Stress Analysis Problem Solution: Maximum Shear Stress

_______________________________________________________________________
PROBLEM (8.79) A point in a structure is subjected to state of stress with
x
σ
= 15 ksi y
σ
x
z
τ
= 10 ksi
acting as shown on a three-dimensional element in Fig. P8.79. Calculate two values of y
σ
for which the
maximum shear stress equals 13 ksi.
SOLUTION
1()
2
avg x z
σ
σσ =+
1(15 0) 7.5
2ksi=+=
22
()
2
xz
x
z
R
σσ
τ
−
=+
22
15 0
()1
2
−0=+
12.5ksi
=
We have
1,3 avg
R
σ
σ =±
17.5 12.5 20 ksi
σ
=+ =
37.5 12.5 5 ksi
σ
=− =−
Assume:
max 1 20 ksi
σ
σ ==
Then
ymin 1 max
2
σ
σστ −
=−
==
=− 20 2(13) 6 ksi
Assume :
min 3 5ksi
σ
σ −==
Then
ymax min max
2
σ
σσ τ +
+ =
==
=− 52(13)21ksi
R
τ
=13
C
τ
=−13
σavg =7.5
τ (ksi)
σ
σ
(ksi)
1
O
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.