remodeling or revision of building regulations.
At the present, US codes and standards are primarily concerned with avoiding structural failure (i.e., a strength requirement), and deal with excessive vibrations (i.e., a serviceability requirement) only to a limited degree [2,3]. Empirical serviceability requirements usually do not involve the frequency of the loading or the natural frequency of the structure. Many researchers believe these requirements are inadequate for controlling the human-induced vibrations. This paper provides a survey of the historical developments in modeling human dynamic loads, perception criteria used in structural vibrations, and various techniques that are used to mitigate the human-induced vibrations.
2. Human-induced dynamic loads * Corresponding author. Tel.: +1 208 282 4695; fax: +1 208 282 4538. E-mail address: [email protected] (A. Ebrahimpour).
Live loads are produced by the use and occupancy of a structure. Human loads comprise the large portion of the live loads in floors of offices and residential
0045-7949/$ - see front matter Ó 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.compstruc.2005.03.023
A. Ebrahimpour, R.L. Sack / Computers and Structures 83 (2005) 2488–2494
3. Human perception of structural vibrations The most frequently cited reference for human perception of vibration is by Reiher and Meister [13]. The Reiher–Meister scale is based on a displacement range of 0.01–10 mm and frequency range of 1–100 Hz. The modified Reiher–Meister scale was proposed by Lenzen [14] for vibrations due to walking impact. For floors with less than 5% critical damping, Lenzen suggested the original scale be applied if the displacement is increased by a factor of ten. Wiss and Parmelee [15] suggested that a constant product of frequency and displacement existed for a given combination of human response and damping. Allen and Rainer [16] developed vibration criteria in terms of acceleration and damping intended for quiet human occupancies such as residen-
tial buildings and offices. As damping increases, the steady-state response due to walking becomes a series of transient responses; resulting in a less significant response. Murray [17] suggested a human perception scale for required damping as a function of the product of initial displacement and frequency, which are the same parameters used in the Wiss–Parmelee scale. Allen et al. [18] suggested a design procedure for assembly floors subjected to rhythmic activities such as dancing and exercises. The International Standards Organization (ISO) [19] recommends vibration limits in terms of acceleration root-mean-squared (rms) and frequency. As shown in Fig. 1, a baseline curve is used by ISO and different multipliers are used for different occupancies. The vibration serviceability criteria for floors have been categorized into two broad categories. These are: criteria for steel beam and concrete slab construction, and wood/lightweight construction. The following sections describe the research in each category. 3.1. Criteria in steel beam and concrete slab construction Allen and Rainer [16] developed a vibration criterion for floors due to footstep loading which were based on tests on 42 long span floor systems. Ellingwood and Tallin [20] recommended a criterion for commercial floors. It is based upon a specified maximum deflection with a prescribed point load placed anywhere on the structure (i.e., a stiffness requirement). Updated guidelines for preventing annoying vibrations in steel framed floor systems are presented in a guide jointly published by the
25 Rhythmic Activities, Outdoor Footbridges
10 5
Peak Acceleration (%Gravity)
buildings. In assembly structures such as ballrooms, grandstands, health clubs, as well as pedestrian bridges, human-induced dynamic loads are the principal source of live loads. In general, the human live loads are classified into two broad categories: in situ and moving. Periodic jumping to music, sudden standing of a crowd, and random in-place movements are examples of in situ activities. Walking, marching, and running are examples of moving activities. Tilden [4] and Fuller [5] were among the first researchers to experimentally quantify the dynamic load effects of individuals and groups, respectively. Tilden considered both in situ and moving loads. Fuller attempted to experimentally quantify the crowd dynamic effect due to a group of people on a gymnasium balcony. Greimann and Klaiber [6] predicted the spectator dynamic loads on the Iowa Sate University stadium during a football game. Structural vibrations have been recorded as a result of spectator movements in rock concert in Canada [7]. Tuan and Saul [8] defined various types of in situ movements by measuring the load-time histories for individual subjects on a small piezoelectric force platform. Ebrahimpour and Sack [9] used a large instrumented force platform to measure in situ loads by individuals and groups of two and four people. In a subsequent study, Ebrahimpour and Sack [10] constructed a 3.7 m by 4.6 m floor system and measured forces of up to forty people performing in situ harmonic movements. They also recommended simple design values for coherent crowd harmonic movements. Only a very few studies of human moving loads have been reported. Canadian researchers measured dynamic forces of individuals and small groups of people [11]. Ebrahimpour et al. [12] measured the input forces imposed by moving groups of people using a set of instrumented platforms, mathematically modeled the loads, performed simulations, and suggested simple design loads for serviceability criteria.
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Indoor Footbridges, Shopping Malls, Dining & Dancing
2.5
1
Offices, Residences
0.5 0.25 ISO Baseline Curve For RMS Acceleration
0.1 0.05 1
3
4 5
8 10
25
40
Frequency, Hz Fig. 1. Peak accelerations for human comfort for vibrations due to human activities [19].
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American Institute of Steel Construction and the Canadian Institute of Steel Construction [21]. Criteria are provided both for walking and rhythmic excitations. In the walking criterion, the floor is acceptable if the peak acceleration, as determined by a simplified relation, does not exceed the ISO recommended acceleration limit. The rhythmic excitation design criterion is based on the natural frequency of the floor being larger than a minimum acceptable level. The minimum acceptable frequency level is a function of the ISO peak acceleration limit and the type of occupancy. 3.2. Criteria in wood/lightweight construction Research on human-induced vibration of lightweight wooden floors have been carried out by Smith and Chui [22], Ohlsson [23], Kalkert et al. [24], Foschi et al. [25], Dolan et al. [26], and Al-FoqahaÕa et al. [27]. Smith and Chui [22] developed methods for predicting dynamic behavior of lightweight wood floors. They recommended that root-mean-squared acceleration response of the floor under heel-drop impact be kept less than 0.45 m/ s2 and that floor natural frequency must be more than 8 Hz. The second requirement is to avoid the frequency band that humans are especially sensitive to (4–8 Hz). Ohlsson [23], presented a design approach for footstep loading in lightweight wood floors with frequencies higher than 8 Hz. For transient vibration, the method is based on determining the peak floor velocity response due to a unit impulse ((mm/s)/N s) and the product of damping coefficient and frequency. Both quantities are used to enter a vibration perception chart. Dolan et al. [26] proposed a stringent frequency requirement; they recommended that the floor fundamental frequency be greater than 15 Hz and 14 Hz for unoccupied and occupied floors, respectively.
4. Structural vibration control Vibration control may be achieved in several ways: passive, semi-active, and active. For a survey of structural control, with particular emphasis on mitigation of wind and seismic responses of buildings, see Housner et al. [28], Soong and Spencer [29], and Spencer and Nagarajaiaj [30]. The following sections describe vibration control, as applied to floor vibrations. 4.1. Tuned mass dampers A tuned mass damper (TMD) is one way of passively controlling the floor vibration. Lenzen [14] used a TMD to provide artificial damping in a floor to dampen the vibration in less than five cycles. The spring and dashpot unit had a frequency of about one cycle per second below the natural frequency of the floor and had a viscous
damping equivalent of 7.5%. Setareh and Hanson [31] provided both analytical study and experimental verification for selecting TMDs to decrease floor vibrations under rhythmic human activities. He presented a detail set of recommendations for design and placement of one or more TMDs. Several of these devices were installed in the balcony of a renovated historic theater in Detroit, Michigan. Several TMDs have been employed in BellagioÕs pedestrian bridges in Las Vegas [32]. It was anticipated that under certain conditions, such as festivals or large gatherings, excessive human-induced vibrations would be possible. Six TMDs, each weighing 1360 kg, were installed in each bridge. Tests on the bridges indicated that damping has been increased from 0.6% to more than 8%. Other successful applications of TMD systems have been recorded in real floors; for example, the cantilevered dance floors of the Terrace on the Park building in Flushing, NY [33,34]. TMD systems are typically effective over a narrow frequency band and must be tuned to a particular natural frequency. They are not effective if the structure has several closely spaced natural frequencies [34,35]. 4.2. Semi-active control During the 1980s, the auto industry researched, developed and tested various types of semi-active shock absorbers. That research produced a new type of control actuator that has applications in civil, mechanical, and aerospace engineering. These devices were developed in response to a need in the auto industry to provide improved ride comfort in vehicles. There are two broad classes of SA actuators: those that dissipate energy via damping and those that store energy by varying stiffness. There has also been an intensive effort since the mid 1980s to develop control systems for civil structures. The past effort has produced a range of designs that include fully active systems, entirely passive systems and designs that rely on a mix of those two (hybrid systems). Active control systems invariably require line power to achieve vibration mitigation. Passive designs require no power, and are usually less expensive than active designs, but are incapable of achieving the protection that an active system can provide. Spencer and Sain asserted that ‘‘Control strategies based on semi-active devices appear to combine the best features of both passive and active control systems and to offer the greatest likelihood for near-term acceptance of control technology as a viable means of protecting civil engineering structural systems. . .’’ [36]. Semi-active control systems provide a much needed technology between fully active structural control systems and passive designs. The term semi-active describes a system that consists of a variable actuator that requires very little power to operate. Both the semi-active (SA) hydraulic system and fully active (FA) hydraulic
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system designs include actuators, valving, etc. But the power required for the SA system is that necessary to modulate the valve position only. That power is typically many orders of magnitude less than that required to achieve a similar FA design. The utility of a SA design is realized when it is used to dissipate energy. Mitigating the motion of a structure during an earthquake, or attenuating the response of a beam due to dynamic loading are examples of applications where the motion of the structure can be harnessed to make a SA design functional. For these applications, analysis has shown that, if the hydraulic pump is removed from a FA hydraulic design, and the plumbing is altered, then the (now SA) system can provide attenuation that is equivalent to what would have been expected had the FA design been implemented. SA friction dampers, mounted as braces on a structure are examples of a SA control system. Hydraulic semi-active vibration dampers (SAHD), provide a combination of both damping and stiffness. Sack and Patten [37] conducted tests using a single-lane bridge 12.3 m in length that they subjected to vehicle loadings. They significantly reduced peak deflection by as much as 15% using feedback linearization to produce a suboptimal controller design. They also demonstrated the effectiveness of semi-active control on a full-scale experiment on an in-service bridge on interstate highway I-35 in Oklahoma. This application was the first full-scale implementation of semi-active control in the United States on a civil structure, and the results showed deflection reduction of more than 70% when compared to the vibration deflection of the bridge operated without dampers attached [38,39]. Setareh [40] and Koo et al. [41,42] proposed the use of a new class of semi-active tuned mass dampers, called ground-hook tuned mass dampers (GHTMD). Ground-hook control was initially introduced for vehicle application. Unlike the ‘‘skyhook’’ control that is designed to control the vibration of the sprung mass for the comfort of a rider, the ‘‘ground-hook’’ is intended to reduce the vibration of the unsprung mass (i.e., the tire and axle assembly). The ground-hook control is used for the stability of the vehicle. Because the structureÕs mass is similar to the unsprung mass of a vehicle, the ground-hook control is applicable in the control of structures attached to a TMD. Setareh obtained optimum design parameters for GHTMD in a floor structure, based on minimization of the acceleration response of the floor, mass ratios (damper to structure), and floor damping ratios. Koo et al. [42] suggested four control strategies for use in GHTMDs: two velocity-based and two displacement-based. In each case, two types of semi-active damping were considered: continuous and on-off. The study concluded that the on-off displacement-based control performs best in minimizing the structural vibrations.
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4.3. Active control Hanagan and Murray [33] and Hanagan et al. [43] developed an active electro-magnetic actuator that uses a piezoelectric velocity sensor and a feedback loop to generate control forces, thus adding damping to the supporting structure. Significant results were obtained on the office floor of a light manufacturing facility and a chemistry laboratory. High initial cost, maintenance, reliability, and the number of actuators needed to effectively reduce vibration levels were issues that were noted with this system. 4.4. Passive control using advanced materials 4.4.1. Damping in viscoelastic materials Ungar and Kerwin [44] and Ungar [45] used the concept of damping in viscoelastic materials in terms of strain energy and developed a model that expressed the overall damping in terms of the damping of individual layers. When viscoelastic material is added to a system, its influence on the overall system damping depends on how much strain energy is stored in the viscoelastic material under load. Therefore, the amount of damping material can be minimized by placing it where it will store the most strain energy [46]. Viscoelastic dampers have been used as vibration control to reduce wind-induced sway in tall buildings. They have been used in the World Trade Center Towers in New York City, Columbia SeaFirst building in Seattle, and Two Union Square building in Seattle, as documented by Mahmoodi and Keel [47] and Mahmoodi et al. [48]. Aiken et al. [49], Chang et al. [50], and Lai et al. [51] studied the feasibility of viscoelastic dampers in mitigating seismic responses of buildings. 4.4.2. Composites and viscoelastic materials The work in aerospace on dynamic behavior and damping in composite orthogrid and isogrid systems are closely related to the passive control of floor vibrations. Chen [52] and Chen and Gibson [53] investigated the damping properties of a composite isogrid panel with an embedded viscoelastic layer. Modal analysis showed that large shear deformation occurs in the region between the ribs and the face skin (i.e., the location of viscoelastic layer), which is caused by the mismatch in stiffness. Although not specifically used for vibration control, advanced composites such as carbon fiber reinforced polymer (CFRP) strips are used in civil engineering to strengthen existing structures [54]. These materials have high strength- and stiffness-to-weight ratios, are easily cut and fabricated on the job site, require no temporary bracings, and can conform to contours (even with obstacles present). Compared with steel, the installation and labor costs may offset the high material cost associated with advanced composites.
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Recently Ebrahimpour and Martell [55] retrofitted laboratory-constructed floors with laminates of carbon fiber reinforced polymer (CFRP) and constrained layers of viscoelastic material (see Fig. 2). The CFRP and viscoelastic retrofit uses high damping with some increase in stiffness to improve the vibration performance of the floor. In this study, the damping ratio of the floor increased from 2.4% to 11.7% (i.e., by 388%) with the addition of CFRP and viscoelastic layers. Fig. 3 shows a normalized deflection graph for the mass–drop test on an unmodified floor and a floor retrofitted with CFRP and viscoelastic materials (for comparison, maximum displacements are adjusted to one). Along with her experimental research, Martell [56] performed an analytical study of an indoor footbridge with a concrete deck and two steel beams. Fig. 4 shows the cross-section of the footbridge. The footbridge did not meet the recommended AISC vibration criterion [21]. A CFRP laminate (5 mm thick by 29 mm wide) and a constrained viscoelastic layer (7.6 mm thick by 29 mm wide) were attached to the bottom flange of each
Fig. 4. Footbridge cross-section.
Fig. 5. AISC recommended vibration criterion for the footbridge.
steel beam, along the entire span of the footbridge. As shown in Fig. 5, this retrofit decreased the peak acceleration and slightly increased the natural frequency of the structure, allowing it to meet the AISC recommended vibration serviceability criterion for an indoor footbridge. Fig. 2. Schematic of the experimental floor system and the data acquisition system.
Fig. 3. Laboratory floor mass–drop displacement responses.
5. Conclusions Coherent crowd harmonic movements may produce resonant or near-resonant structural vibrations that are uncomfortable and intolerable for some occupants. This paper presented a survey of the historical developments in modeling human dynamic loads, perception criteria used in structural floor vibrations, and the techniques used to mitigate the human-induced vibrations. Two of the techniques were explained in more detail, namely: semi-active control and passive control using advanced materials. Previous work on bridges establishes a reasonable basis by which a semi-active controller might be designed to provide vibration mitigation for vibration of building floor systems. The hardware, software, installation of the devices and selection of a controller design are dependent upon the structural system under consideration.
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Experience on full-scale bridges shows a deflection reduction of as much as 70% and significant acceleration reduction over the system with no controls. Passive control using CFRP laminate and constrained viscoelastic material seems appropriate for retrofitting floors with excessive vibrations. Laboratory and analytical results clearly indicate that occupantinduced vibration performance will be improved due to a significant increase in the overall structural damping and a slight increase in the stiffness.
[20] [21]
[22] [23]
[24]
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