Explicit inelastic stiffness for beam elements with uniform and nonuniform cross sections

The quasi-plastic-hinge approach proposed by Attalla in 1994 for material nonlinear analysis is formulated using the total form expressions, which is generally computationally inefficient as numerical integrations and finite-difference schemes are required to obtain the elastic-plastic flexibility coefficients. To overcome the above drawback, the quasi-plastic-hinge approach is formulated in an incremental form for beams with uniform cross sections, by which the elastic-plastic flexibility coefficients are explicitly given. The procedure is directly extended to nonuniform beams through use of different moment-curvature relations for the two ends of the beam, or indirectly through subdivision of the beam into a number of inner segments. The elastic-plastic flexibility coefficients derived for both cases are also explicitly given. For comparison, three steel frames composed of nonuniform cross sections are studied, from which the accuracy of the proposed approaches for treating frames with uniform and nonuniform cross sections is verified.