Inelastic stability of tapered frames with residual stress effect

The instability of a structure due to external critical loading is identified as that the external loading causes the stiffness matrix to become singular or the determinant of the stiffness matrix to become zero. A numerical analysis technique for determining the inelastic buckling loads for steel tapered frames with residual stress effect is presented. In this proposed method, tapered members are modeled as a series of uniform segments and each segment is modeled as several discrete elements. The geometric and material nonlinear responses of structure are generated by an incremental load approach with a secant type of iteration method at each load level to satisfy equilibrium equations. The stability functions are utilized to account for the reduction of member bending stiffness due to the geometric nonlinearity. Effective area and effective moment of inertia are applied to represent the material nonlinearity in structural members.