sm12 22 23

________________________________________________________________________
PROBLEMS (12.22 and 12.23) A beam of rectangular cross section is supported and loaded as
shown in Figs. 12.14 and 12.15. What is the strain energy of the beam caused by shear deformation?
SOLUTION (12.22)
w
x
2
wL
2
wL
6
25
wL
Vwx
α =− + =
22 2
00
3()
25 2
LL
sVwL
Udxx
AG AG
α
==−
∫∫
dx
23 2 2
0
3
5324
L
wx xLLx
AG
=−+=
23
1
20 wL AG
SOLUTION (12.23)
6
5
α
=
AB a
VP
L
=−
=
VP
BC
222
2
2
00
3'
25
LL
sVPa
Udx dxP
AG AG L
α
⎡⎤
== +
⎢⎥
⎣⎦
∫∫∫
0
a
dx
2
3()
5Pa La
AGL
=+
a
P
B
aP
L
A
C
L
x
P
-Pa/L
V
x
x’
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.