To properly evaluate the overall nonlinear structural response, a three-dimensional model is required. Specific analysis requirements are outlined in ASCE/SEI 7 and include items such as diaphragm flexibility, effective seismic weight, effective member stiffnesses, expected material properties, additional inherent damping not associated with inelastic behavior of the structural members, inclusion of effects, and inclusion of inherent torsion.
A wide range of modeling approaches can be used, including line elements with discrete plastic hinges, fiber elements that distribute strength and stiffness across the member cross section and length, and high-definition finite element models that can simulate such effects as local and global buckling and fracture. The NIST guidelines (NIST, 2017a) provide a good overview of these approaches and their relative benefits.
Regardless of the modeling approach used, it is important to capture the expected strength and deformation capacity of the elements and connections being modeled, as well as the effects of slip, strain hardening, in-cycle and cyclic strength degradation, and pinching. This appendix permits these parameters to be established by test data, analyses, or other supporting evidence. When analytical approaches are used to establish these parameters, it is important that the analytical procedure is benchmarked against test data to provide confidence that the values predicted by analysis are meaningful.
Even when test data are used to establish hysteretic properties and shape, it is important to recognize that these properties are often dependent on loading history, as well as the specific material properties and condition of the element. Even when high fidelity finite element models, benchmarked against test data, are used, there is significant uncertainty as to the strengths, stiffnesses, and deformations that the real structure will undergo in response to a specific earthquake motion. One means to account for these uncertainties would be to perform many analyses, varying the hysteretic properties with each analysis to fully define the possible response. Given the significant time and data involved in nonlinear seismic analysis, running such permutations of modeling parameters is not deemed practical at this time. Instead, this appendix recommends the use of best estimate properties, considering the potential variation in material and cross-section properties, construction quality, and loading history.
The NIST guidelines (NIST, 2017c) present a series of models that can be used for structural steel beams, columns, braces, and their connections, as well as for systems other than steel structures. The NIST guidelines (NIST, 2017b) provide guidelines for models relevant to steel moment frames. Other resources include Modeling and Acceptance Criteria for Seismic Design and Analysis of Tall Buildings (ATC-72) (ATC, 2010), ANSI/AISC 342 (AISC, 2022c), and various university research reports.
When analytical approaches are used to predict hysteretic behavior dominated by buckling or other instability phenomena, it is important to include estimates of geometric imperfections in the model. This is particularly important for braces, other than buckling-restrained, because the behavior of these braces is typically dominated by buckling. Similarly, flexure of shapes with thin compression (noncompact) flanges should consider local imperfections. It is typically not necessary to model initial imperfections in columns because they are typically designed to ensure that axial demands are below the likely buckling level.
If nonlinear seismic analysis is to provide meaningful estimates of structural response, it is important to capture all significant sources of stiffness and strength in the structure. This often requires modeling of some or all of the gravity load-resisting system as well as the seismic force-resisting system. In addition, structural elements that are not part of the intended seismic force-resisting system can be damaged by deformations the structure undergoes during the seismic response. These effects can be evaluated either by directly including representation of these elements in the model or by evaluating these elements for the imposed deformations and forces outside the analysis.
Modeling parameters determined in accordance with the requirements of this appendix are intended to provide reasonable best estimate values for analysis.