1. Stability and Determinacy of Structures

2. The stability of a structure can be divided into:
external stability
(ii) internal stability

3. The reactive forces should be non parallel and non concurrent.
External Stability
If the supports can provide the required number of independent reaction components for static equilibrium of the structure it called externally stable.
The reactive forces should be non parallel and non concurrent.

4. Stable support system

5. Unstable support systems
Parallel reaction (unstable)
Concurrent reaction (unstable) P

6. Internal Stability
If it can maintain its geometry under the action of all kinds of forces tending to deform it. (geometry of unstable, known as mechanisms).

7. Unstable structures (mechanisms)

8. Stability and Determinacy in Beams
If r = number of reactions c = number of internal hinges Then ;- If r < 3+c -----> the system is unstable If r = 3+c -----> the system is stable and determinacy If r > 3+c -----> the system is stable and indeterminacy

9. Examples

10. Stability And Determinacy In Trusses
If m=number of bars(members) r = number of reactions j = number of joints Then: m+r < 2j ----> unstable m+r =2j -----> stable and determinate m+r > 2j > stable and indeterminate

11. Examples

12. Examples

13. Examples

14. Stability and Determinacy of Rigid Frames
If m=total number of members r=number of reactions j=number of joints c=number of internal hinges then: - if 3m+r < 3j+c > the frame is unstable if 3m+r = 3j+c > the frame is statically determined provide it is also stable if 3m+r > 3j+c > the frame is statically indeterminate

15. Examples

16. Examples

17. H.W.

18. The End