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Problem #1: A steel rod of diameter d=50 mm and yield strength Oy = 300 MPa supports an axial force P and a vertical force F acting at the end of a 0.8 m-long arm, as shown in Figure 1. The axial force P is a multiple a of the vertical force F, so that P=aF. Using a safety factor of n=2, answer the following questions: a) Based on the maximum shear stress criterion, determine (as a function of a) the largest permissible value of F. b) Base on the maximum distortional strain energy criterion, determine (as a function of a) the largest permissible value of F. c) Plot the results obtained in parts a) and b) for the range -100 < O < 100, and calculate the exact numerical results for a=50. Problem #2: A closed, thin walled cylindrical pressure vessel of mean diameter d = 250 mm and wall thickness t = 5 mm is subjected to an internal pressure pi = 2.8 MPa, a torque (along its longitudinal axis) of T = 31.36 kN-m, and an axial thrust (in tension) of F = 45 kN. The ultimate strengths of the material are OUT = 210 MPa (in tension) and Ouc = 500 MPa (in compression). a) Use the maximum principal stress criterion to determine if the tube will fail by fracture. b) Use the Mohr-Coulomb criterion to determine if the tube will fail by fracture. c) Assume that the value of the torque T was not given. Use the maximum principal stress criterion to determine the critical value T at which the tube would just fail. (Use all other parameter values given above.) d) Assume that the value of the torque T was not given. Use the Mohr-Coulomb criterion to determine the critical value of T at which the tube would just fail. (Use all other parameter values given above.) 1.2 m d z F , 0.8m Figure 1

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