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University of Anbar Engineering College Civil Engineering Department Strength of Materials Second Classroom Sheet No. 4 (Torsion) Q1: A solid steel shaft of diameter (12 in) is fixed at its ends A &B and carries a disk at C. Using all 10 ksi , then determine the maximum safe angle of rotation that can be given to the disk. Ans: 1o 30' A D=0.5" 12" B C 8" Q2: A solid steel shaft of circular cross section has a length of 300 mm and is tapered from 50-mm diameter at the small end to 100-mm diameter at the large end, as shown in Figure. The shaft is subject to a twisting moment of 1000 N.m applied at each end. For G = 80 GPa, determine the angle of twist between the ends and the peak shearing stress. Ans. 0.48°, 40.7 MPa Q3: The aluminum rod AB (G=27 GPa) is bonded to the brass rod BD (G=39 GPa). Knowing the portion CD of the brass rod I hollow and has an inner diameter (40mm), determine the angle of twist at point (A). Ans: 6.02o Q4: Determine the maximum shearing stresses in the aluminum core and steel shell, where a torque (100 N.m) applied at the free end. Use G=77.2 GPa for steel and G=27 GPa for aluminum. Ans: st 1.253 MPa, al 0.328 MPa Q5: The shaft has a radius (c) and is subjected to a uniform torque per unit length of (t o). If it is fixed at its far end (A), determine the angle of twist of end (B). Let shear modulus is (G). Ans: to L2 c 4G Q6: The steel shaft shown subjected to a uniform distributed torque of 60 lb.in/in. Determine the absolute maximum shear stess in the shaft. Use Gsteel= 11x103 ksi. Ans: 5.5 ksi. 60 lb.in/in 0.5" 1.0" B C A 5" 20" Q7: Check adequacy of the rod has a torque (T=50 N.m). Where the allowable shearing stress in all wall points is not exceed ( allowable 4.0 MPa ). Ans: A 3.94 MPa, B 2.36 MPa , Adequate because 4MPa .