For [nonlinear|kb:Nonlinear] static and nonlinear [direct-integration|kb:Comparison of FNA and direct-integration time-history analysis] [time-history|kb:Time-history analysis] analyses, users may simulate [post-yield|kb:Material nonlinearity] behavior by assigning concentrated plastic *hinges* to [frame|kb:Frame] and [tendon|kb:Tendon] objects. Elastic behavior occurs over element length, and then deformation beyond the elastic limit occurs entirely within hinges, which are modeled as discrete points. Inelastic behavior is obtained through integration of the plastic strain and plastic curvature which occurs within a user-defined hinge length. Hinge length is typically on the order of element depth (FEMA-356). To model the plasticity distributed over element length, users may insert a series of hinges.

!Figure 1.png|align=right,border=1,width=250pxpxpxpx,hspace=10!

Plasticity may be associated with force-displacement behaviors, including axial and shear deformation, or moment-rotation, including torsion and bending. These types of hinges may be assigned (uncoupled) to any of the six DOF, and may coincide at the same point. DOF not specified remain elastic. Post-yield behavior is described by the general backbone relationship shown to the right. Strength loss, indicated by a negative stiffness slope, while permitted, is discouraged to mitigate load redistribution (which may lead to progressive collapse) and to ensure numerical convergence. {new-tab-link:http://www.csiberkeley.com/}CSI{new-tab-link} Software automatically limits negative slope to 10% of elastic stiffness. Frame Hinge Overwrite options are available. For informational purposes, additional limit states (IO, LS, CP) may be specified which are reported in analysis, but do not affect results. Unloading from the point of plastic deformation follows the slope of initial stiffness.

*P-M2-M3 hinges* are also available for coupled axial and biaxial-bending behavior. The 3D interaction (yield) surface may be defined explicitly, or automatically through AISC-LRFD eqn. H1-1a and H1-1b (Φ=1) or FEMA-356 eqn. 5-4 for steel, or ACI 318-02 (Φ=1) for concrete. Post-yield behavior is interpolated from one or more user-defined P-θ curves, where θ represents the relationship between M2 and M3. During analysis, an energy-equivalent moment-rotation curve is generated relative to the input P-θ curve(s) and the interaction-surface yield point. The [P-M2-M3 hinge|kb:P-M2-M3 hinge moment-rotation curve] article provides further description.

Additional information on hinges can be found in the {new-tab-link:http://www.csiberkeley.com/}CSI{new-tab-link} [_Analysis Reference Manual_|doc:Analysis Reference Manual] (Frame Hinge Properties, page 131).

{list-of-resources2:label=hinge|drafts-root=Hinge drafts}