Abstract
The present paper investigated the static analysis for the coupled torsional-warping response of open thin-walled doubly
symmetric beams subjected to various twisting moments and bimoments. The static equilibrium torsional-warping
coupling differential equations and associated boundary conditions for the thin-walled beams are derived using total
potential energy variational principle. The exact closed-form solutions for the beams having a cantilever, simply-supported,
fixed-fixed and fixed-fork boundary conditions and under various torsional and warping moments are determined. The
present solution is shown to successfully capture the coupled torsional-warping static response of the thin-walled beams
with various boundary conditions and by excluding and including axial static force effects. The validity and the accuracy of
the numerical results based on the present solution are accomplished throughout the numerical examples presented and
compared with well-established ABAQUS finite beam model solution and other exact solution available in the literature.