ME 221 Statics
Lecture #32
Section 6.9
ME221
Lecture #32
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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 Friday, November 21
ME221
Lecture #32
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Quiz #7
Friday, November 21
Analysis of Structures
Method of Joints or
Method of Sections
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Lecture #32
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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 FBC
(2) - Reactions
Ax, Ay and Cy
PAY
PAx
Ax
a
A
Ay
ME221
Lecture #32
PCy
b
PCx
C
C
y
4
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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Lecture #32
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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 #32
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12 kN
A
C
12 kN
FGEE
G
I
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 #32
H
Anypt
J
0
7
Frames
Are designed to support,
prevent or transmit loads
(forces, no moments). At
least one member is not a
two-force member.
Machines
Are designed to transmit force, motion or energy
(forces and moments). Will always have at least one
member with multiple forces.
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Frames and Machines
• Frames and machines have at least one
multi-force member
– Frames are designed to support loads
– Machines are designed to transmit and modify loads
• Just like trusses, frames and machines need to
be disassembled to determine member forces
– Need to draw a FBD for each member
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Lecture #32
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D
Disassembly Exposes
Internal Forces
E
C
B
W
• First, reactions of entire structure
A
• Second, disassemble and solve for
internal forces
D
Cx
Cy
E
T
C
Cx
T
Cy
FBE
A
Ax
Ax
Ay
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FBE
Ay
Lecture #32
W
FBE
W
B
FBE
FBE is a
two force
member
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Notes on Previous Problem
• Without recognizing BE is a two force member,
the problem is not tractable.
• MUST draw a FBD for entire structure and
each disassembled part
• Each FBD may have three unknown forces
which are found from SFx = 0; SFy = 0;
SMz = 0
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General Procedure
• Draw FBD for entire structure and solve for
reaction forces SFx = 0; SFy = 0; SMz = 0
• Disassemble into component parts
– Recognize two force members
– Draw FBD and solve for reaction forces - using
SFx = 0 ; SFy = 0 ; SMz = 0
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Frame Example
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Lecture #32
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