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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 8mmdiameter 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  mtorque 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‘lUU 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 3.5in.—outerdjameter pipes is m '
for use. Knowing that the wall thickness of the available pipes
ies from 0.25 in. to 0.50 in. in 0.0625in. 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 2.5mlong steel shaft of 30mm 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 8.2ft length will not exceed 3°. The shaftdiskbelt 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 1.6mlong tubular steel shaft of 42min 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.
 Fall '11
 Wu

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