(7) A solid shaft of diameter X=18 mm and length of Y=0.8 m experiences torque using a short rod that is Z=569 mm long and is fixed at theopen end of shaft experiencing the torque. The torque is created with the application of a 750 N perpendicular force. The set-up is illustratedbelow in Figure Q7.Given the shaft has a shear modulus of 80 GPa, calculate the angle of twist in terms of degrees?State your answer to the nearest whole number.YmFigure Q7X mm750 NAZ mm

Answered: (7) A solid shaft of diameter X=18 mm…

Mechanics of Materials (MindTap Course List)

9th Edition

ISBN:9781337093347

Author:Barry J. Goodno, James M. Gere

Publisher:Barry J. Goodno, James M. Gere

Chapter1: Tension, Compression, And Shear

Section: Chapter Questions

Problem 1.3.17P: A stepped shaft ABC consisting of two solid, circular segments is subjected to torques T}and...

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A motor driving a solid circular steel shaft with diameter d = 1.5 in, transmits 50 hp to a gear at B, The allowable shear stress in the steel is 6000 psi. Calculate the required speed of rotation (number of revolutions per minute) so that the shear stress in the shaft does not exceed the allowable limit.
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.
What is the maximum power that can be delivered by a hollow propeller shaft (outside diameter 50 mm, inside diameter 40 mm, and shear modulus of elasticity 80 GPa) turning at 600 rpm if the allowable shear stress is 100 MPa and the allowable rate of twist is 3.0°/m?
A full quarter-circular fillet is used at the shoulder of a stepped shaft having diameter D2= 1.0 in. (see figure), A torque T = 500 lb-in. acts on the shaft. Determine the shear stress at the stress concentration for values as follows: D1= 0.7,0.8, and 0.9 in. Plot a graph showing versus D?
Compare the angle of twist 1 for a thin-walled circular tube (see figure) calculated from the approximate theory for thin-walled bars with the angle of twist 2 calculated from the exact theory of torsion for circular bars, Express the ratio 12terms of the non-dimensional ratio ß = r/t. Calculate the ratio of angles of twist for ß = 5, 10, and 20. What conclusion about the accuracy of the approximate theory do you draw from these results?
A long, thin-walled tapered tube AB with a circular cross section (see figure) is subjected to a torque T. The tube has length L and constant wall thickness t. The diameter to the median lines of the cross sections at the ends A and B are dAand dB, respectively. Derive the following formula for the angle of twist of the tube: Hint: If the angle of taper is small, you may obtain approximate results by applying the formulas for a thin-walled prismatic tube to a differential element of the tapered tube and then integrating along the axis of the tube.
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The hollow rod shown below is 2.99 meters long and is subjected to a torque of 988 Nm at end B. The diameter of the rod is 30 mm and has a wall thickness of 5 mm. The shear modulus of the material is 80 GPa, calculate the angle of twist in radians at B. TNm B meters
Problem 3
A metal shaft ABCD with variable cross-section is subjected to three external torques (T₁=28 kip- in, T2=8 kip-in, and T3=10 kip-in) as shown in the figure below. Each torque is acting at the locations marked with circular points along the shaft. Note that a 16-inch long segment of the shaft at the free end (right) has a 1-inch diameter bore. The dimensions (lengths and diameters) of the shaft are given in the figure. Assume deformation is linear elastic and take G=12×106 psi. D [3" 16"- X C T₁ 2" -32"- T₂ 1" diam. bore B -16"- A T3 the bar has a uniform diameter d along its full length, but external torques remain the same and are applied at the same locations. If the failure shear stress for the material is equal to Tfail = 10 ksi, and the factor of safety is equal to 2, determine the required (uniform) diameter d for the bar. Assume that the bar is solid for its entire length.
A solid constant-diameter circular shaft is subjected to torques TA = 420 lb- ft, TB = 1,040 lb- ft, TC = 850 lb-ft, andTD = 230 lb-ft, acting in the directions shown in the figure. The bearings shown allow the shaft to turn freely. (a) Plot a torque diagram showing the internal torque in segments (1), (2), and (3) of the shaft. Use the right-hand rule. (b) If the allowable shear stress in the shaft is 6,000 psi, what is the minimum acceptable diameter for the shaft?
A shaft has an external diameter (ED) of 350 mm and an internal diameter of 150 mm. i. Calculate the maximum shear stress in the shaft when it is transmitting 3700 kW at 100 rpm. ii. Find the angle of twist in a length of 20 x ED. (Assume G=75GN/m2). iii. If the hollow shaft is replaced by a solid shaft of the same weight and length, what power can it transmit for the same maximum shear stress?

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