ENGI 1313 Mechanics I

Lecture 30: Examples on Method of Sections Shawn Kenny, Ph.D., P.Eng.

Assistant Professor Faculty of Engineering and Applied Science Memorial University of Newfoundland [email protected]

Lecture 30 Objective

 to illustrate the method of sections by example

2 © 2007 S. Kenny, Ph.D., P.Eng.

ENGI 1313 Statics I – Lecture 30

3

Example 30-01

 The Howe bridge truss is subjected to the loading shown. Determine the force in members DE, EH, and HG, and state if the members are in tension or compression.

© 2007 S. Kenny, Ph.D., P.Eng.

ENGI 1313 Statics I – Lecture 30

4

Example 30-01 (cont.)

Determine the force in truss members DE, EH, and HG

 Cut Along Section?

 Truss chords • • • ED EH GH  What Section to Use?

 Right  Calculate Support Reaction Forces?

 Yes, at G

© 2007 S. Kenny, Ph.D., P.Eng.

ENGI 1313 Statics I – Lecture 30

Example 30-01 (cont.)

Determine the force in truss members DE, EH, and HG

 Support Reaction G  What equilibrium equation?



M A



0 G y



16 m

 

20 kN

  

20 kN

  

40 kN



12 m

 

0 G y



45 kN

G y 5 © 2007 S. Kenny, Ph.D., P.Eng.

ENGI 1313 Statics I – Lecture 30

6

Example 30-01 (cont.)

Determine the force in truss members DE, EH, and HG

 Draw Section FBD  Assume all truss member forces are in tension

G y F ED F EH 40kN F GH G y © 2007 S. Kenny, Ph.D., P.Eng.

ENGI 1313 Statics I – Lecture 30

7

Example 30-01 (cont.)

Determine the force in truss members DE, EH, and HG

 Equilibrium Equation?

45



M H kN

   

0 F ED F ED

 

45 kN



45 kN



0

 

F GH

 

F x F ED

 

0 45 kN

 

F EH



F y



G y



0



40 kN



5 kN

F ED F EH 40kN F GH G y G y © 2007 S. Kenny, Ph.D., P.Eng.

ENGI 1313 Statics I – Lecture 30

Example 30-02

 Determine the force in members OE, LE, and LK of the Baltimore truss and state if the members are in tension or compression.

8 © 2007 S. Kenny, Ph.D., P.Eng.

ENGI 1313 Statics I – Lecture 30

9

Example 30-02 (cont.)

Determine the force in truss members OE, LE, and LK

 Where to Start?

 What are the key truss joints (nodes)?

• • Joint E Joint L  Any particular characteristics?

• • 5 unknowns @ E Zero-force @ L

© 2007 S. Kenny, Ph.D., P.Eng.

ENGI 1313 Statics I – Lecture 30

Example 30-02 (cont.)

Determine the force in truss members OE, LE, and LK

 Joint FBD at L  

F LE



F y



0



0

 

F LM

 

F x F LK



0

F LM L F LK 10 © 2007 S. Kenny, Ph.D., P.Eng.

F LE ENGI 1313 Statics I – Lecture 30

Example 30-02 (cont.)

Determine the force in truss members OE, LE, and LK

 Section Cut?

 Draw FBD  Examine FBD  Known?

 Unknown?

 To Be Determined?

A x F ML F OE E F DE A y 11 © 2007 S. Kenny, Ph.D., P.Eng.

ENGI 1313 Statics I – Lecture 30

Example 30-02 (cont.)

Determine the force in truss members OE, LE, and LK

 Next Step?

 Reduce unknowns • Find what support reaction?

• A y

A x

 What equilibrium equation?



M I



0

A y A x F ML F OE E F DE A y 12 © 2007 S. Kenny, Ph.D., P.Eng.

ENGI 1313 Statics I – Lecture 30

Example 30-02 (cont.)

Determine the force in truss members OE, LE, and LK

 Support Reaction A y

A x A y

A y



M I



0

  

2 kN



12 m

 

2 kN



10 m

 

5 kN

  

3 kN A y



6 .

375 kN

13 © 2007 S. Kenny, Ph.D., P.Eng.

ENGI 1313 Statics I – Lecture 30

Example 30-02 (cont.)

Determine the force in truss members OE, LE, and LK

 Next Step?

14

 Find F ML  What equilibrium equation?



M E



0 F ML

  

6 .

375

 

2 kN kN 2

  

2 kN F ML

 

9 .

75 kN



9 .

75 kN F LK



F ML

© 2007 S. Kenny, Ph.D., P.Eng.

A x A y = 6.375kN

ENGI 1313 Statics I – Lecture 30 F ML F OE E F DE

Example 30-02 (cont.)

Determine the force in truss members OE, LE, and LK

 Next Step?

 Find F OE  What equilibrium equation?

  

F y



0 F OE F OE

  

2 2 2



2 2

  

6 .

375 kN



2 kN



2 kN

A x

3 .

365 kN

F ML F OE E F DE 15 © 2007 S. Kenny, Ph.D., P.Eng.

A y = 6.375kN

ENGI 1313 Statics I – Lecture 30

References

 Hibbeler (2007)  http://wps.prenhall.com/esm_hibbeler_eng mech_1

16 © 2007 S. Kenny, Ph.D., P.Eng.

ENGI 1313 Statics I – Lecture 30