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Problem 6.1 In Active Example 6.1, suppose that in
addition to the 2-kN downward force acting at point D,
a 2-kN downward force acts at point C. Draw a sketch of
the truss showing the new loading. Determine the axial
forces in members AB and AC of the truss.
C
5 m
5 m
A
D
B
2 k
N
3 m
3 m
Solution: The new sketch, a free-body diagram of the entire truss
and a free-body diagram of the joint at Aare shown. The angle ˛
between CD and BD is
Solving yields
386
Problem 6.2 Determine the axial forces in the
members of the truss and indicate whether they are in
tension (T) or compression (C).
C
800 N
0.7 m
0.7 m
A
B
0.4 m
20⬚
Solution: We start at joint A
Fx:7
p65 FAB C7
p65 FAC ⊲800 N⊳sin 20°D0
FAC
FAB
Next we move to joint C
Fx:7
p65 FAC FBC D0)FBC D521 N
FAC
Problem 6.3 Member AB of the truss is subjected to a
1000-lb tensile force. Determine the weight Wand the
axial force in member AC.
A
B
W
C
60 in
Problem 6.4 Determine the axial forces in members
BC and CD of the truss. 600 lb
D
E
3 ft
3 f
t
3 f
t
3 ft
A
C
B
388
Problem 6.5 Each suspended weight has mass mD
20 kg. Determine the axial forces in the members of
the truss and indicate whether they are in tension (T)or
compression (C).
0.32 m
0.16 m0.16 m
0.4 m
A
B
CD
mm
Solution: Assume all bars are in tension. Start with joint D
Fy:5
p61 TAD 196.2ND0
196.2 N
Now work with joint C
Finally work with joint A
Fy:5
p29 ⊲TAB CTAC⊳5
p61 TAD D0
TAC D211 N⊲T⊳
TAD D306 N⊲T⊳
Problem 6.6 Determine the largest tensile and com-
pressive forces that occur in the members of the truss,
and indicate the members in which they occur if
(a) the dimension hD0.1m;
(b) the dimension hD0.5m.
Observe how a simple change in design affects the
maximum axial loads.
0.6 m
0.4 m
h
1.2 m
0.7 m
1 kN
C
D
B
A
Solution: To get the force components we use equations of the
form TPQ DTPQePQ DTPQXiCTPQYjwhere Pand Qtake on the
and FyDTABY CTACY 1kND0.
At joint B:
FxDTABX CTBCX CTBDX D0,
Solve simultaneously to get
TBC D0,T
CD D2.88 kN.
0.6 m 1.2 m
CY
−TAB
B
y
x
(b) For this part of the problem, we set hD0.5 m. The unit vectors
TAB D1.35 kN,
TBD D1.74 kN,
and TCD D1.60 kN.
390
Problem 6.7 This steel truss bridge is in the Gallatin
National Forest south of Bozeman, Montana. Suppose
that one of the tandem trusses supporting the bridge is
loaded as shown. Determine the axial forces in members
AB, BC, BD, and BE.
BDF
A
FAC
Now work with joint C
Fy:FBC 10 kip D0)FBC D10 kip
FAC FCE
FBC
C
10 kip
FBD D42.5 kip⊲C⊳, FBE D11.74 kip⊲T⊳
Problem 6.8 For the bridge truss in Problem 6.7,
determine the largest tensile and compressive forces that
occur in the members, and indicate the members in
which they occur.
Solution: Continuing the solution to Problem 6.7 will show the
392
Problem 6.9 The trusses supporting the bridge in
Problems 6.7 and 6.8 are called Pratt trusses. Suppose
that the bridge designers had decided to use the truss
shown instead, which is called a Howe truss. Determine
the largest tensile and compressive forces that occur
in the members, and indicate the members in which
they occur. Compare your answers to the answers to
Problem 6.8.
17 ft 17 ft 17 ft 17 ft
A
BDF
H
GEC
8 ft
10 kip 10 kip 10 kip
Solution: We start with the entire structure in order to find the
reaction at A. We have to assume that either Aor His really a roller
Now we examine joint A
Fy:8
p353 FAB CAD0)FAB D35.2 kip
Fx:17
p353 FAB CFBD D0)FBD D31.9 kip
Fy:8
p353 FAB FBC D0)FBC D15 kip
FBD
B
Next work with joint C
Fy:FBC C8
Finally from joint Ewe find
Fy:FDE 10 kip D0)FDE D10 kip
FDE
FBC DFFG D15 kip⊲T⊳
FCD DFDG D11.74 kip⊲C⊳
Problem 6.10 Determine the axial forces in members
BD,CD, and CE of the truss.
F
300 mm
300 mm
C
E
G
Solution: The free-body diagrams of the entire truss and of joints
394
Problem 6.11 The loads F1DF2D8 kN. Determine
the axial forces in members BD,BE, and BG.
3 m
B
D
E
F2
F1
3 m
GyD9kN
Problem 6.12 Determine the largest tensile and
compressive forces that occur in the members of the
truss, and indicate the members in which they occur if
(a) the dimension hD5 in;
Observe how a simple change in design affects the
maximum axial loads.
A
B
C
E
D
h
A
20
hh
396
Problem 6.13 The truss supports loads at Cand E.
If FD3 kN, what are the axial forces in members BC
and BE?AB
D
G
1 m
1 m 1 m 1 m
(1) Joint G:
from which
p2GD5p2
BD D5
(3) Joint E :
FyDBE
p22FCDE D0,
6.13 (Continued)
(4) Joint A:
FyDAyAC
p2D0,
(5) Joint C :
FyDBC CAC
Problem 6.14 If you don’t want the members of the
truss to be subjected to an axial load (tension or compres-
sion) greater than 20 kN, what is the largest acceptable
magnitude of the downward force F?12 m
A
F
B
Solution: Start with joint A
A
36.9°
30.5°
F
FAB
FAC
C
FCD
Finally examine joint D
Fy:FBD D0
FBD
D
DxFCD
398
c
2008 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they
currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
Problem 6.15 The truss is a preliminary design for a
structure to attach one end of a stretcher to a rescue
helicopter. Based on dynamic simulations, the design
engineer estimates that the downward forces the stretcher
will exert will be no greater than 1.6 kN at Aand at B.
What are the resulting axial forces in members CF,DF,
and FG?
300
mm
290
mm
390
mm
200 mm
480 mm
150 mm
A
B
D
C
G
F
E
Solution: Start with joint C
1.6 kN
Now use joint F
Fx:59
p3706 FFG 29
p3145 FDF C39
p3825 FCF D0
Problem 6.16 Upon learning of an upgrade in the heli-
copter’s engine, the engineer designing the truss does
new simulations and concludes that the downward forces
the stretcher will exert at Aand at Bmay be as large as
1.8 kN. What are the resulting axial forces in members
DE,DF, and DG?
Next work with joint F
Fx:59
p541 TDG C29
p3145 TDF CTCD D0
Fy:21
p541 TDG C48
p3145 TDF TBD D0
400
Problem 6.17 Determine the axial forces in the
members in terms of the weight W.
A
BE
D
C
1 m
1 m
0.8 m 0.8 m 0.8 m
W
Solution: Denote the axial force in a member joining two points
I,Kby IK. The angle between member DE and the positive xaxis
is ˛Dtan10.8D38.66°. The angle formed by member DB with the
positive xaxis is 90°C˛. The angle formed by member AB with the
Problem 6.18 The lengths of the members of the truss
are shown. The mass of the suspended crate is 900 kg.
Determine the axial forces in the members.
12 m
12 m
5 m
13 m
13 m
C
D
B
A
40⬚
27.4°
FAC
FCD
FBC
FBD D1.807 kN D1.807 kN⊲T⊳
402
c
2008 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they
currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
Problem 6.19 The loads F1D600 lb and F2D
300 lb. Determine the axial forces in members AE,BD,
and CD.
F2
F1
D
A
B
C
4 ft
3 ft
G
E
6 ft
4 ft
Solution: The reaction at Eis determined by the sum of the
Joint E :
FyDECAE D0,
F1
0.6D300
0.6D500 lb⊲C⊳ .
FxDBC BD cos ˛D0,
Problem 6.20 Consider the truss in Problem 6.19. The
loads F1D450 lb and F2D150 lb. Determine the axial
forces in members AB,AC, and BC.
Solution: From the solution to Problem 6.19 the angle ˛D36.87°
0.8D625 lb⊲T⊳ .
0.6D375 lb⊲C⊳
EG
BD
F2
404
Problem 6.21 Determine the axial forces in members
BD,CD, and CE of the truss.
CE
G
FD
H
A
B
4 f
t
4 f
t
4 ft4 ft4 ft
12 kip
