1. Determinacy and Stability of Structures
Theory of Structure - I

2. Lecture Outlines Introduction Equations of Equilibrium
Types of Supports and Restraints
Stability and Determinacy
Idealized Structure
Department of Civil Engineering
University of Engineering and Technology, Taxila, Pakistan

3. Introduction Free Body Diagram
Simplified picture of the structure, isolated from its supports, on which are shown all the external forces that act on the structure.
These forces include the applied loads and the reactions that the supports exert on structure.
Department of Civil Engineering
University of Engineering and Technology, Taxila, Pakistan

4. FREE BODY DIAGRAM Department of Civil Engineering
University of Engineering and Technology, Taxila, Pakistan

5. Equations of Equilibrium
For complete static equilibrium in 2D, three requirements must be met:
1. External Horizontal forces balance (translation).
2. External Vertical forces balance (translation).
3. External Moments balance about any point (rotational).
Department of Civil Engineering
University of Engineering and Technology, Taxila, Pakistan

6. The above requirements may be stated mathematically as:
1. SFx = 0
2. SFy = 0
3. SMz = 0
Positive
Positive
Sign Conventions
Positive
Department of Civil Engineering
University of Engineering and Technology, Taxila, Pakistan

7. Types of Supports and Restraints
Roller Support
Fixed Support
Hinge Support
Simple Support
Department of Civil Engineering
University of Engineering and Technology, Taxila, Pakistan

8. Department of Civil Engineering
University of Engineering and Technology, Taxila, Pakistan

9. Department of Civil Engineering
University of Engineering and Technology, Taxila, Pakistan

10. Department of Civil Engineering
University of Engineering and Technology, Taxila, Pakistan

11. Hinge Support Roller Support Department of Civil Engineering
University of Engineering and Technology, Taxila, Pakistan

12. Department of Civil Engineering
University of Engineering and Technology, Taxila, Pakistan

13. Department of Civil Engineering
University of Engineering and Technology, Taxila, Pakistan

14. Department of Civil Engineering
University of Engineering and Technology, Taxila, Pakistan

15. Department of Civil Engineering
University of Engineering and Technology, Taxila, Pakistan

16. Stability and Determinacy
Determinate Structure
A structure for which all the unknown reactions can be determined using the equations of equilibrium is referred to as a determinate structure.
Department of Civil Engineering
University of Engineering and Technology, Taxila, Pakistan

17. Determinate Structure
Department of Civil Engineering
University of Engineering and Technology, Taxila, Pakistan

18. Indeterminate Structure
The structure possesses more unknown reactions than equations of equilibrium, is referred to as an indeterminate structure.
Department of Civil Engineering
University of Engineering and Technology, Taxila, Pakistan

19. Indeterminate Structure
Department of Civil Engineering
University of Engineering and Technology, Taxila, Pakistan

20. Unstable Structure
A structure in which there are an insufficient number of reactions to prevent motion from taking place, is called an unstable structure.
Department of Civil Engineering
University of Engineering and Technology, Taxila, Pakistan

21. Unstable Structure Department of Civil Engineering
University of Engineering and Technology, Taxila, Pakistan

22. Idealized Structure
The structure is made in a line form and the supports are replaced with the reactions.
This new line shape of a structure along with the symbolic reactions and applied loadings (similar to free body diagram), is called the IDEALIZED STRUCTURE.
Department of Civil Engineering
University of Engineering and Technology, Taxila, Pakistan

23. Department of Civil Engineering
University of Engineering and Technology, Taxila, Pakistan

24. Department of Civil Engineering
University of Engineering and Technology, Taxila, Pakistan

25. Department of Civil Engineering
University of Engineering and Technology, Taxila, Pakistan

26. Department of Civil Engineering
University of Engineering and Technology, Taxila, Pakistan

27. Department of Civil Engineering
University of Engineering and Technology, Taxila, Pakistan

28. Thank You Department of Civil Engineering
University of Engineering and Technology, Taxila, Pakistan