HW-Chapter3

HW-Chapter3 - 1" Knowing that each of the shafts AB,...

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Unformatted text preview: 1" Knowing that each of the shafts AB, BC, and CD consists of a solid circular rod, determine (a) the shaft in which the maximum shear- ing stress occurs, (b) the magnitude of that stress. 60X - "I 1\Xom \ (1A5 = mm Fig. P3.“ and A112 .112 Knowing that an 8-mm-diameter hole has been drilled through each of the shafts AB, BC, and CD, determine (a) the shaft in which the maximum shearing stress occurs, (b) the magnitude of that stress. 3.17 The allowable stress is 50 MPa in the brass rod AB and 25 MP; in the aluminum rod BC. Knowing that a torque of magnitude T = 1250 N - m is applied at A, determine the required diamete' of (a) rod AB, (b) rod BC. Fig. P3.” and P3." 3.18 The solid rod BC has a diameter of 30 mm and is made of an alu~ minum for which the allowable shearing stress is 25 MPa. Rod A15 is hollow and has an outer diameter of 25 mm; it is made of a brass for which the allowable shearing stress is 50 MPa. Determine (a) the largest inner diameter of rod AB for which the factor of safety is the same for each rod, (1)) the largest torque that can be applied at A. ‘m.i\ In W (a) Fig. P3.30 Fig. P339 3.28 3.29 3.30 Fig. P337 and P3.28 A torque of magnitude T = 120 N - m is applied to shaft AB U the gear train shown. Knowing that the allowable shearing stres: is 75 MPa in each of the three solid shafts, determine the require: diameter of (a) shaft AB, (1)) shaft CD, (c) shaft EF. ((1) For a given allowable shearing stress, determine the ratio T, u of the maximum allowable torque T and the weight per unit lengti w for the hollow shaft shown. (b) Denoting by (T/w)0 the value rr this ratio for a solid shaft of the same radius Cg, express the rat) T/w for the hollow shaft in terms of (T/w)o and cl/cz. While the exact distribution of the shearing stresses in a hollow qliz.» drical shaft is as shown in Fig. P3.30a, an approximate value can hr obtained for 7,...“ by assuming that the stresses are uniformly distril— uted over the area A of the cross section, as shown in Fig. P330? and then further assuming that all of the elementary shearing force act at a distance from 0 equal to the mean radius 5(0. + (:2) of tlri cross section. This approximate value 1'0 = T/Arm, where T is tl’r applied torque. Determine the ratio Twin/1'0 of the true value rr the maximum shearing stress and its approximate value To for v; ues of Cl/Cg respectively equal to 1.00, 0.95. 0.75, 0.50 and 0. 3.35 The electric motor exerts a 500 N - m-torque on the aluminum shi ABCD when it is rotating at a constant Knowing that C = 27 GPa and that the torques exerted on pulleys B and C are as ShOWL detemiine the angle of twist between (a) B and C, (b) B and D. Fig. P3.35 rls. r‘l-UU I.” The solid spindle AB has a diameter d, = 1.5 in. and is made of ; steel with c = 11.2 x 106 psi and Ta“ = 12 ksi, while sleeve CD 5 made of a brass with G = 5.6 X 106 psi and Ta" = 7 ksi. Deter- ‘:‘.ine the largest angle through which end A can be rotated. The solid spindle AB has a diameter ds = 1.75 in. and is made of ; steel with G = 11.2 X 106 psi and Ta" = 12 ksi, while sleeve CD 5 made of a brass with G = 5.6 X 106 psi and “ran = 7 ksi. Deter- ";ne (0) the largest torque T that can be applied at A if the given elowable stresses are not to be exceeded and if the angle of twist '5 sleeve CD is not to exceed 0.375°, (b) the corresponding angle :rough which end A rotates. Fig. P339 and P3.“ irsion - .rque T,, in the hollow shaft is (a) 3.41 'IVvo shafts, each of Erin. diameter, are connected by the gear: shown. Knowing that C = 11.2 X 106 psi and that the shaft at .7 is fixed, determine the angle through which end A rotates Whfl a 1.2 kip - in. torque is applied at A. Fig. P3.4'l \ solid shaft and a hollow shaft are made of the same material and is of the same weight and length. Denoting by n the ratio c1 /L‘2, ~E.mv that the ratio T;/T,, of the torque T, in the solid shaft to the V(l - n2)/(l + :12) if the .mmum shearing stress is the same in each shaft, (12) (l - 112V 1 ‘— nz) if the angle of twist is the same for each shaft. 1. torque T is applied as shown to a solid tapered shaft AB. Show integration that the angle of twist at A is 7TL Fig. P3.6'l 3.63 An annular plate of thickness t and modulus G is used to con' shaft AB of radius r, to tube CD of radius r2. Knowing th; torque T is applied to end A of shaft AB and that end D of :- CD is fixed, ((1) determine the magnitude and location of the rr mum shearing stress in the annular plate, (12) show that the a:- through which end B of the shaft rotates with respect to end C the tube is Fig. P3.“ stress of 8 ksi. A series of 3.5-in.—outer-djameter pipes is m ' for use. Knowing that the wall thickness of the available pipes ies from 0.25 in. to 0.50 in. in 0.0625-in. increments, choose lightest pipe that can be used. 3.74 The two solid shafts and gears shown are used to transmit 16 hp ' the motor at A operating at a speed of 1260 rpm to a machine at D. Knowing that the maximum allowable shearing stress is S ' determine the required diameter (a) of shaft AB, (b) of shaft C D rig. p313 Fig. P3.74 and P3.75 179 A 2.5-m-long steel shaft of 30-mm diameter rotates at a frequency 3.81 of 30 Hz. Determine the maximum power that the shaft can trans- mit, knowing that G = 77.2 GPa, that the allowable shearing stress is 50 MPa, and that the angle of twist must not exceed 7.5°. A steel shaft must transmit 210 hp at a speed of 360 rpm. Knowing that G = 11.2 X 106 psi, design a solid shaft so that the maximum shearing stress will not exceed 12 ksi and the angle of twist in an 8.2-ft length will not exceed 3°. The shaft-disk-belt arrangement shown is used to transmit 3 hp from point A to point D. (a) Using an allowable shearing stress of 9500 psi, determine the required speed of shaft AB. (b) Solve part (1, assuming that the diameters of shafts AB and CD are, respec- tively, 0.75 in. and 0.625 in. A 1.6-m-long tubular steel shaft of 42-min outer diameter d1 is to be made of a steel for which 1'," = 75 MPa and C = 77.2 CPa. Knowing that the angle of twist must not exceed 4° when the shaft is subjected to a torque of 900 N - m, determine the largest inner diameter (12 that can be specified in the design. Fig. P182 and P333 D . Fig. p331 Problems 183 ...
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This note was uploaded on 12/03/2011 for the course EMA 3702 taught by Professor Wu during the Fall '11 term at FIU.

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HW-Chapter3 - 1" Knowing that each of the shafts AB,...

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