THE BENEFITS OF USING VISCOUS DAMPERS IN A 42-STORY BUILDING

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1 THE BENEFITS OF USING VISCOUS DAMPERS IN A 42-STORY BUILDING Chukwuma G. Ekwueme, Gary C. Hart, Kingsley C. Ozegbe, Can Simsir, Weidlinger Associates, Inc. Gregg E. Brandow, Brandow and Johnston, Inc. ABSTRACT This paper describes a study that demonstrates how viscous damping devices can be used to improve the performance of tall buildings. The study uses a 42-story building that was developed as part of the Tall Buildings Initiative of the Pacific Earthquake Engineering Research (PEER) Center a case study. The original design consists of a dual system with special reinforced concrete moment-resisting frames and special reinforced concrete shear walls in the building core. A new structural design was developed that eliminated the core shear walls and utilized a viscous damping system to improve the building s performance. A preliminary design was developed using the ASCE 7 procedures for the systems with dampers and structural optimization using genetic algorithms was used to optimize the design. Then, time history analyses were used to compare the behavior of the modified building with dampers to the behavior of the original design for the service level earthquake. The study shows that optimization of the damping system leads to significant savings in the cost of the supplemental damping system. However, further refinement is needed to obtain a good correlation between the preliminary analyses using the response spectrum procedure and the results of the time history analyses. INTRODUCTION A case study building that was developed as part of the Pacific Earthquake Engineering Research (PEER) Center s Tall Building s Initiative was used to study the effectiveness of viscous damping devices in improving the seismic performance of tall buildings. The building is a 42-story building (with a penthouse) located in Los Angeles, California. There are four additional levels below grade. The lateral load resisting system consists of a dual system with two four-bay concrete special moment-resisting frames in each direction and special concrete shear walls in the building core. Figure 1 shows a threedimensional view of a computer model of the building developed using the structural analysis software ETABS (CSI, 21). Figure 2 shows a typical floor plan of the levels above grade. The building was designed to satisfy the requirements of the Los Angeles Tall Buildings Structural Design Council (LATBSDC) Criteria for alternative design of tall buildings (LATBSDC, 28). The criteria require tall buildings to provide serviceable behavior when subjected to frequent earthquakes and have a very low probability of collapse under extremely rare earthquakes. These performance criteria are

2 achieved by allowing only limited yielding of ductile elements when a building is subjected to a service level ground motion, which has a 5% probability of being exceeded in 3 years (43 year return period); and by ensuring that the deformation capacities of structural elements are not exceeded during the Maximum Considered Earthquake (MCE). Full details of the building and its design are contained in Ghodsi and Ruiz (21). Computer models of the original design, in both ETABS and PERFORM 3D (CSI, 27), were provided by the original designers of the building and these were modified to perform analyses of buildings without core shear walls and with dampers. Figure 1 Three Dimensional Rendering of Computer Model for PEER Case Study Building

3 FRAME A A N FRAME 2 PIER PIER 3 PIER PIER 2 PIER 3 PIER 1 FRAME B C C.5 D E FRAME F F Figure 2 Typical Floor Plan of 42-Story Building with Core Shear Walls BUILDING WITHOUT CORE SHEAR WALLS As a first step in evaluating the effectiveness of viscous dampers in improving the earthquake response of tall buildings, the PEER Case Study Building was modified by eliminating the core shear walls. A typical floor plan of the building without core shear walls is shown in Figure 3. Gravity loads in the core are supported by columns placed so that the access to the building core is not affected. The lateral load resisting system then consists only of two four-bay moment-resisting frames in each direction. As expected, the response of the building without core shear walls is significantly different than that of the original design. Table 1 shows the periods of the first three modes of vibration of both buildings. The building without core shear walls is significantly more flexible and the story drifts are larger as shown in Figures 4 (a) and (b) for the 43-year earthquake in the east west and north-south directions, respectively. Both buildings satisfy the LATBSD criterion that requires the maximum drift at the roof level to be less than.5 times the building height during the service level earthquake. However, for comparison purposes, viscous damping devices will be used to limit the maximum story drift ratio for the building without core shear walls to.3 for the 43-year earthquake. This will result in service level performance that is similar to the building with core shear walls from a drift control perspective.

4 FRAME A A N FRAME 2 FRAME B C C.5 D E FRAME F F Figure 3 Typical Floor Plan of 42-Story Building without Core Shear Walls Table 1 Periods of Vibration of 42-Story Building with and without Core Shear Walls Period (seconds) With Core Shear Walls Dominant Direction Period (seconds) Without Core Shear Walls Dominant Direction East-West Direction North-South Direction North-South Direction East-West Direction Torsion Torsion

5 With Core Shear Walls Without Core Walls 3 2 With Core Shear Walls Without Core Walls (a) East West Direction (b) North-South Direction Figure 4 Comparison of Maximum Story Drifts for 43-Year Earthquake for 42-Story Building with and without Core Shear Walls PRELIMINARY DESIGN OF BUILDINGS WITH VISCOUS DAMPING SYSTEMS USING ASCE 7-5 PROVISIONS ASCE 7-5 contains design requirements for the design of structures with supplemental damping systems (ASCE, 25). Three types of analysis are permitted: 1. Equivalent Lateral Force Static procedures 2. Response Spectrum Procedure 3. Nonlinear Procedures The equivalent lateral force and response spectrum procedures are based on an assumed ductility, at the maximum earthquake-induced displacement. The fundamental period of the structure, T 1, is modified to obtain the effective stiffness as follows: T T 1D 1 where T 1D is the effective fundamental period at the design displacement. The spectral acceleration and displacement for each mode (or for the first mode and residual modes when using the equivalent lateral force procedure) are then modified to account for the additional damping due to the supplemental damping devices. Figure 5 provides a conceptual illustration of the ASCE 7-5 provisions.

6 Base Shear Design Earthquake Demand (Inherent Damping Only) V = 1 C D V R Y V Y Initial Stiffness with Period T 1 Design Earthquake Demand ( Inherent+Viscous+Hysteretic Damping) Idealized Elasto-Plastic Pushover Curve Pushover Curve V 1 Effective Stiffness with Period T 1D D T 1D = = D T Y 2 1D 2 1 D Y D 1D Roof Displacement Figure 5 Conceptual Description of ASCE 7 Requirements for Structures with Damping Systems For damping systems with viscous damping devices, the viscous damping in the mth mode of vibration for a structure with j devices is given by: Vm j W mj 4W m (1) where W mj is the work done by the jth damping device in one complete cycle of response corresponding to the mth mode of vibration. For linear or nonlinear dampers, W mj is given by (Kargahi and Ekwueme, 28): W mj C jrj Tm (2) where C j is the damping constant, is velocity exponent and rj is the displacement across the device j. W m is the maximum strain energy in the mth mode of vibration at the modal displacements im and is given by: W 1 2 F m im im i (3)

7 Since the displacement is not known at the start of the analysis, and since the contribution of the supplemental damping system depends on the deformation of the structure, the ASCE procedure involves iteration. First, the value of total damping contributed by the supplemental damping devices is assumed. The deformation of the structure, which includes inter-story drifts and corresponding velocities, is computed using this selected value of damping. Then, the damping that corresponds to the deformation of the structure is calculated using Equation (1) and compared to the value of damping that was initially assumed. If the calculated damping is significantly different from the assumed damping, the assumed damping is modified and the process is repeated until the difference between the assumed and calculated damping is negligible. The iterative process is performed for each mode of vibration and to obtain the modal response. The ASCE provisions for buildings with damping systems do not permit the use of the equivalent lateral force procedure for buildings over 1 feet. The response spectrum procedure is permitted if at least two damping devices that are configured to resist torsion are utilized in each story and the total effective damping in the fundamental mode is less than 35 percent of critical. In this paper, the response spectrum procedure is used as part of an optimization process to develop a preliminary design of the damping system. The results of the response spectrum procedure will be verified by nonlinear time history analyses. OPTIMIZATION OF VISCOUS DAMPING SYSTEMS USING GENETIC ALGORITHMS Kargahi and Ekwueme (24) have previously used genetic algorithms for the optimization of viscous damping systems for the rehabilitation of concrete buildings using nonlinear static analyses. In this paper, the methodology is modified for use in the design of new buildings using the ASCE 7-5 provisions for damping systems. The optimization is particularly beneficial for tall buildings because the number of locations where dampers can be placed makes developing an efficient damper design extremely difficult. Using the 42-story building as an example, if four types of dampers are selected for use in the building and only one type of damper is used at each story, there are 42 4 or 3,111,696 unique combinations of damper system designs. The problem is further complicated by the fact that the cost of viscous dampers is related to damping force and stroke - response parameters are not known until after the structural analysis is complete. Thus, while engineers can usually develop a feel for what constitutes an effective design for smaller buildings quite quickly, selecting an efficient damper design for tall buildings is practically impossible without an optimization process of some sort. This study adapts structural optimization using genetic algorithms to develop efficient damper system designs for tall buildings. Unlike classic optimization approaches, optimizations with genetic algorithms are capable of solving large, complex and nonlinear problems that may have discontinuous objective functions and local minima. The method has its roots in the concepts of survival of the fittest and similar biological processes. The optimization starts with the mapping of a set of discrete design variables in a manner such that each unique design can be represented by a string of binary numbers. A number of strings are then randomly generated to represent a set of starting designs that form the initial population. The optimization then consists of repeating three basic procedures reproduction, crossover and mutation. Reproduction involves selecting the members of the population for mating based on fitness. A random selection is performed in which the probability of a design with a high fitness (which is a function of the total cost of the damping devices) has a greater probability of being selected for mating than one with a low fitness. Crossover involves an exchange of binary numbers between pairs of strings at locations above a randomly

8 selected point along the strings lengths. This process creates a new population that typically has a greater overall fitness than the preceding generation. Mutation involves randomly reversing the value in binary strings (from to 1 or vice versa) based on a pre-selected probability of mutation (typically less than 5%). This allows new genetic material to enter the population and improve fitness if certain characteristics dominate the population. The three basic procedures are repeated for a selected number of iterations. The fittest member of all generations is selected as the best design at the end of the optimization process. For the 42-story building, the design of damping system was optimized for the service level earthquake by determining the cheapest damper configuration that limits the maximum story drift to.3 in/in for the 43-year earthquake. Since damping force is a good measure of the cost of viscous damping devices, fitness was based on the inverse of the sum of damping forces in all devices. A fitness penalty was applied if a design did not satisfy the design criteria so that the fitness, f is given by: f j 1 F cj p (4) where F cj is the maximum damping force in device j and p is the penalty which is equal to: i p 1. ;.3 hi max i p.1 ;.3 hi max (5) Since the building is expected to be at or close to yield during the serviceability level earthquake, the system ductility,, for the calculations using the ASCE 7-5 procedures for damping systems was set to 1.. Ground motion parameters were selected so that the spectral values for the equivalent ASCE 7-5 spectrum were close to the spectral site specific response spectrum for the 43-year earthquake as shown in Figure 6. To verify accuracy of the ASCE 7-5 damping calculations, the results of the ETABS response spectrum analysis of the entire structure without core shear walls were compared to results of the ASCE 7-5 procedure for the same building. The first five modes in either direction were used and the contribution of supplemental devices to the total building damping was set to zero. Figures 7(a) and 7(b) show the comparison of the two analysis methods in the east-west and north-south directions, respectively. This figures indicates that the ASCE 7-5 procedures yield reasonably accurate results for the service level earthquake.

9 Spectral Acceleration (g) Year, Site-Specific Equivalent ASCE 7 Spectrum Period (Seconds) Figure 6 Site Specific Response Spectrum and Equivalent ASCE 7 Spectrum for 43-year Earthquake (2.5% Damping) ETABS ASCE ETABS ASCE (a) East West Direction (b) North-South Direction Figure 7 Comparison of Maximum Story Drifts for 43-Year Earthquake for 42-Story Building without Core Shear Walls or Dampers

10 After it had been determined that the ASCE 7 damping procedures provide good estimates of building response, the optimization of the damping system was performed for a selected properties of viscous damping devices. For each of the 42 stories of the building, the maximum story damping force, F ci is given by: F ci Cv i where C is the damping coefficient, is the velocity exponent and v i is the maximum story velocity. Linear dampers with a velocity exponent of 1. were used and possible values of, 5, 15 and 3 kipsec/in were selected for the damping coefficient at each story. Figures 8(a) and 8(b) show the results of the optimization in the east-west and north-south directions, respectively. When compared to values of damping coefficient used over the height of the building to satisfy the story drift limit of.3, there are savings of about 3% in the east-west direction and 22% in north-south direction Fitness 35 3 C= 1 All Floors 25 Average of Population Best of Population Number of Iterations Figure 8(a) Optimization of Damping System Design in East-West Direction

11 Fitness C= 17 All Floors Average of Population Best of Population Number of Iterations Figure 8(b) Optimization of Damping System Design in North-South Direction RESPONSE OF BUILDING WITHOUT CORE SHEAR WALLS AND WITH VISCOUS DAMPING DEVICES Figure 9 shows a typical floor plan of the 42-story building with building designed with viscous damping devices to account for the elimination of core shear walls. The damping devices are placed so that there is no change to the architectural functionality of the building core when compared to the building with core shear walls. Figures 1(a) and 1(b) show a comparison of story drift ratios, obtained using ASCE 7 procedure, in the east-west and north south directions, respectively. As intended, the maximum story drift ratio is limited to.3 in/in. Nonlinear time history analyses were then performed using PERFORM 3D to verify the accuracy of the response spectrum analysis procedures for dampers. Figure 11 compares the response spectra of the two horizontal components of the selected ground motion acceleration time history to the site-specific spectrum of the 43-year earthquake. Figure 12 compares story drift ratios calculated with the time history analysis to those obtained from the ASCE 7 procedures for the building without core walls and without dampers. The figures show that the ASCE 7 response spectrum procedure provides reasonable estimates of story drift. However, the distribution of drift over the height of the building is different from that obtained from time history analyses. In the east west direction, the ASCE 7 procedure underestimates the story drift at several floors. The time history analyses of the building with dampers did not show good correlation with the ASCE 7 procedures for structures with damping systems, with significantly less reduction in response than was predicted by the response spectrum procedure. This could be partly due to the fact that response spectrum procedure is based on deformations that are slightly different from those determined from time history analyses, as indicated Figure 12. In addition, the mode shapes used for the response spectrum procedure consider the entire story drift (and corresponding velocities) when computing the forces in the damping devices. The story drift for each story consists of racking, or shear, deformation and rigid body rotation due to the displacement of the floors below the story. Since the damping devices are only impacted by the racking deformation of each story, the ASCE 7 procedures would overestimate the effect of dampers

12 if the entire story drift is used. The impact rigid story rotation is greater for buildings with only shear walls than for buildings with moment frames such as the case-study building being considered. However, for tall buildings, the effect of story rotation accumulates over a large number of stories and may have a larger impact than expected. Figure 13 shows the results of the time history analyses of the 42-story building with and without damping devices, with the damping coefficients increased by a factor of 5 so that an appreciable reduction in response is achieved. The figure shows that the damping devices reduce the story drifts significantly, except at the upper stories of the building. Figure 14 shows that the damping devices reduce the roof accelerations considerably, in spite of the fact that story drifts in the upper stories are not reduced FRAME A A N FRAME 2 Typical Damper Location FRAME B C C.5 D E FRAME F F Figure 9 Typical Floor Plan of 42-Story Building with Viscous Damping Devices

13 With Core Walls Without Core Walls (No Dampers) Without Core Walls (Optimized Dampers) Figure 1(a) Story Drift Ratios in the East-West Direction during the 43-Year Earthquake from the ASCE 7 Damping Procedure With Core Walls Without Core Walls (No Dampers) Without Core Walls (Optimized Dampers) Figure 1(b) Story Drift Ratios in the North-South Direction during the 43-Year Earthquake from the ASCE 7 Damping Procedure

14 Year Target Spectrum (2.5% Damping) Set3 H1 Set3 H2 Spectral Acceleration (g) Period (sec) ASCE 7 (Response Specrum) PERFORM (Time History) 3 2 ASCE 7 (Response Spectrum) PERFORM (Time History) (a) East West Direction (b) North-South Direction Figure 12 Comparison of Maximum Story Drifts for 43-Year Earthquake Obtained from ASCE 7 Response Spectrum Procedure and Time History Analyses for Building No Core Walls and No Dampers

15 No Core Walls, No Dampers No Core Walls, Optimized Dampers 3 2 No Core Walls, No Dampers No Core Walls, Optimized Dampers (a) East West Direction (b) North-South Direction Figure 13 Comparison of Maximum Story Drifts for 43-Year Earthquake Obtained from Time History Analyses for Building with and without Dampers No Core Walls, No Dampers No Core Walls, Optimized Dampers Acceleration (g) Time (sec) Figure 14 Comparison of Acceleration at Level 43 for Building with and without Dampers

16 CONCLUSIONS The analyses of the PEER case study building shows that dampers can be effective in improving the response of tall buildings at the service level earthquake. Significant reduction in story drifts and floor accelerations can be achieved. This would result in less damage to drift sensitive non-structural components such as cladding and partitions, and less damage to acceleration-sensitive components such as ceilings, elevators and building contents. The efficiency of damping systems is improved considerably by the use of the optimization procedure. Based on the amount of damping force, the cost of the damping system may be reduced by up to 3% as a result of the optimization when using the ASCE 7 procedures for the design of structures with damping systems. However, more work needs to be done to achieve good correlation between the results of the ASCE 7 procedures and nonlinear time history analyses. One improvement would be to incorporate the effect of rigid story rotation on the effectiveness of the dampers, an approach that was not incorporated in this study. This is because while the impact of rigid story rotation is not significant in shorter buildings, it may be substantial in tall buildings. Additional work that will need to be studied includes verifying the effectiveness of the damping systems during the Maximum Considered Earthquake, when significant yielding is expected to occur in elements of the lateral load resisting system. Additional time history analyses will need to be performed and the optimization will need to be based not only on maximum drifts, but also by checking that building elements are in compliance with the acceptance criteria. ACKNOWLEDGEMENT This work was funded in part by Taylor Damping Devices and therefore we wish to express our appreciation to Mr. Doug Taylor and Mr. David Lee. REFERENCES American Society of Civil Engineers (ASCE), 25, Minimum Design Loads for Buildings and Other Structures, ASCE/SEI 7-5, American Society of Civil Engineers, Reston, Virginia. CSI (Computers and Structures, Inc.), 29, ETABS Version 9.6., Extended 3D Analysis of Building Systems, Computers and Structures, Inc, Berkeley, California. CSI (Computers and Structures, Inc.), 21, PERFORM 3D Version 4..3, Nonlinear Analysis and Performance Assessment of 3D Structures, Computers and Structures, Inc, Berkeley, California. Ghodsi, T. and Flores Ruiz, J.A., 21, Pacific Earthquake Engineering Research/Seismic Safety Commission Tall Building Design Case Study 2, The Structural Design of Tall And Special Buildings, Vol. 19, P , John Wiley & Sons, Ltd. Kargahi, M. and Ekwueme, C.G., 24, Optimization of Viscous Damper Properties for Reduction of Seismic Risk in Concrete Buildings, 13th World Conference on Earthquake Engineering, Paper No. 127, Vancouver, B.C., Canada, August 1-6.

17 Los Angeles Tall Buildings Structural Design Council (LATBSDC), 28, An Alternative Procedure for Seismic Analysis and Design of Tall Buildings Located in the Los Angeles Region, Los Angeles Tall Buildings Structural Design Council, Los Angeles, California.

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