Hibbeler R.C. Structural Analysis
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670 ANSWERS TO SELECTED P ROBLEMS
Chapter 5
5–1.
5–2.
5–3.
5–5.
5–6.
5–7.
5–9.
5–10.
5–11.
5–13.
5–14.
5–15.
5–17.
5–18.
5–19.
5–21.
5–22.
5–23.
5–25.
,
,
5–26.
h
3
= 93.75 ft
h
2
= 75.00 ft
h
1
= 43.75 ft
C
y
= 85 kC
x
= 46.7 k
A
y
= 95.0 kA
x
= 46.7 k
B
x
= 46.7 k, B
y
= 5.00 k
M
D
= 10.8 kN
#
m
F
C
= 11.7 k
F
A
= 10.8 k
F
B
= 6.77 k
T = 4.32 kN
A
y
= 15.5 kN
C
y
= 9.55 kN
A
x
= 0
T
hanger
= 1.31 kN
T
E
= T
D
= 8.75 kN
T
F
= 7.0 kN
T
max
= 5.20 kN
y = (38.5x
2
+ 577x)(10
-3
) m
T
max
= 6.93 MN
T
min
= 6.25 MN
M
max
= 6.25 k
#
ft
V
max
=;5 k
T
hanger
= 10 k
T
max
= 117 k
T
min
= 100 k
T
max
= 10.9 k
T
min
= 13.0 k
T
max
= 14.4 k
w = 51.9 lb/ft
T
max
= 431 kN
T
min
= 400 kN
T
B
= 10.3 k
T
O
= 7.03 k
y = 0.0356x
2
F
max
= 12.5 kN
P
2
= 6.25 kN
P
1
= 2.50 kN
P = 71.4 lb
y
D
= 2.10 m
T
AB
= 2.99 kN
T
CD
= 3.72 kN
T
BC
= 1.60 kN
y
B
= 2.43 m
T
max
= 6.41 kN
l = 20.2 ft
F
BC
= 46.7 lb
F
BA
= 83.0 lb
F
CD
= 88.1 lb
5–27.
,
,
5–29.
Chapter 6
6–15.
6–17.
6–18.
6–19.
6–21.
6–22.
6–23.
6–25.
6–26.
6–27.
6–30.
6–31.
6–33.
6–34.
6–35.
6–37.
6–57.
6–58.
6–59.
6–61.
6–62.
6–63. (M
C
)
max( + )
= 16.8 k
#
ft
(M
C
)
max( + )
= 20.0 kN
#
m
(V
B
)
max
= 1.46 k
(M
C
)
max
= 44.1 kN
#
m
(F
CF
)
max( + )
= 7.54 k (T)
(F
CD
)
max( + )
= 12.0 k (T)
(M
B
)
max( + )
= 12.3 kN
#
m
(V
BC
)
max( - )
=-8.21 kN
(V
CD
)
max(-)
=-6 k
(M
H
)
max( + )
= 19.2 k
#
ft
(V
DE
)
max( + )
= 5.07 k
(M
C
)
max( - )
=-118 k
#
ft
(V
DE
)
max( - )
=-52.9 k
(M
C
)
max
= 105 k
#
ft
(V
BC
)
max
= 7 k
(M
D
)
max
= 61.25 k
#
ft
(V
AB
)
max
= 2.73 k
(M
G
)
max( + )
= 46.7 kN
#
m
(V
BC
)
max( + )
= 17.8 kN
(M
G
)
max( - )
=-9.81 kN
#
m
(V
BC
)
max( + )
= 7.15 kN
(V
C
+
)
max( + )
= 33.0 k
(M
E
)
max( + )
= 51.25 k
#
ft
(A
y
)
max( + )
= 20.5 k
(V
C
)
max( - )
=-23.6 kN
(M
C
)
max( + )
= 72.0 kN
#
m
(B
y
)
max( + )
= 87.6 kN
(V
D
)
max
= 5.40 k
(M
A
)
max
=-86.4 k
#
ft
(M
D
)
max
=-4 k
#
ft
(V
A
+
)
max( + )
= 40.1 k
(M
C
)
max( + )
= 151 k
#
ft
(A
y
)
max( + )
= 70.1 k
(B
y
)
max( + )
= 24.75 k
(M
C
)
max( + )
= 112.5 k
#
ft
(M
B
)
max( - )
=-37.5 k
#
ft
(B
y
)
max( + )
= 12.4 k
(V
C
)
max
= 20 kN
(M
C
)
max
= 142 kN
#
m
T
AD
= 4.08 k
A
y
= 1.94 k
D
y
= 8.06 k
A
x
= 3 k
C
y
= 0.216 kC
x
= 0.276 k
A
y
= 3.78 kA
x
= 2.72 k
B
y
= 0.216 k, B
x
= 2.72 k
7–5.
7–6.
7–7.
7–9.
F
FG
= 3.25 k (C)
F
CF
= 2.48 k (T)
F
DG
= 2.48 k (C)
F
AF
= 6.00 kN (T)
F
BE
= 4.00 kN (T)
F
AB
= 13.3 kN (C)
F
FE
= 13.3 kN (T)
F
AE
= 10.0 kN (C)
F
FB
= 10.0 kN (T)
F
CD
= 2.00 kN (T)
F
BC
= 2.67 kN (C)
F
ED
= 2.67 kN (T)
= 3.33 kN (C)F
BD
= 3.33 kN (T)F
EC
F
DE
= 20.5 k (C)
F
CF
= 14.0 k (C)
F
BG
= 14.5 k (C)
F
AH
= 21.5 k (C)
F
CD
= 0
F
EF
= 20.0 kN (C)
= 17.3 k (T)F
BC
F
FG
= 20.0 k (C)
= 0.833 k (T)F
CG
F
AB
= 2.00 k (C)
= 19.3 k (C)F
GH
= 24.2 k (T)F
BH
F
DE
= 20.5 k (C)
F
CE
= 22.5 k (T)
F
AG
= F
BF
= F
DF
= 0
F
DE
= 13.75 k (C)
F
BG
= 7.00 k (C)
F
AH
= 14.25 k (C)
F
CD
= 9.00 k (T)
F
EF
= 11.0 k (C)
F
CE
= 11.25 k (T)
F
DF
= 11.25 k (C)
= 17.7 k (T)F
BC
= 19.7 k (C)F
FG
F
CG
= 0.417 k (T)
F
BF
= 0.417 k (C)
= 9.67 k (C)F
GH
= 7.67 k (T)F
AB
F
BH
= 12.1 k (T)
F
AG
= 12.1 k (C)
F
FC
= 5.0 k (C)
F
FE
= 0.833 k (C)
F
ED
= 15.8 k (C)
= 5.83
k (T)F
CD
6–65.
6–66.
6–67.
6–69.
6–70.
6–71.
6–73.
6–74.
6–75.
6–77.
6–78.
6–79.
6–81.
Chapter 7
7–1.
7–2.
7–3.
= 8.25
k (C)F
DF
= 8.25 k (T)F
EC
F
BC
= 12.5 k (T)
F
GB
= 5.0 k (C)
F
GF
= 7.5 k (C)
= 1.18
k (T)F
BF
= 1.18 k (C)F
GC
F
HG
= 4.17 k (C)
F
AH
= 14.2 k (C)
F
AB
= 9.17 k (T)
= 5.89
k (C)F
AG
= 5.89 k (T)F
HB
F
CD
= 40.0 kN (C)
F
BE
= 40.0 kN (C)
F
AF
= 70.0 kN (C)
F
BC
= 0
F
DE
= 20.0 kN (C)
= 28.3 kN (T)F
BD
F
AB
= 0
F
EF
= 20.0 kN (C)
= 28.3 kN (T)F
BF
= F
CE
= 0F
AE
F
CD
= 30.0 kN (C)
F
BE
= 20.0 kN (C)
F
AF
= 60.0 kN (C)
F
BC
= 10.0 kN (T)
F
DE
= 10.0 kN (C)
F
CE
= F
BD
= 14.1 kN (C)
F
AB
= 10.0 kN (T)
F
EF
= 10.0 kN (C)
F
AE
= F
BF
= 14.1 kN (C)
M
max
= 10.5 k
#
ft
V
abs
max
= 12.5 k
M
max
= 130 k
#
ft
M
max
= 97.2 k
#
ft
M
max
= 164 kN
#
m
V
abs
max
= 67.5 kN
M
max
= 555 k
#
ft
M
max
=-39 kN
#
m
V
max
= 10 kN
M
max
= 64.5 kN
#
m
M
max
= 67.8 kN
#
m
(F
BC
)
max
= 2.37 k (T)
(M
C
)
max( + )
= 4.375 k
#
ft
(M
C
)
max( + )
= 34.0 kN
#
m
A
NSWERS TO SELECTED PROBLEMS 671
7–10.
7–11.
7–13.
7–14.
7–15.
7–17.
7–18.
7–19. Pinned:
A
x
= 6.00 kN
M
A
= 16.2 k
#
ft; M
B
= 9 k
#
ft; M
C
= 7.2 k
#
ft
A
y
= 12 k; B
y
= 16 k; C
y
= 4 k
A
x
= 0; B
x
= 0; C
x
= 0
M
H
= 27.0 k
#
ft
M
L
= 20.25 k
#
ft
M
I
= 9.00 k
#
ft
= 40.3 kN
#
mM
A
M
D
= 7.20 k
#
ft
M
F
= 4.05 k
#
ft
M
B
= 3.78 kN
#
m
M
A
= 4.86 kN
#
m
F
AB
= 9.00 kN (T)
F
CF
= 5.00 kN (C)
F
DE
= 4.00 kN (C)
= 22.7 kN (T)F
AF
= 22.7 kN (C)F
BC
= 5.33 kN (T)F
EF
F
BF
= 15.0 kN (C)
F
AC
= 15.0 kN (T)
= 5.33 kN (C)F
CD
F
CE
= 6.67 kN (C)
F
DF
= 6.67 kN (T)
F
AB
= 0
F
CG
= 5.50 k (C)
F
DF
= 2.00 k (C)
F
DE
= 1.50 k (T)
= 2.12 k (C)F
EF
F
AG
= 10.5 k (C)
F
BC
= 5.00 k (T)
= 7.78 k (T)F
BG
F
FG
= 5.00 k (C)
F
CD
= 1.50 k (T)
= 4.95 k (T)F
CF
F
DG
= F
AC
= 0
F
AB
= 2.75 k (T)
F
CG
= 1.00 k (C)
F
DF
= 0.250 k (C)
F
DE
= 1.50 k (T)
= 2.12 k (C)F
EF
F
AG
= 7.75 k (C)
F
BC
= 7.75 k (T)
F
BG
= 3.89 k (T)
F
AC
= 3.89 k (C)
F
CD
= 3.25 k (T)
Fixed:
7–21.
7–22.
7–23.
7–25.
7–26.
7–27.
F
EI
= 17.5 kN (C)
F
HI
= 4.00 kN (C)
F
EH
= 17.5 kN (T)
F
GH
= 17.0 kN (T)
F
EF
= 16.5 kN (C)
F
FH
= 17.5 kN (C)
M
B
= 30.0 kN
#
m
B
y
= 14.0 kN
B
x
= 10.0 kN
M
A
= 30.0 kN
#
m
A
y
= 14.0 kN
= 10.0 kNA
x
F
DE
= 10.0 kN (T)
F
CE
= 15.0 kN (C)
F
EF
= 14.0 kN (C)
F
CG
= 4.00 kN (C)
F
EG
= 15.0 kN (T)
F
DE
= 20.0 kN (T)
F
CE
= 27.5 kN (C)
F
CG
= 4.00 kN (C)
F
EF
= 24.0 kN (C)
F
EG
= 27.5 kN (T)
F
DE
= 3.00 k (C)
F
DF
= 3.125 k (T)
F
FG
= 1.00 k (C)
F
CD
= 2.00 k (T)
F
DG
= 3.125 k (C)
M
B
= 9.00 k
#
ft
B
y
= 1.875 k
B
x
= 1.50 k
M
A
= 9.00 k
#
ft
A
y
= 1.875 k
= 1.50 kA
x
F
CE
= 1.06 k (T)
F
CF
= 1.77 k (T)
M
B
= 18.0 kN
#
m
B
y
= 9.00 kN
B
x
= 6.00 kN
M
A
= 18.0 kN
#
m
A
y
= 9.00 kN
A
x
= 6.00 kN
B
y
= 18.0 kN
B
x
= 6.00 kN
A
y
= 18.0 kN
672 ANSWERS TO SELECTED P ROBLEMS
8–6.
8–7.
8–9.
8–10.
8–11.
8–13.
8–14.
8–15.
8–17.
8–18.
8–19.
8–21.
8–22.
8–23.
8–25.
=
90
kN
#
m
3
EI
T¢
C
=
18
kN
#
m
2
EI
u
B
a = 0.152 L
a = 0.152
L
= 3.86
mm T¢
C
= 0.00171 radu
C
=
Pa
3
4EI
c
¢
C
=
Pa
2
4EI
u
C
=
Pa
3
4EI
c
¢
C
=
Pa
2
4EI
u
C
a =
L
3
a = 0.153 L
a = 0.153
L
=
50,625 k
#
ft
3
EI
T¢
C
=
3937.5 k
#
ft
2
EI
u
C
= 0.322 in. T¢
max
= 0.00268 radu
B
= 0.322 in. T¢
max
= 0.00268 radu
B
v
3
=
w
24EI
(-x
4
3
+ 8ax
3
3
- 24a
2
x
2
3
+ 4a
3
x
3
- a
4
)
=-
7wa
4
12EI
v
C
v
1
=
wax
1
12EI
(2x
2
1
- 9ax
1
)
=-
7wa
3
6EI
u
B
=
w
0
L
4
120EI
v
max
v =
w
0
x
960EIL
(40L
2
x
2
- 16x
4
- 25L
4
)
u
A
=
5w
0
L
3
192EI
(v
2
)
max
=
wL
4
1823EI
v
B
=
wa
3
24EI
(a - 4L)
u
B
=-
wa
3
6EI
7–29.
7–30.
7–31.
7–33.
7–34.
Chapter 8
8–1.
8–2.
8–3.
8–5.
v
3
=
wa
3
24EI
(4x
3
+ a - 4L)
v
1
=
w
24EI
(-x
1
4
+ 4ax
3
1
- 6a
2
x
1
2
)
v
B
=-
11PL
3
48EI
v
C
=
-PL
3
6EI
u
A
=-
3PL
2
8EI
v
max
=
Pa
24EI
(4a
2
- 3L
2
)
v
2
=
Pa
6EI
[3x
2
(x
2
- L) + a
2
]
v
1
=
Px
1
6EI
[x
1
2
+ 3a(a - L)]
u
A
=
Pa(a - L)
2EI
= 2.99 kN (C)F
HL
= 1.86 kN (T)F
KL
= 2.52 kN (C)F
HG
= 5.43 kN (C)F
HL
= 5.29 kN (T)F
KL
= 4.02 kN (C)F
HG
F
FH
= 3.125 k (C)
F
EH
= 0.500 k (T)
F
FG
= 0
F
JK
= 0.500 k (T)
F
GF
= 0
F
GK
= 3.125 k (C)
B
y
= 1.875 k
B
x
= 2.00 k
A
y
= 1.875 k
= 2.00 kA
x
F
JK
= 0.500 k (C)
F
GF
= 0
F
GK
= 1.875 k (C)
M
B
= 12.0 k
#
ft
B
y
= 1.125 k
B
x
= 2.00 k
M
A
= 12.0 k
#
ft
A
y
= 1.125 k
= 2.00 kA
x
F
CI
= 25.0 kN (C)
F
DI
= 17.5 kN (T)
F
DE
= 4.50 kN (T)
A
NSWERS TO SELECTED PROBLEMS 673
8–26.
8–27.
8–29.
8–30.
8–31.
8–33.
8–34.
8–35.
8–37.
8–38.
8–39.
Chapter 9
9–1.
9–2.
9–3.
9–5. = 2.95 mm T¢
E
v
= 3.38 mmT¢
B
v
= 0.536 mmT¢
A
v
= 0.536 mm T¢
A
v
=
10,368 k
#
ft
3
EI
T¢
D
=
1008 k
#
ft
2
EI
u
D
=
10,368 k
#
ft
3
EI
T¢
D
=
1008 k
#
ft
2
EI
u
D
=
169 kN
#
m
3
EI
T¢
C
=
75 kN
#
m
2
EI
u
D
=
25 Pa
3
6EI
T¢
C
=
3Pa
2
EI
u
C
=
25 Pa
3
6EI
T¢
C
=
3Pa
2
EI
u
C
¢
max
=
0.00802M
0
L
2
EI
T
u
A
=
M
0
L
24EI
=
3Pa
3
4EI
T¢
C
=
5Pa
2
12EI
u
B
=
3Pa
3
4EI
T¢
C
=
5Pa
2
12EI
u
B
F =
P
4
=
9Pa
3
4EI
T¢
C
=
7Pa
2
4EI
u
B
=
9Pa
3
4EI
T¢
C
=
7Pa
2
4EI
u
B
9–6.
9–7.
9–9.
9–10.
9–11.
9–13.
9–14.
9–15.
9–17.
9–18.
9–19.
9–21.
9–22.
9–23.
9–25.
9–26.
9–27.
9–29.
9–30.
9–31.
9–33.
9–34.
9–35.
= 0.455 in.¢
B
= 0.00448 radu
B
=
6637.5 N
#
m
3
EI
T¢
B
=
3150 N
#
m
2
EI
u
B
¢
B
=
6637.5 N
#
m
3
EI
T
u
B
=
3150 N
#
m
2
EI
= 0.282 in.
T¢
C
= 0.00670u
C
= 0.145 in.T¢
C
= 0.00156 radu
C
= 0.145 in.T¢
C
= 0.00156 radu
C
=
Pa
2
6EI
u
A
=
5Pa
2
6EI
u
C
=
5Pa
2
6EI
u
C
=
2Pa
3
3EI
T¢
C
=
PL
2
16EI
u
B
=
PL
3
48EI
T¢
C
u
B
=
PL
2
16EI
¢
C
=
PL
3
48EI
T
= 0.507 in.
c
¢
A
v
= 0.0341 in.T¢
A
v
= 0.0341 in.T¢
A
v
= 4.91 mmT¢
C
v
=
170 k
#
ft
AE
:¢
D
h
¢
D
h
=
170 k
#
ft
AE
:
= 0.0582 in.T¢
A
v
¢
F
v
= 0.0392 in.T
= 0.0392 in.T¢
F
v
=
199 kN
#
m
AE
T¢
D
v
= 2.95 mmT¢
E
v
674 ANSWERS TO SELECTED P ROBLEMS
10–3.
10–5.
10–6.
10–7.
10–9.
10–10.
10–11.
10–13.
10–14.
10–15.
10–17.
M
A
= 45.0 kN
#
m
A
x
= 24.0 kN
A
y
= 33.0 kN
C
y
= 39.0 kN
M
C
= 10.4 k
#
ft
C
y
= 5.65 k
C
x
= 0
4.35 kA
y
=
M
A
= 6.25 k
#
ft
A
y
= 3.125 k
A
x
= 3.00 k
C
y
= 1.875 k
29.6 kA
y
=
42.4 kC
y
=
A
x
= 21.75 k
= 3.75 kC
x
C
y
= 0.900 k
A
x
= 0
A
y
= 0.900 k
B
y
= 7.20 k
M
A
= 200 lb
#
ft
A
y
= 75 lb
A
x
= 0
B
y
= 75 lb
=
2640 k
#
ft
3
EI
¢
C
= 1.50 mm¢
B
= 17.1 kC
y
= 17.1 kA
y
A
x
= 0
= 37.7 kB
y
B
y
=
5P
2
M
A
=
PL
2
A
x
= 0
A
y
=
3P
2
M
A
=
9wL
2
128
B
y
=
7wL
128
A
y
=
57wL
128
A
x
= 0
9–37.
9–38.
9–39.
9–41
9–42.
9–43.
9–45.
9–46.
9–47.
9–49.
9–50.
9–51.
9–53.
9–54.
9–55.
9–57.
9–58.
9–59.
9–61.
Chapter 10
10–1.
10–2.
A
y
= 2.625 k
B
y
= 30.75 k
C
y
= 14.625 k
C
x
= 0
M
A
=
w
0
L
2
15
B
y
=
w
0
L
10
A
y
=
2w
0
L
5
A
x
= 0
(¢
C
)
v
=
417 k
#
ft
3
EI
T
=
79.1
k
#
ft
3
EI
:(¢
C
)
h
=
79.1 k
#
ft
3
EI
:(¢
C
)
h
= 0.0401 in. :(¢
C
)
h
= 0.414(10
-3
) radu
A
= 0.414(10
-3
) radu
A
= 2.81 mmT(¢
C
)
v
= 2.81 mmT(¢
C
)
v
=
1148 k
#
ft
3
EI
;¢
C
h
¢
C
h
=
1148 k
#
ft
3
EI
;
¢
B
y
=
wL
4
4EI
=
5wL
4
8EI
¢
C
h
=
440 k
#
ft
3
EI
T(¢
D
)
v
=
1397 k
#
ft
3
EI
T¢
D
¢
D
=
1397 k
#
ft
3
EI
T
¢
A
=
22.95 kN
#
m
3
EI
T
u
A
=
9
kN
#
m
2
EI
=
w
0
L
4
120EI
T¢
C
¢
C
=
w
0
L
4
120EI
T
= 0.469 in.T¢
B
= 0.00448 radu
B
ANSWERS TO SELECTED PROBLEMS 675
10–18.
10–19.
10–21.
10–22.
10–23.
10–25.
10–26.
10–27.
10–29.
10–30.
10–31. 4.63 kN (T)F
CD
=
F
DB
= 0.586 k (C)
F
AB
= 0.414 k (T)F
AD
=
F
CB
= 0.414 k (T)F
DC
=
1.41 k (T)F
AC
=
F
DE
= 3.96 kN (C)
14.0 kN (C)F
BD
=
5.61 kN (T)F
BE
=
F
CD
= 10.0 kN (C)
14.1 kN (T)F
CB
=
6.04 kN (T)F
AB
=
F
AE
= 6.04 kN (T)
8.54 kN (C)F
AD
=
7.91 kN (C)F
AC
=
F
DA
= 4.94 k (T)
F
AB
= 10.1 k (C)
5.10 k (T)F
DB
=
F
DC
= 6.58 k (T)
F
AC
= 8.23 k (C)
3.06 k (C)F
CB
=
F
BC
= 0
F
BD
= 0.667 k (T)
0.667 k (C)F
AB
=
A
y
= 15.0 kN
B
y
= 7.50 kN
A
x
= 1.53 kN
1.53 kNB
x
=
A
y
= 0
B
y
= 0
2.65 kNA
x
=
2.65 kNB
x
=
4.65 kA
y
=
4.65 kD
y
=
A
x
= 2.59 k
D
x
= 5.41 k
A
x
= 2.27 k
A
y
= 22.5 k
D
y
= 22.5 k
-2.27 kD
x
=
M
D
= 19.5 k
#
ft
D
y
= 15.0 k
D
x
= 2 k
A
y
=-15.0 k 10–33.
10–34.
10–35.
10–37.
10–38.
10–39.
10–45.
Chapter 11
11–1.
11–2.
11–3.
11–5.
11–6.
11–7.
11–9.
M
CD
=-2.61 k
#
ft
M
CB
= 2.61 k
#
ft
M
BC
=-66.0 k
#
ft
M
BA
= 66.0 k
#
ft
M
AB
=-167 k
#
ft
M
BC
=-41.25 kN
#
m
M
BA
= 41.25 kN
#
m
M
DC
= 40.5 k
#
ft
M
CD
=-9 k
#
ft
M
CB
= 9 k
#
ft
M
BC
=-13.5 k
#
ft
M
BA
= 13.5 k
#
ft
M
AB
=-49.5 k
#
ft
-4.09 kN
#
mM
DC
=
-8.18 kN
#
mM
CD
=
8.18 kN
#
mM
CB
=
-8.18 kN
#
mM
BC
=
8.18 kN
#
mM
BA
=
4.09 kN
#
mM
AB
=
M
BC
=-19.25 kN
#
m
M
BA
= 19.25 kN
#
m
20.4 kN
#
mM
CB
=
M
AB
=-18.5 kN
#
m
48 k
#
ftM
CB
=
-84 k
#
ftM
BC
=
84 k
#
ftM
BA
=
M
AB
=-102 k
#
ft
M
C
=-10.6 k
#
ft
M
B
=-8.76 k
#
ft
M
A
=-4.62 k
#
ft
C
y
= 0.241 k
F
AC
= 28.0 k
F
CD
= 7.48 kip
C
y
=
P
3
C
x
= 0
28.1 k (T)F
BC
=
F
BC
= 16.3 k (T)
F
AB
= 18.4 k (T)
22.8 k (C)F
BD
=
53.4 kNF
CB
=
19.2 kNF
DB
=
676 ANSWERS TO SELECTED P ROBLEMS
12–7.
12–14.
12–15.
12–19.
12–22.
12–23.
12–25.
12–26.
Chapter 13
13–1.
M
CB
= 348 k
#
ft
M
BC
=-301 k
#
ft
M
BA
= 301 k
#
ft
M
AB
=-348 k
#
ft
7.54 k
#
ftM
CB
=
-7.54 k
#
ftM
CD
=
-14.2 k
#
ftM
DC
=
14.2 k
#
ftM
DA
=
24.0 k
#
ftM
CD
=
-24.0 k
#
ftM
CB
=
-24.0 k
#
ftM
BC
=
24.0 k
#
ftM
BA
=
M
AB
= M
DC
= 0
-196 k
#
ftM
CD
=
M
CB
= 196 k
#
ft
104 k
#
ftM
BC
=
-104 k
#
ftM
BA
=
-55.7 k
#
ftM
DC
=
-175 k
#
ftM
CD
=
175 k
#
ftM
CB
=
-218 k
#
ftM
BC
=
218 k
#
ftM
BA
=
128 k
#
ftM
AB
=
M
D
= 20.6 kN
#
m
M
C
=-41.1 kN
#
m
M
B
=-41.1 kN
#
m
M
A
= 20.6 kN
#
m
M
D
= 146 k
#
ft
D
y
= 96.0 k
D
x
= 29.3 k
M
A
= 146 k
#
ft
A
y
= 96.0 k
A
x
= 29.3 k
M
CB
= 0
M
BC
=-19.4 k
#
ft
M
BA
= 19.4 k
#
ft
M
AB
=-2.30 k
#
ft
C
y
= 6 kN
M
A
= 30 kN
#
m
B
y
= 33 kN
A
y
= 33 kN
A
x
= 011–10.
11–11.
11–13.
11–14.
11–15.
11–17.
11–18.
11–19.
11–21.
11–22.
11–23.
Chapter 12
12–1.
12–2.
M
C
=-122 k
#
ft
M
B
=-187 k
#
ft
M
A
=-230 k
#
ft
M
B
= M
C
=-84.0 k
#
ft
M
DC
=-56.7 k
#
ft
M
AB
= 25.4 k
#
ft
-6.32 kN
#
mM
CB
=
-9.43 kN
#
mM
BC
=
6.32 kN
#
mM
CD
=
3.32 kN
#
mM
DC
=
-3.32 kN
#
mM
DA
=
-25.9 kN
#
mM
AD
=
M
CB
=-80.0 kN
#
m
M
DA
=-64.0 kN
#
m
M
CD
= 80.0 kN
#
m
M
DC
= 64.0 kN
#
m
-13.4 k
#
ftM
CB
=
13.4 k
#
ftM
DA
=
13.4 k
#
ftM
CD
=
-13.4 k
#
ftM
DC
=
-34.9 kN
#
mM
BD
=
-34.9 kN
#
mM
BC
=
69.8 kN
#
mM
BA
=
-40.8 k
#
ftM
BC
=
40.8 k
#
ftM
BA
=
-2.11 k
#
ftM
AB
=
M
BC
=-0.540 kN
#
m
M
BA
= 0.540 kN
#
m
M
AB
=-1.98 kN
#
m
M
CB
= 16.7 k
#
ft
M
AB
=-42.9 k
#
ft
M
CB
=-36 k
#
ft
M
BC
=-72 k
#
ft
M
BA
= 72 k
#
ft
M
AB
=-126 k
#
ft
-27.2 k
#
ftM
CD
=
27.2 k
#
ftM
CB
=
0.923 k
#
ftM
BC
=
-0.923 k
#
ftM
BA
=
-24.5 k
#
ftM
AB
=
M
BA
= 24 k
#
ft
M
AB
=-10.5 k
#
ft
A
NSWERS TO SELECTED PROBLEMS 677
13–2.
13–3.
13–5.
13–6.
13–7.
13–9.
13–10.
M
DB
= 28.3 k
#
ft
M
BD
=-28.3 k
#
ft
M
BA
= 28.3 k
#
ft
M
AB
= M
CD
= 0
M
DC
=-28.3 k
#
ft
M
DB
= 28.3 k
#
ft
M
BD
=-28.3 k
#
ft
M
BA
= 28.3 k
#
ft
M
DC
=-1.75 k
#
ft
M
CD
=-3.51 k
#
ft
M
CB
= 3.51 k
#
ft
M
BC
=-3.51 k
#
ft
M
BA
= 3.51 k
#
ft
M
AB
= 1.75 k
#
ft
M
DC
= 0
M
EC
=-2.77 k
#
ft
M
CE
=-5.53 k
#
ft
M
CD
=-604 k
#
ft
M
CB
= 610 k
#
ft
M
FB
= 2.77 k
#
ft
M
BF
= 5.53 k
#
ft
M
BC
=-610 k
#
ft
M
BA
= 604 k
#
ft
M
AB
= 0
M
DC
= 0
M
EC
=-2.77 k
#
ft
M
CE
=-5.53 k
#
ft
M
CD
=-604 k
#
ft
M
CB
= 610 k
#
ft
M
FB
= 2.77 k
#
ft
M
BF
= 5.53 k
#
ft
M
BC
=-610 k
#
ft
M
BA
= 604 k
#
ft
M
AB
= 0
369 k
#
ftM
BC
=
-75.1 k
#
ftM
CB
=
75.1 k
#
ftM
CA
=
37.6 k
#
ftM
AC
=
M
CB
= 348 k
#
ft
M
BC
=-301 k
#
ft
M
BA
= 301 k
#
ft
M
AB
=-348 k
#
ft
13–11.
Chapter 14
14–1.
14–2.
14–3.
14–5.
14–6.
14–7.
14–9.
X(10
6
)
113.4 28.8 -75 0 -38.4 -28.8 0 0 0 0
28.8 21.6 0 0 -28.8 -21.6 0 0 0 0
-75 0 150 0 0 0 0 0 -75 0
0 0 0 100 0 -100 0 0 0 0
-38.4 -28.8 0 0 151.8 0 0 -75 -38.4 28.8
-28.8 -21.6 0 -100 0 143.2 0 0 28.8 -21.6
00000010000-100
0000-75 0 0 75 0 0
00-75 0 -38.4 28.8 0 0 113.4 -28.8
0 0 0 0 28.8 -21.6 -100 0 -28.8 121.6
H
K =
X(10
6
)
203.033 -53.033 -53.033 53.033 -15000 000
-53.033 53.033 53.033 -53.033 0 0 0 0 0 0
-53.033 53.033 256.066 0 0 0 -53.033 -53.033 -150 0
53.033 -53.033 0 256.066 0 -150 -53.033 -53.033 0 0
-150 0 0 0 300 0 -150 0 0 0
000-150 0 150 0 0 0 0
00-53.033 -53.033 -150 0 203.033 53.033 0 0
00-53.033 -53.033 0 0 53.033 53.033 0 0
00-150 0 0 0 0 0 150 0
0 0 0 0000 000
H
K =
q
2
= 6.57 k (C)
q
2
= 12.7 lb (C)
D
1
=-0.00172 in.
q
3
= 3.33 k (T)
q
2
= 0
q
1
= 33.3 k (C)
D
2
=-0.0230 in.
D
1
= 0
K = H
510.72 0 -201.39 0 -154.67 -116 -154.67 116
0 174 0 0 -116 -87.0 116 -87.0
-201.39 0 201.39 0 0000
00000000
-154.67 -116 0 0 154.67 116 0 0
-116 -87.0 0 0 116 87.0 0 0
-154.67 116 0 0 0 0 154.67 -116
116 -87.0 0 0 0 0 -116 87.0
X
M
EB
= 47.3 k
#
ftM
FC
=
M
BC
=-274 k
#
ftM
CB
=
M
BE
= 94.6 k
#
ftM
CF
=
M
BA
= 180 k
#
ftM
CD
=
M
AB
= M
CD
= 0
M
DC
=-28.3 k
#
ft
678 ANSWERS TO SELECTED P ROBLEMS
Chapter 16
16–1.
16–2.
16–3.
16–5.
16–6.
16–7.
R
9
= 24.5 kN
R
8
= 5.54 kN
R
7
= 35.5 kN
R
6
= 5.54 kN
K =
I
763.125 0 26.25 26.25 0 -13.125 0 -750 0
0 763.125 -26.25 0 -26.25 0 -750 0 -13.125
26.25 -26.25 140 35 35 -26.25 0 0 26.25
26.25 0 35 70 0 -26.25 0 0 0
0 -26.25 35 0 70 0 0 0 26.25
-13.125 0 -26.25 -26.25 0 13.175 0 0 0
0 -750 0 0 0 0 750 0 0
-750 0 0 0 0 0 0 750 0
0 -13.125 26.25 0 26.25 0 0 0 13.125
Y
(10
6
)
K =
I
851250 0 22500 22500 -11250 0 -440000 0 0
0 1055760 -14400 0 0 -1050000 0 -5760 -14400
22500 -14400 108000 30000 -22500 0 0 14400 24000
22500 0 30000 60000 -22500 0 0 0 0
-11250 0 -22500 -22500 11250 0 0 0 0
0 -1050000 0 0 0 1050000 0 0 0
-840000 0 0 0 0 0 140000 0 0
0 -5760 14400 0 0 0 0 5760 14400
0 -14400 24000 0 0 0 0 14400 48000
Y
R
9
= 19.6 kN
#
m g
R
8
= 26.4 kN
c
R
7
= 6.79 kN :
R
6
= 2.72 kN
#
m b
R
5
= 21.6 kN
c
R
4
= 3.21 kN :
I
511.29 0 22.5 -11.25 0 22.5 -500 0 0
0 511.25 -22.5 0 -500 0 0 -11.25 -22.5
22.5 -22.5 120 -22.5 0 30 0 22.5 30
-11.25 0 -22.5 11.25 0 -22.5 0 0 0
0 -500 0 0 500 0 0 0 0
22.5 0 30 -22.5 0 60 0 0 0
-500 0 0 0 0 0 500 0 0
0 -11.25 22.5 0 0 0 0 11.25 22.5
0 -22.5 30 0 0 0 0 22.5 60
Y
(10
6
)K =
14–10.
14–11.
14–13.
14–14.
14–15.
Chapter 15
15–1.
15–2.
15–3.
15–5.
15–6.
15–7.
15–9.
15–10.
15–11.
R
4
= 160 kN
#
m
R
3
= 120 kN
R
2
= 80 kN
#
m
Q
6
= 25.5 k
Q
5
= 21.0 k
Q
4
= 25.5 k
M
2
= M
3
= 44.2 kN
#
m
R
6
= 30.8 kN
#
m
R
5
= 28.9 kN
R
4
= 2.30 kN
#
m
R
3
= 7.725 kN
R
2
= 41.4 kN
R
6
= 14.0 kN
#
m
R
5
= 22.0 kN
R
4
= 85.75 kN
R
3
= 32.25 kN
R
6
= 12.4 kN
R
5
= 34.5 kN
R
4
= 1.93 kN
R
6
= 39.6 kN
R
5
= 86.6 kN
#
m
R
4
= 40.2 kN
R
3
= 7.85 kN
M
3
= 116 kN
#
m
M
1
= 27.5 kN
#
m
M
3
= 22.5 kN
#
m
M
1
= 90 kN
#
m
F
0.40533 0.096 0.01697 -0.11879 -0.33333 0
0.096 0.128 0.02263 -0.15839 0 0
0.01697 0.02263 0.129 -0.153 0 0.17678
-0.11879 -0.15839 -0.153 0.321 0 -0.17678
-0.33333 0 0 0 0.33333 0
0 0 0.17678 -0.17678 0 0.25
V
K = AE
q
3
= 3.55 k (T)
q
5
= 1.64 k (C)
D
5
= 0.00546 m
D
6
= 0.0133 m
q
5
= 33.3 kN
A
NSWERS TO SELECTED PROBLEMS 679
K =
I
4833.33 0 0 -4833.33 0 0 0 0 0
0 130.90 7854.17 0 -130.90 7854.17 0 0 0
0 7854.17 628333.33 0 -7854.17 324166.67 0 0 0
-4833.33 0 0 4909.01 0 5454.28 -75.75 0 5454.28
0 -130.90 -7854.17 0 4158.68 -7854.17 0 -4027.78 0
0 7854.17 314166.67 5454.28 -7854.17 1151964.64 -5454.28 0 261805.55
000-75.75 0 -5454.28 75.75 0 -5454.28
000 0-4027.78 0 0 4027.78 0
0 0 0 5454.28 0 261805.55 -5454.28 0 523611.11
Y