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Compression Members

Compression Members. Compression Members. Compression members are susceptible to BUCKLING BUCKLING – Loss of stability Axial loads cause lateral deformations (bending-like deformations). P is applied slowly P increases Member becomes unstable - buckles. Column Theory.

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Compression Members

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  1. Compression Members

  2. Compression Members • Compression members are susceptible to BUCKLING • BUCKLING – Loss of stability • Axial loads cause lateral deformations (bending-like deformations) P is applied slowly P increases Member becomes unstable - buckles

  3. Column Theory Axial force that causes Buckling is called Critical Load and is associated to the column strength • Pcr depends on • Length of member • Material Properties • Section Properties

  4. P P y z Column Theory - Euler Elastic Buckling Governing Equation Solution Apply Boundary Conditions

  5. Column Theory - Euler Buckling

  6. Elastic Buckling Column Theory - Euler Buckling

  7. Assumptions • Column is perfectly straight • The load is axial, with no eccentricity • The column is pinned at both ends No Moments Need to account for other boundary conditions

  8. Other Boundary Conditions Free to rotate and translate Fixed on top Free to rotate Fixed on bottom Fixed on bottom Fixed on bottom

  9. Other Boundary Conditions In general K: Effective Length Factor LRFD Commentary Table C-C2.2 p 16.1-240

  10. Effective Length Factor

  11. Column Theory - Column Strength Curve

  12. Example I A W12x50 is used as a column to support a compressive load of 145 kips. The length is 20 ft and the ends are pinned. Without regard to LRFD or ASD investigate the stability of the column For a W12x50 OK – Column is Stable

  13. Example I A W12x50 is used as a column to support a compressive load of 145 kips. The length is 20 ft the bottom is fixed and the top is free. Without regard to LRFD or ASD investigate the stability of the column For a W12x50 NG – Column is Unstable

  14. AISC Requirements CHAPTER E pp 16.1-32 Nominal Compressive Strength AISC Eqtn E3-1

  15. AISC Requirements LRFD

  16. AISC Requirements ASD

  17. AISC Requirements ASD – Allowable Stress

  18. To compute Fcr – ELASTIC BUCKLING Recall Assumptions

  19. Assumptions • Column is perfectly straight • The load is axial, with no eccentricity • The column is pinned at both ends

  20. To compute Fcr – ELASTIC BUCKLING Accounts for Imperfections

  21. To compute Fcr – INELASTIC BUCKLING

  22. Design Strength

  23. Alternatively Inelastic Buckling

  24. In Summary

  25. Example A W14x74 of A992 steel has a length of 20 feet and pinned ends. Compute the design strength for LRFD and the allowable compressive strength for ASD Slenderness Ratio

  26. Example

  27. Example LRFD ASD

  28. Homework 4.3-1 4.3-4 4.3-6

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