Torsion Part-II | Circular Bars of Linearly Elastic Materials | Torsion Formula | Angle of Twist

Shear stress in circular bars ____________________ Torsion Part-I | Torsional Deformations of a Circular Bar | Mechanics of Materials | Mech Engg.    • Torsion | Torsional Deformations of a Circ...   ____________________ Torsion Part-II | Circular Bars of Linearly Elastic Materials | Torsion Formula | Angle of Twist Mechanics of Materials Chapter # 3 | Torsion Chapter 3 is concerned with the twisting of circular bars and hollow shafts acted upon by torsional moments. First, we consider uniform torsion which refers to the case in which torque is constant over the length of a prismatic shaft, while nonuniform torsion describes cases in which the torsional moment and/or the torsional rigidity of the cross-section varies over the length. As for the case of axial deformations, we must relate stress and strain and also applied loading and deformation. For torsion, recall that Hooke’s Law for shear states that shearing stresses are proportional to shearing strains, with the constant of proportionality being G, the shearing modulus of elasticity. Both shearing stresses and shearing strains vary linearly with increasing radial distance in the cross-section, as described by the torsion formula. The angle of twist, 6, is proportional to the internal torsional moment and the torsional flexibility of the circular bar. Most of the discussion in this chapter is devoted to linear elastic behavior and small rotations of statically determinate members. However, if the bar is statically indeterminate, we must augment the equations of statical equilibrium with compatibility equations (which rely on torque-displacement relations) to solve for any unknowns of interest, such as support moments or internal torsional moments in members. Stresses on inclined sections also are investigated as a first step toward a more complete consideration of plane stress states in later chapters. Finally, a number of specialized and advanced topics (such as strain energy, shear flow in thin-walled tubes, and stress concentrations in torsion) are introduced.