Question

Problem 1 A half solid, half shell Steel shaft ABCD is fixed to a rigid wall at its end A and has the dimensions shown in the figure below. Torques Ti and T2 are applied at sections B and D in the indicated directions, respectively. A solid concentric copper shaft is incased in the shell part of the steel shaft between the rigid wall at end A and the solid portion of the steel shaft at C. Shear modulus of steel is Gst -78 GPa and shear modulus of copper is Gcu 45 GPa. 50 cm 25 ci 75 cm Steel Steel Hollow NLCopper T2 12 kNm solid Copper shaft Diameter = 5 cm WALL Hollow Steel shel Outer Diameter 12 cm Inner Diameter 8 cm (a) Draw a free-body diagram of the shaft ABCD, find the reaction torque at A, and calculate the internal torque for parts AB and BD (b) Make a section cut between A and B, draw a free-body diagram of either left or right portion of the cut; and calculate the internal torque carried by the solid copper shaft and the internal torque carried by the steel shell. (c) For part AB: Calculate the magnitude of the shear stress at the inner radius of the steel shell. Calculate the magnitude of the shear stress at the surface of solid copper shaft. (d) For part AB: Calculate the magnitude of the shear strain at the inner radius of the steel shell. Calculate the magnitude of the shear strain at the surface of solid copper shaft. (e) Calculate the angle of rotation of section D with respect to section A.

Answer 1

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