New Criteria for use of Nonlinear Dynamic Analysis in Design ASCE 7-16 and PEER TBI VII

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1 New Criteria for use of Nonlinear Dynamic Analysis in Design ASCE 7-16 and PEER TBI VII Ronald O. Hamburger, SE, Senior Principal Simpson Gumpertz & Heger Inc. San Francisco, CA Abstract Jack P. Moehle, PhD, PE Ed & Diane Wilson Professor Structural Engineering University of California at Berkeley Nonlinear dynamic analysis has become an increasingly important tool for performance-based seismic design. Following concepts first introduced in the Pacific Earthquake Engineering Research Center s Guidelines for Performancebased Seismic Design of Tall Buildings (TBI I) (PEER, 2010), the 2009 NEHRP Provisions (BSSC, 2009) and ASCE 7-16 (ASCE, 2017) substantially improved the requirements for use of nonlinear dynamic analysis that had been specified in building codes and standards for many years. In an update to its Tall Building Guidelines (TBI II) (PEER, 2017) PEER further improved these recommendations, making them consistent with design criteria in ACI 314 (ACI ) and AISC 360 (AISC, 2016a) and in better alignment with standard load and resistance factor design approaches. Introduction Nonlinear dynamic analysis, also called nonlinear time history analysis and nonlinear response history analysis, is a powerful tool for predicting the performance of structures subjected to strong earthquake motion. For the simplest, single-degree-offreedom (SDOF) systems having a single concentrated mass, m, supported by a single structural element with stiffness k, as illustrated in Figure 1, response history analysis predicts the structure s response to a time-varying ground motion history, u(t) in the figure, in terms of its time-varying deformation relative to its base, x(t); and the amount of force, F(t), experienced by the structural element supporting the mass as a function of time. These quantities are obtained by stepwise numerical solution of the equation of motion for the structure: 0 Eq,-1 Figure 1- Earthquake Response of SDOF Structure Other parameters in Equation 1 include: the mass s velocity at time t, relative to its base;, its acceleration at time t, relative to its base; and,, the structure s velocitydependent resistance to motion, also termed damping. The structure s stiffness, k(x) is expressed as a function of the structure s deformation, x(t). A number of different formulations for k(x), commonly called hysteretic relationships, can be used, such as those illustrated in Figure 2. The intent is to replicate the actual changes in stiffness and strength that occur in structural elements as they are subjected to repeated cycles of deformation at varying amplitudes beyond their elastic limit. For many years, response history analysis was regarded as a research tool, impractical for use in the design office. Initially this was because of the difficulty of solving the complex equations of motion for multi-degree-of-freedom structures, prior to the advent of high speed computers. Then, after the necessary computing power was available, engineers lacked software that could perform these computations. Finally, it was recognized that the results of such analysis were highly 1

2 dependent on the hysteretic relationships employed and the specific characteristics of the specific ground motions used as input. Lacking consensus as to the appropriate way to model structures or even to select and scale ground motions, engineers resorted to other, simpler techniques for estimating structural response to earthquakes and building codes ignored the use of nonlinear dynamic analysis. Figure 2 Representative hysteretic relationships This began to change in the 1980s, when seismic base isolation was introduced to the engineer s toolkit of earthquake-resistant technologies. Seismic isolation enabled the practical use of nonlinear dynamic analysis in design because in isolated structures, almost all nonlinear behavior occurs in the isolators, the hysteretic response of which can often be represented by the simple strain hardening behavior illustrated in Figure 2b. Further, early base isolated buildings, which consisted of rigid superstructures mounted on flexible elastomeric bearings, largely behaved as SDOF systems, enabling the simplest form of Eq. 1 to be utilized and greatly simplifying the computation effort so that it could be handled by software available at that time. SEAOC s Tentative Seismic Isolation Design (SEAOC 2006) publication, subsequently adopted in the 1988 UBC (ICBO, 1988) appendix on seismic isolation, presented the first codification of requirements for nonlinear dynamic analysis. The requirements specified that hysteretic relationships be benchmarked against test data for prototypes of the actual isolators employed. In addition, recognizing the variability inherent in results obtained from nonlinear dynamic analysis, SEAOC recommended performing analysis for a suite of not less than 3 ground motions. Under the SEAOC recommendations, only two response parameters were of interest: the isolator displacement demand and the isolator force. If 7 or more motions were used, SEAOC permitted use of the mean results for design. If fewer than 7 ground motions were used, SEAOC required that the maximum value of these parameters obtained from the analysis, thought to be a conservative estimate of mean response, be used for design. However, SEAOC also required consideration of uncertainty in hysteretic properties, by requiring analysis for bounding assumptions on the stiffness of the isolators. The intent was to obtain reasonable, but undefined reliability. The next major development in the adoption of nonlinear dynamic analysis criteria in building codes occurred as part of the ATC-33 project to develop the FEMA 273/274 (ATC, 1997) Guidelines and Commentary for Seismic Rehabilitation, which today have evolved into the ASCE 41 (ASCE, 2013) standard. FEMA 273/274 was one of the first performancebased seismic design criteria and attempted to directly define performance as a function of calculated response. FEMA 273/274 included nonlinear dynamic analysis as one of four permitted analysis procedures. The guidelines for use of nonlinear dynamic analysis were based on the SEAOC base isolation provisions, but were broadened for application to structures with multi-degree of freedom response and elements of widely different hysteretic characteristics. Unlike the base isolation provisions, which required use of bounded properties, FEMA 273/274 specified use of bestestimate properties to model hysteretic behavior. FEMA 273/274 classified elements either as being deformationcontrolled or force-controlled. Deformation-controlled elements are those capable of exhibiting ductile behavior, with appreciable nonlinear response capacity. Force-controlled elements are those with little ductility, and which consequently were required to resist design shaking while remaining elastic. Commentary to FEMA 273/274 indicated an intent that designs meeting the specified criteria would have less than a 10% probability of having poorer performance than intended when subjected to design earthquake shaking. However, the acceptance procedures inherent in the documents were not compatible with this goal. For deformation-controlled behaviors, the Guidelines permitted mean results from suites of 7 or more ground motions to be compared against mean estimates of element deformation capacity. This results in approximately a 45% probability that performance would not be as good as desired, even if the mean response obtained from the suite of analyses was unbiased. This was recognized by the authors of the Guidelines and accepted because it was viewed that for ductile elements, modest demands beyond the capacity would not be catastrophic. However, for forcecontrolled behaviors better reliability was desired. The Guidelines required that mean demand be less than a conservative estimate of capacity, taken as mean minus one standard deviation. Reliability calculations were not done at the time that the Guidelines were prepared. It can be shown, however, given uncertainties in the use of nonlinear analysis, this results in a probable failure rate of about 30%, far from that intended. 2

3 Following publication of FEMA 273/274, ASCE adapted the nonlinear response history requirements of those Guidelines into the 2002, 2005, and 2010 editions of its ASCE 7 Standard for Minimum Design Loads for Buildings and Other Structures (ASCE, 2002, 2005, 2010), where it became the design criteria for new buildings with the same inherent lack of reliability as the FEMA 273/274 guidelines. FEMA P695 and ASCE 7-10 In response to attempts by construction product suppliers to obtain building code acceptance of their products and establish new systems with beneficial R coefficients, FEMA sponsored the ATC-63 project. That project published the FEMA P-695 methodology for qualifying design criteria for new structural systems, including the R, C d and o coefficients assigned to these systems. FEMA P-695 presented a procedure for computing the notional collapse fragility associated with a structural system and associated design procedures and indicated that new structural systems should be demonstrated capable of producing structures with not greater than a 10% probability of collapse, conditioned on the occurrence of MCE shaking. The 10% collapse goal was selected because using the procedures, the developers of the methodology determined that selected structural systems already covered by the building code, and believed to be capable of superior performance, were marginally capable of meeting this goal. It should be noted that the FEMA P-695 methodology incorporates a number of conservative assumptions including neglecting the contribution to earthquake resistance of structural components that are not designed as part of the seismic force resisting system. Many engineers familiar with the FEMA P-695 methodology believe that the real collapse fragility of modern codeconforming systems is significantly better than suggested by the 10% collapse probably goal. Regardless, commentary to the ASCE 7-10 standard adopted this goal as the intent of its seismic design requirements for Risk Category II structures and adopted goals of 5% and 3% conditional probabilities of collapse for Risk Category III and IV structures, respectively. Further, ASCE 7-10 revised the definition of maximum considered earthquake shaking such that instead of having a 2% - 50 year exceedance probability, it produced a 1 % - 50 year collapse probability for structures having a 10% conditional probable of collapse at MCE shaking. With the adoption of these criteria, the profession assented to the proposition that the safety goal of the building code requirements was obtained by designing structures that would not have greater than a 10% probability of collapse should they experience MCE shaking. PEER TBI Guidelines V1 In 2009, in response to the growing practice of engineers using performance-based seismic design procedures as a means of avoiding some prescriptive building code requirements, PEER engaged in a partnership with numerous public and private organizations to develop recommendations for performancebased seismic design of tall buildings. PEER engaged in an extensive program of research into technical and social aspects of tall building development and response in earthquakes and in 2010, published TBI I. These guidelines required evaluation of building response at two earthquake shaking levels, a service level, having a 43-year return period, and the MCE R level defined by ASCE Service level evaluations were specified assuming linear analysis and are not of interest here. MCE R level evaluation, however, was conducted with nonlinear dynamic analysis. Departing from the FEMA 273/274 Guidelines, and ASCE 41, TBI I required both global and also element level evaluations of performance. Global evaluations included limitations on mean story drift ratios, mean residual story drift ratios, and maximum values of both peak transient and residual story drift. Evaluations of residual drift were intended to guard against tall buildings being placarded as unsafe following strong earthquakes, and potentially resulting in entire districts surrounding such buildings being declared unsafe for fear the tall building would fall in aftershocks. Limitations were placed on story drift both as a means of controlling damage and also to assure that predicted response remained within the valid range of modeling, though that term was not specifically used. Like ASCE 41, TBI I parsed elements into deformation- and force-controlled behaviors. However, unlike ASCE 41, rather than specifying acceptable levels of deformation for deformation-controlled elements, TBI I only required that in the analysis, the strength of these elements be degraded to nil values should the valid range of modeling be exceeded. If, in an analysis, one or more deformation-controlled elements exceeded their valid range of modeling, degraded to zero strength and the analysis completed with otherwise acceptable response, performance was considered acceptable. Like FEMA 273/274 and ASCE 41, this approach assumes that excessive demand on a ductile element is likely not critical to performance, however, it requires that the nonlinear analysis demonstrate that the overall structural performance is acceptable in the event that a deformation-controlled element fails. TBI I divided force-controlled elements into critical and noncritical categories, where critical elements are defined as those the failure of which would lead to partial or total structural collapse. Noncritical elements are defined as those, the failure 3

4 of which, would not typically result in collapse or life endangerment, with conventional coupling beams in concrete core walls cited as an example. Under TBI I force-controlled elements were evaluated using the acceptance criteria:, Eq. 3 where,, is the expected value of element strength, computed using mean values of material strength and the appropriate strength formulation found in ACI 318 or AISC 360 and is the strength reduction, or resistance factors obtained from the same standards. is the demand, computed as 1.5 times the mean value of demand obtained from the suite of analyses, or, if the demands were limited by a ductile mechanism, such as is the case for column axial loads in a special moment frame, the mean demand plus 1.3 times the standard deviation in demand obtained from the analyses. In the case where demand is limited by a ductile mechanism, could not be taken less than 1.2 times the mean demand. This latter requirement is intended to guard against artificially low computed standard deviations, which often occur when spectral matching of ground motions is used. At the time TBI I was developed the most common type of tall building being designed utilized central reinforced concrete cores to provide lateral resistance. In these designs, the shear resistance of the concrete cores was considered a critical forcecontrolled behavior. Therefore, the PEER TBI team calibrated Eq. 3 such that for reinforced concrete shear walls with modest flexural ductility demand, there would be less than a 10% probability of shear failure at MCE shaking (Hamburger, 2014; Wallace, 2014). The reliability provided by Eq. 3 for other types of force-controlled elements, e.g., columns in special moment frames, was not explicitly evaluated. ASCE 7-16 Chapter 16 Following publication of TBI I, the BSSC Provisions Update Committee (PUC) initiated work to develop the 2014 NEHRP Provisions (BSSC, 2014) which would serve as the basis for the ASCE 7-16 standard. One of the goals adopted by the PUC was to update the ASCE 7 procedures for linear and nonlinear response history analysis. The PUC felt that the reliability basis instituted by PEER in TBI I represented a significant improvement in the procedures and set about forming the new Chapter 16 based on that work, but substantially extending the TBI procedures so they were calibrated not only to shear walls but also other force-controlled behaviors (Haselton, et. al. 2017a). The requirements included in the 2014 NEHRP Provisions were modified and adopted into ASCE 7-16 Chapter 16. In a major departure from past practice, ASCE 7-16 requires that a minimum suite of 11 ground motions be used for nonlinear dynamic analysis. For Risk Category II structures, not more than 1 of the 11 motions can result in unacceptable response. Unacceptable response is defined as lack of convergence in the analysis, calculation of demands beyond the valid range of modeling for the elements, calculation of story drift ratios exceeding 4.5%, or calculation of demands on critical force-controlled components that exceed their capacity. This requirement was developed for consistency with the goal of not greater than a 10% probability of collapse given MCE R shaking, which in the 2016 edition of the standard has moved forward from commentary to the body of Chapter 1. As reported in Haselton, et al. (2017b), while 1 or fewer collapses in 11 analyses is not a statistically significant indicator that the collapse rate is less than 10%, if 2 or more analyses in a suite of 11 produce unacceptable response this is a statistically significant indicator that the true collapse rate exceeds 10%. ASCE 7-16 adopted other global evaluation criteria from PEER TBI I including limitations on mean transient story drift and residual drift. ASCE 7-16 also adopts element level acceptance evaluations for force- and deformation-controlled behaviors targeted at the limiting 10% collapse probability goal. ASCE 7-16 classifies force-controlled controlled elements as non-critical, ordinary, or critical. Critical elements are those the failure of which results in collapse of a substantive portion of the structure. Noncritical elements are those the failure of which would not result in collapse. Ordinary elements are those the failure of which would result in local collapse only. ASCE 7-16 established element acceptance criteria for forcecontrolled elements as: Eq. 4 where is the mean demand predicted by analysis; is the non-seismic portion of the demand; is the expected element capacity; is the occupancy importance factor specified by the standard; and is a load factor taken as 1.0 for noncritical elements, 1.5 for ordinary elements, and 2.0 for critical elements, reflecting the acceptable increased collapse probability for noncritical and ordinary elements, respectively. Equation 4 was calibrated to provide the desired 10% collapse probability targeted at elements for which the predictive equations in the ACI and AISC standards do not have significant bias, such as buckling of steel columns. Commentary to the standard permits engineers to adjust Eq. 4 where it can be demonstrated that the ACI or AISC predictive equations do entail bias. ASCE 7-16 also adopted criteria for deformation-controlled elements, recognizing only ordinary and critical deformationcontrolled elements. The criteria is that mean deformation 4

5 demand obtained from the analyses cannot exceed 0.3 or 0.5 times the mean deformation at which loss of gravity load carrying capacity occurs, as demonstrated by laboratory testing, respectively, for critical and ordinary elements. Again, this acceptance criteria is targeted at not exceeding a 10% failure probability for MCE R shaking. Recognizing that most laboratory testing of ductile elements does not load the element to a point at which gravity load failure occurs, it is not practically possible to implement this acceptance criteria. Recognizing this, ASCE 7-16 permits use of the ASCE 41 collapse prevention acceptance criteria as an alternative, which as discussed earlier in this paper, is not capable of achieving the desired reliability. PEER TBI VII In 2016, PEER, with support from the Pankow Foundation, initiated a project to update its Tall Building Design Guidelines. Goals of the project included making the guidelines compatible with the updated standards produced by ACI, AISC, and ASCE as well as taking advantage of the lessons learned in the design of tall buildings since the document was first published. Although the PEER team made many updates and improvements to the Guidelines, this paper focuses only on the development of acceptance criteria for nonlinear analysis used to demonstrate, implicitly, that the structure is capable of meeting the collapse reliability goals established in ASCE TBI II refers to and directly coordinates with ASCE 7-16, ACI , and AISC However, it makes modifications to the requirements of these standard documents, particularly ASCE One of the most significant exceptions to ASCE 7-16 is the ASCE 7 requirement that structures designed using nonlinear dynamic analysis also must be demonstrated to meet all pertinent criteria of ASCE 7 Chapter 12, except drift limits and load combinations incorporating overstrength. TBI II does not require ASCE 7 Chapter 12 compliance, adopting instead the service level event evaluation previously adopted in TBI I. The TBI II authors felt that the design earthquake evaluation contained in Chapter 12 was of limited use considering that design earthquake shaking has a different return period at each site and also that the focus of TBI II is to enable innovation as well as provide more reliable buildings. It is generally agreed that some requirements of Chapter 12 and related standards, e.g., shear design requirements for concrete walls, will not by themselves provide the reliability targeted by the code. The authors believed that assuring minimal damage for a Service Level earthquake shaking level with uniform return period and relying on the nonlinear dynamic analysis procedures for MCER shaking is a more consistent way to achieve the performance objectives. TBI II retains the ASCE 7-16 requirement for a minimum of 11 ground motions. However, it provides additional guidance on the selection of ground motions for this suite for sites with strong contribution from sources having significantly different characteristics. Examples of such sites include Seattle, where significant contribution to hazard occurs both due to Cascadia subduction zone events and also shallow crustal faults such as the Seattle Fault zone. Similar situations exist in the Los Angeles basin where significant contribution to hazard occurs from a major San Andreas event, and also the several thrust ramps present beneath the basin. In such cases, TBI II recommends that the suite include at least 5 motions representative of each source type. The purpose of this is to obtain a significant representation of each contributor to the hazard. TBI I did not require consideration of accidental eccentricity in nonlinear dynamic analysis because it was viewed that for tall buildings, it was extremely unlikely that the structure would experience simultaneous accidental displacement of mass at all levels. However, since publication of TBI I, Charney (Hazelton, et. al. 2017b) and others performed analytical research suggesting that it is important to include accidental torsion in the analysis for torsionally irregular structures. Therefore, ASCE 7-16 requires inclusion of accidental torsion in nonlinear analysis for all structures having torsional irregularity as defined by ASCE 7. In lieu of this requirement TBI II permits engineers to compute a twisting index, in each direction as the ratio of the maximum drift in a direction computed from elastic analysis with accidental torsion to that computed without accidental torsion. If this twisting index is less than 1.2 at all levels, accidental torsion need not be included in the analysis. This approach is similar to that contained in ASCE 7, but somewhat simpler and a more direct evaluation of the effects of torsion on response. The limiting value of 1.2 was judgmentally selected considering the computed value for buildings having different plan shape and arrangement. Like TBI I and ASCE 7-16, TBI II evaluates both global and element-specific acceptance criteria. Global acceptance checks are similar to those in ASCE One exception is that for Risk Category III structures, ASCE 7-16 does not permit any unacceptable response. TBI II permits one unacceptable response if a suite of not less than 20 motions is evaluated. The reason for this is that even if a structure truly has a conditional collapse probability at MCE R shaking less than the 5% targeted by ASCE 7 for Risk Category III structures, there is still a significant probability that at least one motion in a suite of 11 will produce unacceptable response. By expanding the suite to 20 motions, the level of assurance remains similar to that obtained for Risk Category II structures with a suite of 11 motions. 5

6 Element level acceptance evaluation is significantly different from that in ASCE 7. TBI II continues the practice of TBI I of not requiring specific acceptance values for deformationcontrolled elements; instead it is required that calculated demands must be within the valid range of modeling or that the element resistance degrades to zero strength when such demands exceed the valid modeling range. As long as predicted response of the structure as a whole is acceptable, it is presumed that failure of the individual element is tolerable. The acceptance evaluation for force-controlled elements is significantly different than required by ASCE There are several reasons for this. First, the authors felt that having load combinations different from those used in traditional design, as specified in ASCE 7 Chapter 2 and the International Building Code, is confusing to engineers. Further, the acceptance evaluation procedures in ASCE 7-16 Chapter 16 could result in the design of members that do not meet the minimum criteria of ACI 318 and AISC 360. Accordingly, TBI II adopts the following four load combinations: Eq Eq Eq Eq. 8 Eqs. 5 and 6 are intended to be used to evaluate forcecontrolled demands when the demand is limited by formation of a ductile yield mechanism, in which case E M is the demand associated with development of this mechanism, with all elements having their expected strength. These equations were calibrated to provide the same level of safety inherent in ACI 318, AISC 360, and AISC 341 (AISC 2016b). Eqs. 7 and 8 are intended for use in the more general case when demand on a force-controlled element is not limited by a ductile yield mechanism. Parameters used in the equations include: D is dead load; L is the service live load defined in the building code, with the load factor on L permitted to be reduced to 0.5 where uniform live load does not exceed 100 psf; Q T is the total demand predicted by analysis and Q ns is the non-seismic portion of the total predicted demand; I e is the occupancy importance factor, is a resistance factor, B is a bias factor explained later, and R n is the nominal resistance specified either by ACI 318 or ACI 360. For critical force-controlled elements, the resistance factor, is taken as the value of the resistance factor specified by the applicable materials industry standard. For ordinary and noncritical elements, is assigned a value of 0.9 and 1.0, respectively. Presently, ACI 318 and AISC 360 specify resistance factors targeted at the reliability goals associated with loadings other than seismic, as indicated in AISC 7-16 Table 1.3.1a. Both ACI and AISC are in the process of developing nonlinear modeling and acceptance criteria guidance for use in performance-based design. These efforts may result in values of resistance factors that are different than the present ones. In that event, it will be necessary to reevaluate the load factor of 1.3 placed on seismic demand in Eq. 7 an Eq. 8, as the 1.3 value was calibrated to produce the reliability targets indicated in AISC 7-16 Table 1.3.1b, that is, collapse risks of 10%, 5%, and 2.5%, respectively, for Risk Category II, III, and IV structures when subject to MCE R shaking. The calibration of the 1.3 load factor assumed a coefficient of variation in demand prediction of 0.3, based on review of statistics from analyses of real buildings. It assumes an additional uncertainty in the true value of mean demand resulting from the use of a limited suite of ground motions of 0.2 based on work by Huang et. al. (2008). It further assumes an average resistance factor, specified by the materials standard of 0.85; a bias in resistance of 1.1, and coefficient of variation in resistance of 15%. The bias in resistance is the ratio between the true mean value of resistance and that obtained using the equation for nominal resistance specified by the material standard. It includes allowance for material oversterngth and also any inherent conservatism in the predictable equation. The value of 1.1 for the bias and 15% for the coefficient of variation in element strength was computed based on data presented in Ellingwood et. al. (1980). TBI II recommends use of a bias value, B = 1.0 for most structural elements, unless data are available to show that the inherent bias associated with the predictive equation for nominal resistance exceeds 1.1. Commentary to the guidelines recommends that for shear in concrete walls, with limited flexural ductility demand, the bias factor B may be taken as having a value of In a major departure from TBI I and also ASCE 7-16 Chapter 16, Eqs 5 through 8 require the consideration of vertical earthquake shaking, represented by the term 0.2S MS D, where S MS is the short period, site-adjusted, maximum considered earthquake shaking parameter obtained in accordance with ASCE 7-16 Chapter 11. Where vertical response is directly considered in the nonlinear analysis, and Q T includes vertical response effects, the 0.2S MS D may be neglected. The authors considered inclusion of vertical earthquake shaking as necessary to achieve the target reliability goals. 6

7 Summary Once regarded as purely a research tool, nonlinear dynamic analysis has become an important addition to the engineer s toolkit, particularly when using performance-based approaches to design of major structures. For many years, the FEMA 273/274 Guidelines and ASCE 41 standard based on those guidelines set the state of practice for use of nonlinear analysis in evaluation and design. The PEER TBI I Guidelines, published in 2010, made substantive improvements to that practice, many of which have been reflected in ASCE The updated PEER TBI Guidelines, published in 2017, further advance the state of practice for nonlinear dynamic analysis as a design tool. Importantly, the TBI II Guidelines provide a reliability-based approach to evaluation of a design acceptability that is consistent with the other industry design standards and design approaches commonly employed by engineers. Members of the ASCE 7 and ASCE 41 committees have acknowledged the important improvements introduced in TBI II and are considering updates to those standards for compatibility. References ACI, 2014, Building Code Requirements for Reinforced Concrete Structures, ACI , American Concrete Institute, Farmington Hills, MI AISC, 2010, Specification for Structural Steel Buildings, ANSI/AISC , American Institute of Steel Construction, Chicago, IL AISC 2016a, Specification for Structural Steel Buildings, ANSI/AISC , American Institute of Steel Construction, Chicago, IL AISC 2016b, Seismic Provisions for Steel Buildings, ANSI/AISC , American Institute of Steel Construction, Chicago, IL ASCE, 2002, Minimum Design Loads for Buildings and Other Structures, ASCE 7-02, American Society of Civil Engineers, ASCE, 2005, Minimum Design Loads for Buildings and Other Structures, ASCE 7-05, American Society of Civil Engineers, ASCE, Seismic Evaluation and Rehabilitation of Buildings, ASCE 41-06, American Society of Civil Engineers, ASCE, 2010, Minimum Design Loads for Buildings and Other Structures, ASCE 7-10, American Society of Civil Engineers, ASCE, 2016, Minimum Design Loads for Buildings and Other Structures, ASCE 7-16, American Society of Civil Engineers, ATC, 1997, Guidelines and Commentary for Seismic Rehabilitation of Buildings, FEMA 273/274, Federal Emergency Management Agency, Washington, D.C. ATC, 2009, Quantification of Building Seismic Performance Factors, FEMA P-695, Federal Emergency Management Agency, Washington, D.C. BSSC, 2014, NEHRP Recommended Seismic Provisions for New Buildings and Other Structures, FEMA P-1050, Federal Emergency Management Agency, Washington, D.C. Ellingwood, B., Galambos, T.V., MacGregor, J.G., and Cornell, C.A., 1980, Development of a Probability Based Load Criterion for American National Standard A58, Building Code Requirement for Minimum Design Loads in Buildings and Other Structures, NBS Special Publication 577, National Bureau of Standards, Washington, D.C. Hamburger, R.O. 2014, Shear Design of Reinforced Concrete Structural Walls for Tall Buildings Proceedings of the 10 th National Conference on Earthquake Engineering, Anchorage, Alaska, July 2014, Earthquake Engineering Research Institute, Oakland, CA Haselton, C. B., Fry, A., Hamburger, R.O., Baker, J.W., Zimmerman, R.B., Luco, N., Elwood, K. J. Hooper, J.D., Charney, F.A., Pekelnikcy, R.G., and Whittaker, A.S., 2017a, Response History Analysis for the Design of New Buildings in the NEHRP Provisions and ASCE/SEI 7 Standard: Part II Structural Analysis Procedures and Acceptance Criteria, Earthquake Spectra, Volume 33, Issue 2, Earthquake Engineering Research Institute, Oakland, CA Haselton, C. B., Fry, A., Hamburger, R.O., Baker, J.W., Zimmerman, R.B., Luco, N., Elwood, K. J. Hooper, J.D., Charney, F.A., Pekelnikcy, R.G., and Whittaker, A.S., 2017b, Response History Analysis for the Design of New Buildings in the NEHRP Provisions and ASCE/SEI 7 Standard: Part I Overview and Specification of Ground Motions, Earthquake Spectra, Volume 33, Issue 2, Earthquake Engineering Research Institute, Oakland, CA Huang, Y.N., Whittaker, A.S., Luco, N., 2008, Maximum Spectral Demands in the Near-Fault Region, Earthquake 7

8 Spectra Vol 24 No. 1, Earthquake Engineering Research Institute, Oakland, CA ICBO, 1988, Uniform Building Code, International Conference of Building Officials, Whittier, CA PEER, 2010, PEER TBI Guidelines for Performance-based Seismic Design of Tall Buildings, Pacific Earthquake Engineering Research Center, Berkeley, California PEER, 2017, PEER TBI Guidelines for Performance-based Seismic Design of Tall Buildings, Version 2.0, Pacific Earthquake Engineering Research Center, Berkeley, California SEAOC, 1986, Tentative Seismic Isolation Design Requirements, Structural Engineers Association of California, Sacramento, CA Wallace, J. 2014, Design of Tall Buildings on the West Coast of the United States, Proceedings of the 10 th National Conference on Earthquake Engineering, Anchorage, Alaska, July 2014, Earthquake Engineering Research Institute, Oakland, CA 8