Hibbeler engineering mechanics (solutions manual) statics 12th edition engineering mechanics chapter 7

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•7–1. Determine the internal normal force and shear
force, and the bending moment in the beam at points C and
D. Assume the support at B is a roller. Point C is located just
to the right of the 8-kip load.

8 kip
40 kip и ft
A

C
8 ft

545

D
8 ft

B
8 ft

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7–2. Determine the shear force and moment at points C
and D.

500 lb

300 lb

200 lb
B

A

C
6 ft

546

4 ft

E

D
4 ft

6 ft

2 ft


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7–3. Determine the internal normal force, shear force, and
moment at point C in the simply supported beam. Point C is
located just to the right of the 1500-lb – ft couple moment.

500 lb/ft

B

A
C
6 ft

547

1500 lb и ft
6 ft

30Њ


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*7–4. Determine the internal normal force, shear force,
and moment at points E and F in the beam.

C

A

E

D

45Њ

F

B

300 N/m
1.5 m

548

1.5 m

1.5 m

1.5 m


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•7–5. Determine the internal normal force, shear force,
and moment at point C.

0.2 m

400 N
1m

A

B
C
1.5 m
3m

549

2m


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7–6. Determine the internal normal force, shear force, and
moment at point C in the simply supported beam.

4 kN/m

A

B

C
3m

550

3m


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7–7. Determine the internal normal force, shear force, and
moment at point C in the cantilever beam.

w0

A
L
––
2

551

B

C
L
––
2


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*7–8. Determine the internal normal force, shear force,
and moment at points C and D in the simply supported
beam. Point D is located just to the left of the 5-kN force.

5 kN
3 kN/m

A

B
C
1.5 m

552

1.5 m

D
3m


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•7–9. The bolt shank is subjected to a tension of 80 lb.
Determine the internal normal force, shear force, and
moment at point C.

C
90Њ

A

553

6 in.

B


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7–10. Determine the internal normal force, shear force,
and moment at point C in the double-overhang beam.

3 kN/m

A
1.5 m

554

B

C
1.5 m

1.5 m

1.5 m


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7–11. Determine the internal normal force, shear force,
and moment at points C and D in the simply supported
beam. Point D is located just to the left of the 10-kN
concentrated load.

10 kN
6 kN/m

A

B
D

C
1.5 m

555

1.5 m

1.5 m

1.5 m


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*7–12. 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.

5 kip

0.5 kip/ft

A
6 ft

556

B

D

C
6 ft

6 ft

6 ft


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•7–13. Determine the internal normal force, shear force,
and moment at point D of the two-member frame.

250 N/m
B
A

D
2m

1.5 m
C

E
4m

557

300 N/m


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7–14. Determine the internal normal force, shear force,
and moment at point E of the two-member frame.

250 N/m
B
A

D
2m

1.5 m
C

E
4m

558

300 N/m


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7–15. 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.

300 lb/ft
200 lb/ft

200 lb/ft
D

F

E
A
4 ft

4 ft

C

B
4 ft

*7–16. Determine the internal normal force, shear force,
and moment in the cantilever beam at point B.
6 kip/ft

B

A
3 ft

559

12 ft

4 ft


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•7–17. Determine the ratio of a>b for which the shear force
will be zero at the midpoint C of the double-overhang beam.

w0

C
A
a

560

C
b/2

B
B
b/2

a

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7–18. Determine the internal normal force, shear force,
and moment at points D and E in the overhang beam. Point
D is located just to the left of the roller support at B, where
the couple moment acts.

2 kN/m

6 kN и m

C
A

D
3m

B

E

1.5 m

1.5 m

3

5
4

5 kN

561


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7–19. Determine the distance a in terms of the beam’s
length L between the symmetrically placed supports A
and B so that the internal moment at the center of the
beam is zero.

w0

w0

A

B
a
––
2

a
––
2
L

562


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*7–20. Determine the internal normal force, shear force,
and moment at points D and E in the compound beam.
Point E is located just to the left of the 10-kN concentrated
load. Assume the support at A is fixed and the connection at
B is a pin.

10 kN

2 kN/m
B

C
A
1.5 m

563

D
1.5 m

E
1.5 m

1.5 m


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•7–21. Determine the internal normal force, shear force,
and moment at points F and G in the compound beam. Point
F is located just to the right of the 500-lb force, while point G
is located just to the right of the 600-lb force.

500 lb
2 ft

2 ft

600 lb

A
F

B
D

C

1.5 ft
E
G

2 ft

564

2 ft

2 ft


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7–22. The stacker crane supports a 1.5-Mg boat with the
center of mass at G. Determine the internal normal force,
shear force, and moment at point D in the girder. The trolley
is free to roll along the girder rail and is located at the
position shown. Only vertical reactions occur at A and B.

2m

1m1m

5m

A

B
C

7.5 m

D
2m
3.5 m

G

565


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7–23. Determine the internal normal force, shear force,
and moment at points D and E in the two members.

0.75 m
1m

B

D

60 N

0.75 m
A

60Њ

30Њ

2m

566

E
C


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*7–24. Determine the internal normal force, shear force,
and moment at points F and E in the frame. The crate
weighs 300 lb.

1.5 ft

1.5 ft

1.5 ft

1.5 ft
0.4 ft

A
4 ft

B

567

F

C

E

D


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•7–25. Determine the internal normal force, shear force,
and moment at points D and E of the frame which supports
the 200-lb crate. Neglect the size of the smooth peg at C.

4.5 ft
C

4 ft

E
2 ft
B

1.5 ft
D
1.5 ft

568

A


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7–26. The beam has a weight w per unit length. Determine
the internal normal force, shear force, and moment at point
C due to its weight.

B
L
––
2

L

––
2

C

u
A

569