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A solid shaft and a hollow shaft are made of the same material and are of the same weight and length. Denoting by n the ratio c1/c2 show that the ratio Ts/Th of the torque Ts in the solid shaft to the torque Th in the hollow shaft is (a)
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Mechanics of Materials, 7th Edition
- 1. A steel shaft is subjected to the torques shown. The shaft is solid with a diameter of 1 in and G = 12,000 ksi. Determine: (a) internal torque (lb ft) in each segment. Include the necessary diagram to show these internal forces (b) maximum shear stress (psi) in each segment (c) rotation angle of pulley D w/r to the support of A. Follow the rule of signs given in the lecture. Include the necessary FBDs of sections.arrow_forwardThe motor on the left provides a torque of 5500 N•m to the gear shaft shown. The motor runs machines connected to gears B, C and D requiring torques of 3000 N•m, 1500 N•m and 1000 N•m respectively. A, B, C and D are spaced 2000 mm apart and the diameter of the shaft is 75 mm. The shear modulus of the shaft material is 80x109 N/m2. Determine: Minimum diameter required (in millimeters) if the shearing stress in the shaft is limited to 100x106 N/m2 Rotation of D with respect to A Note: Draw the Free Body Diagram, Compute for all of the necessary elements, Include the units/dimensions, use the proper formula and round-off all the answers and final answers to 3 decimal places.arrow_forwardA steel shaft of diameter 60 mm and length 3.5 m is fixed at its ends A and B. If two torques of the same direction are applied, a 500 Nm torque at C (Im from the left end) and a 200 Nm torque at D (1m from the right end), determine the maximum internal torque in the shaft.arrow_forward
- 2. In the gear system shown, the motor applies a torque of 600 N-m to the gear at A. Shafts (1) and (2) are solid shafts, and the bearings shown allow free rotation of the shafts. (a) Determine the torque TE provided by the gear system at gear E. (b) If the allowable shear stress in each shaft must be limited to 70 MPa, determine the minimum permissible diameter for each shaft. 72 teeth B 24 teeth (1) 30 teeth 60 teeth (2) Earrow_forward1. The hollow steel shaft (G=12 000000 Psi) must transmit a torque of 300000 lb-in. The total angle of twist must not exceed 3 degrees per 100 ft. the maximum shearing strength must not exceed 16000 Psi. (a) Find the inside diameter "d" if the outside diameter is equal to 12 inches. (b) Find the maximum torsional shear stress and (c) Find the maximum torsional shear strain.arrow_forwardThe 70-mm-diameter solid shaft shown is subjected to torques of 600 N·m and 1400 N·m at points B and C, respectively, determine the maximum shear stress in the shaft. (Unit: MPa)arrow_forward
- I at nd. end 3.8 Attaching a hollow shaft to a solid shaft creates the steel shaft. Determine the maximum torque T that may be applied to the ends of the shaft in the 3.5-m length without exceeding a shear stress of 70 MPa or a twist angle of 2.5°. For steel, use G = 83 GPa. =12 T 120mm Alvern de ww08 1914 90 ****************** 2.5m 2007 099 wwg/ 1.8m Oarrow_forward1. The 40-mm-diameter steel shaft is subjected to the torques shown. Determine the angle of twist of end B with respect to A. Use the sign convention for internal torques and take G= 75GPa. FBDs of cut sections OR an internal torque diagram is required for full credit. 80 N-m 20 N-m 30 N-m 600 mm 800 mm 200 mmarrow_forwardÀ solid 0.96-in.diameter shaft is subjected to the torques shown. The bearings shown allow the shaft to turn freely. Determine the shear stress magnitude in shaft (1). 10 Ib-A 50 Ib-ft 70 Ib-ft (1) (2) 30 Ib-f (3) 827 psi O 880 psi O 956 psi 691 psi O 739 psiarrow_forward
- A 88-N·m torque is applied to a hollow shaft having the cross section shown. Neglecting the effect of stress concentrations, determine the shearing stress at points a and b. The shearing stress at point a is MPa. The shearing stress at point b is MPa.arrow_forwardL1=1.8 L2=.9 d1370 d2=53 Compound shaft ACB is fixed at A and consisting of two solid circular sections AC & CB, as shown, and is subjected to the given distributed torque. The diameter of part AC is DI, and the diameter of part CB is D2. The material of the shaft having a shear modulus of 69 GPa. Determine (a) the maximum shear stress (KPa) developed in shaft AB, (b) the angle of twist of point B. The values of LI, L2, D1, and D2 are given in table below for each student. DI 50 Nm/m C 0.2 m LI L2arrow_forwardThe compound shaft carries the two torques shown. The shear moduli are 28 GPa for aluminum, 83 GPa for steel, and 35 Gpa for bronze. If T = 1168.7 Nm, U = 4515 Nm, x = 3.01 m, y = 2.36 m, z = 1.35 m, d = 90 mm, and e = 83 mm, find the angle of rotation of the free end of the shaft. Round off the final answer to two decimal places. U T Aluminum Steel Bronzearrow_forward
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