1. Introduction to Axially Loaded Compression Members
Chapter 5
Introduction to Axially Loaded Compression Members

2. Compression Members
Chords of Trusses
Columns
Bracing Members
Columns are straight vertical members whose lengths are considerably greater than their thicknesses

3. Residual Stresses
The stresses that remain in a material after the original cause of the stresses, such as external forces, heat gradient, has been removed.
Caused by :
Uneven cooling of hot rolled sections
Uneven cooling welded materials
Cambering
Affect strength
Could be 10 to 15 ksi or more
Structural Steel Design by McCormac and Csernak, 5th Edition, Int. 2012

4. Structural Steel Design by McCormac and Csernak, 5th Edition, Int. 2012

5. Column Failure Modes
Local Buckling
Torsional Buckling
Flexural Buckling
(Euler buckling)

6. Euler Buckling depends on
Length, L
Material, E
Euler Buckling depends on
Cross section, A or I or r
End support condition

7. Columns are Long and slender members subjected to an axial compressive force.
Buckling is Lateral deflection of columns
Buckling result in instability of columns, and causes sudden failure.
Buckling occurs when load P > Pcr the critical load

8. Column with Pin Support (Ideal)
Ideal column :
perfectly straight before loading
Linear-Elastic Homogeneous material
P is applied thru c.g.
The flexural differential equation

10. Buckling Load of an elastic column is calculated using Euler Formula
𝑃 𝑐𝑟 = 𝜋 2 𝐸 𝐼 𝐿 2
Dividing both sides by cross sectional area A
And since the radius of gyration 𝑟= 𝐼 𝐴
Euler Buckling Stress is the defined as 𝐹 𝑒 = 𝑃 𝐴
𝐹 𝑒 = 𝜋 2 𝐸 ( 𝐿 𝑟 ) 2
Structural Steel Design by McCormac and Csernak, 5th Edition, Int. 2012

11. Column Strength Curve

12. Structural Steel Design by McCormac and Csernak, 5th Edition, Int. 2012

13. End restraint and Effective Lengths of Columns
K is the Effective Length Factor
KL is the Effective Length of Column
Structural Steel Design by McCormac and Csernak, 5th Edition, Int. 2012

14. Structural Steel Design by McCormac and Csernak, 5th Edition, Int. 2012

15. Structural Steel Design by McCormac and Csernak, 5th Edition, Int. 2012

16. For short columns , the failure stress will equal the yield stress.
For intermediate columns , the member will fail by both yielding and buckling.
The strength of long columns is predicted by Euler formula (elastic buckling control)
Structural Steel Design by McCormac and Csernak, 5th Edition, Int. 2012

17. Structural Steel Design by McCormac and Csernak, 5th Edition, Int. 2012

19. AISCM 14th Edition

20. AISCM 14th Edition

21. AISCM 14th Edition

22. AISCM 14th Edition

23. AISCM 14th Edition

24. Stiffened Elements Unstiffened Elements
Structural Steel Design by McCormac and Csernak, 5th Edition, Int. 2012

25. Control of Local Buckling
Limiting values for the width thickness ratio
AISCS section B4 and Table B4.1a of AISCS
Structural Steel Design by McCormac and Csernak, 5th Edition, Int. 2012

26. Structural Steel Design by McCormac and Csernak, 5th Edition, Int. 2012

27. Structural Steel Design by McCormac and Csernak, 5th Edition, Int. 2012

28. Structural Steel Design by McCormac and Csernak, 5th Edition, Int. 2012

29. Structural Steel Design by McCormac and Csernak, 5th Edition, Int. 2012

30. Structural Steel Design by McCormac and Csernak, 5th Edition, Int. 2012

31. Structural Steel Design by McCormac and Csernak, 5th Edition, Int. 2012

32. Structural Steel Design by McCormac and Csernak, 5th Edition, Int. 2012

33. Structural Steel Design by McCormac and Csernak, 5th Edition, Int. 2012

34. Structural Steel Design by McCormac and Csernak, 5th Edition, Int. 2012

35. Structural Steel Design by McCormac and Csernak, 5th Edition, Int. 2012

36. Structural Steel Design by McCormac and Csernak, 5th Edition, Int. 2012

37. Structural Steel Design by McCormac and Csernak, 5th Edition, Int. 2012

38. Structural Steel Design by McCormac and Csernak, 5th Edition, Int. 2012

39. Structural Steel Design by McCormac and Csernak, 5th Edition, Int. 2012

40. Structural Steel Design by McCormac and Csernak, 5th Edition, Int. 2012

41. HW # 4 : Problems 5-3 and 5-8
Structural Steel Design by McCormac and Csernak, 5th Edition, Int. 2012