Transcript ENGI 1313 Mechanics I Lecture 29: Zero Force Members and Method of Sections Shawn Kenny, Ph.D., P.Eng. Assistant Professor Faculty of Engineering and Applied Science Memorial University.

ENGI 1313 Mechanics I
Lecture 29:
Zero Force Members and Method of
Sections
Shawn Kenny, Ph.D., P.Eng.
Assistant Professor
Faculty of Engineering and Applied Science
Memorial University of Newfoundland
[email protected]
Lecture 29 Objective
to examine zero force members in truss
structures
 to understand the method of sections for
establishing forces in truss members

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© 2007 S. Kenny, Ph.D., P.Eng.
ENGI 1313 Statics I – Lecture 29
Comprehension Quiz 29-01

In the method of joints, ______ equations of
equilibrium are typically applied at each joint.





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A) two
B) three
C) four
D) six
Answer: A
© 2007 S. Kenny, Ph.D., P.Eng.
ENGI 1313 Statics I – Lecture 29
Example 29-01

4
Identify the zero force members in the
following truss structure.
© 2007 S. Kenny, Ph.D., P.Eng.
ENGI 1313 Statics I – Lecture 29
Example 29-01 (cont.)

What Tools are Available?
Method of joints by inspection
 Equilibrium equations

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
F
0

F
0
x
y
© 2007 S. Kenny, Ph.D., P.Eng.
ENGI 1313 Statics I – Lecture 29
Example 29-01 (cont.)

What are the Known Forces?
Fy
Fx
By
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© 2007 S. Kenny, Ph.D., P.Eng.
ENGI 1313 Statics I – Lecture 29
Example 29-01 (cont.)

What are the Zero Force Members?

# Equilibrium Equations < # Unknowns
Fy
?
Fx
?
?
?
?
?
?
By
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© 2007 S. Kenny, Ph.D., P.Eng.
?
ENGI 1313 Statics I – Lecture 29
?
?
Example 29-01 (cont.)

What are the Zero
Force Members?
Fy
Fx
By
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© 2007 S. Kenny, Ph.D., P.Eng.
ENGI 1313 Statics I – Lecture 29
Example 29-01 (cont.)
Truss Members Supporting the Load
 Why Have Zero Force Members?

Increase truss frame rigidity
 Support other applied load conditions

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© 2007 S. Kenny, Ph.D., P.Eng.
ENGI 1313 Statics I – Lecture 29
Comprehension Quiz 29-02

Determine the number of zero-force members.
F1





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A) 0
B) 1
C) 2
D) 3
E) 4
F3
Answer: D
© 2007 S. Kenny, Ph.D., P.Eng.
F2
ENGI 1313 Statics I – Lecture 29
Analysis of Long or Complex Trusses

How to Determine Truss
Member Forces of
Internal Chords?

?
Method of joints?
?
?
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© 2007 S. Kenny, Ph.D., P.Eng.
ENGI 1313 Statics I – Lecture 29
Method of Sections

Cut Truss Member

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Newtown’s 3rd Law
© 2007 S. Kenny, Ph.D., P.Eng.
ENGI 1313 Statics I – Lecture 29
Method of Sections (cont.)

Why Cut?



Where to Cut?



Force calculation
Total # unknowns < 3
What Equations?

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Limit # joint calculations
Directly calculate force
for interior members
Minimize # reactions to
calculate
© 2007 S. Kenny, Ph.D., P.Eng.


F  0
F  0
M  0
ENGI 1313 Statics I – Lecture 29
x
y
Method of Sections (cont.)

What Section to Use?
Minimize unknowns
 Minimize calculations

Section Left
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© 2007 S. Kenny, Ph.D., P.Eng.
Section Right
ENGI 1313 Statics I – Lecture 29
Method of Sections (cont.)
1.
Determine Truss Support Reactions

2.
3.
4.
5.
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If necessary
Select Cut-Line on Truss
Select Truss Section to Analyse
Draw FBD of Cut Truss Section
Apply Equilibrium Equations
© 2007 S. Kenny, Ph.D., P.Eng.
ENGI 1313 Statics I – Lecture 29
Comprehension Quiz 29-03

A cut is made through GH,
BG and BC to determine
the forces. Which section
will you choose for
analysis?




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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
© 2007 S. Kenny, Ph.D., P.Eng.
ENGI 1313 Statics I – Lecture 29
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

a
a

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Answer: D
© 2007 S. Kenny, Ph.D., P.Eng.
ENGI 1313 Statics I – Lecture 29
References
Hibbeler (2007)
 http://wps.prenhall.com/esm_hibbeler_eng
mech_1

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© 2007 S. Kenny, Ph.D., P.Eng.
ENGI 1313 Statics I – Lecture 29