1.5.1 Beams
Guidelines for nonlinear modeling and acceptance criteria for beams are provided in ANSI/AISC 342, and guidelines and criteria for beams in seismically designed moment frames are included in NIST (2017b). Whereas the guidelines and criteria in ANSI/AISC 342 are more geared to nonlinear static analysis, the NIST guidelines (2017b) focus more specifically on nonlinear response history (dynamic) analysis.
The following commentary pertains to specific subsections of the requirements for beams:
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(a) It is generally anticipated that beams that are characterized as deformation components and modeled inelastically will have low axial loads. The criteria to ignore the effect of axial loads up to is based on judgment as a practical matter. There are instances where larger axial forces may develop, such as in beams of braced frames, where the axial load effect should be accounted for in the beam analysis model and acceptance criteria. ANSI/AISC 342, Section C3, includes provisions for modeling flexural members with significant axial loads.
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(b) ANSI/AISC 342, Chapter C, specifies flexural modeling parameters for beams where hinges are located away from connections and for beams where hinges form close to fully restrained (FR) beam-column connections. These modeling parameters are generally intended to represent the first-cycle envelope response from tests under reverse cyclic loading. Alternatively, NIST (2017b) includes modeling guidelines for first-cycle and cyclic-envelope response of beam hinges based on a systematic calibration to available test data for FR beam-column connections.
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(c) Most fiber-type beam and beam-column models available in computer programs do not consider deterioration due to local buckling and/or low-cycle fatigue and fracture. In the absence of other information to establish their maximum permissible range of application, the effective plastic rotations in fiber-type models should be limited to the plastic rotations at peak moments [e.g., the modeling parameter, , as specified in ANSI/ASCE 342, or , the modeling parameter specified in NIST (2017b)]. The plastic rotations in the fiber models may be calculated based on the member chord rotation, as illustrated in ASCE/ SEI 41 (ASCE, 2017), Figure 9-3. Where fiber-type beam hinge or distributed plasticity models are used, the strain-hardening modulus of steel may be taken as of the elastic modulus.
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(d) It is preferred to locate the concentrated hinge or fiber hinge at the expected plastic hinge location, which is typically located a beam depth or more away from the column face. However, for practicality, the hinge may be located at the beam end (in other words, at the face of the column), in which case, the plastic hinge properties in the analysis model may need to be adjusted to reconcile the moments and rotations with those at the actual hinge rotation. Chapter 4 of NIST (2017b) provides information on making such adjustments.
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(e) Depending on the steel beam size, composite action with the concrete floor system can significantly increase the beam stiffness and strength. While it may be possible to conservatively neglect composite beam action, this is not always the case, such as in cases where the composite action may push yielding from the beam into the column, potentially leading to a weak story condition due to hinging in the columns. Chapter 4 of NIST (2017b) provides information on adjusting the beam model to account for composite action.
1.5.2 Links
Guidelines for nonlinear modeling and acceptance criteria for links are provided in ANSI/AISC 342, Section C2. Link behavior and modeling criteria are typically distinguished between flexural or shear links, depending on the primary yielding mechanism. Links may be modeled in nonlinear analyses with either rotational flexural hinges or as discrete shear springs, where the hinge or spring properties are related to the link yielding behavior. Information and guidance on modeling of links employed in a variety of structural system configurations are provided in the following references: Koboевич et al. (2012), Malakoutian et al. (2013), Borello and Fahnestock (2013), and Chen et al. (2019).
1.5.3 Columns
Generally, yielding is limited to flexural response of columns with low- to moderate-axial loads, where higher axial and shear load effects (excluding local panel-zone action) are treated as force-controlled actions. Guidelines for nonlinear modeling and acceptance criteria for flexural response of columns are provided in Section C3 of ANSI/AISC 342, and modeling guidelines for columns in seismically designed moment frames are included in NIST (2017b). Whereas the guidelines and criteria in ANSI/AISC 342 are more geared to nonlinear static analysis, the NIST guidelines (2017b) focus more specifically on nonlinear response history (dynamic) analysis. For unique scenarios where column instability must be directly captured in the model, axial-flexural interaction, distributed inelasticity over the length of the member, and initial imperfections are required (Imanpour et al., 2016a, 2016b). Where fiber-type column hinge or distributed plasticity models are used, the strain-hardening modulus of steel may be taken as 3% of the elastic modulus.
1.5.4 Braces (Except Buckling-Restrained Braces)
Guidelines for nonlinear modeling and acceptance criteria for braces that may undergo a flexural buckling response are provided in ANSI/AISC 342, Sections C3, C7, and E1. Additional guidelines for modeling braces are included in Chapter 5 of NIST (2017c). Whereas the guidelines and criteria in ANSI/AISC 342 focus on concentrated hinge/spring models, the NIST guidelines (2017c) focus on fiber-type beam-column models. In addition to the brace itself, the brace end connections may undergo inelastic action that should be modeled. Additional information and guidance on modeling braces, brace end connections, and gusset plates are provided by Huang and Mahin (2010), Hsiao et al. (2012), Lai and Mahin (2013), Karamanci and Lignos (2014), and Sizemore et al. (2017).
1.5.5 Buckling-Restrained Braces
Due to their stable hysteretic response, modeling of buckling restrained braces is relatively straightforward. However, one does need to take care to specify the initial stiffness and inelastic parameters to account for (a) the effective length of the unbonded (yielding) core region relative to the overall brace length; (b) cyclic hardening parameters, considering the difference in tension versus compression loading; and (c) the end connections. Ideally, the modeling parameters should be calibrated to representative tests from the buckling-restrained brace manufacturer. Information and guidance on modeling of buckling-restrained braces is provided in NIST (2015), Fahnestock et al. (2007), and Uriz and Mahin (2008).
1.5.6 Steel Plate Shear Walls
Guidelines for nonlinear modeling and acceptance criteria for steel plate shear walls as deformation controlled (inelastic) elements are provided in ANSI/AISC 342. Research papers relevant to modeling of steel plate shear walls include Bhowmick et al. (2009), Shishkin et al. (2009), and Berman (2011).
1.5.7 Composite Plate Shear Walls
Composite plate shear walls may be designed as uncoupled or coupled wall systems. Uncoupled composite plate shear walls are expected to undergo significant flexural yielding and plasticity at the base of the walls. These uncoupled walls are expected to be flexure critical—that is, undergo flexural yielding and plasticity before the wall in-plane shear strength is reached. In regions of significant flexural yielding, the steel plates undergo yielding and cyclic local buckling, eventually leading to their fracture due to low-cycle fatigue. The concrete infill is confined by the steel plates, but it also undergoes cyclic inelastic behavior, eventually leading to crushing. As such, the nonlinear models should explicitly account for the effects of (a) steel yielding, cyclic local buckling, and low-cycle fatigue leading to fracture and (b) concrete confinement and cyclic crack opening and closing behavior leading to crushing failure. Examples of effective stress-strain curves that implicitly account for these effects are provided in Agarwal et al. (2020) and Bruneau et al. (2019).
Coupled composite plate shear walls consist of composite walls coupled together using composite coupling beams—for example, filled box sections. Coupled systems are expected to undergo significant flexural yielding and plasticity at each end of the coupling beams located along the height of the walls and also to undergo flexural yielding and plasticity at the base of the composite plate shear walls. The composite coupling beams and composite walls are expected to be flexure critical—in other words, undergo flexural yielding and plasticity before shear strength or failure is reached. In regions of significant flexural yielding, the steel plates of the coupling beams and walls undergo yielding and cyclic local buckling, eventually leading to their fracture due to low-cycle fatigue. The concrete infill is generally confined by the steel plates, and it also undergoes cyclic inelastic behavior, eventually leading to crushing. As such, the nonlinear models should explicitly account for the effects of (a) steel yielding, cyclic local buckling, and low-cycle fatigue leading to fracture and (b) concrete confinement and cyclic crack opening and closing behavior leading to crushing failure. Examples of effective stress-strain curves that implicitly account for these effects are provided in Agarwal et al. (2020) and Bruneau et al. (2019).