Approximate analysis of non-uniform torsion. (15th November 2021) - Trahair, Nicholas; Papangelis, John
Highlights: Exact analysis of non-uniform torsion is difficult. Addition of uniform and warping torsion stiffnesses leads to approximate solutions. Computer programs are not needed. Approximations are generally of acceptable accuracy. Superposition allows solutions for many torque distributions. Abstract: It is difficult to obtain closed form exact solutions for the non-uniform torsion of beams. Advanced finite element methods easily produce very accurate solutions, but simple programs are not widely available. One simple program is validated by comparing its solutions with closed form solutions. A simple approximate method is proposed which combines the uniform and warping torsion stiffness approximations. The determination of the warping stiffness approximation is simplified by using the moment-area method. The approximate twist rotations are compared with the accurate solutions, are shown to be of generally acceptable accuracy, and in most cases to be conservative. Approximate solutions for the central twist rotations of simply supported beams with off-centre torques can be combined using superposition to find solutions for a wide range of torque loadings. A worked example is given.