1. Truss and Frame Analysis
Chapter 4
Truss and Frame Analysis

2. Trusses
Account for the majority of the structures constructed in the world today
A pin connected truss has all of its members ideally in pure axial tension or pure axial compression
All members are considered to be two-force members

3. Trusses (Cont’d)

4. Truss Behavior
A truss is typically a network of triangles that all lie in the same plane
It is a stable shape that prevents “racking” when lateral forces are applied
Trusses are connected by frictionless pins

5. Truss Behavior (Cont’d)
All the forces on a truss are applied at the joints
The selfweight of the members are negligible and is either neglected or applied equally at the joints as a concentrated load

6. Truss Behavior (Cont’d)

7. Truss Behavior (Cont’d)

8. Truss Behavior (Cont’d)

9. Method of Joints
This method constructs a free-body diagram of each joint
The principles of equilibrium are used to solve for the unknown joint forces
Fx = 0
Fy = 0
Because all of the forces at a joint act through the joint, it is considered to be a concurrent system

10. Steps for Using the Method of Joints
Solve the external support reactions of the truss
Draw free-body diagrams of each joint in the truss
Begin at a joint that does not have many potential unknown forces

11. Steps for Using the Method of Joints (Cont’d)
Flip-flop the joint forces that act at one end of a member to the opposite end of that member
Go on to another joint until the truss is completed

12. Method of Joints Example

13. Method of Joints Example

14. Method of Sections
Involves cutting the truss through the members whose forces are to be determined
The equations for equilibrium are used to determine the forces that act on the members that have been cut

15. Steps for Using the Method of Sections
Solve the support reactions of the complete truss
Section the truss through the members that are to be found

16. Steps for Using the Methods of Sections (Cont’d)
Work with only one piece of the truss as the new free-body diagram
Write and solve the appropriate equilibrium equations

17. Method of Sections Example

18. Method of Sections Example

19. Method of Sections Example

20. Method of Sections Example

21. Method of Sections Example

22. Frames Assumed to be pin-connected
Considered to have the ability to develop reactions forces while being free to rotate
Key concept to frame analysis is Newton's concept of action and reaction

23. Newton’s First Law of Motion
If the algebraic sum of all forces in a system is equal to zero, then the system will retain its present state

24. Newton’s Second Law of Motion
If the algebraic sum of the forces in a system is not equal to zero, then the net result will be that the system will accelerate or decelerate
The acceleration or deceleration of the system will be directly proportional to the force that is applied and inversely proportional to the mass of the system

25. Newton’s Second Law of Motion (Cont’d)
The system will accelerate in a straight line to the force (in the same direction)

26. Newton’s Third Law of Motion
When an object transmits a force to another object, the net result is the receiving object will transmit a force of equal magnitude in the opposite direction

27. Frame Analysis
The analysis of pin-connected frames is based on the concepts of isolating a free-body and writing algebraic equations

28. Steps for Performing Frame Analysis
Determine the external support (pins, rollers, etc.) for complete structure
Explode the frame into separate free-body diagrams of each member

29. Steps for Performing Frame Analysis (Cont’d)
Use the three equilibrium equations to solve for unknown pin reactions
Continue until all pin reactions are solved