1. ME 201 Engineering Mechanics: Statics
Chapter 6 – Part A
6.1 Simple Trusses
6.2 Method of Joints
6.3 Zero Force Members

2. Simple Truss
A structure composed of slender members joined together at their end points
“Planar Truss”

3. Simple Truss
To Design members and connections of a truss, necessary to determine forces developed in each member
Assumptions:
All loadings are applied at the joints
Members are joined together by smooth pins
Assumptions satisfactory for bolted or welded joints

4. Simple Truss Each truss member acts as a 2-force member
Force directed along axis of member
Tension – pull, elongation
Compression – push, shorten
Several analytical approaches to solving

5. Method of Joints
If truss is in equilibrium, each joint must also be in equilibrium
Approach:
Sketch Free Body Diagram of Entire Truss
Solve for Reactions
Sketch Free Body Diagrams of Each Joint
2 unknown limit per FBD
∑ Fx =0 ∑ Fy =0 ∑ Mo =0

6. Example Problem Given: F = 500 N θ = 45º Find: Force in each member θ

7. Example Problem Solution
45º
2 m B Ax
500 N Ay Cy θ
2 m B C A F
Given:
F = 500 N
θ = 45º
Find:
Force in each member
Solution:
1-FBD
2-Support Reactions
45º
2 m B
500 N A C

8. Example Problem Solution
45º
2 m B
500 N A C
Given:
F = 500 N
θ = 45º
Find:
Force in each member
Solution:
1-FBD
2-Support Reactions
3-Joint FBDs
Joint A
Joint B
Joint C
500 N AC AB
500 N BC AB
45º
500 N BC AC
45º

9. Example Problem SolutionBC AB
Joint B
45º
500 N AC AB
Joint A
Given:
F = 500 N
θ = 45º
Find:
Force in each member
Solution:
1-FBD
2-Support Reactions
3-Joint FBDs B A C
500 T
707 C
Results shown in a force diagram

10. Zero Force Members Zero Force Members support NO loading Used for:
Stability
Changing Applied Loads

11. Zero Force Members
If only 2 members form a truss joint AND no external load or support reaction is applied to the joint, then the members must be Zero Force Members X X X X

12. Zero Force Members
If 3 members form a truss joint for which 2 members are collinear, the 3rd member is a Zero Force Member, provided no external force or support reaction is applied to the joint. X X