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# Hinge FAQ

## Default hinge properties are derived from which source?

Answer: Automatic hinge properties for steel members are based on Table 5-6 of FEMA-356, and for concrete members, Tables 6-7 and 6-8.

Overwrite options are available for the manual definition of hinge behavior or certain hinge properties.

## How is yield rotation calculated?

Answer: The yield rotation of a hinge is calculated as yielding curvature (My/EI) multiplied by hinge length.

For the automatic FEMA frame hinges, the yield rotation is specified in the code (ASCE 41-06, Table 5-6) as the chord rotation of the full member length due to plastic moment at one end. Specifically, the yield rotation is Mp/(6*E*I/L), where Mp = Z*fy, and L is the frame object (not element) length and this is how the yield rotation is determined in the program.

## Why do hinge results deviate from the defined hinge backbone?

Answer: Several reasons as to why hinge results may deviate from a given backbone curve include:

• A sufficient number of multiple states should be specified on the Results Saved for Nonlinear Load Cases menu when running nonlinear static analysis.
• Strength loss (degradation), indicated by the negative slope of a backbone curve, is automatically limited to 10% of the frame-element elastic stiffness. Rationale is explained in the CSI Analysis Reference Manual (Strength Loss, page 135). A hinge-overwrite option is available through the Assign > Frame > Hinge Overwrites menu such that users may specify steeper strength degradation by using a small relative length on the order of 0.02.

• The backbone curve for a coupled hinge is only valid if the yield point on the interaction surface does not change. This may occur with P-M2-M3 hinges, for example, when P or M3 change, causing M2 to deviate from the backbone curve. Please keep in mind that the backbone curve represents a triaxial relationship between each of these parameters. See test problem Hinge response when yield point changes for an example.

## Should frame plasticity be modeled using nonlinear material properties or frame hinges?

Answer: Frame hinges must be specified to model nonlinear frame behavior. Nonlinear material parameters are then associated with hinge response, including the interaction surface and the moment-rotation curves which describe post-yield behavior. When implementing fiber hinges, material definition controls the stress-strain relationships of individual fibers.

## What is the difference between hinge and hysteretic-link application?

Isotropic, kinematic, Takeda, and pivot hysteresis models are available for single DOF hinges. For isotropic hysteresis, hinges unload elastically, parallel to the initial stiffness tangent (A-B slope), while for other hysteresis types, unloading follows a more complex nonlinear relationship.

For links, several additional hysteretic models are available. Hysteretic behavior may be specified for multiple degrees-of-freedom using a single link.

Additional information can be found in the Hinge and link comparison article.

## Can PM and PMM hinges be used to model energy dissipation?

Answer: Yes, energy is dissipated for PM and PMM hinges. In fact, these always use isotropic dissipation, which dissipates more energy than the kinematic, Takeda, and Pivot rules available for the single DOF hinges.

## How does the plastic-hinge deformation-curve scale factor affect analysis?

Answer: For response, please see the CSI Analysis Reference Manual (Scaling the Curve, page 135).

## Why are two hinges shown, one on each side, when only one hinge is defined?

Answer: The graphical display of two hinges is merely a convention which shows the same hinge on either side of a meshed joint into which other members frame.

## How are hinges assigned to steel pipe sections?

Answer: To assign hinges to a steel pipe section, define a User Hinge, then assign this hinge type to the section. As an alternative, fiber hinges may be assigned. The software will then automatically determine the fiber layout according to the section shape.

## Why is fiber-hinge state always given as A ≤ B, even when plastic behavior is achieved?

Answer: Hinge states A, B, C, D, and E are used to define the moment-rotation curve of a coupled P-M2-M3 hinge. These parameters are not applicable to fiber P-M2-M3 hinges, therefore fiber-hinge state is always given as A ≤ B because computation does not involve their values.

Fiber-hinge response is derived from the nonlinear constitutive model defined for each material within the frame-element cross section. Plastic force-displacement and moment-rotation curves are obtained by integrating the axial behavior of the individual fibers which populate the cross section.

Users may display the cross-section moment-rotation curve, or individual fiber stress-strain curves, through the Display > Show Hinge Results menu.

## What is the difference between deformation-controlled (ductile) and force-controlled (brittle) hinge types?

Answer: For steel members, ductile hinges are based on effective strengths, which are the expected material properties, and according to FEMA-356, are recommended for deformation-controlled actions.

For steel members, brittle hinges are based on minimum strengths, which are the lower bounds of material properties, and are recommended for force-controlled actions.

For reinforcement in concrete members, minimum strengths are currently being used for both deformation-controlled and force-controlled hinges.

## Does unbraced length influence the FEMA P-M hinge interaction surface?

Answer: The hinge interaction surface is considered to be a property of the cross section, and not the entire member. Therefore unbraced length is not considered during interaction-surface calculation. The interaction surface envelopes all yield points which characterize the onset of plasticity in extreme fibers under combined loading conditions. Hinge capacity is associated with the frame or tendon cross section local to hinge location. Flexural and buckling capacity are two parameters which are associated with unbraced length.

Users who wish to consider unbraced length during interaction-surface calculation have the option to manually define P-M hinge properties and yield criteria. Moment-rotation curves may be developed through nonlinear analysis of members modeled using shell elements which would capture localized buckling of slender members.

## Why are plastic-hinge colors not displayed when viewing FNA deformation?

Answer: Please note that hinges are not active during Fast Nonlinear Analysis (FNA), only during nonlinear static and direct-integration time-history analyses.

FNA is based upon the mode-superposition method, intended for primarily linear-elastic systems which may have a limited number of predefined nonlinear elements. An elastic building with isolation and damping devices, for instance, would be suitable for dynamic-linear analysis.