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5.2.1.4 Parabolic Function

The tangent modulus model in Equation 5.3 is suitable for P/Py > 0.5, but is not sufficient to represent the stiffness degradation for cases with small axial forces and large bending moments. A gradual stiffness degradation of the plastic hinge is required to represent the distributed plasticity effects associated with bending actions. We shall introduce the hardening plastic-hinge model to represent the gradual transition from elastic stiffness to zero stiffness associated with a fully developed plastic hinge. When the hardening plastic hinges are present at both ends of an element, the incremental force-displacement relationship maybe expressed as [19]:

mA mb P

0 0

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