e following is TRUE for a hollow circular shaft subjected to a uniformly distributed in the elastic range such as what is shown in the figure? a b A B
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- A steel punch consists of two shafts: upper shaft and lower shaft. Assume that the upper shaft has a diameter d1= 24 mm and the bottom shaft has a diameter d2= 16 mm. The punch is used to insert a hole in a 4 mm plate, as shown in the figure. If a force P - 70 kN is required to create the hole, what is the average shear stress in the plate and the average compressive stress in the upper and lower shaft of the punch?A solid circulai' aluminum bar AB is fixed at both ends and loaded by a uniformly distributed torque 150N·n/m. The bar has diameter d = 30 mm. Calculate the reactive torques at the supports and the angle of twist at midspan. Assume that G = 28 GPa.A high-strength steel drill rod used for boring a hole in the earth has a diameter of 0.5 in. (see figure). The allowable shear stress in the steel is 40 ksi and the shear modulus of elasticity is 11,600 ksi. What is the minimum required length of the rod so that one end of the rod can be twisted 30º with respect to the other end without exceeding the allowable stress? If the shear strain in part (a) is limited to 3.2 × 10-3 , what is the minimum required length of the drill rod?
- 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 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?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 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.A square tube section has side dimension of 20 in. arid thickness of 0.5 in. If the section is used for a 10-ft-long beam subjected to 1250 kip-in, torque at both ends, calculate the maximum shear stress and the angle of twist between the ends. Use G = 11,600 ksi.A circular tube of aluminum is subjected to torsion by torques T applied at the ends (see figure). The bar is 24 in. long, and the inside and outside diameters are 1.25 in. and 1.75 in., respectively. It is determined by measurement that the angle of twist is 4° when the torque is 6200 lb-in. Calculate the maximum shear stress in the tube, the shear modulus of elasticity G, and the maximum shear strain (in radians). If the maximum shear strain in the tube is limited to 2.5 × 10-3 and the inside diameter is increased to 1.375 in., what is the maximum permissible torque?
- Repeat Problem 11.3-9. Use two C 150 × 12.2 steel shapes and assume that E = 205 GPa and L = 6 m.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 torque T is applied to a thin-walled tube having a cross section in the shape of a regular hexagon with constant wall thickness t and side length b (see figure). Obtain formulas for the shear stress rand the rate of twist