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. Chapter Outline Simple Trusses The Method of Joints
The Method of Sections

4. Simple Trusses
A truss composed of slender members joined together at their end points
Planar Trusses
Planar trusses used to support roofs and bridges
Roof load is transmitted to the truss at joints by means of a series of purlins

5. Simple Trusses
Planar Trusses
The analysis of the forces developed in the truss members is 2D
Similar to roof truss, the bridge truss loading is also coplanar

6. Simple Trusses “All loadings are applied at the joint”
Assumptions for Design
“All loadings are applied at the joint”
- Weight of the members neglected
“The members are joined together by smooth pins”
- Assume connections provided the center lines of the joining members are concurrent

7. Simple Trusses Form of a truss must be rigid to prevent collapse
The simplest form that is rigid or stable is a triangle

8. Trusses
Method of Joints
Method
of Sections

9. 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

10. 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

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

13. Solution
FBD of each pin shows the effect of all the connected members and external forces applied to the pin
FBD of each member shows only the effect of the end pins on the member

14. 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

15. Example 3
Determine the force members GB,AB of the truss. State if the members are in tension or compression. Use joint method of analysis

16. Assignment 3
Question 1
Determine the force in each member of the truss and state if the members are in tension or compression. P1=40kN and P2=20kN.

17. Assignment 3
Question 2
Using the method of joints, determine the force in each member of the trust shown. State whether each member is in tension or compression.
20 kN

18. Assignment 3
Question 3
The Howe Bridge truss is subjected to the loading shown. Determine the force in members JI, GF and GD. State if the members are in tension or compression. Use joint method of analysis.

19. Assignment 3
Question 4 For the Truss shown below, find the reaction forces at the supports A & B

20. Assignment 3
Question 5 For the truss shown below determine the internal force members CD,FC and EC. State if the members are in tension or compression. Apply joint method of analysis