Accurate Stiffness Matrix for Nonprismatic Members

In this note, the transfer matrix method is adopted to deduce general expressions for the components of the stiffness matrix and equivalent node load vector of nonprismatic members, and the effect of warping is not considered. State vectors are introduced to describe the nodal forces and displacements of a structural member. The relation between the state vectors of the left node and the right node of the member is given by a matrix referred to as the transfer matrix. It is found that the stiffness matrix of the member can be expressed in terms of the transfer matrix. Therefore, an accurate expression for the stiffness matrix can be obtained as long as the corresponding transfer matrix can be accurately determined. The method proposed is a general procedure for the stiffness matrix derivation of both continuous nonprismatic members and discontinuous nonprismatic members. The correctness of the obtained stiffness expressions is verified by two simple numerical examples.