For nonlinear static and nonlinear direct-integration time-history analyses, users may simulate post-yield behavior by assigning concentrated plastic hinges to frame and tendon objects. Elastic behavior occurs over element length, 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, typically on the order of element depth (FEMA-356). To model the plasticity distributed over element length, users may insert a series of hinges. Multiple hinges may also coincide at the same point.
Plasticity may be associated with force-displacement behaviors, including axial and shear deformation, or moment-rotation, including torsion and bending. Hinges may be assigned (uncoupled) to any of the six DOF. Post-yield behavior is described by the general backbone relationship shown to the right. The modeling of strength loss is discouraged, to mitigate load redistribution (which may lead to progressive collapse) and to ensure numerical convergence.
CSI
Software automatically limits negative slope to 10% of elastic stiffness, though 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.
Fiber hinges are available to model the coupled [P-M2-M3] behavior of nonlinear frame objects. 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.
Additional information on hinges can be found in the
CSI
Analysis Reference Manual (Frame Hinge Properties, page 131).
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