Index Archetype Models

General considerations for developing index archetype models are

summarized in Table 5-2. These considerations should be used as a guide in establishing index archetype models, as follows:

 Model Idealization. Definition of index archetype models includes selection of the type of idealization used to represent structural behavior.

At the one extreme are nonlinear continuum finite element models, which, in theory, are capable of representing the underlying structural mechanics most directly. At the other extreme are phenomenological models, which represent the overall force-deformation response through

is an example of such a phenomenological model, in which moment-rotation behavior is related to beam-column design parameters through semi-empirical models that are calibrated to beam-column subassembly tests.

In between these two extremes are models that utilize both continuum and phenomenological representations. A “fiber-type” model of a reinforced concrete shear wall is an example of such a combined model, where flexural effects are modeled with uniaxial stress-strain behavior for reinforcing steel and concrete, and where shear behavior (or combined shear-flexural behavior) is represented through a stress-resultant (force-based) phenomenological model. Regardless of type, models must be validated against test data and other substantiating evidence to assess how accurately they capture nonlinear response and critical limit state behavior.

Table 5-2 General Considerations for Developing Index Archetype Models

Model Attributes Considerations

Mathematical Idealization  Continuum (physics-based) versus phenomenological elements

Plan and Elevation Configurations

 Number of moment frame bays, regularity.

 Planar versus 3-D wall representations, openings, coupling beams, regularity.

 Number of bracing bays, bracing configuration, regularity.

 Variations to reflect diaphragm effects on stiffness and 3-D force distributions

2-D versus 3-D Component Behavior

 Prevalence of 2-D versus 3-D systems in design practice

 Impact on structural response, including provisions for 3-D (out-of-plane failures) in 2-D models

2-D versus 3-D System Behavior

 Characteristics of index archetype configurations, such as diaphragm flexibility

 Impact on structural response that is specific to certain structural systems

 Elevation and Plan Configurations. Representation of elevation and plan configurations in index archetype models will depend on both the index archetype configurations and the structural system behavior.

While vertical and horizontal irregularities will certainly influence collapse, for the purpose of evaluating general design provisions,

currently permissible elevation and plan irregularities in ASCE/SEI 7-05

are not addressed in index archetype models. As illustrated by examples in Chapter 9, two-dimensional, three-bay frames of regular proportions are judged sufficient to represent typical behavior of reinforced concrete moment frame systems. The extent to which this type of model will suffice for studies of other moment frame types should be established based on the specific behavioral effects of the specific moment frame system. For walls, the issue of planar versus three-dimensional response is a key consideration, as is the presence of wall openings, boundary elements, and coupling beams. For example, reinforced concrete walls with large boundary members (e.g., flanged walls) are likely to exhibit more shear-critical behavior than planar walls without boundary members. For braced frame systems, one or two bays of framing are likely to be sufficient unless the system relies on the specific interaction between two adjacent bays. Representation of alternative brace

configurations is likely to be a dominant variable in collapse assessment of braced-frame systems. Where diaphragm flexibility has a significant effect on the lateral system response and performance, this flexibility should be incorporated in the index archetype model.

 Two-Dimensional versus Three-Dimensional Component Behavior.

The need for models that simulate two-dimensional versus

three-dimensional behavior will generally depend on: (1) the type of structural configurations common in the design space; and (2) the expected influence of three-dimensional effects on structural response. For most structural framing types, two-dimensional models are likely to be sufficient. However, there may be cases where three-dimensional behavior (e.g., out-of-plane torsional-flexural instability of laterally unbraced beam-columns or braces) or three-dimensional geometry (e.g., reinforced-concrete C-shaped core walls) are important to simulate. For wall systems, two-dimensional wall models may be sufficiently accurate for some system configurations (e.g., wooden shear walls, planar

reinforced concrete walls) but less accurate and perhaps inappropriate for others (e.g., C-shaped and I-shaped reinforced concrete core walls).

 Two-Dimensional versus Three-Dimensional System Behavior.

System behavior involves the interaction of multiple seismic-force-resisting components distributed spatially within a structure.

Introduction of different spatial combinations, however, could lead to an intractable number of index archetype configurations and corresponding index archetype models. Building code provisions regarding plan configuration and three-dimensional effects (e.g., redundancy, accidental torsion) are usually not system specific, so in most cases, a

two-flexibility may require three-dimensional index archetype model configurations if important diaphragm effects cannot be suitably incorporated in two-dimensional models.

5.3.1 Index Archetype Model Idealization

Index archetype models should provide the most basic (generic)

representation of an index archetype configuration that is still capable of distinguishing between significant behavioral modes and key design features of the proposed seismic-force-resisting system. Index archetype models should be developed in cooperation with the peer review panel.

The mathematical idealization of index archetype models should capture all significant nonlinear effects related to the collapse behavior of the system.

This can be done through: (1) explicit simulation of failure modes through nonlinear analyses; or (2) evaluation of non-simulated¹ failure modes using alternative limit state checks on demand quantities from nonlinear analyses.

Analytical models are generally distinguished by overall topology and element type. Topology refers to two-dimensional or three-dimensional modeling configurations. The choice of topology (2-D or 3-D) is largely a function of the index archetype configurations. The choice of element type depends on structural component behavior and the nature of component degradation. Two-dimensional topologies (e.g., planar frames or walls) do not preclude the modeling of three-dimensional effects (e.g., out-of-plane instabilities). Conversely, three-dimensional topologies (e.g., space frames or C-shaped walls) do not necessarily employ element types that capture all three-dimensional behavioral effects. Thus, the modeling decisions should be made on a case-by-case basis, depending on the specific features of the structure system archetypes.

For simulating collapse, component models must capture strength and stiffness degradation under large deformations. Structural components are usually idealized as a combination of one-dimensional line-type elements (beam-columns or axial struts) and two-dimensional continuum elements (plane-stress or plate/shell finite elements). Three-dimensional continuum elements (brick finite elements) may be appropriate and necessary in some cases. Within each element type, element formulations can be further distinguished by the extent to which the underlying structural behavior is modeled explicitly or through phenomenological representations. For

1 The term “non-simulated” is used to describe potential modes of collapse failure that are not explicitly captured by the index archetype model (i.e., not explicitly simulated), but is evaluated by alternative methods of analysis and included in the evaluation of collapse performance.

example, nonlinear beam-column elements can range in sophistication from fiber-type continuum elements, in which the geometry and materials in the cross section are modeled explicitly, to concentrated spring models, in which the inelastic response is idealized through uni-axial or multi-axial springs.

Provided that they are accurately calibrated to the appropriate range of design and behavioral parameters, concentrated spring models will usually be sufficient for simulating nonlinear response of columns, beams, and beam-column connections in frame systems. These models have the practical advantage of providing a straight-forward approach to characterizing strength and inelastic deformation characteristics. However, concentrated spring models generally cannot represent behavioral effects beyond those present in the underlying data. Continuum models, which generally model the physical behavior at a more fundamental level, can, if properly formulated and validated, represent a broader range of behavioral effects that do not rely as much on tests to represent the specific parameters of the index archetype designs.

Wall systems will typically require two-dimensional continuum models that can capture significant nonlinear stress and strain variations within the walls.

Continuum models may include traditional two-dimensional plane stress/strain finite elements, or alternative formulations that utilize combinations of formal finite element approaches and engineering assumptions to represent the nonlinear behavior (including the effects of strength and stiffness degradation).

In the case of moment frame systems, for example, an index archetype model might consist of the two-dimensional, three-bay frame shown in Figure 5-3.

This model incorporates one-dimensional line-type elements with either concentrated spring or discrete component models to simulate the nonlinear degrading response of beams, columns, beam-column connections, and panel zones. Significant frame behaviors are captured in a two-dimensional representation, and the three-bay configuration captures differences between interior and exterior columns. The additional leaning column elements capture P-delta effects of the seismic mass that is not tributary to the frame.

For shear wall systems, an index archetype model might be as simple as a cantilever element that accounts for inelastic flexure and shear behavior at the base of the wall. However, where punched shear wall geometries are included in the index archetype configurations, then the corresponding index archetype models would need to be more complicated.

Figure 5-3 Example of index archetype model for moment resisting frame systems