SOLUTION
8–51. Determine the horizontal displacement at C. Take
E=29(103)
ksi,
I=150
in4
for each member. Use the method
of virtual work.
AB
CD
10 ft
8
k
8 ft
© 2018 Pearson Education, Inc., 330 Hudson Street, NY, NY 10013. All rights reserved. This material is protected under all copyright laws as they
currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
SOLUTION
EI
29(10
3
)(150)
*8–52. Solve Prob. 8–51 using Castigliano’s theorem.
AB
CD
10 ft
8
k
8 ft
SOLUTION
mM
(10)(10x
2
)
(x
3
)(8x
3
)
8–53. Determine the horizontal displacement of the rocker at
B. Take
E=29(103)
ksi,
I=150
in4
for each member. Use the
method of virtual work.
AB
CD
10 ft
8
k
8 ft
SOLUTION
AB
CD
10 ft
8
k
8 ft
8–54. Solve Prob. 8–53 using Castigliano’s theorem.
414
SOLUTION
1800 kN #m3
EI
8–55. Determine the vertical displacement of point C.
EI is constant. Use the method of virtual work.
A
3 m
4 m
20 kN
C
B
80 kN
?
m
Ans.
(
∆C)v=
1800 kN #m3
EI
T
415
SOLUTION
0M
0M
1
EI
A
3 m
4 m
20 kN
C
B
80 kN
?
m
*8–56. Solve Prob. 8–55 using Castigliano’s theorem.
EI
SOLUTION
EI
8–57. Determine the slope at A and the vertical displacement
at B. Use the method of virtual work. EI is constant.
4
m
4
m
3 m
A
C
B
60 kN
EI
SOLUTION
EI
4 m
4 m
3 m
A
C
B
60 kN
8–58. Solve Prob. 8–57 using Castigliano’s theorem.
EI
SOLUTION
B
C
A
y
z
x
1.5 m
2 kN
1 m
8–59. The bent rod has an
E=200
GPa,
G=75
GPa,
and a
radius of 30 mm. Use Castigliano’s theorem and determine the
vertical deflection at C. Include the effects of bending, shear,
and torsional strain energy.
419
*8–60. Determine the slope at A. Take
E=29(103)
ksi.
The
moment of inertia of each segment of the frame is indicated in
the figure. Assume D is a pin support. Use the method of
virtual work.
BC
AD
12 ft
IAB 5 600 in4
IBC 5 900 in4
ICD 5 600 in4
5 ft 5 ft
12 k
SOLUTION
1
#uA=
LL
0
m
u
M
EI
dx =
L5
0
(1 –0.1x)(6x)dx
EIBC
+
L5
0
(0.1x)(6x)dx
EIBC
+0+
0
u
A=
(75 –25 +25)
EI
BC
=
75(144)
29(10
3
)(900)
=0.414(10 –3) rad
A
Ans.
Ans.
u
A=0.414(10 –3) radA
SOLUTION
EI
BC
29(10
3
)(900)
BC
AD
12 ft
IAB 5 600 in4
IBC 5 900 in4
ICD 5 600 in4
5 ft 5 ft
12 k
8–61. Solve Prob. 8–60 using Castigliano’s theorem.