Solid Mechanics Ent251/4

SOLID MECHANICS ENT251/4 ASSIGNMENT 3

Question 1 [4-4] The copper shaft is subjected to the axial loads as shown in Figure 1. Determine the displacement of end A with respect to end D if the diameters of each segment are dAB = 20 mm, dBC = 25 mm and dCD = 12 mm. The modulus of elasticity of the shaft is E = 126 GPa.

Figure 1

Question 2 [4-36] The A-36 steel pipe has an outer radius of 20 mm and an inner radius of 15 mm. The modulus of elasticity of the pipe is E = 200 GPa. If it fits snugly between the fixed walls before it is loaded, determine the reaction at the walls when it is subjected to the load as shown in Figure 2.

Figure 2

Question 3 [4-41] The support consists of a solid red brass post surrounded by a stainless steel tube. The modulus of elasticity of the brass and steel are Ebr = 101 GPa and Est = 193 GPa. Before the load is applied, the gap between these two parts is 1 mm. Given the dimensions as shown in Figure 3, determine the greatest axial load that can be applied to the rigid cap A without causing yielding of any one of the materials. The yield strength of the brass is σY.br = 70 MPa.

Figure 3 Question 4 [5-1]

A shaft as shown in Figure 4 is made of a steel alloy having an allowable shear stress of allow = 84 MPa and diameter of 37.5mm. (a) Determine the maximum torque T that can be transmitted. (b) Determine the maximum torque T’ if a 25-mm-diameter hole is bored through the shaft. (c) Sketch the shear–stress distribution along a radial line in case (a) and (b).

Figure 4

Question 5 [5-53] The turbine as shown in Figure 5 develops 150 kW of power, which is transmitted to the gears such that C receives 70% and D receives 30%. The bearing support at E allows the shaft to turn freely about its axis. If the rotation and the shear modulus of elasticity of the 100-mm-diameter A-36 steel shaft are  = 800 rev/min and G = 75GPa respectively, determine; (a) absolute maximum shear stress in the shaft. (b) angle of twist of end E of the shaft relative to B.

Figure 5