The following will be discussed in this chapter: Torsional loads on circular shafts, net torque due to internal stresses, axial shear components, shaft deformations, shearing strain, stresses in elastic range, normal stresses, torsional failure modes, angle of twist in elastic range,. | Third Edition CHAPTER MECHANICS OF MATERIALS Ferdinand P. Beer E. Russell Johnston, Jr. John T. DeWolf Torsion Lecture Notes: J. Walt Oler Texas Tech University © 2002 The McGraw-Hill Companies, Inc. All rights reserved. Third Edition MECHANICS OF MATERIALS Beer • Johnston • DeWolf Contents Introduction Statically Indeterminate Shafts Torsional Loads on Circular Shafts Sample Problem Net Torque Due to Internal Stresses Design of Transmission Shafts Axial Shear Components Stress Concentrations Shaft Deformations Plastic Deformations Shearing Strain Elastoplastic Materials Stresses in Elastic Range Residual Stresses Normal Stresses Example Torsional Failure Modes Torsion of Noncircular Members Sample Problem Thin-Walled Hollow Shafts Angle of Twist in Elastic Range Example © 2002 The McGraw-Hill Companies, Inc. All rights reserved. 3-2 Third Edition MECHANICS OF MATERIALS Beer • Johnston • DeWolf Torsional Loads on Circular Shafts • Interested in stresses and strains of circular shafts subjected to twisting couples or torques • Turbine exerts torque T on the shaft • Shaft transmits the torque to the generator • Generator creates an equal and opposite torque T’ © 2002 The McGraw-Hill Companies, Inc. All rights reserved. 3-3 Third Edition MECHANICS OF MATERIALS Beer • Johnston • DeWolf Net Torque Due to Internal Stresses • Net of the internal shearing stresses is an internal torque, equal and opposite to the applied torque, T = ∫ ρ dF = ∫ ρ (τ dA) • Although the net torque due to the shearing stresses is known, the distribution of the stresses is not • Distribution of shearing stresses is statically indeterminate – must consider shaft deformations • Unlike the normal stress due to axial loads, the distribution of shearing stresses due to torsional loads can not be assumed uniform. © 2002 The McGraw-Hill Companies, Inc. All rights reserved. 3-4 Third Edition MECHANICS OF MATERIALS Beer • Johnston
