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FIGURE 5.5 Parabolic plastic-hinge stiffness degradation function with a0 = 0.5 based on the load and resistance factor design sectional strength equation.

FIGURE 5.5 Parabolic plastic-hinge stiffness degradation function with a0 = 0.5 based on the load and resistance factor design sectional strength equation.

Fully plastic

LRFD plastic strength (a =1.0)

Fully plastic

LRFD plastic strength (a =1.0)

FIGURE 5.6 Smooth stiffness degradation for a work-hardening plastic hinge based on the load and resistance factor design sectional strength curve.

M/Mp

FIGURE 5.6 Smooth stiffness degradation for a work-hardening plastic hinge based on the load and resistance factor design sectional strength curve.

The parameter z represents a gradual stiffness reduction associated with flexure at sections. The partial plastification at cross-sections in the end of elements is denoted by 0 < z < 1. Z maybe assumed to vary according to the parabolic expression (Figure 5.5):

where a is the force-state parameter obtained from the limit state surface corresponding to the element end (Figure 5.6):

0 0

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