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2E4: SOLIDS & STRUCTURES Lecture 10

2E4: SOLIDS & STRUCTURES Lecture 10. Dr. Bidisha Ghosh Notes: http://www.tcd.ie/civileng/Staff/Bidisha.Ghosh/Solids & Structures. Moment curvature equation. A quick touch on bending before learning buckling! Moment at any section Moment-curvature equation :

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2E4: SOLIDS & STRUCTURES Lecture 10

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  1. 2E4: SOLIDS & STRUCTURESLecture 10 Dr. BidishaGhosh Notes: http://www.tcd.ie/civileng/Staff/Bidisha.Ghosh/Solids & Structures

  2. Moment curvature equation A quick touch on bending before learning buckling! Moment at any section Moment-curvature equation: Buckling is an effect of combined compression & bending

  3. Compression on A Slender Column From knowledge of bending, Solve this equation….. 1. 2. So,

  4. Compression on A Slender Column For any buckling to happen the second condition has to be true and that means,

  5. Compression on A Slender Column The strut will buckle at the lowest load, i.e. the EULER BUCKLING LOAD this formula is for a pin-ended column. Notes: 1. Radius of Gyration,

  6. Slenderness Ratio, Effective Length Euler buckling load for pin-ended column, Hence, using radius of gyration, Slenderness ratio = (defined as) This critical load/buckling load is dependant on end conditions. It can be shown the general form of buckling load Effective length, (defined as) Effective Slenderness Ratio,

  7. Different End-Conditions

  8. Different End-Conditions

  9. Classification of Columns CD is Euler curve showing behaviour of long columns For slenderness ratio less than 30, columns are called struts. They fail by yielding or crushing, generally not buckling. Euler formula should not be used for slenderness ratio <120

  10. How things fail? Buckling

  11. How things fail? Tension

  12. How things fail? Compression

  13. How things fail? Bending

  14. How things fail? Shear

  15. How things fail? Corrosion

  16. How things fail? Fatigue

  17. How things fail? Torsion

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