PROBLEM 6.164
Using the method of joints, determine the force in each member of
the truss shown. State whether each member is in tension or
compression.
SOLUTION
Reactions:
0: 16 kN
Cx
M A
0: 9 kN
yy
F A
0: 16 kN
x
F C
PROBLEM 6.165
Using the method of joints, determine the force in each
member of the double-pitch roof truss shown. State whether
each member is in tension or compression.
SOLUTION
Free body: Truss:
PROBLEM 6.165 (Continued)
Free body: Joint B:
22 1
0: (7.8262 kN) 0
55 2
xBD BC
FF F  
or
0.79057 7.8262 kN
BD BC
FF
(1)
11 1
0: (7.8262 kN) 2 kN 0
55 2
yBD BC
FF F  
Free body: Joint C:
21
0: (1.8861 kN) 0
52
yCD
FF 
1.4911 kN
CD
F
1.491 kN
CD
FT
11
0: 7.00 kN (1.8861 kN) (1.4911 kN) 0
25
xCE
FF  
5.000 kN
CE
F
5.00 kN
CE
FT

PROBLEM 6.165 (Continued)
Free body: Joint F:
12
0: (3.3544 kN) 0
25
xFG
FF 
4.243 kN
FG
F
4.24 kN
FG
FC
11
0: 1.75 kN (3.3544 kN) ( 4.243 kN) 0
52
yEF
FF  
2.750 kN
EF
F
2.75 kN
EF
FT

Add Eqs. (1) and (2):
2 10.607
GH
F
5.303
GH
F
5.30 kN
GH
FC
Subtract Eq. (1) from Eq. (2):
2 2.121 kN
EG
F
1.0605 kN
EG
F
1.061 kN
EG
FC
PROBLEM 6.166
A stadium roof truss is loaded as shown. Determine the
force in members AB, AG, and FG.
SOLUTION
We pass a section through members AB, AG, and FG, and use the free body shown.
PROBLEM 6.167
A stadium roof truss is loaded as shown. Determine the
force in members AE, EF, and FJ.
SOLUTION
We pass a section through members AE, EF, and FJ, and use the free body shown.
PROBLEM 6.168
Determine the components of all forces acting on member
ABD of the frame shown.
SOLUTION
Free body: Entire frame:
PROBLEM 6.169
Determine the components of the reactions at A and E if the frame is loaded
by a clockwise couple of magnitude 36 N · m applied (a) at B, (b) at D.
SOLUTION
Free body: Entire frame:
The following analysis is valid for both parts (a) and (b) since the point of application of the couple is
immaterial.
0: 36 N m (0.4 m) 0
Ex
MA 
90 N 90.0 N
xx
A 
A
PROBLEM 6.169 (Continued)
From Eq. (1):
0
30 N 0
yy
y
AE
E


30 N 30 N
yy
E E
PROBLEM 6.170
Knowing that the pulley has a radius of 50 mm, determine the
components of the reactions at B and E.
SOLUTION
Free body: Entire assembly:
0 : (300 N)(350 mm) (150 mm) 0
Ex
MB 
700 N
x
B 700 N
x
B
PROBLEM 6.171
For the frame and loading shown, determine the components of the
forces acting on member CFE at C and F.
SOLUTION
Free body: Entire frame:
PROBLEM 6.172
For the frame and loading shown, determine the reactions at A, B, D,
and E. Assume that the surface at each support is frictionless.
SOLUTION
Free body: Entire frame:
0: (1000 lb)sin30 0
x
FAB 
500 0AB 
(1)
0: (1000 lb)cos30 0
y
FDE 
866.03 0DE 
(2)
PROBLEM 6.173
Water pressure in the supply system exerts a downward force of 135 N
on the vertical plug at A. Determine the tension in the fusible link DE
and the force exerted on member BCE at B.
SOLUTION
Free body: Entire linkage:
0: 135 0
y
FC 
135 NC