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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. Column Theory - Euler Buckling

  5. Column Theory - Euler Buckling

  6. 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

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

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

  9. Effective Length Factor

  10. Column Theory - Column Strength Curve

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

  12. AISC Requirements LRFD

  13. AISC Requirements ASD

  14. AISC Requirements ASD – Allowable Stress

  15. Design Strength

  16. Alternatively Inelastic Buckling

  17. In Summary

  18. LOCAL BUCKLING • A.Flexural Buckling • Elastic Buckling • Inelastic Buckling • Yielding • B. Local Buckling – Section E7 pp 16.1-39 • and B4 pp 16.1-14 • C. Lateral Torsional Buckling

  19. Local Stability - Section B4 pp 16.1-14 Local Stability: If elements of cross section are thin LOCAL buckling occurs The strength corresponding to any buckling mode cannot be developed

  20. Local Stability - Section B4 pp 16.1-14 Local Stability: If elements of cross section are thin LOCAL buckling occurs The strength corresponding to any buckling mode cannot be developed

  21. Local Stability - Section B4 pp 16.1-14 Local Stability: If elements of cross section are thin LOCAL buckling occurs The strength corresponding to any buckling mode cannot be developed

  22. Local Stability - Section B4 pp 16.1-14 • Stiffened Elements of Cross-Section • Unstiffened Elements of Cross-Section

  23. Local Stability - Section B4 pp 16.1-14 • Compact • Section Develops its full plastic stress before buckling (failure is due to yielding only) • Noncompact • Yield stress is reached in some but not all of its compression elements before buckling takes place (failure is due to partial buckling partial yielding) • Slender • Yield stress is never reached in any of the compression elements (failure is due to local buckling only)

  24. Local Stability - Section B4 pp 16.1-14 If local buckling occurs cross section is not fully effective Avoid whenever possible Measure of susceptibility to local buckling Width-Thickness ratio of each cross sectional element: l If cross section has slender elements - l> lr Reduce Axial Strength (E7 pp 16.1-39)

  25. Slenderness Parameter - Section B5 pp 16.1-12 Cross Sectional Element l Slenderness Stiffened Unstiffened b t h tw l=b/t=bf/2tw l=h/tw

  26. Slenderness Parameter - Limiting Values AISC B5 Table B4.1 pp 16.1-16

  27. Slenderness Parameter - Limiting Values AISC B5 Table B4.1 pp 16.1-17

  28. Slenderness Parameter - Limiting Values AISC B5 Table B4.1 pp 16.1-18

  29. Slenderness Parameter - Limiting Values

  30. Slenderness Parameter - Limiting Values

  31. Slender Cross Sectional Element:Strength Reduction E7 pp 16.1-39 Reduction Factor Q: Q: B4.1 – B4.2 pp 16.1-40 to 16.1-43

  32. Slender Cross Sectional Element:Strength Reduction E7 pp 16.1-39 Reduction Factor Q: Q=QsQa Qs, Qa: B4.1 – B4.2 pp 16.1-40 to 16.1-43

  33. Example I Investigate a W14x74, grade 50 in compression for local stability W14x74: bf-10.1 in, tf=0.785 in FLANGES - Unstiffened Elements Flange is not slender, OK

  34. Example I Investigate a W14x74, grade 50 in compression for local stability W14x74: bf-10.1 in, tf=0.785 in WEB - Stiffened Element Web is not slender, OK

  35. Example I Investigate a W14x74, grade 50 in compression for local stability W14x74: bf-10.1 in, tf=0.785 in PART 1 – Properties: Slender Shapes are marked with “c”

  36. 1.5 t = 0.1875 7.652 in 8 in Example II Determine the axial compressive strength of an HSS 8x4x1/8 with an effective length of 15 ft with respect to each principal axis. Use Fy=46 ksi. HSS 8x4x1/8 Ag=2.70 in2 h/t=66.0 rx=2.92 in2 b/t=31.5 ry=1.71 in2

  37. HSS 8x4x1/8 Maximum OK Ag=2.70 in2 rx=2.92 in2 ry=1.71 in2 h/t=66.0 b/t=31.5 Example II Inelastic Buckling Nominal Strength

  38. HSS 8x4x1/8 Ag=2.70 in2 rx=2.92 in2 ry=1.71 in2 h/t=66.0 b/t=31.5 Example II Local Buckling SLENDER

  39. HSS 8x4x1/8 Ag=2.70 in2 rx=2.92 in2 ry=1.71 in2 h/t=66.0 b/t=31.5 Example II Local Buckling Stiffened Cross-Section – Rectangular w/ constant t Qs=1.0 AISC E7.2 Case (b) applies provided that Code allows f=Fy to avoid iterations Aeff: Summation of Effective Areas of Cross section based on reduced effective width be

  40. be Example II Aeff:

  41. Aeff: 1.5 t = 0.1875 be 7.652 in 8 in Example II Loss of Area

  42. Example II Loss of Area Reduction Factor

  43. Example II Local Buckling Strength Inelastic Buckling Same as before Nominal Strength

  44. Example II Local Buckling Strength Nominal Strength CONTROLS Lateral Flexural Buckling Strength LRFD ASD

  45. Column Design Tables Assumption : Strength Governed by Flexural Buckling Check Local Buckling Column Design Tables Design strength of selected shapes for effective length KL Table 4-1 to 4-2, (pp 4-10 to 4-316) Critical Stress for Slenderness KL/r table 4.22 pp (4-318 to 4-322)

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