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 providesthe accuracy of distributed plasticity methods with the computational efficiency that is greater than that ofdistributed plasticity methods but less than that of plastic-hinge based methods. This method accounts forthe effect of spread of plasticity accurately without discretization through the cross-section of a beam-columnelement, which is achieved by the following procedures. First, nonlinear equations describing therelationships between generalized stresses and strains of the cross-section are derived analytically. Next,nonlinear force-deformation relationships for the beam-column element are obtained through lengthwiseintegration of the generalized strains. Elastic-plastic flexibility coefficients are then calculated bydifferentiating the above element force-deformation relationships. Finally, an elastic-plastic stiffness matrixis obtained by making use of the flexibility-stiffness transformation. Adding the conventional geometricstiffness matrix to the elastic-plastic stiffness matrix results in the tangent stiffness matrix, which canreadily be used to evaluate the load carrying capacity of steel frames following standard nonlinearanalysis procedures. The accuracy of the proposed method is verified by several examples that aresensitive to the effect of spread of plasticity.