1. Lecture 30: Examples on Method of Sections
ENGI 1313 Mechanics I
Lecture 30: Examples on Method of Sections

2. Lecture 30 Objective
to illustrate the method of sections by example

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.

4. Determine the force in truss members DE, EH, and HG
Example (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

5. Determine the force in truss members DE, EH, and HG
Example (cont.)
Determine the force in truss members DE, EH, and HG
Support Reaction G
What equilibrium equation? Gy

6. Determine the force in truss members DE, EH, and HG
Example (cont.)
Determine the force in truss members DE, EH, and HG
Draw Section FBD
Assume all truss member forces are in tension Gy
FED
40kN
FEH
FGH Gy

7. Determine the force in truss members DE, EH, and HG
Example (cont.)
Determine the force in truss members DE, EH, and HG
Equilibrium Equation? Gy
FED
40kN
FEH
FGH Gy

8. 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.

9. Determine the force in truss members OE, LE, and LK
Example (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 E L

10. Determine the force in truss members OE, LE, and LK
Example (cont.)
Joint FBD at L
FLE
FLK
FLM L

11. Determine the force in truss members OE, LE, and LK
Example (cont.)
Section Cut?
Draw FBD
Examine FBD
Known?
Unknown?
To Be Determined? Ay Ax E
FML
FOE
FDE

12. Determine the force in truss members OE, LE, and LK
Example (cont.)
Next Step?
Reduce unknowns
Find what support reaction? Ay
What equilibrium equation? Ax Ay Ay Ax E
FML
FOE
FDE

13. Determine the force in truss members OE, LE, and LK
Example (cont.)
Support Reaction Ay Ax Ay

14. Determine the force in truss members OE, LE, and LK
Example (cont.)
Next Step?
Find FML
What equilibrium equation?
Ay = 6.375kN Ax E
FML
FOE
FDE

15. Determine the force in truss members OE, LE, and LK
Example (cont.)
Next Step?
Find FOE
What equilibrium equation?
Ay = 6.375kN Ax E
FML
FOE
FDE

16. References Hibbeler (2007)