 # G.17.4.1.6 Frame element hinge properties

Discrete hinge properties for frame elements are usually based on FEMA-356 criteria. As per section 5.5.2.2.2 of FEMA 356, in lieu of relationships derived from experiment or analysis, the generalized load deformation curve shown in the figure below, with parameters a, b, c, as defined in tables1.5.6 and 1.5.7, shall be used for components of steel moment frames. Modification of this curve shall be permitted to account for strain-hardening of components as follows:
1. a strain-hardening slope of 3% of the elastic slope shall be permitted for beams and columns unless a greater strain-hardening slope is justified by test data; and
2. where panel zone yielding occurs, a strain-hardening slope of 6% shall be used for the panel zone unless a greater strain-hardening slope is justified by test data. ### Generalized Force-Deformation Relationship for Components

• Point A is the origin
• Point B represents yielding. No deformation occurs in the hinge up to point B, regardless of the deformation value specified for point B. The displacement (rotation or axial elongation as the case may be) will be subtracted from the displacements at points C, D and E. Only plastic deformation beyond point B will be exhibited by hinge.
• Point C represents ultimate capacity of plastic hinge. At this point hinge strength degradation begins (hinge starts shedding load) until it reaches point D.
• Point D represents the residual strength of the plastic hinge. Beyond point D the component responds with substantially strength to point E.
• Point E represents total failure. At deformation greater than point E the plastic hinge will drop load to zero.

The parameters Q and QCE (Qy) in Figure 1-6 are generalized component load and generalized component expected strength, respectively. For beams and columns, θ is the total elastic and plastic rotation of the beam or column, θy is the rotation at yield. For braces Δ is total elastic and plastic displacement, and Δy is yield displacement.

Use of equations (1-6-1) and (1-6-2) to calculate the yield rotation, θy, where the point of contraflexure is anticipated to occur at the mid-length of the beam or column, respectively, shall be permitted.

For beams:

 θy = Z·FyeLb /(6·EIb) (1-6-1)

For columns:

 θy = Z·FyeLc /(6·EIc) (1 - P/Pye) (1-6-2)

Q and QCE are the generalized component load and generalized component expected strength, respectively. For flexural actions of beams and columns, QCE refers to the plastic moment capacity, which shall be calculated using equations (1-6-3) and (1-6-4):

For beams:

 QCE = MCE = Z·Fye (1-6-3)

For columns:

 QCE = MCE = 1.18·Z·Fye (1 - P/Pye) (1-6-4)

where
 E = Modulus of elasticity Fye = Expected yield strength of the material I = Moment of inertia Lb = Beam length Lc = Column length MCE = Expected flexural strength of a member or Joint, kip-in. P = Axial force of the member Pye = Expected axial yield force of the member = AgFye Q = Generalized component load QCE = Generalized component expected strength = Effective expected strength, which is defined as the statistical mean value of yield strengths, Qy, for a population of similar components, and includes consideration of strain hardening and plastic section development.