C-C2C2 Additional requirements

The analysis requirements of ASCE/SEI 7 (ASCE, 2022), are general with the primary intent of provisioning for stability, in part by developing minimum design forces for a variety of systems. Required strength relates to a sufficient first-yield strength within the system. While limitations on system irregularity help to avoid unexpected or known undesirable behavior, the requirements of ASCE/SEI 7 do not ensure a well-proportioned system with controlled or distributed yielding. The Provisions are intended to expand on the basic requirements of ASCE/SEI 7 to provide a well-proportioned system with controlled yielding and large inelastic drift capacity. This is accomplished to varying degrees depending on the intended ductility of the system by promoting inelastic behavior in designated components, while limiting inelastic behavior elsewhere. The required strength of designated yielding members (DYM) or components is determined by elastic analysis methods for the prescribed load combinations, while that of other elements, which are intended to remain essentially elastic, is determined by a pseudo-capacity design approach that varies from system to system.

An alternative to using elastic analysis is to use the plastic design method as a more direct way to achieve the objective of a desired yield mechanism for the structural system (Goel and Chao, 2008). In the plastic design approach, the desired yield mechanism is first selected by identifying the DYM and those that are intended to remain elastic, designated as non-DYM. The required strength of the DYM is determined by using a mechanism-based plastic analysis for each appropriate load combination. Any expected overstrength of the DYM or structure beyond the elastic limit up to the formation of targeted yield mechanism (within its maximum deformation limit) must be properly considered in the analysis. The second step of determining the required strength of non-DYM can be carried out by one of the following possible methods:

• (a) A static elastic analysis of suitably selected structural subassemblages consisting of non-DYM with loads applied to keep them in equilibrium under the expected forces from the DYM and other applicable loads
• (b) A nonlinear static pushover analysis of the entire structure up to a target drift level by modeling the DYM to behave inelastically, while the non-DYM are modeled (or “forced”) to behave elastically in order to be able to determine their required strength
• (c) A nonlinear dynamic analysis of the structure as modeled for the pushover analysis mentioned previously, using an appropriately selected ensemble of ground motions

Typical seismic analysis of structures uses applied external loads. The Specification requires that second-order effects be considered in order to arrive at appropriate member design forces. These second-order effects consist of magnification of member forces due to the presence of gravity load acting through the sidesway displacement of the structure ( $P-\Delta$ effect) and magnification of member moments due to the presence of member axial force ( $P-\delta$ effect).

Determining the required strength of non-DYM is the same in the capacity design and plastic mechanism design methods. In a static elastic analysis approach, a set of forces that represent the fully yielded capacity of the DYM, applicable gravity loads, and lateral forces, as required for equilibrium, are applied on appropriately selected portions of the structure. $P-\Delta$ corrections, such as notional lateral loads or the $B_{2}$ factor, are not applicable as those effects are represented in the calculated lateral forces. The $P-\Delta$ effect can be thought of as having contributed to the formation of the fully yielded condition. $P-\delta$ effects are not relieved by the formation of the plastic mechanism, and where such effects occur, adjustments (such as the $B_{1}$ factor) must be applied in order to arrive at appropriate design forces.