576 the solid steel shaft shown in figure p576 has a

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Unformatted text preview: and d, find the magnitude of maximum torsional shear stress in the shaft and the rotation of the section at B. Text A Figure P5.71 January, 2010 2.5L M. Vable Mechanics of Materials: Torsion of Shafts 5 245 5.72 A uniformly distributed torque of q in.·lb/in. is applied to the entire shaft, as shown in Figure P5.72. In addition to the distributed torque a concentrated torque of T = 3qL in.·lb is applied at section B. Let the shear modulus be G and the radius of the shaft r. In terms of q, L, G, and r determine (a) the rotation of the section at B; (b) the magnitude of maximum torsional shear stress in the shaft. 3qL in lb L q in lb/in Figure P5.72 B L 2L Design problems 5.73 A steel shaft (Gst = 80 GPa) and a bronze shaft (Gbr = 40 GPa) are securely connected at B, as shown in Figure P5.69. The magnitude of maximum torsional shear stresses in steel and bronze are to be limited to 160 MPa and 60 MPa, respectively. Determine the maximum allowable torque Text to the nearest kN·m that can act on the shaft. 5.74 A steel shaft (Gst = 80 GPa) and a bronze shaft (Gbr = 40 GPa) are securely connected at B, as shown in Figure P5.74. The magnitude of maximum torsional shear stresses in steel and bronze are to be limited to 160 MPa and 60 MPa, respectively, and the rotation of section B is limited to 0.05 rad. (a) Determine the maximum allowable torque T to the nearest kN·m that can act on the shaft if the diameter of the shaft is d = 100 mm. (b) What are the magnitude of maximum torsional shear stress and the maximum rotation in the shaft corresponding to the answer in part (a)? Text 1.5 m 3m Figure P5.74 5.75 A steel shaft (Gst = 80 GPa) and a bronze shaft (Gbr = 40 GPa) are securely connected at B, as shown in Figure P5.74. The magnitude of maximum torsional shear stresses in steel and bronze are to be limited to 160 MPa and 60 MPa, respectively, and the rotation of section B is limited to 0.05 rad. (a) Determine the minimum diameter d of the shaft to the nearest millimeter if the applied torque T = 20 kN · m. (b) What are the magnitude of maximum torsional shear stress and the maximum rotation in the shaft corresponding to the answer in part (a)? 5.76 The solid steel shaft shown in Figure P5.76 has a shear modulus of elasticity G = 80 GPa and an allowable torsional shear stress of 60 MPa. The allowable rotation of any section is 0.03 rad. The applied torques on the shaft are T1 = 10 kN·m and T2 = 25 kN· m. Determine (a) the minimum diameter d of the shaft to the nearest millimeter; (b) the magnitude of maximum torsional shear stress in the shaft and the maximum rotation of any section. T1 T2 d B Figure P5.76 1m 1.5 m C 2.5 m The diameter of the shaft shown in Figure P5.76 d = 80 mm. Determine the maximum values of the torques T1 and T2 to the nearest kN·m that can be applied to the shaft. Printed from: http://www.me.mtu.edu/~mavable/MoM2nd.htm 5.77 Composite Shafts 5.78 An aluminum tube and a copper tube, each having a thickness of 5 mm, are securely fastened to two rigid bars, as shown in Figure P5.78. The bars force the tubes to rotate by equal angles. The two tubes are 1.5 m long, and the mean diameters of the aluminum and copper tubes are 125 mm and 50 mm, respectively. The shear moduli for aluminum and copper are Gal = 28 GPa and Gcu = 40 GPa. Under the January, 2010 M. Vable Mechanics of Materials: Torsion of Shafts 5 246 action of the applied couple section B of the two tubes rotates by an angle of 0.03 rad Determine (a) the magnitude of maximum torsional shear stress in aluminum and copper; (b) the magnitude of the couple that produced the given rotation. Aluminum F A B Copper Figure P5.78 5.79 F Solve Problem 5.78 using Equations (5.18a) and (5.18b). 5.80 An aluminum tube and a copper tube, each having a thickness of 5 mm, are securely fastened to two rigid bars, as shown in Figure P5.78. The bars force the tubes to rotate by equal angles. The two tubes are 1.5 m long and the mean diameters of the aluminum and copper tubes are 125 mm and 50 mm, respectively. The shear moduli for aluminum and copper are Gal = 28 GPa and Gcu = 40 GPa. The applied couple on the tubes shown in Figure P5.78 is 10 kN·m. Determine (a) the magnitude of maximum torsional shear stress in aluminum and copper; (b) the rotation of the section at B. 5.81 Solve Problem 5.80 using Equations (5.18a) and (5.18b). 5.82 Solve Example 5.14 using Equations (5.18a) and (5.18b). 5.83 The composite shaft shown in Figure P5.83 is constructed from aluminum (Gal = 4000 ksi), bronze (Gbr = 6000 ksi), and steel (Gst = 12,000 ksi). (a) Determine the rotation of the free end with respect to the wall. (b) Plot the torsional shear strain and the shear stress across the cross section 30 in kips 1.5 in 2 in 25 in Aluminum Steel Bronze Figure P5.83 5.84 Solve Problem 5.83 using Equations (5.18a) and (5.18b). 5.85 If T = 1500 N · m in Figure P5.85, determine (a) the magnitude of maximum torsional shear stress in cast iron and copper; (b) the rotation of the section at D with respect to the section at A. T Figure P5.85 T A B Printe...
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This note was uploaded on 04/08/2010 for the course ENGR 232 taught by Professor Smith during the Spring '10 term at Aarhus Universitet.

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