Compression Test of Steel Columns Experiment # 5 Compression Test of Steel Columns

Objectives : 1) To study some of the important parameters which affect column buckling, such as slenderness ratio (L/r) and least radius of gyration (r). 2) To determine the relationship between critical stress versus slenderness ratio of steel columns. 3) To confirm the validity of Euler’s analysis of Pcr ,the critical buckling load and the relationship of Pcr to column slenderness.

Compression Members :  Columns: structural members which undergo compressive stress. Column Strength : Its ability to support loads without experiencing excessive stress. Column Design : 2) Column Stability : Its ability to support loads without experiencing sudden change in its configuration. Material Failure Column Failure : 2) Buckling

Material Failure: ■ The failure of a short column resulting from the compression axial force looks like: P Safe Failure

Buckling : ■ However, when a compression member becomes longer, the role of the geometry and stiffness (Young’s Modulus) becomes more and more important. ■ For a long (slender) column, buckling occurs way before the normal stress reaches the strength of the column material. P Pcr : Safe : Buckling Load Increase σcr : Buckling Stress Pcr : Buckling Load

Buckling Stress: ■ What does buckling stress (σcr) depend on ? - Modulus of Elasticity (E) - Length of the column (L) - Dimensions of the cross section (r for a rod) Pcr ■ The expression for critical stress is called Euler’s (1707-1783) formula. For a both end pinned column we have:

Euler’s Formula: ■ An important parameter in Euler’s formula is: Pcr is called slenderness ratio. Column length Le : effective length rg : radius of gyration Support condition

An Example: ■ For example for a rod with both ends pinned we have : Pcr - Both ends pinned : Le = L Radius of gyration : And the slenderness ratio is :

Effective Length: ■ How to figure out Le based on the supports conditions ?

Buckling Curve: ■ If the critical stress (σcr ) vs. slenderness ratio is plotted : stress Slenderness ratio

Buckling Curve: ■ If the critical stress (σcr ) vs. slenderness ratio is plotted : stress Slenderness ratio

Experiment Procedure: ■ For this experiment several steel columns with different lengths and cross section diameters are put under compression and the buckling loads are measured. Then the corresponding critical stresses are compared with those calculated from Euler’s formula.

Experiment Procedure: ■ Finally, experimental and theoretical critical stresses are plotted vs. slenderness ratio : KL/rg Euler’s Formula Experimental Stresses Short Intermediate Long σy σcr (psi)

Thank you ! Questions?