An analytical method for calculating torsional constants for arbitrary complicated thin-walled cross-sections

Abstract

In this paper, an analytical method is proposed for calculating torsional constants for complicated thin-walled cross-sections with arbitrary closed or open rib stiffeners. This method uses the free torsional theory and the principle of virtual work to build governing equilibrium equations involving unknown shear flows and twisting rate. After changing the form of the equations and combining these two unknowns into one, torsional function, which is a function of shear flow, shear modulus, and twisting rate, is included in the governing equations as only one of the unknowns. All the torsional functions can be easily obtained from these homogeneous linear equations, and torsional constants can be easily obtained from the torsional functions. The advantage of this method is that we can easily and directly obtain torsional constants from the torsional functions, rather than the more sophisticated shear flow and twisting rate calculations. Finally, a complicated thin-walled cross-section is given as a valid numerical example to verify the analytical method, which is much more accurate and simpler than the traditional finite element method.