Chapter 7 | Solution to Problems | Transformations of Stress and Strain | Mechanics of Materials

Problem 7.26: The steel pipe AB has a 102-mm outer diameter and a 6-mm wall thickness. Knowing that arm CD is rigidly attached to the pipe, determine the principal stresses and the maximum shearing stress at points H & K. Problem 7.55: Determine the principal planes and the principal stresses for the state of plane stress resulting from the superposition of the two states of stress shown. Problem 7.66: For the state of plane stress shown, determine the maximum shearing stress when (a) σx = 14 ksi and σy = 4 ksi, (b) σx = 21 ksi and σy = 14 ksi. (Hint: Consider both in-plane and out-of-plane shearing stresses.) Problem 7.85: The 38-mm-diameter shaft AB is made of a grade of steel for which the yield strength is σY = 250 MPa. Using the maximum shearing-stress criterion, determine the magnitude of the torque T for which yield occurs when P = 240 kN. Problem 7.86: Solve Prob. 7.85, using the maximum-distortion-energy criterion. Problem 7.95: The cast-aluminum rod shown is made of an alloy for which σUT = 70 MPa and σUC = 175 MPa. Knowing that the magnitude T of the applied torques is slowly increased and using Mohr’s criterion, determine the shearing stress τ0 that should be expected at rupture. Problem 7.100: The maximum gage pressure is known to be 1150 psi in a spherical steel pressure vessel having a 10-in. outer diameter and a 0.25-in. wall thickness. Knowing that the ultimate stress in the steel used is σU = 60 ksi, determine the factor of safety with respect to tensile failure.