1. Truss Analysis
Engineering
Mr. Cumber
2009

2. Bellwork
What are two applications of trusses besides bridges?

3. Non-Bridge Trusses

4. Non-Bridge Trusses

5. Non-Bridge Trusses

6. Statics Not Moving Forces in X and Y directions = 0 Newton’s 2nd Law aP a q a b

7. Importance

8. Methods Method of Joints Method of Sections a q c P Fbc Fac P a b PRx Ry
Fab

9. Method of Joints Good when few members When all forces are needed
To check Method of Sections data

10. Execution Cut each joint, draw forces Fill in angles
Break down forces into X and Y components
Add like forces, solve for unknowns

11. Class Example
If P = 300 N, a = 60, q = 30, what is the force on member [bc]? c P a q a b

12. Example Step One: Cut Joint Step Two: Fill in Forces
Step Three: Fill in Angles 60 30
Fbc
Fac
300

13. Example Step Four: Break Forces into X and Y components
Fxac
Fxbc
Fxac = Fac cos 60
Fyac = Fac sin 60
Fxbc = Fbc cos 30
Fybc = Fbc sin 30 60 30 60
Fybc
Fyac 30
Fbc
Fac
300

14. Example Step Five: Sum like forces and set = to 0, solve!
SFx = 0 = -Fxac + Fxbc
(right is positive)
SFy = 0 = Fyac + Fybc
(down is positive)
Complete w/Mr. Cumber on board
Fxac = Fac cos 60
Fyac = Fac sin 60
Fxbc = Fbc cos 30
Fybc = Fbc sin 30

15. Practice
If P = 500 N, a = 72, q = 18, what is the force on member [ac]? P c a q a b

16. Method of Sections Good when there are lots of members
When only one specific member force is needed

17. Execution Cut truss into two sections (through the member you need)
Treat section as a single rigid body
Draw Forces and Angles
Determine X and Y Components
Solve for SFx and SFy = 0

18. Class Example
If P = 300 N, a = 60, q = 30, what is the force on member [bc]?
ab = 20 cm
ac = 10 cm
bc = 17.3 cm c P a q a b

19. Example Step One: Cut Truss Step Two: Draw Forces and Angles
Step Three: Determine components
Fxbc
Fxbc = Fbc cos 30
Fybc = Fbc sin 30 30
Fybc
300
Fbc Rx Ry
Fab

20. Example Step Four: Sum like forces and set = to 0, solve!
SFx = 0 = Fxbc + Fab + Rx
(right is positive)
SFy = 0 = Fybc + Ry
(down is positive)
SM = 0 (New Equation! – for Rx and Ry)
Complete w/Mr. Cumber on board

21. Important Notes Either method should give the same answer
Use to check
Choosing a method wisely will save lots of work
Figure out reaction forces first - you might need them later.