What is the maximum torque 8 the tube can transmit if

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Unformatted text preview: 00 mm at A to 50 mm at B. The shaft between B and C has a constant radius of 50 mm. The shear modulus of the material is G = 40 GPa. Determine (a) the angle of rotation of wheel C with respect to the fixed end; (b) the maximum shear strain in the shaft 10 kN ⋅ m 2.5 kN ⋅ m Figure P5.36 x A C B 7.5 m 2m – ax 5.37 The radius of the tapered shaft in Figure P5.37 varies as R = Ke . Determine the rotation of the section at B in terms of the applied torque Text, length L, shear modulus of elasticity G, and geometric parameters K and a. Text m Figure P5.37 x 5.38 The radius of the tapered shaft shown in Figure P5.37 varies as R = r ( 2 – 0.25 x ⁄ L ) . In terms of Text, L, G, and r, determine (a) the rotation of the section at B; (b) the magnitude of maximum torsional shear stress in the shaft. Printed from: http://www.me.mtu.edu/~mavable/MoM2nd.htm Distributed torques 5.39 The external torque on a drill bit varies as a quadratic function to a maximum intensity of q in.·lb/in., as shown in Figure P5.39. If the drill bit diameter is d, its length L, and its modulus of rigidity G, determine (a) the maximum torsional shear stress on the drill bit; (b) the relative rotation of the end of the drill bit with respect to the chuck. L x ⎛ x2⎞ q ⎜ ------⎟ in. ⋅ lb/in. ⎝ L 2⎠ Figure P5.39 January, 2010 M. Vable Mechanics of Materials: Torsion of Shafts 5 235 5.40 A circular solid shaft is acted upon by torques, as shown in Figure P5.40. Determine the rotation of the rigid wheel A with respect to the fixed end C in terms of q, L, G, and J. TA 2qL in lb TB in q in A Figure P5.40 B 0.5 L 0 .5 L Design problems -5.41 A thin steel tube (G = 12,000 ksi) of 1-in. thickness has a mean diameter of 6 in. and a length of 36 in. What is the maximum torque 8 the tube can transmit if the allowable torsional shear stress is 10 ksi and the allowable relative rotation of the two ends is 0.015 rad? Determine the maximum torque that can be applied on a 2-in. diameter solid aluminum shaft (G = 4000 ksi) if the allowable torsional shear stress is 18 ksi and the relative rotation over 4 ft of the shaft is to be limited to 0.2 rad. 5.42 A hollow steel shaft (G = 80 GPa) with an outside radius of 30 mm is to transmit a torque of 2700 N·m. The allowable torsional shear stress is 120 MPa and the allowable relative rotation over 1 m is 0.1 rad. Determine the maximum permissible inner radius to the nearest millimeter. 5.43 5.44 A 5-ft-long hollow shaft is to transmit a torque of 200 in.·kips. The outer diameter of the shaft must be 6 in. to fit existing attachments. The relative rotation of the two ends of the shaft is limited to 0.05 rad. The shaft can be made of steel or aluminum. The shear modulus of elasticity G, the allowable shear stress τallow, and the specific weight γ are given in Table P5.44. Determine the maximum inner -diameter to the nearest 1 in. of the lightest shaft that can be used for transmitting the torque and the corresponding weight. 8 TABLE P5.44 τallow (ksi) G (ksi) Material γ (lb/in.3) Steel 12,000 18 0.285 Aluminum 4,000 10 0.100 Transmission of power Power P is the rate at which work dW ⁄ dt is done; and work W done by a constant torque is equal to the product of torque T and angle of rotation φ. Noting that ω = d φ ⁄ dt , we obtain P = Tω = 2πf T (5.16) where T is the torque transmitted, ω is the rotational speed in radians per second, and f is the frequency of rotation in hertz (Hz). Power is reported in units of horsepower in U.S. customary units or in watts. 1 horsepower (hp) is equal to 550 ft·lb/s = 6600 in·lb/s and 1 watt (W) is equal to 1 N·m/s. Use Equation (5.16) to solve Problems 5.38 through 5.40. 5.45 A 100-hp motor is driving a pulley and belt system, as shown in Figure P5.45. If the system is to operate at 3600 rpm, determine the -minimum diameter of the solid shaft AB to the nearest 1 in. if the allowable stress in the shaft is 10 ksi. Printed from: http://www.me.mtu.edu/~mavable/MoM2nd.htm 8 Figure P5.45 5.46 The bolts used in the coupling for transferring power in Problem 5.45 have an allowable strength of 12 ksi. Determine the minimum --number (> 4) of 1-in. diameter bolts that must be placed at a radius of 5 in. 4 8 5.47 A 20-kW motor drives three gears, which are rotating at a frequency of 20 Hz. Gear A next to the motor transfers 8 kW of power. Gear B, which is in the middle, transfers 7 kW of power. Gear C, which is at the far end from the motor, transfers the remaining 5 kW of power. A single solid steel shaft connecting the motors to all three gears is to be used. The steel used has a yield strength in shear of 145 January, 2010 M. Vable Mechanics of Materials: Torsion of Shafts 5 236 MPa. Assuming a factor of safety of 1.5, what is the minimum diameter of the shaft to the nearest millimeter that can be used if failure due to yielding is to be avoided? What is the magnitude of maximum torsional stress in the segment between gears A and B? Stretch yourself 5.48 A circular shaft has a constant torsional rigidity GJ and is acted upon by a distributed torque t(x). If at section A the internal torque is zero, show that the relativ...
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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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