Characterize Behavior

System behavior is characterized through the use of structural system archetypes. The concept of an archetype is described in Chapter 4.

Establishment of archetypes begins with identifying the range of features and behavioral characteristic that describe the bounds of the proposed seismic-force-resisting system.

Archetypes provide a systematic means for characterizing permissible configurations and other significant features of the proposed system. Like building code provisions, archetypical systems are intended to represent typical applications of a seismic-force-resisting system, recognizing that it is practically impossible to envision or attempt to quantify performance of all possible applications. They should, however, reflect the degree of

irregularity permitted within standard building code provisions.

The challenge in defining and assessing structural system archetypes is in narrowing the range of parameters and attributes to the fewest and simplest

possible, while still being reasonably representative of the variations that would be permitted in actual structures. In addition to ground motion intensity (Seismic Design Category), the following characteristics are considered in defining structural system archetypes: (1) building height; (2) fundamental period; (3) structural framing configurations; (4) framing bay sizes or wall lengths; (5) magnitude of gravity loads; and (6) member and connection design and detailing requirements. Structural system archetypes are assembled into bins called performance groups, which reflect major divisions, or changes in behavior, within the archetype design space. The collapse safety of the proposed system is then evaluated for each

performance group.

In the collapse assessment process, only framing components that are specifically designated as part of the seismic-force-resisting system are included in the archetypes. While it is recognized that other portions of the building (e.g., components of the gravity system or certain nonstructural components) can significantly affect collapse behavior, such components, which are not controlled by seismic-force-resisting system design

requirements, cannot be relied upon for reducing collapse risk.

2.6 Develop Models

Development of structural models for collapse assessment is discussed in Chapter 5. Structural system archetypes provide the basis for preparing a finite number of trial designs and developing a corresponding number of idealized nonlinear models that sufficiently represent the range of intended applications for a proposed system. Index archetype models are developed to provide the most basic (generic) idealization of an archetypical

configuration, while still capturing significant behavioral modes and key design features of the proposed seismic-force-resisting system.

Designs consider the range of seismic criteria for each applicable Seismic Design Category, variations in gravity loads, and other distinguishing features including alternative geometric configurations, varying heights, and different tributary areas that impact seismic design or system performance.

To the extent possible, nonlinear models include explicit simulation of all significant deterioration mechanisms that could lead to structural collapse.

Recognizing that it is not always possible (or practical) to simulate all possible collapse modes, the Methodology includes provisions for assessing the effects of behaviors that are not explicitly simulated in the model, but could trigger collapse.

Nonlinear models must account for the seismic mass that is stabilized by the seismic-force-resisting system, including the destabilizing P-delta effects associated with the seismic mass. In most cases, elements are idealized with phenomenological models to simulate complicated component behavior. In some cases, however, two-dimensional or three-dimensional continuum finite element models may be required to properly characterize behavior. Models are calibrated using material, component, or assembly test data and other substantiating evidence to verify their ability to simulate expected nonlinear behavior.

2.7 Analyze Models

Collapse assessment is performed using both nonlinear static (pushover) and nonlinear dynamic (response history) analysis procedures described in Chapter 6. Nonlinear static analyses are used to help validate the behavior of nonlinear models and to provide statistical data on system overstrength and ductility capacity. Nonlinear dynamic analyses are used to assess median collapse capacities and collapse margin ratios.

Nonlinear response is evaluated for a set of pre-defined ground motions that are used for collapse assessment of all systems. Two sets of ground motion records are provided for nonlinear dynamic analysis. One set includes 22 ground motion record pairs from sites located greater than or equal to 10 km from fault rupture, referred to as the “Far-Field” record set. The other set includes 28 pairs of ground motions recorded at sites less than 10 km from fault rupture, referred to as the “Near-Field” record set. While both Far-Field and Near-Field record sets are provided, only the Far-Field record set is required for collapse assessment. This is done for reasons of practicality, and in recognition of the fact that there are many unresolved issues concerning the characterization of near-fault hazard and ground motion effects. The Near-Field record set is provided as supplemental information to examine issues that could arise due to near-fault directivity effects, if needed.

The record sets include records from all large-magnitude events in the Pacific Earthquake Engineering Research Center (PEER) Next-Generation

Attenuation (NGA) database (PEER, 2006a). Records were selected to meet a number of sometimes conflicting objectives. To avoid event bias, no more than two of the strongest records have been taken from any one earthquake, yet the record sets have a sufficient number of motions to permit statistical evaluation of record-to-record (RTR) variability and collapse fragility.

Strong ground motions were not distinguished based on either site condition or source mechanism. The Far-Field and Near-Field record sets are provided in Appendix A, along with background information on their selection.

For collapse evaluation, ground motions are systematically scaled to increasing earthquake intensities until median collapse is established.

Median collapse is the ground motion intensity in which half of the records in the set cause collapse of an index archetype model. This process is similar to, but distinct from the concept of incremental dynamic analysis (IDA), as proposed by Vamvatsikos and Cornell (2002).

Figure 2-3 shows an example of IDA results for a single structure subjected to a suite of ground motions of varying intensities. In this illustration, sidesway collapse is the governing mechanism, and collapse prediction is based on lateral dynamic instability, or excessive lateral displacements.

Using collapse data obtained from IDA results, a collapse fragility can be defined through a cumulative distribution function (CDF), which relates the ground motion intensity to the probability of collapse (Ibarra et al., 2002).

Figure 2-4 shows an example of a cumulative distribution plot obtained by fitting a lognormal distribution to the collapse data from Figure 2-3.

While the IDA concept is useful for illustrating the collapse assessment procedure, the Methodology only requires calculation of the median collapse point, which can be calculated with fewer nonlinear analyses than would otherwise be required to calculate the full IDA curve. An abbreviated process for calculating the median collapse point is described in Chapter 6.

Figure 2-3 Incremental dynamic analysis response plot of spectral acceleration versus maximum story drift ratio.

Figure 2-4 Collapse fragility curve, or cumulative distribution function.