B4 The short concrete cylinder having a diameter of 50 mm is subjected to a torque of 500 Nm and an axial tensile force of 2 kN. Find: 500 Nm 500 Nm 2kN 2kN (a) the tensile stress in the concrete;
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- Two sections of steel drill pipe, joined by bolted flange plates at Ä are being tested to assess the adequacy of both the pipes. In the test, the pipe structure is fixed at A, a concentrated torque of 500 kN - m is applied at x = 0.5 m, and uniformly distributed torque intensity t1= 250 kN m/m is applied on pipe BC. Both pipes have the same inner diameter = 200 mm. Pipe AB has thickness tAB=15 mm, while pipe BC has thickness TBC= 12 mm. Find the maximum shear stress and maximum twist of the pipe and their locations along the pipe. Assume G = 75 GPa.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 tube AB is fixed at one end and free at the other. The tube is subjected to concentrated torques as shown in the figure. If the outer radius of the tube is 1.5 in, and the thickness is 3/4 in., calculate the strain energy stored in the tube. Let G= 11,800 ksi.
- A circular steel tube with an outer diameter of 75 mm and inner diameter of 65 mm is subjected to torques 7"at its ends. Calculate the maximum permissible torque 7jliajl if the allowable normal strain is ea= 5 X 10"4 Assume that G = 15 GPa.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?Solve the preceding problem if the length L = 56 in., the inner radius r1— 1.25 in., the angle of twist is 0.5°, and the allowable shear strain is 0.0004 rad.
- Solve the preceding problem if the shaft has an outer diameter d2=150 mm and inner diameter d1= 100 mm. Also, the steel has a shear modulus of elasticity G = 75 GPa, and the applied torque is 16 kN ·m.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 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 solid copper bar of circular cross section has length L = 1.25 m and shear modulus of elasticity G = 45 GPa. The bar is designed to carry a 250 N · m torque acting at the ends. If the allowable shear stress is 30 M Pa and the allowable angle of twist between the ends is 2.5°, what is the minimum required diameter?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)?A copper rod of length L = 18.0 in. is to be twisted by torques T (see figure) until the angle of rotation between the ends of the rod is 3.0°. (a) If the allowable shear strain in the copper is 0.0006 rad, what is the maximum permissible diameter of the rod? (b) If the rod diameter is 0.5 in., what is the minimum permissible length of the rod?