1. Columns Zach Gutzmer, EIT Civil and Environmental Engineering South Dakota State University

2. What is a Column? The two main type of structural elements are: – Axial elements – Beam elements

3. What is a Column? Axial elements are subjected to loads only along the member’s axis.

4. What is a Column? Beam elements are subjected to loads along the member’s axis AND loads transverse to the member’s axis.

5. Columns A column is a beam element with a relatively high axial load. *For today’s discussion, we will assume the loads in the transverse direction are negligible compared to the high axial load.

6. Column Failure Modes Columns can fail if the applied load exceeds the yield stress of the material. – This is a strength failure Columns can also fail by buckling. – This is a stability failure

7. What is Buckling?

10. Buckling Buckling is a phenomena of compression members. Once the buckling load, or critical load, is reached, the column will instantly loose stability and “kick out” to one side. Once buckled, the column’s ability to carry load is greatly reduced.

11. Buckling Example Wooden Ruler: – Area = l x w = 1.25in x 0.125 in = 0.1563 in – σ ult = 3.78 ksi – P ult = σ ult x Area = 591 lbs An approximate load of 600 lbs will crush the ruler.

12. Buckling Example Critical buckling load P cr : – E = modulus of elasticity = 1,900,000 psi – I = moment of inertia = 2.035 x 10 -4 in 4 – K = effective length factor = 1.0 – L = Length = 36 in – π = delicious P cr = 2.94 lbs !!!

13. Buckling Example The ruler will buckle before it can crush/yield. If a member buckles before it yields: - Elastic buckling If a member buckles after it yields: - Inelastic buckling What happens to the member after the load is removed?

14. Buckling Equation P cr = critical buckling load E = modulus of elasticity I = moment of inertia K = effective length factor L = Length If we wanted to increase the column capacity of our ruler, what factors could we change?

15. Effective Length Factor K depends on the type of supports on the column We can also change the effective length by adding bracing along the height of the column

16. What is the effective length for:

17. 12 feet and 8.4 feet depending on axis

18. Ruler Example If we leave the ruler’s supports at pinned – pinned but added a brace in the middle (L = 18”): – P cr = 11.8 lbs If we change the ruler’s supports to fixed – fixed (k = 0.5) with no brace: – P cr = 11.8 lbs If we change the ruler’s supports to fixed – fixed (k = 0.7, L = 18”) and add a brace: – P cr = 24 lbs To make the ruler crush before it buckles, we would need a brace every 2.5 inches!

19. Buckling Behavior There is a ‘weak’ and ‘strong’ axis for buckling – Buckling will always occur about the ‘weak’ axis Axis aa is the weak axis Axis bb is the strong axis The ‘weak’ axis is the axis with the lower moment of inertia Do all shapes have a ‘strong’ and ‘weak’ axis?