1. Lecture 27: Structural Analysis
ENGI 1313 Mechanics I
Lecture 27: Structural Analysis

2. Chapter 6 Objectives
to show how to determine the forces in the members of a truss using the method of joints and the method of sections
to analyze the forces acting on the members of frames and machines composed of pin-connected members

3. Lecture 27 Objective to develop an understanding of truss structures
to examine forces in truss elements

4. What are Trusses? Common Structural Element
Framework of bar or strut members connected at nodal points (joints)
Stable form is a triangle
Build by adding two members (AD & DB) and node (joint) D
3 Bar or strut members
(AB, BC, AC)
3 Nodes or joints
(A, B, C)

5. What are Trusses? (cont.)
Early Use
Greek and Roman architecture used wood trusses
Truss Designs
Significant number developed and patented over the years

6. Truss Applications
Provide Span Support for Roofing, Flooring or Transportation
Bibliotheque Nationale de France

7. Truss Applications (cont.)
Memorial University “The Works”

8. Truss Applications (cont.)
Saynatsalo Town Hall, Finland

9. Truss Applications (cont.)
Pont de Québec

10. Truss Applications (cont.)
Lifting Structures

11. Truss Node (Joint) Connection
Gusset Plate Joint
Riveted or bolted connection
Considered to act as a pin connection
I-35 Mississippi Bridge prior to 2007 Failure

12. Truss Node (Joint) Connection (cont.)
Bolted or Pinned Joint

13. Planar Truss Deck Load Stringer Beam Truss Joint Reaction ForcesAx FB FC FD
Truss Joint Loads Ay Ey

14. Planar Truss (cont.) Roof Load Purlin Truss Joint Reaction ForcesFC FA FD
Reaction Forces FE FA
Truss Joint Loads Ax Ay Ey

15. Truss Analysis
Assumptions
Loads & reactions applied at truss joints

16. Truss Analysis (cont.) Assumptions Self-weight is generally neglected
Typical applied loads >>> bar or strut weight
Reaction Forces
Truss Joint Loads
Self-Weight
0.5WAB
0.5WAB
WAB

17. Truss Analysis (cont.) Assumptions
Truss nodes or joints act as smooth pins
Bolted or welded connections require force lines of action to be concurrent

18. Compressive Euler Buckling
Truss Analysis (cont.)
Two-Force Member
Based on assumptions
Load effects
Tension
Elongation
Compression
Shortening
Buckling may occur
Compressive Euler Buckling

19. Truss Analysis (cont.) Equilibrium Equations Statically Determinate
What equations are available?
Statically Determinate
m  # truss members
j  # truss joints
r  # reaction forces

20. Unstable Configuration Rigid or Stable Configurations
Truss Analysis (cont.)
Rigid or Stable Truss
Does not collapse under applied load
Unstable Configuration
Rigid or Stable Configurations

21. Textbook Problems

22. Textbook Problems

23. Textbook Problems

24. Textbook Problems

25. Textbook Problems

26. References Hibbeler (2007)