Home Work #5 Due Date:25 Mar, 2010 (Turn in your assignment at the mail box of S581 outside the ME general office) The solutions must be written on single-side A4 papers only.

HW 3-Problem #1 A solid circular bar ABC consists of two segments, as shown in the figure. One segment has diameter d1=50mm and length L1=1.25m; the other segment has diameter d2=40mm and length L2=1.0m. What is the allowable torque Tallow if the shear stress is not to exceed 30MPa and the angle of the twist between the ends of the bar is not to exceed 1.5 °.(Assume G=80Gpa)

Solution to Problem #1 377

HW 3-Problem #2 A solid circular bar ABCD with fixed supports at ends A and D is acted upon by two equal and oppositely directed torque To, as shown in the figure. The torques are applied at ponits B and C, each of which is located at distance x from on end of the bar.(The distance x may vary from zero to L/2.) (a) For what distance x will the angle of twist at points B and C be a maximum? (b) What is the corresponding angle of the twist Φmax?(Hint: Use Eqs.3-46a and b of example 3-9 to obtain the reactive torques.)

Solution to Problem #2

HW 3-Problem #3 The composite shaft shown in the figure is manufactured by shrink-fitting a steel sleeve over a brass core so that the two parts act as a single solid bar in torsion. The outer diameter of the two parts are d1=40mm for the brass core and d2=50mm for the steel sleeve. The shear moduli of elasticity are Gb=36GPa for the brass and Gs=80GPa for the steel. Assuming that the allowable shear stresses in the brass and steel are τb=48MPa and τs=80MPa, respectively, determine the maximum permissible torque Tmax that may be applied to the shaft.(Hint: Use Eqs.3-44a and b to find the torque.)

Solution to Problem #3 Continue in next slides

Solution to Problem #3 1521