12–36. (Continued)
616
617
12–37. (Continued)
d
Ans.
c
Ans.
T
Ans.
d
Ans.
B
Ans.
Ans.
618
12–37. (Continued)
Ans.
Ax=3.50
kN d
MA=7.00
kN #mB
Ay=5.20
kNT
Bx=7.00
kN d
MB=14.0
kN #mB
By=0
Cx=7.00
kN d
MC=14.0
kN #mB
Cy=0
Dx=3.50
kN d
MD=7.00
kN #mB
Dy=5.20
kN
c
d
Ans.
c
Ans.
d
Ans.
B
Ans.
Ans.
B
Ans.
619
620
12–38. (Continued)
d
Ans.
B
Ans.
T
Ans.
d
Ans.
B
Ans.
T
Ans.
622
SOLUTION
12–39. Use the portal method of analysis and draw the
moment diagram for column AFE.
4 m
6 m
30 kN
15 kN
A
D
EH
I
L
K
G
J
FC
B
4 m
623
SOLUTION
*12–40. Solve Prob. 12–39 using the cantilever method of
analysis. All the columns have the same cross-sectional area.
4 m
6 m
30 kN
15 kN
A
D
EH
I
L
K
G
J
FC
B
4 m
624
SOLUTION
+
SΣFx=0;
4V–3=0
V=0.75
k
+
SΣFx=0;
4V′–9=0
V′=2.25
k
Ay=2.925
k
c
NA=–2.925
k
Ans.
Ax=2.25
kS
VA=2.25
k
Ans.
MA=20.25
k#ftA
Ans.
Ans.
Ay=2.925
k
c
NA=–2.925
k
Ax=2.25
kS
VA=2.25
k
MA=20.25
k#ftA
12–41. Use the portal method and determine
(approxi mately) the axial force, shear force, and moment
at A.12 ft
18 ft
20 ft 20 ft
3 k
6
k
ABC
DEF
GH
I
12 in
2
8 in
2
10 in
2
626
SOLUTION
12–43. Draw (approximately) the moment diagram for girder
PQRST and column AFKP of the building frame. Use the
portal method.
12 kN
24 kN
24 kN
6 m 6 m 8 m 8 m
4 m
4
m
4
m
PQR ST
KLMNO
FGHIJ
AB CDE
627
12–43. (Continued)
SOLUTION
*12–44. Draw (approximately) the moment diagram for
girder PQRST and column AFKP of the building frame. All
columns have the same cross-sectional area. Use the cantilever
method.
12 kN
24 kN
24 kN
6 m 6 m 8 m 8 m
4
m
4
m
4
m
PQR ST
KLMNO
FGHIJ
AB CDE
629
*12–44. (Continued)
630
SOLUTION
+
SΣFx=0;
10 –6V=0;
V=1.667
kN
The equilibrium of each segment is shown on the FBDs.
12–45. Draw the moment diagram for girder IJKL of the
building frame. Use the portal method of analysis. Each column
has the cross-sectional area indicated.
20 kN
24 (10
23
) m
2
Area 16 (10
23
) m
2
16 (10
23
) m
2
24 (10
23
) m2
4 m 5 m 4 m
4 m
4
m
JKL
G
F
EH
DCBA
I
40 kN
631
SOLUTION
12–46. Draw the moment diagram for girder IJKL of the
building frame. Use the cantilever method of analysis. Each
column has the cross-sectional area indicated.
20 kN
24 (10
23
) m
2
Area 16 (10
23
) m
2
16 (10
23
) m
2
24 (10
23
) m2
4 m 5 m 4 m
4 m
4 m
JKL
G
F
EH
DCBA
I
40 kN