Approximate Closed-form Formulae for Buckling Analysis of Rectangular Tubes under Torsion

The buckling torque may be much less than the yield torque in very thin rectangular tubes under torsion. In this paper, simple closed-form formulae are presented for buckling analysis of long hollow rectangular tubes under torsion. By the presented formulae, one can obtain the critical torque or the critical angle of twist of the tube in terms of its geometrical parameters and material constants. First, an approximate function for critical angle of twist, including a part in terms of the Poisson’s ratio and another part in terms of geometrical parameters with unknown coefficients are considered. Then, the unknown coefficients are found by a minimax optimization method and also by using the accurate results obtained by the finite element method. The formulae can be used for a wide range of dimensions of hollow rectangular tubes. The numerical studies show that the maximum error of the presented formulae is less than 10%.