Validation of the 2000 NEHRP Provisions Equivalent Lateral Force and Modal Analysis Procedures for Buildings with Damping Systems

Transcription

1 Validation of the Equivalent Lateral Force and Modal Analysis Procedures for Buildings with Damping Systems Oscar M. Ramirez, a) Michael C. Constantinou, b) M.EERI, Andrew S. Whittaker, c) M.EERI, Charles A. Kircher, d) M.EERI, Martin W. Johnson, e) M.EERI, and Christis Z. Chrysostomou f) Equivalent lateral and modal analysis procedures for yielding buildings with damping systems were developed, validated, and incorporated in the. Key to the implementation of the procedures was the validation process that demonstrated the accuracy of the proposed procedures. The procedures for implementing yielding, viscoelastic, linear viscous, and nonlinear viscous dampers were tested using the results of nonlinear response-history analysis on sample three- and six-story frames and were found to be robust. [DOI: / ] INTRODUCTION The 2000 edition of the NEHRP Recommended Provisions for Seismic Regulations for New Buildings and Other Structures (BSSC 2001), hereafter referred to as the 2000 NEHRP Provisions, includes newly developed linear procedures for implementing passive energy dissipation devices in new buildings. Two types of linear procedures are presented: equivalent lateral (ELF) and modal or response-spectrum analysis (RSA). The development and validation of the analysis methods for buildings with damping systems have been the result of the collective efforts of members of Technical Subcommittee 12 of the Building Seismic Safety Council and researchers at the University at Buffalo. These efforts are described in Ramirez et al. (2000). The companion paper by Whittaker et al. (2003) [this issue, see pages ] describes the evolution of analysis/design procedures for buildings with damping systems, establishes the need for the simplified procedures of the, presents in part the equivalent a) Professor and Director, Centro Experimental de Ingeniera, Universidad Tecnologica de Panama, Panama, Rep. de Panama b) Professor and Chairman, Department of Civil, Structural and Environmental Engineering, University at Buffalo, State University of New York, Buffalo, NY c) Associate Professor, Department of Civil, Structural and Environmental Engineering, University at Buffalo, State University of New York, Buffalo, NY d) Principal, Kircher & Associates, 1121 San Antonio Rd., Suite D-202, Palo Alto, CA e) Principal, ABS Consulting, 300 Commerce Dr., Suite 200, Irvine, CA f) Lecturer, Department of Civil Engineering, Higher Technical Institute, 2152 Nicosia, Cyprus 981 Earthquake Spectra, Volume 19, No. 4, pages , November 2003; 2003, Earthquake Engineering Research Institute

2 982 O. M. RAMIREZ ET AL. lateral and the response-spectrum analysis procedures of the and describes the application of these procedures for linear viscous, nonlinear viscous, viscoelastic and hysteretic damping systems. This paper presents some of the validation studies of the procedures for buildings with damping systems. The accuracy of the analysis procedures is investigated by comparison with the results of nonlinear response-history analysis. Complete information on the validation studies are presented in Ramirez et al. (2000). The simplified analyses were performed using the ELF and RSA methods except as modified below: 1. In the application of the, the load combination factors CF 1 and CF 2 described in Ramirez et al. (2000) were used instead of either of the corresponding factors in ATC (1997) or the coefficients C mfd and C mfv presented in the. This modification is of minor significance in the application of the methods of analysis and was made for convenience because it was easier to utilize equations rather than tables when performing spreadsheet analysis. 2. In the application of the methods of analysis, the procedures described in the companion paper by Whittaker et al. (2003) for the calculation of the effective damping, the effective period and the added strength and stiffness were followed. The procedures described in the are valid for linear viscous damping systems and for viscoelastic and yielding damping systems but are only approximate for nonlinear viscous damping systems. 3. The correction factors presented by Ramirez et al. (2000) were used in selected examples to demonstrate the significance of the correction procedure for multi-degree-of-freedom systems. Such factors are not presented in either the or FEMA-274 (ATC 1997). One goal of the studies described in both this paper and Ramirez et al. (2000) was to determine whether building frames equipped with dampers could be designed for lower base shear strengths than undamped building frames but achieve similar levels of performance, measured herein using displacements and plastic hinge rotations. The examples presented below involve three- and six-story special steel moment-resisting frame buildings with linear viscous, nonlinear viscous, viscoelastic, and yielding damping systems installed in diagonal or chevron brace configurations. To study the performance of damped building frames with smaller base shear strengths than that required for undamped special moment-resisting frames, termed V in the 1997 NEHRP Provisions (BSSC 1998), the example frames were designed for a base shear strength in the range of 0.6V to V. The seismic performance of the undamped and damped building frames was studied using nonlinear response-history analysis. Twenty scaled earthquake histories that matched on average a response spectrum with parameters S DS 1.0, S D1 0.6 and T s 0.6 second were used for the analysis. No near-field or soft-

3 VALIDATION OF SIMPLIFIED ANALYSIS PROCEDURES FOR DAMPED BUILDINGS 983 Figure 1. Reference frame details. soil histories were included in the set of 20 histories. Ramirez et al. (2000) provides complete information on the histories and scaling procedures used for the analytical studies. REFERENCE AND DAMPED FRAME ANALYSIS AND DESIGN REFERENCE THREE- AND SIX-STORY FRAMES Because the vast majority of buildings in the United States are less than six stories in height, three- and six-story frames were selected as reference frames. The reference frames are special steel moment-resisting frames without damping systems. Two perimeter frames are placed along each axis of each building. The buildings are regular in configuration with plan dimensions of m by m. The assumed occupancy is office space. The three-story building is m in height and the six-story building is m in height. The reactive weights at each floor level of each building are shown in Figures 1a and 1b. These weights were held constant for all of the damped frames although some minor reduction in reactive weight was achieved with the use of smaller section sizes in the damped frames. The reference (undamped) frames were designed to meet the minimum base shear and maximum limits (0.02 times the story height) of Section 5.3 of the 1997 NEHRP Provisions. For special steel moment-resisting frames, the 1997 NEHRP Provisions assign values of 8 to the response modification factor and 5.5 to the deflection amplification factor. The resulting section sizes for the two reference frames are shown in Figures 1a (three-story) and 1b (six-story). One column size was adopted for the threestory frame. Column sizes were changed every second story in the six-story frame. The nominal yield strength of all steel was assumed to be 345 MPa. Torsional effects were not considered in the analysis and design of the reference frames.

4 984 O. M. RAMIREZ ET AL. For the three-story frame, the weight of structural steel is 215 kn and the fundamental period is 1.07 second as determined by eigenvalue analysis using IDARC2D (Valles et al. 1996). Nonlinear static analysis of the frame predicts a maximum strength of between 2223 and 2775 kn depending on the lateral distribution used for the analysis: strengths between 1.37 and 1.70 times the minimum strength required by the 1997 NEHRP Provisions. This substantial increase in strength is associated with having to satisfy of limit of 2% of the story height under the design lateral s. For the six-story frame, the weight of structural steel is 504 kn and the fundamental period is 1.90 second. Nonlinear static analysis of the frame predicts a maximum strength of between 2748 and 3646 kn depending on the lateral distribution used for the analysis: strengths between 1.30 and 1.73 times the minimum strength required by the 1997 NEHRP Provisions. THREE-STORY AND SIX-STORY FRAMES WITH DAMPING SYSTEMS Building frames with damping systems may be designed in accordance with the for a base shear of not less than 0.75V, where V is the base shear for the building frame without a damping system. The frames shown in Figures 1a and 1b were redesigned to have base shear strength in the range of 0.6V to V, which resulted in different member sections. Damping systems were then added to these frames and proportioned in accordance with the to meet the criteria. Six frames were designed: five three-story frames with approximate base shear strengths of 0.60V, 0.75V, 0.80V, 0.9V, and V, and one six-story frame with a base shear strength of approximately 0.75V. These frames were termed 3S-60, 3S-75, 3S-80, 3S-90, 3S-100, and 6S-75, respectively. Table 1 summarizes the characteristics of these six frames. Listed in the table are (a) the ratio of the strength of the frame to that of the corresponding reference frame as determined by simple plastic analysis assuming beam-sway mechanisms (see Ramirez et al. for details), (b) the ratio of the weight of the steel sections in the frame to that of the corresponding reference frame, and (c) the ratio of the fundamental period of the frame to that of the corresponding reference frame. The data of Table 1 show that the base shear strengths of the frames with damping systems are substantially lower than the base shear strengths of the reference frames that were designed to meet the criteria of the 1997 NEHRP Provisions. A total of nine examples utilizing the six frames of Table 1 were analyzed. The frames with the damping systems in these examples are described in Table 2 and illustrated in Figures 2 and 3. Detailed calculations are presented in Ramirez et al. (2000). NONLINEAR RESPONSE HISTORY ANALYSIS was performed using IDARC2D (Valles et al. 1996), a program with elements for modeling damping devices. Complete details of the models used for the analysis are presented in Ramirez et al. (2000). The nine example frames listed in Table 2 were analyzed as follows. Example frames 1, 2, 3, 5, 6, 8, and 9 were analyzed for both the design-basis earthquake (DBE) and the maximum considered earthquake (MCE). The DBE set of earthquake histories consisted of the 20-scaled mo-

5 VALIDATION OF SIMPLIFIED ANALYSIS PROCEDURES FOR DAMPED BUILDINGS 985 Table 1. Characteristics of example frames exclusive of the damping systems Frame Strength ratio Weight ratio Period ratio 3S S S S S S tions noted above and described in Ramirez et al. (2000) and in the companion paper by Whittaker et al. (2003). The amplitudes of the DBE acceleration histories were multiplied by 1.5 to establish the MCE histories: the inverse of the process adopted in the to generate a DBE spectrum from an MCE spectrum. Peak response quantities were obtained for each history and values are presented in the tables below for minimum, maximum, mean ( ), and 1 responses. Example frames 2 and 4 were analyzed to assess the degree of inelastic action in frames with and without damping systems. Frame 7 was analyzed for MCE shaking only. Table 2. Properties of the example frames Example Frame Frame Damping System 1 EVD 2 Properties 3 1 3S-60 LV 10% C 0.8 kn-s/mm all stories 2 3S-75 LV 10% C 0.9 kn-s/mm all stories 3 3S-90 LV 10% C 1.0 kn-s/mm all stories 4 3S-100 LV 20% C 2.14 kn-s/mm all stories 5 6S-75 LV 10% See Figure 3e for details 6 3S-80 NLV 10% C 14.5 kn-(s/mm) 0.5 all stories 7 3S-80 NLV 20% C 32 kn-(s/mm) 0.5 all stories 8 3S-75 VES 8.5% 3M ISD110; A mm 2, h 140 mm 9 3S-75 TMY - b 305 mm, h 457 mm, t 25 mm, F y 248 MPa 1. LV linear viscous; NLV nonlinear viscous with a exponent of 0.5; VES viscoelastic solid; TMY triangular metallic yielding. 2. EVD equivalent viscous damping ratio; damping ratio calculated assuming elastic response 3. See Ramirez et al. (2000) for complete details.

6 986 O. M. RAMIREZ ET AL. Figure 2. Details of example frames 1 through 5 (all braces TS 8 8). PRESENTATION AND INTERPRETATION OF RESULTS ACCURACY OF THE SIMPLIFIED NEHRP PROCEDURES data are presented for representative cases in Tables 3 through 15. Complete details are presented in Ramirez et al. (2000). Included in the tables are (a) peak interstory s, (b) peak interstory velocities (for the viscous dampers only), (c) peak

7 VALIDATION OF SIMPLIFIED ANALYSIS PROCEDURES FOR DAMPED BUILDINGS 987 Figure 3. Details of example frames 6 through 9 (all braces TS 8 8). damper s, (d) story shear s at the time of maximum, and (e) maximum story shears (that include including the viscous as appropriate). Data are presented for the equivalent lateral (ELF) and response-spectrum analysis (RSA) methods of the and for the nonlinear response-history analysis. Included in the presentation of the ELF and RSA results are data for two characterizations of the higher-mode periods, namely, T m and T m, where T m is the period in mode m from eigenvalue analysis (taken as the residual mode period for the ELF) and is the ductility demand calculated from the analysis of the first mode response. Evaluation of the data presented in Tables 3 through 15 led the authors to the following conclusions: 1. The ELF method tends to overestimate and underestimate the damper s and frame-member actions in the lowest and upper stories, respectively. These differences are caused primarily by the contribution of the residual mode to the total response. The residual mode shape has a substantial component associated with the displacements of the lower floors of the building and resembles the second mode of vibration but with substantially larger modal displacements in the lower floors and a larger modal weight.

8 988 O. M. RAMIREZ ET AL. Table 3. DBE analysis of Example Frame 1 (3S-60) with a linear viscous damping system shear at max. disp. 1,2 Nonlinear responsehistory analysis , , , , , , , , , , , , , , , , , , , , , , , , Max. story 3 572, , , , shear 2 938, , , , , , , , Values in bold are results using the revised correction factors of Ramirez et al. (2000) 2. The use of T m instead of T m for calculating higher-mode response contributions produces marginally improved predictions of total response compared with the average results of the nonlinear response-history analysis. 3. The two simplified procedures generally predict conservative estimates of story that fall consistently between the and 1 results of the nonlinear response-history analysis. 4. The use of pseudo- correction factors of Ramirez et al. (2000) improves the predictions of interstory and damper s as can be seen in Tables 3 and 4. Although the improvement is not significant, the correction is simple to implement and as such its use is warranted. 5. The accuracy of the predictions of key design parameters such as the peak damper and the maximum base shear by the two simplified methods varies considerably among the selected examples. Table 16 summarizes these predictions for MCE shaking. However, the results of the simplified analyses are generally within 30% of the average of the results of nonlinear response-history analysis and as such are acceptable for simplified methods of analysis. The pre-

9 VALIDATION OF SIMPLIFIED ANALYSIS PROCEDURES FOR DAMPED BUILDINGS 989 Table 4. MCE analysis of Example Frame 1 (3S-60) with a linear viscous damping system shear at max. disp. 1,2. Nonlinear responsehistory analysis ELF RSA ELF RSA Min. 1 Max , , , , , , , , , , , , , , , , , , , , , , , , Max. story 3 729, , , , shear , , , , , , , , Values in bold are results using the revised correction factors of Ramirez et al. (2000) dicted responses of the simplified methods deviate most from the average results of the nonlinear response-history analysis for the six-story momentresisting frame. EXTENT AND PATTERNS OF DAMAGE The allow the strength of a building frame to be reduced substantially below that of an undamped frame if damping systems are added to the frame. Compare the reference frame of Figure 1a (without damping devices) to the damped frame of Figure 2a (with a linear viscous damping system). These two frames meet the criteria of both the 1997 NEHRP Provisions and the. As noted in Table 1, the frame with the damping system (3S-75) has a base shear strength (calculated by plastic analysis using a pattern of lateral loads proportional to the first mode shape) that is 55% of that of the frame without the damping system. The pattern of plastic hinge formation and some key response quantities were investigated in (a) the three-story reference frame of Figure 1a, (b) the three-story, 3S-75 frame with linear viscous damping system (Example Frame 2, Figure 2b), and (c) the three-story, 3S-100 frame with linear viscous damping system (Example Frame 4, Figure 2d). Note that 3S-75 just meets the criteria of the

10 990 O. M. RAMIREZ ET AL. Table 5. DBE analysis of Example Frame 2 (3S-75) with a linear viscous damping system shear at max. disp Max. story shear whereas case 3S-100 is a stronger and highly damped frame: a frame that is more representative of a design for substantial improvement of performance. The three frames were analyzed using the scaled Northridge Century earthquake history that is described in Ramirez et al. (2000): a DBE-type history that produced responses in the frames that were similar to the average responses calculated using the 20 scaled motions described above. Analyses were performed for this DBE history and an MCE history, which was the DBE history scaled in amplitude by a factor of 1.5. Figures 4 through 6 below present the results of these analyses. Each figure identifies the seismic excitation (DBE or MCE), presents key response quantities such as maximum interstory ratios, roof displacements, base shear s (including the damping component) and plastic hinge rotations, and the location and sequence of the formation of plastic hinges. Comparing the performance of the frames in both the DBE and MCE shaking: 1. The maximum DBE for the reference frame equals 0.028, which exceeds the NEHRP Provisions limit of This is not surprising because the NEHRP Provisions consistently underestimate the maximum inelastic by the ratio of R/C d, which is equal to 1.46 ( 8/5.5). If the limit of 0.02 is factored up by 1.46, the resulting ratio is and quite similar to the calculated maximum of

11 VALIDATION OF SIMPLIFIED ANALYSIS PROCEDURES FOR DAMPED BUILDINGS 991 Table 6. MCE analysis of Example Frame 2 (3S-75) with a linear viscous damping system shear at max. disp Max. story shear Frame 3S-75 (Figure 5) that just meets the criteria of the NEHRP Provisions exhibits smaller s, smaller plastic hinge rotations and substantially smaller base shear s than the undamped reference frame. 3. The maximum DBE and MCE roof displacements in the highly damped Frame 3S-100 (Figure 6) are substantially smaller than those in lightly damped 3S-75. However the performance of 3S-100 as measured in terms of ratios, maximum plastic hinge rotations and maximum base shear s is only marginally better than that of 3S Moment-frame buildings designed with damping systems to meet the minimum criteria of the perform comparably to or better than buildings designed without damping systems to meet the minimum strength and criteria of the 1997 NEHRP Provisions. Moreover, buildings with damping systems offer the distinct advantage of lower base shear s than conventional buildings without damping systems for similar levels of performance. CONCLUSIONS Moment-frame buildings with and without damping systems were analyzed and designed using the simplified ELF and RSA procedures of the. The resultant designs were evaluated by response-history analysis with twenty scaled

12 992 O. M. RAMIREZ ET AL. Table 7. DBE analysis of Example Frame 5 (6S-75) with a linear viscous damping system Max. story shear earthquake histories that matched on average a response spectrum with parameters S DS 1.0, S D1 0.6 and T s 0.6 second were used for the analysis. No near-field or soft-soil histories were included in the set of 20 histories. As such, the results of the study are strictly only valid for moment-frame buildings on rock and firmsoil sites. The two simplified methods of the were validated by the studies reported in this paper and in Ramirez et al. (2000). The simplified methods produced estimates of peak displacements, peak velocities, and peak accelerations (including the viscous component) that were in good overall agreement with the average of results of nonlinear response-history analysis. Although the simplified methods are not

13 VALIDATION OF SIMPLIFIED ANALYSIS PROCEDURES FOR DAMPED BUILDINGS 993 Table 8. MCE analysis of Example Frame 5 (6S-75) with a linear viscous damping system Max. story shear error free, they are simple to apply, converge systematically and produce results of sufficient accuracy for the purpose of design. The greatest differences occurred in the analysis of the three-story frame. Moment-frame buildings on rock or stiff soil sites with damping systems designed to meet the minimum strength and criteria of the performed comparably to, or better than, conventional buildings without damping systems. Buildings with damping systems can be designed for a lower base shear than conventional buildings without damping systems for similar performance. Although the minimum design base shear for a damped building is 75% of that of the corresponding conventionally framed building, the analysis results presented in this paper suggest that the minimum percentage could be lowered further.

14 994 O. M. RAMIREZ ET AL. Table 9. DBE analysis of Example Frame 6 (3S-80) with a nonlinear viscous damping system 1 shear at max. disp. Max. story shear Table 10. MCE analysis of Example Frame 6 (3S-80) with a nonlinear viscous damping system 1 shear at max. disp. Max. story shear

15 VALIDATION OF SIMPLIFIED ANALYSIS PROCEDURES FOR DAMPED BUILDINGS 995 Table 11. MCE analysis of Example Frame 7 (3S-80) with a nonlinear viscous damping system N 1 shear at max. disp. Max. story shear Table 12. DBE analysis of Example Frame 8 (3S-75) with a viscoelastic damping system 1 shear at max. disp. Max. story shear

16 996 O. M. RAMIREZ ET AL. Table 13. MCE analysis of Example Frame 8 (3S-75) with a viscoelastic damping system shear at max. disp Max. story shear Table 14. DBE analysis of Example Frame 9 (3S-75) with a yielding damping system Max. story shear

17 VALIDATION OF SIMPLIFIED ANALYSIS PROCEDURES FOR DAMPED BUILDINGS 997 Table 15. MCE analysis of Example Frame 9 (3S-75) with a metallic yielding damping system Max. story shear Table 16. Summary of key analysis results Frame Example Frame 2 Example Frame 5 2 Example Frame 6 Method 1 ELF RSA NRHA ELF RSA NRHA ELF RSA NRHA quantity quantity Drift (mm) Force Base Shear Frame Example Frame 8 Example Frame 9 Method ELF RSA NRHA ELF RSA NRHA Drift (mm) Force Base Shear Not applicable ELF equivalent lateral ; RSA response-spectrum analysis; NRHA nonlinear response history analysis 2. Three sets of results presented for the six-story frame because damper sizes changed every two stories.

18 998 O. M. RAMIREZ ET AL. Figure 4. DBE and MCE response of reference three-story frame. Figure 5. DBE and MCE response of Frame 3S-75. Figure 6. DBE and MCE response of Frame 3S-100.

19 VALIDATION OF SIMPLIFIED ANALYSIS PROCEDURES FOR DAMPED BUILDINGS 999 ACKNOWLEDGMENTS Financial support for this project was provided by the Multidisciplinary Center for Earthquake Engineering Research, Task on Rehabilitation Strategies for Buildings (Projects No , No , No , and No c). The work was performed under the direction of Technical Subcommittee 12, Base Isolation and Energy Dissipation, of the Building Seismic Safety Council, which was tasked with developing analysis and design procedures for inclusion in the 2000 NEHRP Recommended Provisions for Seismic Regulations for New Buildings and Other Structures. The work of Technical Subcommittee 12 was supported by the Federal Emergency Management Agency. REFERENCES Applied Technology Council (ATC), NEHRP Guidelines for the Seismic Rehabilitation of Buildings and NEHRP Commentary on the Guidelines for the Seismic Rehabilitation of Buildings, 1997 Edition, Report Nos. FEMA-273 and FEMA-274, prepared for and published by the Federal Emergency Management Agency, Washington, D.C. Building Seismic Safety Council (BSSC), NEHRP Recommended Provisions for Seismic Regulations for New Buildings and Other Structures, 1997 Edition, Part 1 Provisions, Part 2 Commentary, Report Nos. FEMA-302 and FEMA-303, prepared for and published by the Federal Emergency Management Agency, Washington, D.C. Building Seismic Safety Council (BSSC), NEHRP Recommended Provisions for Seismic Regulations for New Buildings and Other Structures, 2000 Edition, Part 1 Provisions, Part 2 Commentary, Report Nos. FEMA-368 and FEMA-369, Federal Emergency Management Agency, Washington, D.C. Ramirez, O. M., Constantinou, M. C., Kircher, C. A., Whittaker, A. S., Johnson, M. W., Gomez, J. D., and Chrysostomou, C. Z., Development and Evaluation of Simplified Procedures for Analysis and Design of Buildings with Passive Energy Dissipation Systems, MCEER Report , Revision 1, Multidisciplinary Center for Earthquake Engineering Research, University at Buffalo, State University of New York, Buffalo, NY, 470 pp. Valles, R. E., Reinhorn, A. M., Kunnath, S. K., Li, C., and Madan, A., IDARC2D Version 4.0: A Computer Program for the Inelastic Damage Analysis of Buildings, NCEER Report , National Center for Earthquake Engineering Research, University at Buffalo, State University of New York, Buffalo, NY Whittaker, A. S., Constantinou, M. C., Ramirez, O. M., and Johnson, M. W., Equivalent lateral and modal analysis procedures of the for buildings with damping systems, Earthquake Spectra 19 (4), [this issue] (Received 14 June 2002; accepted 23 April 2003)