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s y
s x
p
z
t
p
r
s y
FIGURE P1.50
Cylindrical pressure vessel.
s y
s x
z
x
t xy
y
s x
s y
FIGURE P1.52
A thin rectangular element in plane stress.
Strength Theories
1.53 Find the torque necessary to initiate yielding in a 10 mm diameter steel shaft. The
yield strength in tension is 180 MN/m 2 , and the shear yield stress is one-half of this
value. Use (a) maximum shear stress theory and (b) the von Mises theory.
Answer: (a) 17.67 Nm (b) 20.39 Nm
1.54 A thin-walled cylinder of radius 1 m is subject to an internal pressure of 700 kN/m 2
.
The yield stress of the material in tension is 250 MN/m 2 . Find the required wall
thickness according to (a) maximum stress theory, (b) maximum shear stress theory,
and (c) von Mises theory. See Problem 1.50 for the fundamental stress formulas for a
cylinder.
Answer:
(a) 2.8 mm, (b) 2.8 mm, (c) 2.43 mm
1.55 A material is found to have a yield stress in a tensile test of
40 , 000 psi. If a sheet
of this material is in a state of plane stress and is subject to the stresses
σ
=
ys
σ
=
150 , 000
x
psi,
xy that corresponds to yield according
to (a) the Tresca theory and (b) the von Mises theory.
σ
=−
30 , 000 psi, and
τ
xy . Find the value of
τ
y
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