method of joints –example
DESCRIPTION
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 PresentationTRANSCRIPT
![Page 1: Method of Joints –Example](https://reader036.vdocument.in/reader036/viewer/2022081507/56815d7c550346895dcb85fe/html5/thumbnails/1.jpg)
![Page 2: Method of Joints –Example](https://reader036.vdocument.in/reader036/viewer/2022081507/56815d7c550346895dcb85fe/html5/thumbnails/2.jpg)
Method of Joints –Example
Using the method of joints, determine the force in each member of the truss.
![Page 3: Method of Joints –Example](https://reader036.vdocument.in/reader036/viewer/2022081507/56815d7c550346895dcb85fe/html5/thumbnails/3.jpg)
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
![Page 4: Method of Joints –Example](https://reader036.vdocument.in/reader036/viewer/2022081507/56815d7c550346895dcb85fe/html5/thumbnails/4.jpg)
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
![Page 5: Method of Joints –Example](https://reader036.vdocument.in/reader036/viewer/2022081507/56815d7c550346895dcb85fe/html5/thumbnails/5.jpg)
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
![Page 6: Method of Joints –Example](https://reader036.vdocument.in/reader036/viewer/2022081507/56815d7c550346895dcb85fe/html5/thumbnails/6.jpg)
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
![Page 7: Method of Joints –Example](https://reader036.vdocument.in/reader036/viewer/2022081507/56815d7c550346895dcb85fe/html5/thumbnails/7.jpg)
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
![Page 8: Method of Joints –Example](https://reader036.vdocument.in/reader036/viewer/2022081507/56815d7c550346895dcb85fe/html5/thumbnails/8.jpg)
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
![Page 9: Method of Joints –Example](https://reader036.vdocument.in/reader036/viewer/2022081507/56815d7c550346895dcb85fe/html5/thumbnails/9.jpg)
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
![Page 10: Method of Joints –Example](https://reader036.vdocument.in/reader036/viewer/2022081507/56815d7c550346895dcb85fe/html5/thumbnails/10.jpg)
Method of Joints –Class Problem
Determine the forces BC, DF and GE. Using the method of Joints.
![Page 11: Method of Joints –Example](https://reader036.vdocument.in/reader036/viewer/2022081507/56815d7c550346895dcb85fe/html5/thumbnails/11.jpg)
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.
![Page 12: Method of Joints –Example](https://reader036.vdocument.in/reader036/viewer/2022081507/56815d7c550346895dcb85fe/html5/thumbnails/12.jpg)
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.
![Page 13: Method of Joints –Example](https://reader036.vdocument.in/reader036/viewer/2022081507/56815d7c550346895dcb85fe/html5/thumbnails/13.jpg)
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.
![Page 14: Method of Joints –Example](https://reader036.vdocument.in/reader036/viewer/2022081507/56815d7c550346895dcb85fe/html5/thumbnails/14.jpg)
Method of Sections – Example
Determine the forces in members FH, GH and GI of the roof truss.
![Page 15: Method of Joints –Example](https://reader036.vdocument.in/reader036/viewer/2022081507/56815d7c550346895dcb85fe/html5/thumbnails/15.jpg)
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
![Page 16: Method of Joints –Example](https://reader036.vdocument.in/reader036/viewer/2022081507/56815d7c550346895dcb85fe/html5/thumbnails/16.jpg)
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
![Page 17: Method of Joints –Example](https://reader036.vdocument.in/reader036/viewer/2022081507/56815d7c550346895dcb85fe/html5/thumbnails/17.jpg)
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
![Page 18: Method of Joints –Example](https://reader036.vdocument.in/reader036/viewer/2022081507/56815d7c550346895dcb85fe/html5/thumbnails/18.jpg)
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
![Page 19: Method of Joints –Example](https://reader036.vdocument.in/reader036/viewer/2022081507/56815d7c550346895dcb85fe/html5/thumbnails/19.jpg)
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.
![Page 20: Method of Joints –Example](https://reader036.vdocument.in/reader036/viewer/2022081507/56815d7c550346895dcb85fe/html5/thumbnails/20.jpg)
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
![Page 21: Method of Joints –Example](https://reader036.vdocument.in/reader036/viewer/2022081507/56815d7c550346895dcb85fe/html5/thumbnails/21.jpg)
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
![Page 22: Method of Joints –Example](https://reader036.vdocument.in/reader036/viewer/2022081507/56815d7c550346895dcb85fe/html5/thumbnails/22.jpg)
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
![Page 23: Method of Joints –Example](https://reader036.vdocument.in/reader036/viewer/2022081507/56815d7c550346895dcb85fe/html5/thumbnails/23.jpg)
Method of Sections – Class Problem
Determine the forces in members CD and CE using method of sections.
![Page 24: Method of Joints –Example](https://reader036.vdocument.in/reader036/viewer/2022081507/56815d7c550346895dcb85fe/html5/thumbnails/24.jpg)
Homework (Due 2/24/03)
Problems:
6-34, 6-37, 6-38, 6-40, 6-45, 6-63
![Page 25: Method of Joints –Example](https://reader036.vdocument.in/reader036/viewer/2022081507/56815d7c550346895dcb85fe/html5/thumbnails/25.jpg)
Truss –Bonus Problem
Determine whether the members are unstable, determinate or indeterminate.
![Page 26: Method of Joints –Example](https://reader036.vdocument.in/reader036/viewer/2022081507/56815d7c550346895dcb85fe/html5/thumbnails/26.jpg)
Truss –Bonus Problem
Determine the loads in each of the members.
![Page 27: Method of Joints –Example](https://reader036.vdocument.in/reader036/viewer/2022081507/56815d7c550346895dcb85fe/html5/thumbnails/27.jpg)
Truss –Bonus Problem
Determine the loads in each of the members.
![Page 28: Method of Joints –Example](https://reader036.vdocument.in/reader036/viewer/2022081507/56815d7c550346895dcb85fe/html5/thumbnails/28.jpg)
Truss –Bonus Problem
Determine the loads in each of the members.