Summary

In this paper, the tangent stiffness matrix of the four-termed element is presented using the principle of stationary potential energy. The accuracy of the element is identical with stability function and the element overcomes the difficulty that the formulae of the stability function are different when the sign of axial force changes. The formulated element can be used for geometric nonlinear analysis by one element per member as well as describe the effect of axial-torsion buckling (Wagner effect) exactly. On the basis of the formulation of the four-termed element, using the flow theory and the Orbison's yielding surface, the second-order elasto-plastic stiffness matrix of the 3D beam-column element is derived. The model can accurately depict the effects of inner gradual plastic-hinge and the internal forces redistribution. Plastic-hinge can form at arbitrary position along the element. The proposed formulation can be used for accurate entire process analysis of space steel frame of tall buildings. The elastic and inelastic analysis can be implemented using same model by the condensation technique that eliminates the internal freedoms so the structure of the analyzing program need not be modified. Theoretically, this model is accurate and shows its advantage on the structural advanced analysis. Its validity is verified by several numerical examples.