CL 231 Autumn 2012Tutorial 4 Tutorial - 4 1. A prospector uses a hand-powered winch (see figure 1) to raise a bucket of ore in his mine shaft. The axle of the winch is a steel rod of diameter d = 0.625 in Also, the distance from the center of the axle to the center of the lifting rope is b = 4.0 in. If the weight of the loaded bucket is W = 100 lb, what is Figure 1 the maximum shear stress in the axle due to torsion? 2. A circular tube of outer diameter d3 = 70 mm and inner diameter d2 = 60 mm is welded at the righthand end to a fixed plate and at the left-hand end to a rigid end plate (see figure 2). A solid circular bar of diameter d1 = 40 mm is inside of, and concentric with, the tube. The bar passes through a hole in the fixed plate and is welded to the rigid end plate. The bar is 1.0 m long and the tube is half as long as the bar. A torque T = 1000 N.m acts at end A of the bar. Also, both the bar and tube are made of an aluminium alloy with shear modulus of elasticity G = 27 GP a. (a) Determine the maximum shear stresses in both the bar and tube. (b) Determine the angle of twist (in degrees) at end A of the bar. Figure 2 3. A solid circular bar of diameter d = 50 mm (see figure 3) is twisted in a testing machine until the applied torque reaches the value T = 500 N.m. At this value of torque, a strain gage oriented at 45o to the axis of the bar gives a reading = 339 × 106 . What is the shear modulus G of the material? 1 what is the maximum torque (To )max that may be applied at section C? Figure 5 6. 2 . (a) If the shaft has a diameter of 30 mm. The shear moduli of elasticity are Gb = 36 GP a for the brass and Gs = 80 GP a for the steel. The composite shaft shown in the figure 6 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. Assuming that the allowable shear stresses in the brass and steel are τb = 48 M P a and τs = 80 M P a. respectively. A stepped shaft ACB having solid circular cross sections with two different diameters is held against rotation at the ends (see figure 5). If the allowable shear stress in the shaft is 43 M P a. A motor drives a shaft at 12 Hz and delivers 20 kW of power (see figure 4). The outer diameters of the two parts are d1 = 40 mm for the brass core and d2 = 50 mm for the steel sleeve. what is the minimum permissible diameter dmin of the shaft? Figure 4 5. determine the maximum permissible torque Tmax that may be applied to the shaft. what is the maximum shear stress τmax in the shaft? (b) If the maximum allowable shear stress is 40 M P a.CL 231 Autumn 2012 Tutorial 4 Figure 3 4. (c) shaft EF . (b) the largest torque that can be applied at A. (b) shaft CD.m is applied to shaft AB of the gear train shown in fig.CL 231 Autumn 2012 Tutorial 4 Figure 6 7. Knowing that the allowable shearing stress is 75 M P a in each of the three solid shafts. Determine (a) the largest inner diameter of rod AB for which the factor of safety is the same for each rod. 7) has a diameter of 30 mm and is made of an aluminum for which die allowable shearing stress is 25 M P a. 8. Figure 8 3 . The solid rod BC (as shown in fig. Rod AB is hollow and has an outer diameter of 25 mm. determine the required diameter of (a) shaft AB. Figure 7 8. A torque of magnitude T = 120 N. it is made of a brass for which the allowable shearing stress is 50 M P a. and sleeve CD is made of a brass with an allowable shearing stress of 7 ksi (as shown in fig. The aluminum rod AB as shown in fig. Knowing that each shaft is solid. (b) shaft BC. of spindle AB. Determine (a) the largest torque T that can be applied at A if the allowable shearing stress is not to be exceeded in sleeve CD. The solid spindle AB is made of a steel with an allowable shearing stress of 12 ksi. determine the angle of twist at A.CL 231 Autumn 2012 Tutorial 4 9. (b) the corresponding required value of the diameter ds . determine the maximum shearing stress in (a) shaft AB. 11). Under normal operating conditions. Knowing that portion CD of the brass rod is hollow and has an inner diameter of 40 mm. (c) shaft CD. the electric motor exerts a torque of 2.m on shaft AB (as shown in fig. Figure 10 11.8 kN. 10). 4 . Figure 9 10. 9 (G = 27 GP a) is bonded to the brass rod BD (G = 39 GP a). 27 lb. 5 .2 × 106 psi) is 8 f t long and its outer and inner diameters are respectively equal to 2. determine (a) the maximum shearing stress.f t/rad.25 in. (b) the angle of twist of the shaft. determine the diameter of the wire for which the torsional spring constant will be 4. 12)is to be determined experimentally by using a torsional pendulum consisting of a 6 − f t steel wire. A hollow steel drive shaft (G = 11. Knowing that G = 11.2 × 106 psi. Figure 12 13.CL 231 Autumn 2012 Tutorial 4 Figure 11 12.50 in and 1. The mass moment of inertia of a gear (shown in fig. Knowing that the shaft transmits 200 hp while rotating at 1500 rpm. 6 × 106 psi for brass. The solid cylinders AB and BC are bonded together at B and are attached to fixed supports at A and C (as shown in fig.7 × 106 psi for aluminium and 5. Figure 13 6 .CL 231 Autumn 2012 Tutorial 4 14. (b) in cylinder BC. 13). determine the maximum shearing stress (a) in cylinder AB. Knowing that the modulus of rigidity is 3.