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 Pcr depends on Length of member Material Properties
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 Elastic BucklingP
Governing Equation
Solution
Apply Boundary
Conditions P y z

5. Column Theory - Euler Buckling

6. Column Theory - Euler Buckling
Elastic Buckling

7. Column is perfectly straight The load is axial, with no eccentricity
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

10. Effective Length Factor

11. Column Theory - Column Strength Curve

12. Example I OK – Column is Stable
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 NG – Column is Unstable
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. Column is perfectly straight The load is axial, with no eccentricity
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