ME 221 Statics
Lecture #31
Sections 6.6 – 6.7
ME221
Lecture #31
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Homework #11
Chapter 6 problems:
– 2, 3, 6 & 7 – Method of Joints
– 32, 36, 47 & 53 – Method of Sections
– 68 & 75
• Due Wednesday, November 19
ME221
Lecture #31
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Exam #3 Results
Scores posted on Angel
Solution posted on Angel
See syllabus for regrade policy
ME221
Lecture #31
3
Trusses
Composed of slender straight pieces connected
together by frictionless pins where all the loads (no
moments) are applied.
Each member will act as a two-force member
(either in tension or compression).
All the forces acting on a truss member are axial.
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Analysis of Trusses Using the Method of Joints
PBy
PBx
B
We need to solve
for:
(1) - Internal forces
FAB, FAC, and FCA
(2) - Reactions
Ax, Ay and Cy
PAx
Ax
PAY
a
A
Ay
ME221
Lecture #31
PCy
b
PCx
C
C
y
5
Using Matrix Notation
1
0
1
 FAB   cos a
 F   sin a
0
0
0
AC

 
cos b 0
 FBC   cos a 0

 =   sin a 0  sin b 0
A
 x  
 1  cos b 0
 Ay   0

  0
0
sin
b
0
C

 y 
Using manual calculations
Look for joints with 2 unknowns
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Lecture #31
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0 0

1 0
0 0

0 0
0 0

0 1
 PAx 
 P 
 Ay 
  PBx 



P
 By 
  PCx 


 PCy 
6
Example
6 kN
A
B
3 kN
0.9 m
C
D
E
1.2 m
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1.2 m
Lecture #31
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6 kN
A
4
B
4
9 5
15
3 kN
C
16
15
16
9
5
4
4
E
D
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Method of Sectioning
If the question is to find internal forces in selected
members of the truss, then one can alternatively
use the method of sectioning.
Example: Determine the force in members FG and FH
12 kN
A
C
12 kN
E
G
I
1.8 m
B
D
F
H
J
4 @ 2.4 m=9.6 m
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Lecture #31
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12 kN
A
C
12 kN
E
G
I
FGE
1.8 m
FGF
B
D
FHF F
12 kN
A
C
H
J
12 kN
E
G
FEG
I
FFG
B
D
F
x
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0
F
y
1.8 m
F
FEH
0
M
Lecture #31
H
Anypt
J
0
10
Trusses: 3-D (Space Trusses)
• Consider all the members as two force members
– Joints are ball & socket
• Generally, use the method of joints
• Determinate structures
– Equation for determining 3j = m + r
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3-D Truss Methodology
•
•
•
•
•
Determine unit vectors based on structure geometry
Solve for reaction forces with entire structure
Draw FBD of joint
Sum forces at joint to determine member forces
Solve joint-by-joint or write out as a system of
equations
– the latter method may also include reaction forces
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Lecture #31
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