4–1. Determine the internal normal force, shear force, and
bending moment in the beam at points C and D. Point D is
located just to the right of the concentrated force and
moment. Assume the support at B is a pin and A is a roller.
15 kN
30 kN ? m
B
ACD
2 m2
m2
m
15 kN>m
4–2. Determine the internal normal force, shear force, and
bending moment at point C. Point C is located just to the left of
the moment.
SOLUTION
ACB
2 m 2 m 2 m
2 m
12 kN
24 kN?m
12 kN>m
4–3. Determine the internal normal force, shear force, and
moment acting at point C and at point D, which is located just
to the right of the roller support at B.
SOLUTION
200 lb>ft200 lb>ft
300 lb>ft
4 ft
A
EF
CB
D
4 ft4 ft4 ft
*4–4. Determine the internal normal force, shear force, and
bending moment at point D. Take
w=150
N>m
.
4 m
A
D
B
C
4 m
4 m
3
m
w
4–5. The beam AB will fail if the maximum internal moment
at D reaches
800
N#m
or the normal force in member BC
becomes 1500 N. Determine the largest load w it can support.
4 m
A
D
B
C
4 m
4 m
3
m
w
4–6. Determine the internal normal force, shear force, and
bending moment in the beam at points C and D. Point C is
located just to the left of the roller support. Assume the support
at B is a roller and A is a pin.
AB
18 kN>m
9 kN>
m
C
D
3 m3 m3 m
4–7. Determine the internal normal force, shear force, and
bending moment acting at point C, located just to the right of
the 12-kN force and
18
kN #m
moment.
A
B
18 kN
18 kN ?m
2 m 2 m 2 m
C
12 kN
133
*4–8. Determine the internal normal force, shear force, and
moment at points E and D of the compound beam.
S
+Σ Fx =0;
NE=0
Ans.
+
c
ΣFy=0;
VE+50 =0
VE=–50 N
Ans.
a+Σ ME=0;
–200 +50(2) –ME=0
ME=–100 N #m
Ans.
Segment DB:
S
+Σ Fx=0;
ND=0
+
c
ΣFy=0;
VD–800 +50 =0
VD=750 N
Ans.
a+ΣMD=0;
–800(2) +6(50) –MD=0
MD=–1300 N #m=–1.30 kN #m
Ans.
Ans.
NE=0
VE=–50 N
ME=–100 N #m
VD=750 N
MD=–1.30 kN #m
2 m
AD BE C
800 N
2 m 2 m 2 m4 m
200 N
m
Segment EC:
SOLUTION
4–9. Determine the internal normal force, shear force, and
moment at point C of the beam.
3 m 3 m
400 N>m
200
N>m
A
C
B
SOLUTION
135
Ans.
NC=0
VC=2.75 k
MC=25.5 k #ft
ND=0
VD=–5.25
k
MD=31.5 k #ft
4–10. Determine the internal normal force, shear force, and
moment in the beam at points C and D. Point D is just to the
right of the 5-kip load.
k
6 ft 6 ft 6 ft 6 ft
0.5 kip>ft
A
CD
B
5 kip
SOLUTION
4–11. Determine the internal normal force, shear force, and
bending moment in the beam at point C.
A
B
3 k
>
ft
9 ft
9 ft
9 ft
C
*4–12. Determine the shear and moment throughout the
beam as a function of x.
SOLUTION
B
A
x
4 m 2 m
600 N
4–13. Determine the shear and moment throughout the
beam as a function of x.
B
A
x
4 m 2 m
15 kN>m
4–14. Determine the shear and moment throughout the
beam as a function of x.
SOLUTION
B
A
x
4 m 2 m
12 kN?m
4–15. Determine the shear and moment in the floor girder as
a function of x. Assume the support at B is a pin and A is a
roller.
2
m1
m1 m
A
B
4 kN
6 kN
*4–16. Determine the shear and moment throughout the
beam as a function of x.
SOLUTION
AB
8 kN
>
m
3 m3 m
x
4–17. Determine the shear and moment in the beam as a
function of x.
4–18. Determine the shear and moment throughout the
beam a function of x.
SOLUTION
6 ft 4 ft
2 k>ft
8 k
x
10 k
40 k?
ft
4–19. Determine the shear and moment throughout the
beam a function of x.
SOLUTION
AB
x
4 ft 4 ft
150 lb>ft
6 ft
250 lb
250 lb
*4–20. Determine the shear and moment in the beam a
function of x.
x
BA
w0
L
__
2
L
__
2
SOLUTION