A round steel shaft of diameter 0.1 m is subjected to an axial tensile load of 400 kN with a superimposed torque of 20 kN-m as shown in the figure. The yield strength of the shaft material is Sy = 500 MPa. S, = 500 MPa (a) Calculate the normal and shear stress at the white square in the diagram. (b) Calculate the principle shear stress at the white square. (c) Calculate the factor of safety corresponding to initial yielding of the shaft using the maximum shear stress theory.
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- A tubular bar with outside diameterd2= 4.0 in, is twisted by torques T = 70,0 kip-in. (see figure). Under the action of these torques, the maximum tensile stress in the bar is found to be 6400 psi. Determine the inside diameter rtf of the bar. If the bar has length L = 48.0 in. and is made of aluminum with shear modulus G = 4,0 × 106 psi, what is the angle of twist d (in degrees) between the ends of the bar? (c) Determine the maximum shear strain y (in radians)?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 segment of a generator shaft with a hollow circular cross section is subjected to a torque T = 240 kip-in, (see figure). The outer and inner diameters of the shaft arc 8.0 in, and 6.25 in., respectively. What is the maximum permissible compressive load /'that can be applied to the shaft if the allowable in-plane shear stress is rAi(m= 6250 psi
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- -8 An aluminum bar of solid circular cross section is twisted by torques T acting at the ends (see figure). The dimensions and shear modulus of elasticity arc L = 1.4 m, d = 32 mm, and G = 28 GPa. Determine the torsional stiffness of the bar. If the angle of twist of the bar is 5º, what is the maximum shear stress? What is the maximum shear strain (in radians)? If a hole of diameter d/2 is drilled longitudinally through the bar, what is the ratio of the torsional stiffnesses of the hollow and solid bars? What is the ratio of their maximum shear stresses if both arc acted on by the same torque? If the hole diameter remains at d/2, what new outside diameter d2will result in equal stiffnesses of the hollow and solid bars?A solid brass bar of diameter d = 1.25 in. is subjected to torques T1as shown in part a of the figure. The allowable shear stress in the brass is 12 ksi. What is the maximum permissible value of the torques T1? If a hole of diameter 0.625 in. is drilled longitudinally through the bar, as shown in part b of the figure, what is the maximum permissible value of the torques T2? What is the percent decrease in torque and the percent decrease in weight due to the hole?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).