16 - Torsion of circular shafts and thin-walled tubes

Abstract

This chapter examines the uniform torsion of circular shafts, thin-walled tubes, and thin-walled open sections. The simplest torsion problem is that of the twisting of a uniform thin circular tube. The torsion of a thin circular tube is a relatively simple problem as the shearing stress may be assumed constant throughout the wall thickness. The case of a solid circular shaft is more complex because the shearing stresses are variable over the cross-section of the shaft. Along any radius of the cross-section, the shearing stresses are normal to the radius and in the plane of the cross-section. The torsional failure of ductile materials occurs when the shearing stresses attain the yield stress of the material. The greatest shearing stresses in a circular shaft occur in a cross-section, along the length of the shaft. When a circular shaft is subjected to longitudinal thrust or tension as well as twisting, the direct stresses due to the longitudinal load must be combined with the shearing stresses to evaluate the principal stresses in the shaft.