Shawn Kenny, Ph.D., P.Eng.Assistant ProfessorFaculty of Engineering and Applied ScienceMemorial University of Newfoundlandspkenny@engr.mun.ca

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.

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Example 29-01 (cont.)

What Tools are Available? Method of joints by inspection Equilibrium equations

0Fx

0Fy

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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

?

?

?

?

? ? ?

?

?

?

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Example 29-01 (cont.)

What are the ZeroForce Members?

Fy

Fx

By

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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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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

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Method of Sections (cont.)

What Section to Use? Minimize unknowns Minimize calculations

Section Left Section Right

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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

18 ENGI 1313 Statics I – Lecture 29© 2007 S. Kenny, Ph.D., P.Eng.

References

Hibbeler (2007) http://wps.prenhall.com/

esm_hibbeler_engmech_1