Plastic analysis

Plastic Analysis

1. PRESENTATION ON Plastic analysis

2. OUTLINES

3.  Elastic limit Elastic limit   

4. Mechanical hinge Plastic hinge Reality Concept Resists zero moment Resists a constant moment M P Mechanical Hinge Plastic Hinge with M P =

5. M – Moment corresponding to working load M y – Moment at which the section yields M P – Moment at which entire section is under yield stress  y C T  y M P

6. Plastic moment Moment at which the entire section is under yield stress C  T A c  y  A t  y 2 c t  A  A  A •NA divides cross-section into 2 equal parts 2 y C  T  A 

7.  y y 2 y C  A  y t c A T   2 y A Similar to  y Z  y  A   y  y    Z Couple due to 2 y 2 y c t y p Plastic modulus Z p   1  is the shape factor Z

8. Shape factor for various cross-sections b d Rectangular cross-section: Section modulus  bd 3 12  I bd 2 y  d 2  6 Z    2  2 4 p c t bd d d b d ⎛ ⎞ Z  A  y  y    2 ⎜ 4 4 ⎟ ⎝ ⎠ Plastic modulus Shape factor = 1.5 Z p Z Dept. of CE, GCE Kannur 16 Dr.RajeshKN 18

9. Circular section

10. Triangular section

11. Methods of Plastic Analysis

12. Basic terminologies

13. 1. Simple beam Equilibrium method: 4 P M  W u . l M P M u  W  4 M P l

14. MECHANISMS OF FAILURE A statically determinate beam will collapse if one plastic hinge is developed Consider a simply supported beam with constant cross section loaded with a point load P at midspan If P is increased until a plastic hinge is developed at the point of maximum moment (just underneath P) an unstable structure will be created. Any further increase in load will cause collapse

15. BEAM MECHANISMS

16. Panel mechanism/sway mechanism

17. PROBLEM

18. SUMMARY