1. Column Buckling - Inelastic A long topic

2. Effects of geometric imperfection Leads to bifurcation buckling of perfect doubly-symmetric columns P v v vovo P MxMx

3. Effects of Geometric Imperfection

4. Geometric Imperfection A F = amplification factor

5. Geometric Imperfection Increases exponentially Limit A F for design Limit P/P E for design Value used in the code is 0.877 This will give A F = 8.13 Have to live with it.

6. Residual Stress Effects

8. Consider a rectangular section with a simple residual stress distribution Assume that the steel material has elastic-plastic stress-strain  curve. Assume simply supported end conditions Assume triangular distribution for residual stresses x y b d  rc  rt E yy    y  y

9. Residual Stress Effects One major constrain on residual stresses is that they must be such that Residual stresses are produced by uneven cooling but no load is present

10. Residual Stress Effects Response will be such that - elastic behavior when x y b d x y bb bb YY YY  Y /b

11. Residual Stress Effects