Page 166 - Shigley's Mechanical Engineering Design

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Load and Stress Analysis 141
(a) Determine the precise location of the critical stress element at the cross section at A.
(b) Sketch the critical stress element and determine magnitudes and directions for all stresses
acting on it. (Transverse shear may be neglected if you can justify this decision.)
(c) For the critical stress element, determine the principal stresses and the maximum shear stress.
3–85* Repeat Prob. 3–84 with F x = 300 lbf, F y = 250 lbf, and F z = 0.
3–86* Repeat Prob. 3–84 with F x = 300 lbf, F y = 250 lbf, and F z = –100 lbf.
3–87* Repeat Prob. 3–84 for a brittle material, requiring the inclusion of stress concentration in the
fillet radius.
3–88 Repeat Prob. 3–84 with F x = 300 lbf, F y = 250 lbf, and F z = 0, and for a brittle material, requir-
ing the inclusion of stress concentration in the fillet radius.
3–89 Repeat Prob. 3–84 with F x = 300 lbf, F y = 250 lbf, and F z = –100 lbf, and for a brittle material,
requiring the inclusion of stress concentration in the fillet radius.
3–90 The figure shows a simple model of the loading of a square thread of a power screw transmitting
an axial load F with an application of torque T. The torque is balanced by the frictional force F f
acting along the top surface of the thread. The forces on the thread are considered to be distrib-
uted along the circumference of the mean diameter d m over the number of engaged threads, n t .
From the figure, d m = d r + p/2, where d r is the root diameter of the thread and p is the pitch of
the thread.
(a) Considering the thread to be a cantilever beam as shown in the cutaway view, show that the
bending stress at the root of the thread can be approximated by
6F
σ b =±
πd r n t p
(b) Show that the axial and maximum torsional shear stresses in the body of the shaft can be
approximated by
4F 16T
σ a =− 2 and τ t = 3
πd r πd r
(c) For the stresses of parts (a) and (b) show a three-dimensional representation of the state
of stress on an element located at the intersection of the lower thread root base and the

d
d m
F
d r

y
F f
x
Problem 3–90 p/2

p/2

T
F