Method of Joints –Example
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Method of Joints –Example . Using the method of joints, determine the force in each member of the truss. Method of Joints –Example . Draw the free body diagram of the truss and solve for the equations. Method of Joints –Example . Solve the moment about C. Method of Joints –Example . - PowerPoint PPT Presentation
Transcript of Method of Joints –Example
Method of Joints –Example
Using the method of joints, determine the force in each member of the truss.
Method of Joints –Example
Draw the free body diagram of the truss and solve for the equations
x x
x
y y
y
0
0 lb
0 2000 lb 1000 lb
3000 lb
F C
C
F E C
E C
Method of Joints –Example
Solve the moment about C
C
y
0 2000 lb 24 ft 1000 lb 12 ft 6 ft
10000 lbC 3000 lb 10000 lb 7000 lb
M E
E
Method of Joints –Example
Look at joint A
y AD
AD AD
x AD AB AB
AB AB
40 2000 lb5
2500 lb 2500 lb C
3 30 2500 lb5 5
1500 lb 1500 lb T
F F
F F
F F F F
F F
Method of Joints –Example
Look at joint D
y AD DB DB
DB DB
x AD DB DE
DE
DE DE
4 4 4 40 2500 lb5 5 5 5
2500 lb 2500 lb T3 305 5
3 32500 lb 2500 lb5 53000 lb 3000 lb C
F F F F
F F
F F F F
F
F F
Method of Joints –Example
Look at joint B
y BD BE
DE
DE DE
x BD BA BE BC
BC
BC DE
4 40 1000 lb5 5
4 42500 lb 1000 lb5 53750 lb 3750 lb C
3 305 5
3 32500 lb 1500 lb 3750 lb5 5
5250 lb 5250 lb T
F F F
F
F F
F F F F F
F
F F
Method of Joints –Example
Look at joint E
y EB EC
DE
EC EC
x EB ED EC
EC
EC EC
4 40 10000 lb5 5
4 43750 lb 10000 lb5 58750 lb 8750 lb C
3 305 5
3 33750 lb 3000 lb5 58750 lb 8750 lb C
F F F
F
F F
F F F F
F
F F
Method of Joints –Example
Look at joint C to check the solution
y CE
x CE CB x
40 7000 lb5
4 8750 lb 7000 lb 0 OK!5
305
3 8750 lb 5250 lb 0 05
F F
F F F C
Method of Joints –Class Problem
Determine the forces BC, DF and GE. Using the method of Joints.
Method of Sections -Truss
The method of joints is most effective when the forces in all the members of a truss are to be determined. If however, the force is only one or a few members are needed, then the method of sections is more efficient.
Few simple guidelines of section truss analysis:• Pass a section through a maximum of 3 members of
the truss, 1 of which is the desired member where it is dividing the truss into 2 completely separate parts,
• At 1 part of the truss, take moments about the point (at a joint) where the 2 members intersect and solve for the member force, using ∑ M = 0,
• Solve the other 2 unknowns by using the equilibrium equation for forces, using ∑ Fx = 0 and ∑ Fy = 0.
Method of Sections -Truss
If we were interested in the force of member CE. We can use a cutting line or section to breakup the truss and solve by taking the moment about B.
Method of Sections – Example
Determine the forces in members FH, GH and GI of the roof truss.
Method of Sections – Example
Draw a free body diagram and solve for the reactions.
RAx
RAy
L
x Ax
Ax
y
Ay
0
0 kN
0
20 kN
F R
R
F
L R
Method of Sections – Example
Solve for the moment at A.
RAx
RAy
L
A
Ay
6 kN 5 m 6 kN 10 m 6 kN 15 m
1 kN 20 m 1 kN 25 m 30 m
7.5 kN12.5 kN
M
L
LR
Method of Sections – Example
Solve for the member GI. Take a cut between the third and fourth section and draw the free-body diagram.
HIHI
HI
1 o
8 m 10 m 8 m15 m 10 m 15 m
5.333 m8 mtan 28.1
15 m
l l
l
Method of Sections – Example
The free-body diagram of the cut on the right side.
H GI
GI GI
1 kN 5 m 7.5 kN 10 m 5.333 m
13.13 kN 13.13 kN T
M F
F F
Method of Sections – Example
Use the line of action of the forces and take the moment about G it will remove the FGI and FGH and shift FFH to the perpendicular of G.
Method of Sections – Example
Take the moment at G
G
oFH
FH FH
1 kN 5 m 1 kN 10 m 7.5 kN 15 m
cos 28.1 8 m
13.82 kN 13.82 kN C
M
F
F F
Method of Sections – Example
Use the line of action of the forces and take the moment about L it will remove the FGI and FFH and shift FGH to point G.
1 o5 mtan 133.25.333 m
Method of Sections – Example
Take the moment at L
oL GH
GH GH
1 kN 5 m 1 kN 10 m cos 43.2 15 m
1.372 kN 1.372 kN C
M F
F F
Method of Sections – Class Problem
Determine the forces in members CD and CE using method of sections.
Homework (Due 2/24/03)
Problems:
6-34, 6-37, 6-38, 6-40, 6-45, 6-63
Truss –Bonus Problem
Determine whether the members are unstable, determinate or indeterminate.
Truss –Bonus Problem
Determine the loads in each of the members.
Truss –Bonus Problem
Determine the loads in each of the members.
Truss –Bonus Problem
Determine the loads in each of the members.
