# G.17.4.1.6 Frame element hinge properties

- 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
- 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 Q_{CE} (Q_{y}) 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, θ_{y} is the rotation at yield. For braces Δ is total elastic and plastic displacement, and Δ_{y} is yield displacement.

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

For beams:

θ_{y} = Z·F_{ye}L_{b} /(6·EI_{b}) | (1-6-1) |

For columns:

θ_{y} = Z·F_{ye}L_{c} /(6·EI_{c}) (1 - P/P_{ye}) | (1-6-2) |

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

For beams:

Q_{CE} = M_{CE} = Z·F_{ye} | (1-6-3) |

For columns:

Q_{CE} = M_{CE} = 1.18·Z·F_{ye} (1 - P/P_{ye}) | (1-6-4) |

= | ||

_{ye}
| = | |

= | ||

_{b}
| = | |

_{c}
| = | |

_{CE}
| = | |

= | ||

_{ye}
| = | _{g}F_{ye} |

= | ||

_{CE}
| = | _{y}, for a population of similar components, and includes consideration of strain hardening and plastic section development. |