Hibbeler R.C. Structural Analysis
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70 CHAPTER 2ANALYSIS OF STATICALLY DETERMINATE STRUCTURES
2
A
B
C
2 m
10 kN
/
m
45
4 m
F2–2
8 kN/m
4 m
1 m
10 kN
B
C
A
2 m
F2–4
A
C
B
2 m 2 m
60 kNm
3 m
F2–1
A
B
C
10 kN
/
m
60
2 m 2 m
F2–3
B
A
C
6 kN
2 kN
2 m
2 m
2 m
2 m
F2–6
FUNDAMENTAL PROBLEMS
F2–1. Determine the horizontal and vertical components
of reaction at the pins A, B, and C.
F2–4. Determine the horizontal and vertical components
of reaction at the roller support A, and fixed support B.
F2–2. Determine the horizontal and vertical components
of reaction at the pins A, B, and C.
F2–5. Determine the horizontal and vertical components
of reaction at pins A, B, and C of the two-member frame.
F2–3. Determine the horizontal and vertical components
of reaction at the pins A, B, and C.
F2–6. Determine the components of reaction at the roller
support A and pin support C. Joint B is fixed connected.
A
B
C
3 ft
4 ft
300 lb
2 ft
2 ft
F2–5
FUNDAMENTAL PROBLEMS 71
2
A
B
C
D
4 ft
2 ft
8 ft
2 k/ft
0.5 k/ft
F2–9
A
B
C
D
3 kN/m
8 kN 8 kN
2 m
2 m
2 m
3 m
4 m
F2–7
A
B
C
D
2 m
3 m
6 kN
4 kN
6 kN
3 m
2 m 2 m
F2–8
F2–7. Determine the horizontal and vertical components
of reaction at the pins A, B, and D of the three-member
frame. The joint at C is fixed connected.
F2–9. Determine the components of reaction at the fixed
support D and the pins A, B, and C of the three-member
frame. Neglect the thickness of the members.
F2–8. Determine the components of reaction at the fixed
support D and the pins A, B, and C of the three-member
frame. Neglect the thickness of the members.
F2–10. Determine the components of reaction at the fixed
support D and the pins A, B, and C of the three-member
frame. Neglect the thickness of the members.
1.5 kN/m
6 m
2 m 2 m 2 m
6 kN
8 kN 8 kN
6 kN
A
B
C
D
F2–10
72 CHAPTER 2ANALYSIS OF STATICALLY DETERMINATE STRUCTURES
2
6 m 6 m 3 m
20 kN 20 kN
26 kN
5
12
13
A
B
Prob. 2–18
12 ft 12 ft
2 k/ft
2 k/ft
3 k/ft
600 k · ft
A
B
60
Prob. 2–19
24 ft
5 k/ft
2 k/ft
10 ft
A
B
Prob. 2–20
4 kN/m
18 kN
6 m
BCA
2 m 2 m
Prob. 2–21
2–18. Determine the reactions on the beam. Neglect the
thickness of the beam.
2–21. Determine the reactions at the supports A and B of
the compound beam. Assume there is a pin at C.
PROBLEMS
2–19. Determine the reactions on the beam.
2–22. Determine the reactions at the supports A, B, D,
and F.
*2–20. Determine the reactions on the beam.
2–23. The compound beam is pin supported at C and
supported by a roller at A and B. There is a hinge (pin) at D.
Determine the reactions at the supports. Neglect the thickness
of the beam.
B
8 k
2 k/ft
4 ft4 ft 4 ft
4 ft8 ft
2 ft
A
C
D
E
F
Prob. 2–22
ADB C
8 ft
3
4
5
8 ft
12 k
15 k · ft
4 k
30
8 k
8 ft
4 ft 2 ft
6 ft
Prob. 2–23
PROBLEMS 73
2
*2–24. Determine the reactions on the beam. The support
at B can be assumed to be a roller.
2–27. The compound beam is fixed at A and supported by
a rocker at B and C. There are hinges (pins) at D and E.
Determine the reactions at the supports.
2–25. Determine the reactions at the smooth support C
and pinned support A. Assume the connection at B is fixed
connected.
*2–28. Determine the reactions at the supports A and B.
The floor decks CD, DE, EF, and FG transmit their loads to
the girder on smooth supports. Assume A is a roller and B
is a pin.
2–26. Determine the reactions at the truss supports A
and B. The distributed loading is caused by wind.
2–29. Determine the reactions at the supports A and B of
the compound beam. There is a pin at C.
12 ft 12 ft
B
A
2 k/ft
Prob. 2–24
80 lb/ft
B
A
C
6 ft
10 ft
30
Prob. 2–25
AB
48 ft
600 lb/ft
400 lb/ft
48 ft
20 ft
Prob. 2–26
6 m
2 m
6 m
2 m 2 m
15 kN
ADBE
C
Prob. 2–27
4 ft 4 ft 4 ft 4 ft
3 ft 1 ft
3 k/ft
10 k
A
C
D
E
F
G
B
Prob. 2–28
A
C
B
4 kN/m
6 m 4.5 m
Prob. 2–29
74 CHAPTER 2ANALYSIS OF STATICALLY DETERMINATE STRUCTURES
2
A
C
B
2 kN/m
6 m 4 m
Prob. 2–30
2–30. Determine the reactions at the supports A and B of
the compound beam. There is a pin at C.
2–33. Determine the horizontal and vertical components
of reaction acting at the supports A and C.
2–31. The beam is subjected to the two concentrated loads
as shown. Assuming that the foundation exerts a linearly
varying load distribution on its bottom, determine the load
intensities and for equilibrium (a) in terms of the
parameters shown; (b) set , .L = 12 ftP = 500 lb
w
2
w
1
*2–32. The cantilever footing is used to support a wall
near its edge A so that it causes a uniform soil pressure
under the footing. Determine the uniform distribution
loads, and , measured in lb/ft at pads A and B,
necessary to support the wall forces of 8000 lb and 20 000 lb.
w
B
w
A
2–34. Determine the reactions at the smooth support A
and the pin support B. The joint at C is fixed connected.
P 2P
w
2
w
1
L
__
3
L
__
3
L
__
3
Prob. 2–31
w
A
A
B
w
B
8 ft2 ft 3 ft
1.5 ft
8000 lb
20 000 lb
0.25 ft
Prob. 2–32
30 kN
50 kN
1.5 m
3 m
1.5 m
B
C
A
3 m
4 m
4 m
2 m
2 m
Prob. 2–33
150 lb/ft
B
A
C
60
10 ft
5 ft
Prob. 2–34
PROBLEMS 75
2
2–35. Determine the reactions at the supports A and B. 2–37. Determine the horizontal and vertical components
force at pins A and C of the two-member frame.
*2–36. Determine the horizontal and vertical components
of reaction at the supports A and B. Assume the joints at C
and D are fixed connections.
2–38. The wall crane supports a load of 700 lb. Determine
the horizontal and vertical components of reaction at the
pins A and D. Also, what is the force in the cable at the
winch W?
30 ft
20 ft
48 ft 48 ft
500 lb/ft
700 lb/ft
A
B
Prob. 2–35
6 m 8 m
4 m
20 kN
7 m
A
B
CD
30 kN
40 kN
12 kN/m
Prob. 2–36
3 m
3 m
200 N/
m
A
B
C
Prob. 2–37
60
4 ft
D
AB
C
E
W
4 ft
700 lb
4 ft
Prob. 2–38
76 CHAPTER 2ANALYSIS OF STATICALLY DETERMINATE STRUCTURES
2
2–39. Determine the resultant forces at pins B and C on
member ABC of the four-member frame.
2–41. Determine the horizontal and vertical reactions at
the connections A and C of the gable frame. Assume that A,
B, and C are pin connections. The purlin loads such as D
and E are applied perpendicular to the center line of each
girder.
*2–40. Determine the reactions at the supports A and D.
Assume A is fixed and B and C and D are pins.
2–42. Determine the horizontal and vertical components
of reaction at A, C, and D.Assume the frame is pin connected
at A, C, and D, and there is a fixed-connected joint at B.
2 ft
150 lb/ft
4 ft
5 ft
5 ft2 ft
A
FE D
BC
Prob. 2–39
A
B
D
C
w
w
L
1.5L
Prob. 2–40
800 lb
600 lb 600 lb
400 lb 400 lb
DG
E
C
F
A
B
120 lb/ft
800 lb
6 ft 6 ft 6 ft 6 ft
10 ft
5 ft
Prob. 2–41
A
C
D
B
50 kN
40 kN
4 m
6 m
1.5 m 1.5 m
15 kN/m
2 m
Prob. 2–42
PROJECT PROBLEM 77
2
2–43. Determine the horizontal and vertical components
at A, B, and C. Assume the frame is pin connected at these
points. The joints at D and E are fixed connected.
*2–44. Determine the reactions at the supports A and B.
The joints C and D are fixed connected.
18 ft 18 ft
10 ft
6 ft
A
B
C
D
E
3 k/ft
1.5 k/ft
Prob. 2–43
4 m
A
C
D
B
3 m 1.5 m
2 m
10 kN/m
3
4
5
Prob. 2–44
PROJECT PROBLEM
2–1P. The railroad trestle bridge shown in the photo is
supported by reinforced concrete bents. Assume the two
simply supported side girders, track bed, and two rails have
a weight of 0.5 k ft and the load imposed by a train is 7.2 k ft
(see Fig. 1–11). Each girder is 20 ft long. Apply the load over
the entire bridge and determine the compressive force in
the columns of each bent. For the analysis assume all joints
are pin connected and neglect the weight of the bent. Are
these realistic assumptions?
>>
Project Prob. 2–1P
PP
8 ft
18 ft
AD
B
C
75
75
The forces in the members of this bridge can be analyzed using either the
method of joints or the method of sections.
3
79
In this chapter we will develop the procedures for analyzing statically
determinate trusses using the method of joints and the method of
sections. First, however, the determinacy and stability of a truss will be
discussed. Then the analysis of three forms of planar trusses will
be considered: simple, compound, and complex. Finally, at the end of
the chapter we will consider the analysis of a space truss.
3.1 Common Types of Trusses
A truss is a structure composed of slender members joined together at
their end points. The members commonly used in construction consist
of wooden struts, metal bars, angles, or channels. The joint connections
are usually formed by bolting or welding the ends of the members to a
common plate, called a gusset plate, as shown in Fig. 3–1, or by simply
passing a large bolt or pin through each of the members. Planar trusses
lie in a single plane and are often used to support roofs and bridges.
Analysis of Statically
Determinate Trusses
The gusset plate is used to connect eight
members of the truss supporting structure
for a water tank.
gusset plate
Fig. 3–1