Mechanics of Materials
11th Edition
ISBN: 9780137605460
Author: Russell C. Hibbeler
Publisher: Pearson Education (US)
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The aluminum shaft, composed of three segments is fastened to rigid supports as A and D.
Calculate the maximum shear stress in each segment when the two torques are applied.
A
400 N-m
850 N-m
L=1.4 m
30 mm diameter
B
L=2.4 m
50 mm diameter
L-1.9 m
30 mm diameter
The 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
Bronze
two solid steel shafts of different diameters are joined together at point C. the diameter of the smaller shaft is 0.5 in, while the diameter of the larger shaft is 1 in. if the supports at both ends, A & B, are unyielding / rigid, and a counterclockwise torque of 500 ft lb at point D, determine the maximum shear stress in the shaft in ksi. The modulus of rigidity for steel is 10800 ksi.Show full solution please
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- Two solid steel shafts of different diameters are joined together at point C. The diameter of the smaller shaft is 0.5 inch, while the diameter of the larger shaft is 1 inch. If the supports at both ends, A & B, are unyielding / rigid, and a counterclockwise torque of 500 ft lb is applied at point D, determine the maximum shear stress in the shaft in ksi. The modulus of rigidity for steel is 10800 ksi. 8 in 5 in 12 inarrow_forwardThe diameter of and LcD = 240 mm. 1. The lengths LAB = LBC = 200 mm parts AB and CD of the bar is 25 mm and the diameter of part BC is 50 mm. The shear modulus of the material is G = 80 GPa. If the torque T = 2.2 kN- m, determine the magnitude of the angle of twist of the right end of the bar relative to the wall in degrees. 4 kN-m 8 kN-m LAB. LBC. 2. The lengths LAB = LBC = 200 mm and LCD = 240 mm. The diameter of parts AB and CD of the bar is 25 mm and the diameter of part BC is 50 mm. The shear modulus of the material is G = 80 GPa. What value of the torque T would cause the angle of twist of the right end of the bar relative to the wall to be zero? 4 kN-m 8 kN-m LAB. T LBCarrow_forwardThe solid-circular member AC, having a diameter D and a shear modulus of 69 GPa, is subjected to the torques 2T and 3T at points A and B, respectively. If tallow = 35 MPa and (fA/C)allow =2o, determine the maximum permissible value of the torque T. Use the table given below and your student ID to find the values of L1, L2, and D. Student ID L1 (m) L2 (m) D (mm) 1131731 1 0.6 78arrow_forward
- A solid shaft has a diameter of 25 mm and is subjected to a torque of 200 Nm at one end.Determine the maximum shear stress in the shaft and the angle of twist over 0.8 m length.Given that the Modulus of Rigidity, G = 85GPa.arrow_forwardThe tube is made of C86100 bronze and has a rectangular cross section asshown in Figure. If it is subjected to the two torques, determine the average shear stress in the tube at points A and B. Also, what is the angle of twist of end C? The tube is fixed at E.arrow_forwardA tapered, wrought iron shaft of length 5 ft, has 2 inch diameter at the fixed end and 0.8 inch diameter at the free end. Determine the angle of twist of the shaft, if it carries a torque, T = 2000 lb-in at the free end. Use G = 10^7 psi for wrought iron.arrow_forward
- A compound shaft consists of two pipe segments. Segment (1) has an outside diameter of 212 mm and a wall thickness of 9 mm. Segment (2) has an outside diameter of 139 mm and a wall thickness of 11 mm. The shaft is subjected to torques TB = 47 kN-m and Tc = 24 kN-m, which act in the directions shown. Determine the maximum shear stress magnitudes 7₁, 72 in each shaft segment. Answers: T1 = i T2 = i (1) (2) MPa. MPa.arrow_forwardThe solid-circular member AC, having a diameter D and a shear modulus of 69 GPa, is subjected to the torques 2T and 3T at points A and B, respectively. If Tallow = 35 MPa and (OA/c)allow =2°. detemine the maximum pemissible value of the torque T. Use the table given below and your student ID to find the values of L1, L2, and D. B A 3T 2T Student L1 (m) L2 (m) D ID (mm) 1131731 1 0.6 78arrow_forwardThe wrench is applied to two forces each of magnitude P. The steel shaft AB has a diameter of 15 mm. If the shear stress in the shaft is not exceed 120 MPa and the angle of twist is not exceed 5; find the largest allowable of P. For steel; use G = 80 GPa.arrow_forward
- The brass wire has a triangular cross section, 2 mm on a side. If the yield stress for brass is tY = 205 MPa, determine the maximum torque T to which it can be subjected so that the wire will not yield. If this torque is applied to the 4-m-long segment, determine the greatest angle of twist of one end of the wire relative to the other end that will not cause permanent damage to the wire. Gbr = 37 GPa.arrow_forwardThe torque of 100 kip - ft is applied in the 16-ft-long hollow steel shaft. Note that the inner diameter of the shaft is two-thirds of its outer diameter D. If the inner diameter is 8 inches, find the angle of twist of the shaft. Use G = 12 x 10^6 psi for steel.arrow_forwardThe electric motor exerts a torque of 800N*m on the steel shaft ABCD when it rotates at a constant speed. Design specifications require that the shaft diameter is uniform from A to D and that the angle of twist between A and D does not exceed 1.5°. If it is known that the maximum shear must be less than or equal to 60MPa and G=77GPa. Determine the diameter which can be used for the axis. The figure is in the attached imagearrow_forward
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