Second order analysis of planar steel frames considering the effect of spread of plasticity

This paper presents a method of elastic-plastic analysis for planar steel frames that provides<br />the accuracy of distributed plasticity methods with the computational efficiency that is greater than that of<br />distributed plasticity methods but less than that of plastic-hinge based methods. This method accounts for<br />the effect of spread of plasticity accurately without discretization through the cross-section of a beam-column<br />element, which is achieved by the following procedures. First, nonlinear equations describing the<br />relationships between generalized stresses and strains of the cross-section are derived analytically. Next,<br />nonlinear force-deformation relationships for the beam-column element are obtained through lengthwise<br />integration of the generalized strains. Elastic-plastic flexibility coefficients are then calculated by<br />differentiating the above element force-deformation relationships. Finally, an elastic-plastic stiffness matrix<br />is obtained by making use of the flexibility-stiffness transformation. Adding the conventional geometric<br />stiffness matrix to the elastic-plastic stiffness matrix results in the tangent stiffness matrix, which can<br />readily be used to evaluate the load carrying capacity of steel frames following standard nonlinear<br />analysis procedures. The accuracy of the proposed method is verified by several examples that are<br />sensitive to the effect of spread of plasticity.