1. Lecture 29: Zero Force Members and Method of Sections
ENGI 1313 Mechanics I
Lecture 29: Zero Force Members and Method of Sections

2. Lecture 29 Objective to examine zero force members in truss structures
to understand the method of sections for establishing forces in truss members

3. Comprehension Quiz 29-01
In the method of joints, ______ equations of equilibrium are typically applied at each joint.
A) two
B) three
C) four
D) six
Answer: A

4. Example 29-01
Identify the zero force members in the following truss structure.

5. Example 29-01 (cont.) What Tools are Available?
Method of joints by inspection
Equilibrium equations

6. Example (cont.)
What are the Known Forces? Fy Fx By

7. Example 29-01 (cont.) What are the Zero Force Members?
# Equilibrium Equations < # Unknowns Fy ? Fx ? ? By

8. Example (cont.)
What are the Zero Force Members? Fy Fx By

9. Example 29-01 (cont.) Truss Members Supporting the Load
Why Have Zero Force Members?
Increase truss frame rigidity
Support other applied load conditions

10. Comprehension Quiz 29-02 Determine the number of zero-force members.
A) 0
B) 1
C) 2
D) 3
E) 4
Answer: D F1 F2 F3

11. Analysis of Long or Complex Trusses
How to Determine Truss Member Forces of Internal Chords?
Method of joints? ? ? ?

12. Method of Sections
Cut Truss Member
Newtown’s 3rd Law

13. Method of Sections (cont.)
Why Cut?
Limit # joint calculations
Directly calculate force for interior members
Where to Cut?
Force calculation
Total # unknowns < 3
What Equations?
Minimize # reactions to calculate

14. Method of Sections (cont.)
What Section to Use?
Minimize unknowns
Minimize calculations
Section Left
Section Right

15. Method of Sections (cont.)
Determine Truss Support Reactions
If necessary
Select Cut-Line on Truss
Select Truss Section to Analyse
Draw FBD of Cut Truss Section
Apply Equilibrium Equations

16. Comprehension Quiz 29-03
A cut is made through GH, BG and BC to determine the forces. Which section will you choose for analysis?
A) Right, fewer calculations
B) Left, fewer calculations
C) Either right or left, same amount of work
D) None as there are too many unknowns
Answer: A

17. Comprehension Quiz 29-04
Can you determine the force in member ED by making the cut at section a-a?
A) No, 4 unknowns
B) Yes, MD = 0
C) Yes, ME = 0
D) Yes, MB = 0
Answer: D a a

18. References Hibbeler (2007)