ENGI 1313 Mechanics I
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Transcript of ENGI 1313 Mechanics I
Shawn Kenny, Ph.D., P.Eng.Assistant ProfessorFaculty of Engineering and Applied ScienceMemorial University of [email protected]
ENGI 1313 Mechanics I
Lecture 29: Zero Force Members and Method of Sections
2 ENGI 1313 Statics I – Lecture 29© 2007 S. Kenny, Ph.D., P.Eng.
Lecture 29 Objective
to examine zero force members in truss structures
to understand the method of sections for establishing forces in truss members
3 ENGI 1313 Statics I – Lecture 29© 2007 S. Kenny, Ph.D., P.Eng.
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 ENGI 1313 Statics I – Lecture 29© 2007 S. Kenny, Ph.D., P.Eng.
Example 29-01
Identify the zero force members in the following truss structure.
5 ENGI 1313 Statics I – Lecture 29© 2007 S. Kenny, Ph.D., P.Eng.
Example 29-01 (cont.)
What Tools are Available? Method of joints by inspection Equilibrium equations
0Fx
0Fy
6 ENGI 1313 Statics I – Lecture 29© 2007 S. Kenny, Ph.D., P.Eng.
Example 29-01 (cont.)
What are the Known Forces?
Fy
Fx
By
7 ENGI 1313 Statics I – Lecture 29© 2007 S. Kenny, Ph.D., P.Eng.
Example 29-01 (cont.)
What are the Zero Force Members? # Equilibrium Equations < # Unknowns
Fy
Fx
By
?
?
?
?
? ? ?
?
?
?
8 ENGI 1313 Statics I – Lecture 29© 2007 S. Kenny, Ph.D., P.Eng.
Example 29-01 (cont.)
What are the ZeroForce Members?
Fy
Fx
By
9 ENGI 1313 Statics I – Lecture 29© 2007 S. Kenny, Ph.D., P.Eng.
Example 29-01 (cont.)
Truss Members Supporting the Load Why Have Zero Force Members?
Increase truss frame rigidity Support other applied load conditions
10 ENGI 1313 Statics I – Lecture 29© 2007 S. Kenny, Ph.D., P.Eng.
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 ENGI 1313 Statics I – Lecture 29© 2007 S. Kenny, Ph.D., P.Eng.
Analysis of Long or Complex Trusses
How to Determine Truss Member Forces of Internal Chords? Method of joints?
?
?
?
12 ENGI 1313 Statics I – Lecture 29© 2007 S. Kenny, Ph.D., P.Eng.
Method of Sections
Cut Truss Member Newtown’s 3rd Law
13 ENGI 1313 Statics I – Lecture 29© 2007 S. Kenny, Ph.D., P.Eng.
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
0Fx
0Fy
0M
14 ENGI 1313 Statics I – Lecture 29© 2007 S. Kenny, Ph.D., P.Eng.
Method of Sections (cont.)
What Section to Use? Minimize unknowns Minimize calculations
Section Left Section Right
15 ENGI 1313 Statics I – Lecture 29© 2007 S. Kenny, Ph.D., P.Eng.
Method of Sections (cont.)
1. Determine Truss Support Reactions If necessary
2. Select Cut-Line on Truss
3. Select Truss Section to Analyse
4. Draw FBD of Cut Truss Section
5. Apply Equilibrium Equations
16 ENGI 1313 Statics I – Lecture 29© 2007 S. Kenny, Ph.D., P.Eng.
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 ENGI 1313 Statics I – Lecture 29© 2007 S. Kenny, Ph.D., P.Eng.
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