A steel circular tube is subjected to torsion by torques T applied at the ends as shown below. The bar is 1.5m long, and the inside and outside diameters are 30mm and 50mm, respectively. It is determined by measurement that the angle of twist is 2.53° when the torque is 4800Nm. Calculate the shear modulus of elasticity “G”.

A steel circular tube is subjected to torsion by torques T applied at the ends as shown below. The bar is 1.5m long, and the inside and outside diameters are 30mm and 50mm, respectively. It is determined by measurement that the angle of twist is 2.53° when the torque is 4800Nm. Calculate the shear modulus of elasticity “G”.

Mechanics of Materials (MindTap Course List)

9th Edition

ISBN:9781337093347

Author:Barry J. Goodno, James M. Gere

Publisher:Barry J. Goodno, James M. Gere

Chapter3: Torsion

Section: Chapter Questions

Problem 3.3.11P: A circular tube of aluminum is subjected to torsion by torques T applied at the ends (see figure)....

See similar textbooks

Similar questions

An aluminum bar has length L = 6 ft and diameter d = 1.375 in. The stress-strain curse for the aluminum is shown in Fig. 1.34. The initial straight, line part of the curve has a slope (modulus of elasticity) of 10.6 × 106 psi. The bar is loaded by tensile forces P = 44.6 k and then unloaded. (a) That is the permanent set of the bar? (b) If the bar is reloaded. what is the proportional limit? hint: Use the concepts illustrated in Figs. l.39b and 1.40.
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 tie-down on the deck of a sailboat consists of a bent bar boiled at both ends, as shown in the figure. The diameter dBof the bar is 1/4 in., the diameter D Wof the washers is 7/8 in., and the thickness is of the fiberglass deck is 3/8 in. If the allowable shear stress in the fiberglass is 300 psi, and the allowable bearing pressure between the washer and the fiberglass is 550 psi, what is the allowable load P allowon the tie-down?
A hollow, circular, cast-iron pipe (Ec =12,000 ksi) supports a brass rod (Ec= 14,000 ksi} and weight W — 2 kips, as shown. The outside diameter of the pipe is dc= 6 in. (a) If the allowable compressive stress in the pipe is S00O psi and the allowable shortening of the pipe is 0.02 in., what is the minimum required wall thickness trmm? (Include the weights of the rod and steel cap in your calculations.) (b) What is the elongation of the brass rod Srdue to both load Wand its own weight? (c) What is the minimum required clearance h?
A prismatic bar with a length L = 1 m and cross-sectional area A = 1200 mm2 is supported at the ends. The bar is then subjected to a temperature increase ?T = 25°C. Calculate the complete stale of stress acting on an inclined section .rs that is cut through the bar at an angle ?? = 45*. Use E = 200 GPa and the coefficient of thermal expansion a = 12×10-6/?.
A wine of length L = 4 ft and diameter d = 0.125 in. is stretched by tensile forces P = 600 lb. The wire is made of a copper alloy having a stress-strain relationship that may be described mathematically by =18,0001+30000.03(=ksi) in which is nondimensional and has units of kips per square inch (ksi). (a) Construct a stress-strain diagram for the material. (bj Determine the elongation, of the wire due to the Forces P. (c) IF the forces are removed, what is the permanent set of the bar? (d) If the forces are applied again, what is the proportional limit?
A solid circular bar of copper (G = 45 GPa) with length L = 315n m and diameter d = 40 mm is subjected to pure torsion by torques T acting at the ends (see figure). Calculate the amount of strain energy U stored in the bar when the maximum shear stress is 32 MPa. From the strain energy, calculate the angle of twist (in degrees).
A circular copper bar with diameter d = 3 in. is subjected to torques T = 30 kip-in. at its ends. Find i lie maximum shear, ion si le. and compressive stresses in the tube and their corresponding strains. Assume that G = 6000 ksi.
A solid circular bar of steel (G = 1L4 × 106 psi) with length L = 30 in, and diameter d = 1.75 in, is subjected to pure torsion by torques T acting at the ends (see figure). Calculate the amount of strain energy V stored in the bar when the maximum shear stress is 4500 psi. From the strain energy, calculate the angle of twist 0 (in degrees).
A steel cable with a nominal diameter of 25 mm (see Table 2-1) is used in a construction yard to lift a bridge section weighing 38 kN. as shown in the figure. The cable has an effective modulus of elasticity E = 140 GPa. (a) If the cable is 14 m long, how much will it stretch when the load is picked up? (b) If the cable is rated for a maximum load of 70 kN, that is the factor of safety with respect to failure of the cable?
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 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?