Second-order inelastic analysis of steel frames using element with midspan and end springs

An efficient method for elastoplastic large-deflection analysis of steel frames using an element with plastic hinges at midspan and two ends is proposed. The need in conventional methods to divide a member into two or more elements to model the distributed loads, and the need to allow for a plastic hinge at its span is eliminated. The formation of plastic hinges is simulated as gradually softening springs. This approach prevents the overestimation of the capacity of a steel frame and also reduces the complexity in data handling. Because the element stiffness matrix is explicitly derived, the additional computational effort for forming the element matrix only involves a few algebraic calculations and is therefore minimal. The saving in the overall computer time and data input and output efforts is considerable since a single element can be used to model one beam member in the ultimate analysis of most practical structures. Most importantly, the linear structural model can be directly used for a second-order inelastic analysis, leading to a convenience and consistency in extending a linear analysis to a nonlinear analysis.