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, and then deformation beyond the elastic limit occurs entirely within hinges, which are modeled as discrete points. Inelastic behavior is obtained through integration of 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 plasticity distributed over element length, users may insert a series of hinges.
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. Values may be exact, or scaled, possibly according to the yield-point coordinates. 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.
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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.
P-M2-M3 hinges are also available for coupled axial and bi-axial-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 yield point on the interaction surface.
Additional information can be found in the
CSI
[_Analysis Reference Manual_] (Frame Hinge Properties, page 131).
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