Q2 / A solid steel [G= 80 GPa] shaft of variable diameter is subjected to the torques shown in Figure. The diameter of the shaft in segments (1) and (3) is 50 mm, and the diameter of the shaft in segment (2) is 80 mm. The bearings shown allow the shaft to turn freely. (a) Determine the maximum shear stress in the compound (b) Determine the rotation angles of pulleys B,C and D with respect to pulley A. shaft. 500 N-m 4,500 N-m (1), 2,800 N-m (2) 1,200 N-m (3) 0.70 m 1.80 m D 0.70 m

Q2 / A solid steel [G= 80 GPa] shaft of variable diameter is subjected to the torques shown in Figure. The diameter of the shaft in segments (1) and (3) is 50 mm, and the diameter of the shaft in segment (2) is 80 mm. The bearings shown allow the shaft to turn freely. (a) Determine the maximum shear stress in the compound (b) Determine the rotation angles of pulleys B,C and D with respect to pulley A. shaft. 500 N-m 4,500 N-m (1), 2,800 N-m (2) 1,200 N-m (3) 0.70 m 1.80 m D 0.70 m

Mechanics of Materials (MindTap Course List)

9th Edition

ISBN:9781337093347

Author:Barry J. Goodno, James M. Gere

Publisher:Barry J. Goodno, James M. Gere

Chapter3: Torsion

Section: Chapter Questions

Problem 3.5.11P: -11 A solid steel bar (G = 11.8 X 106 psi ) of diameter d = 2,0 in. is subjected to torques T = 8.0...

See similar textbooks

Similar questions

The stepped shaft shown in the figure is required to transmit 600 kW of power at 400 rpm. The shaft has a full quarter-circular fillet, and the smaller diameter D1= 100 mm. If the allowable shear stress at the stress concentration is 100 MPa, at what diameter will this stress be reached? Is this diameter an upper or a lower limit on the value of D2?
A hollow tube ABCDE constructed of monel metal is subjected to five torques acting in the directions shown in the figure. The magnitudes of the torques are T1= 1000 lb-in., T2= T4= 500 lb-in., and T3= T5= 800 lb-in. The tube has an outside diameter of d2= 1.0 in. The allowable shear stress is 12,000 psi and the allowable rate of twist is 2.0°/ft. Determine the maximum permissible inside diameter d1, of the tube.
The propeller shaft of a large ship has an outside diameter 18 in. and inside diameter 12 in,, as shown in the figure. The shaft is rated for a maximum shear stress of 4500 psi. If the shaft is turning at 100 rpm, what is the maximum horsepower that can be transmitted without exceeding the allowable stress? If the rotational speed of the shaft is doubled but the power requirements remain unchanged, what happens to the shear stress in the shaft?
A stepped shaft ABC consisting of two solid, circular segments is subjected to torques T}and T2acting in opposite directions, as shown in the figure. The larger segment of the shaft has a diameter of dv- 2.25 in. and a length Lt= 30 in.; the smaller segment has a diameter d2— 1.75 in. and a length L, = 20 in. The torques are T, = 21,000 lb-in. and fz=10.000 lb-in. (a) Find reaction torque TAat support A. (b) Find the internal torque T(x) at two locations: x = L1/2 and x = L1+ L2/2. Show these internal torques on properly drawn free-body diagrams (FBDs).
A propeller shaft for a small yacht is made of a solid steel bar 104 mm in diameter. The allowable stress in shear is 48 MPa, and the allowable rate of twist is 2.0° in 3.5 meters. (a) Assuming that the shear modulus of elasticity is G = 80 GPa, determine the maximum torque that can be applied to the shaft. (b) Repeat part (a) if the shaft is now hollow with an inner diameter of 5d18. Compare values to corresponding values from part (a).
A circular aluminum tube subjected to pure torsion by torques T(sec figure) has an outer radius r2equal to 1.5 times the inner radius r1. (a) If the maximum shear strain in the tube is measured as 400 × 10-6 rad, what is the shear strain y1at the inner surface? (b) If the maximum a1lo-abk rate of twist is 0.125 °/m and the maximum shear strain is to be kept at 400 × 10-6 rad by adjusting the torque T, that is the minimum required outer radius ( r2)Min?
A hollow steel shaft used in a construction auger has an outer diameter d2= 6.0 in. and inner diameter d1= 4.5 in. (see figure). The steel has a shear modulus of elasticity G = 11.0 × 106 psi. For an applied torque of 150 kip-in., determine the following quantities: shear stress at the outer surface of the shaft, shear stress at the inner surface, and rate of twist (degrees per unit of length). Also, draw a diagram showing how the shear stresses vary in magnitude along a radial line in the cross section.
When drilling a hole in a table leg, a furniture maker uses a hand-operated drill (see figure) with a bit of diameter d = 4.0 mm. If the resisting torque supplied by the table leg is equal to 0.3 N · m, what is the maximum shear stress in the drill bit? If the allowable shear stress in the drill bit is 32 MPa, what is the maximum resisting torque before the drill binds up? If the shear modulus of elasticity of the steel is G = 75 GPa, what is the rate of twist of the drill bit (degrees per meter)?
-11 A solid steel bar (G = 11.8 X 106 psi ) of diameter d = 2,0 in. is subjected to torques T = 8.0 kip-in. acting in the directions shown in the figure. Determine the maximum shear, tensile, and compressive stresses in the bar and show these stresses on sketches of properly oriented stress elements. Determine the corresponding maximum strains (shear, tensile, and compressive) in the bar and show these strains on sketches of the deformed elements.
A solid circular bar A BCD with fixed supports at ends A and D is acted upon by two equal and oppositely directed torques T0, as shown in the figure. The torques arc applied at points B and C each of which is located at distance x from one end of the bar. (The distance x may vary from zero to L/2.) For what distance x will the angle of twist at points B and C be a maximum? What is the corresponding angle of twist 0max?
A solid aluminum bar (G = 27 GPa ) of diameter d = 40 mm is subjected to torques T = 300 N - m acting in the directions shown in the figure, Determine the maximum shear, tensile, and compressive stresses in the bar and show these stresses on sketches of properly oriented stress elements. Determine the corresponding maximum strains (shear, tensile, and compressive) in the bar and show these strains on sketches of the deformed elements.
A tubular shaft being designed for use on a construction site must transmit 120 kW at 1,75 Hz, The inside diameter of the shaft is to be one-half of the outside diameter. If the allowable shear stress in the shaft is 45 MPa, what is the minimum required outside diameter d?