ENGI 1313 Mechanics I

1
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 29-01 (cont.)

• What are the Known Forces?

Fy
Fx
By
7
Example 29-01 (cont.)

• What are the Zero Force Members?
• Equilibrium Equations lt Unknowns

Fy
Fx
By
8
Example 29-01 (cont.)

• What are the ZeroForce 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
• Newtowns 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 lt 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)
• http//wps.prenhall.com/esm_hibbeler_engmech_1