sm9 97

Excerpts from this work may be reproduced by instructors for distribution on a not-for-profit basis for testing or
instructional purposes only to students enrolled in courses for which the textbook has been adopted. Any other
reproduction or translation of this work beyond that permitted by Sections 107 or 108 of the 1976 United States
Copyright Act without the permission of the copyright owner is unlawful.
_______________________________________________________________________
PROBLEM (*9.97) A bracket arm is acted upon by a vertical load P = 6 kN at its free end, as
depicted in Fig.P9.97. Calculate the factor of safety
s
nfor the rod of diameter d = 50 mm, according to
the maximum shear stress theory of failure.
Given: The material is an aluminum alloy with a yield strength of y
τ
= 140 MPa (see Table B.4).
*SOLUTION
6 0.2 1.2 6 0.25 1.5
M
kN m T kN m=× = ⋅ =× = ⋅
An element at point A:
33
32 32(1.2) 97.78
(0.05)
xM
M
Pa
d
σππ == =
33
16 16(1.5) 61.12
(0.05)
xz T
M
Pa
d
τππ == =
So
22
max ()
2y
xxz
s
n
τ
σ
ττ
=+=
22
(48.89) (61.12) 78.28
M
Pa=+=
140
s
n
=
Solving,
1.79
s
n=
An element at point B:
max 3
416
3
dt PT
Ad
τττ
π
=+= +
23
4(4 6) 16(1.5) 140
65.19
3 (0.05) (0.05)
s
MPa n
ππ
×
=+= =
or
2.15
s
n=
Figure (a)
x
y
τ
A
x
σ
z
x
x
y
τ
B
y
x
P
z
B
T
A
C
y