1. ANALYSIS OF STRUCTURES

2. Chapter Objectives
Determine the forces in the members of a truss using the method of joints and the method of sections

3. Roof Trusses

4. Definition
Load
Transferred
Load not
Transferred
Load
Transferred

5. Truss Types
Trusses are categorised into 3 groups depending on the shape of the top chord
Triangular Roof Trusses
Crescent roof Trusses
Other Types

6. Triangular Roof Trusses
Simple Triangular geometric shape
Web Bracing
Straight Top Chord

7. Triangular Roof Trusses

8. Crescent Roof Trusses
Top Chord is manufactured with a curved top chord
The Harbour bridge is a good example

9. Other Types Top Chords may be parallel – such as floor joist trusses
Or they may be nearly parallel – such as bridges

11. Roof Truss Members

12. Roof Truss Panel Points

13. Roof Truss Stress Types

14. Parallel Chord Trusses
Top Chord & Bottom Chord are parallel
Used as Rafters
Advantages
Lighter
Larger Spans
Allow for easy access for services
Disadvantages
Cannot be site modified
Generally Deeper

15. Parallel Chord Trusses

16. Transfer of Loads
Click to show load flow on correctly installed trusses
Tensile Load to
Counteract Compressive Load
Compression Load
Internal Wall
Min 12 Clear
No load in this Area

17. Transfer of Loads
Click to show load flow on incorrectly installed trusses
Bottom Chord is not designed to take horizontal load and will fail
Bottom Chord bearing on Internal Wall
Load transmits Horizontally to wall.

18. Trusses
Method of Joints
Method
of Sections

19. The Method of Joints
For truss, we need to know the force in each members
Forces in the members are internal forces
Resultant of internal force in each member has to equal to zero (equilibrium condition)
For external force members, equations of equilibrium can be applied

20. The Method of Joints
Procedure for Analysis
Draw the FBD with at least 1 known and 2 unknown forces
Find the external reactions at the truss support
Choose the joint has the less unknown forces
Apply equilibrium equations
Use known force to analyze the unknown forces

21. Example 1
Determine the force in each member of the truss and indicate whether the members are in tension or compression.

23. Example 2
Determine the force members HC,CG and DF of the truss. State if the members are in tension or compression. Use joint method of analysis

24. The Method of Sections Consider the truss and section a-a as shown
Member forces are equal and opposite to those acting on the other part – Newton’s Law

25. The Method of Sections Free-Body Diagram
Procedure for Analysis
Free-Body Diagram
Choose the section that at least cut almost if not all the required internal forces.
Determine the truss’s external reactions
Use equilibrium equations to solve member forces at the cut session
Draw FBD of the sectioned truss which has the least number of forces acting on it
Find the sense of an unknown member force

26. The Method of Sections Equations of Equilibrium
Procedure for Analysis
Equations of Equilibrium
Summed moments about a point
Find the 3rd unknown force from moment equation

27. Example 3
Determine the force in members GE, GC, and BC of the truss using sectional method of analysis. Indicate whether the members are in tension or compression.

28. Example 3

29. Example 4
Determine the force in members DE, EB, and AB of the truss using sectional method of analysis. Indicate whether the members are in tension or compression

30. Example 4