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# Plastic analysis

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Plastic Analysis of RC section, Plastic hinge formation

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### Plastic analysis

1. 1. Seminar on “Plastic Analysis” By: Shubham Satish Babar Department of Civil Engineering 2015-16
2. 2. 1) Introduction 2) Plastic hinge concept 3) Plastic section modulus & Shape factor 4) Collapse mechanism 5) Determination of collapse load CONTENT-
3. 3. Materials 1) Introduction - •Elastic •Elastic-Perfectly plastic
4. 4. Assumptions •Plane sections remain plane in plastic condition • Stress-strain relation is identical both in compression and tension
5. 5. Process of yielding of a section •Let a cross-section increases gradually. •Within elastic limit, M = σ .Z •Z is section modulus, I/y •Elastic limit –yield stresses reached My = σ y.Z •When moment is increased, yield spreads into inner When moment is increased, yield spreads into inner fibres. Remaining portion still elastic • Finally, the entire cross-section yields
6. 6. Change in stress distribution during yielding Rectangular cross section M<My M=My My<M<Mp M=Mp
7. 7. Inverted T section Example -
8. 8. 2) Plastic hinge concept •When the section is completely yielded, the section is fully plastic • A fully plastic section behaves like a hinge – Plastic hinge Plastic hinge is defined as an yielded zone due to bending in a structural member, at which large rotations can occur at a section at constant plastic moment, MP
9. 9. Moment at which the entire section is under yield stress 3) Plastic section modulus & Shape factor -
10. 10. Couple due to Plastic Modulus NA divides cross-section into 2 equal parts
11. 11. Shape factor for various cross-sections
12. 12. Circular section
13. 13. Triangular section
14. 14. I section
15. 15. Beam mechanism - 4) Collapse mechanism -
16. 16. • Plastic hinges develop at the ends first • Beam becomes a simple beam • Plastic hinge develops at the centre • Beam collapses
17. 17. • Plastic hinge develops at the fixed support first • Beam becomes a simple beam • Plastic hinge develops at the centre • Beam collapses
18. 18. Panel mechanism/sway mechanism
19. 19. Gable Mechanism
20. 20. Methods of Plastic Analysis • Static method or Equilibrium method Lower bound: A load computed on the basis of an assumed equilibrium BM diagram in which the moments are not greater than MP is always less than (or at the worst equal to) the true ultimate load. • Kinematic method or Mechanism method or Virtual work Work performed by the external loads is equated to the internal work absorbed by plastic hinges Upper bound: A load computed on the basis of an assumed mechanism is always greater than (or at the best equal to) the true ultimate load.
21. 21. The Plastic Hinges occur- • At the point of maximum moment. • At the connection involving change in geometry. • Under the concentrated load. • At the point of zero shear in span, loaded by uniformly distribute load.
22. 22. 5) Determination of collapse load - 1. Simple beam
23. 23. • Virtual work method
24. 24. 2. Fixed beam with UDL
25. 25. Equilibrium : Virtual Work :
26. 26. 3. Fixed beam with point load
27. 27. 4. Fixed beam with eccentric point load
28. 28. Virtual Work :
29. 29. 5. Propped cantilever with point load at midspan
30. 30. 6. Propped cantilever with UDL
31. 31. REFERENCES - • “Plastic Analysis” by Dr. Rajesh K. N. (Assistant Professor in Civil Engineering Assistant Professor in Civil Engineering Govt. College of Engineering, Kannur) • Fundamentals of Structural Steel Design by M L Gambhir