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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 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.

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.

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CSI

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] article provides further description.

Additional information on hinges can be found in the

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Analysis Reference Manual (Frame Hinge Properties, page 131).

Articles

Tutorials

TitleDescriptionProgram

Hinge first steps (CSiBridge)

Basic introduction to hinge application in CSiBridge.

CSiBridge

Hinge first steps (SAP2000)

Basic introduction to hinge application in SAP2000.

SAP2000

Pushover analysis first steps

Guidelines for performing pushover analysis.

SAP2000

Test Problems

TitleDescriptionProgram

Hinge response when yield point changes

Behavior of a concentrated plastic hinge when the loading applied to a nonlinear frame object causes the yield point of the interaction surface to change position.

SAP2000

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