Exact dynamic stiffness matrix of a bending-torsion coupled beam including warping

It is known that an allowance for warping stiffness can change the natural frequencies of thin-walled open section beams substantially. The purpose of this paper is to investigate the magnitude of such changes by using an exact member theory. This is achieved by formulating an exact dynamic stiffness matrix for a typical beam member from established theory and linking this to a new and convenient procedure which extends the well-known Wittrick-Williams algorithm to ensure convergence upon any desired natural frequency. Numerical results are given for both single and continuous beams of the channel section for which some comparative results are available in the literature. The effect of warping stiffness on the natural frequencies is discussed and it is concluded that substantial error can be incurred if the effect is ignored.