Page 164 - Shigley's Mechanical Engineering Design

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Load and Stress Analysis 139
assuming simple supports (assume also that bearing C carries the thrust load), (b) draw the shear-
force and bending-moment diagrams, (c) for the critical stress element, determine the torsional
shear stress, the bending stress, and the axial stress, and (d) for the critical stress element, deter-
mine the principal stresses and the maximum shear stress.
y
6.50 in 3 in
3.88 in
D
0.88-in dia.
2.50 in
x
Problem 3–74* 1.30 in A B
3.63 in E

C
1.13-in dia.
3–75 Repeat Prob. 3–74 except for a contact force at E of (F E ) CD = –46.6i – 140j + 406k lbf and a
shaft diameter of 1.0 in.
3–76* Repeat the analysis of Prob. 3–74 for shaft AB. Assume that bearing A carries the thrust load.
3–77* A torque T = 100 N · m is applied to the shaft EFG, which is running at constant speed and con-
tains gear F. Gear F transmits torque to shaft ABCD through gear C, which drives the chain
sprocket at B, transmitting a force P as shown. Sprocket B, gear C, and gear F have pitch diam-
eters of a = 150, b = 250, and c = 125 mm, respectively. The contact force between the gears is
transmitted through the pressure angle φ = 20°. Assuming no frictional losses and consider-
ing the bearings at A, D, E, and G to be simple supports, locate the point on shaft ABCD that
contains the maximum tensile bending and maximum torsional shear stresses. Combine these
stresses and determine the maximum principal normal and shear stresses in the shaft.
y
a
E F G
c = 125 mm
y T = 100 N m T
B
A C D
x z b = 250 mm
Problem 3–77*
d = 30 mm

a
P
P
f = 250 mm g = 125 mm
e = 75 mm a = 150 mm
View a–a
3–78 Repeat Prob. 3–77 with the chain parallel to the z axis with P in the positive z direction.
3–79* Repeat Prob. 3–77 with T = 900 lbf · in, a = 6 in, b = 5 in, c = 10 in, d = 1.375 in, e = 4 in,
f = 10 in, and g = 6 in.
3–80* The cantilevered bar in the figure is made from a ductile material and is statically loaded with
F y = 200 lbf and F x = F z = 0. Analyze the stress situation in rod AB by obtaining the follow-
ing information.