sm12 43 44

________________________________________________________________________
PROBLEMS (12.43 and *12.44) For the truss and loading shown in Fig. P12.43 and Fig.
P12.44, obtain the vertical deflection at point C. Use the work-energy method and assume that all
members are of equal axial rigidity AE.
SOLUTION (12.43)
5
6
AC BC
LL==
3
P
A
4
2
PB
2
P
L
/2
L
/2
C
23
L
L
Apply the method of joints at C and B:
53
88
AC CB AB
FF PF== =P
Therefore,
22
25 5 9
[2( ) ]
22 6466
4
FL PL
AE AE
== ⋅+
∑
U2
19
48 PL AE
=
Hence
2
19 1
48 2 C
PL
UP
δ
AE
==, 19
24
CPL
AE
δ
=
↓
SOLUTION (*12.44)
Using the method of joint of joints at C, B, D, and A:
2
AB BC CD BD
FPF PF PF== =−=P−
20
AD AE DE
FPF F==2P=−
We have
2
AD BC
LL==L
Thus,
22
(1 2 2 1 1 2 2 0 4)
22
FL PL
U
AE AE
==++++++
∑
2
2(1.75 2) PL
AE
=+
Hence,
2
21
(1.75 2) 2C
PL
UP
δ
AE
=+=
Continued on next slide
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Solving
4(1.75 2)
CPL
AE
δ =+↓12.675 PL
AE
=
↓
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
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