Truss Analysis

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 c P q a a b

7. Importance

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

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 q a 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 = 300 + 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 q a 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 q a 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 Fab Ry

20. Example • Step Four: Sum like forces and set = to 0, solve! • SFx = 0 = Fxbc + Fab + Rx • (right is positive) • SFy = 0 = 300 + 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.