1. Determinacy and Stability of Structures
Theory of Structure - I
SWEDISH COLLEGE OF ENGG & TECH ,WAH CANTT

2. Lecture Outlines Introduction Equations of Equilibrium
Types of Supports and Restraints
Stability and Determinacy
Idealized Structure

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.

4. FREE BODY DIAGRAM

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).

6. The above requirements may be stated mathematically as:
1. SFx = 0
2. SFy = 0
3. SMz = 0
Positive
Positive
Sign Conventions
Positive

7. Types of Supports and Restraints
Roller Support
Fixed Support
Hinge Support

9. Hinge Support
Roller Support

14. 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.

15. Determinate Structure

16. Indeterminate Structure
The structure possesses more unknown reactions than equations of equilibrium, is referred to as an indeterminate structure.

17. Indeterminate Structure

18. Unstable Structure
A structure in which there are an insufficient number of reactions to prevent motion from taking place, is called an unstable structure.

19. Unstable Structure

20. 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.