Last Updated on June 2, 2025 by Maged kamel
Steel columns and Euler’s formula and k factors.
Introduction to Compression members. Euler’s formula establishes a relationship between the load-carrying capacity of columns and their slenderness ratio, which is defined as the ratio of the height to the radius of gyration. The higher the slenderness ratio, the lower the carrying capacity.
According to Euler’s formula, the critical stress for a column can be evaluated as Fe=π^2 EI/(L/r)^2, where KL/r is called the slenderness ratio, K is the effective length factor, Fe is the critical stress, E is the modulus of elasticity.
The use of KL instead of L takes into consideration the actual column length and support conditions. There are six conditions in which columns may exist.
For each case, a different k value is to be considered; for columns, these conditions are shown in the next picture, K factor cases for columns.
A detailed description of the Content of the post.
Our subject will be the compression members, especially steel columns.
The first point. What is the definition of compression members?
The second point will be An illustration of the different modes of failure.
The third point illustrates where to use the different steel sections for compression members.
The fourth point is how do we drive the expression for Euler’s equation.
The fifth point is the difference between local buckling and general buckling.
The sixth point is, what are the different modes for failures for short columns? The last point is the Torsional buckling.
Definition of the compression member.
From Prof Alan William’s book Steel Structure Design LRFD -ASD. for the definition of Compression member.
What is a compression member? A compression member is a structural member that carries loads along its longitudinal axis.
Usually, the compression member is free from the effect of the bending moment.
He explored the different types of compression members, for instance, columns, in a framed structure. If you have braced frames, then the bracing itself is a compression member, just like the truss. The top chords of a simply supported truss are compression members.
The failure of a compression member can cause the collapse of a structure, making the design of compression members a crucial subject.
In Professor Varma’s lectures, he shows the formula used to compute stress.l He defined compression members as the structural elements that are subjected to axial compressive forces loaded through the centroid.
The stress can be evaluated as the compression load divided by the area. But in reality, the situation might vary. It is rare how to have a concentric load.
Causes of additional stress to compression members.
1 -The accidental eccentricity of loading concerning the centroid.
2-Residual stresses in the member due to the fabrication process; residual stress can cause both tensile and compression stress.
3- Member out of straightness, which is called crookedness; there is no 100% plumb column section; n AISC (American Institute of Steel Construction) construction, “L/500” refers to an erection tolerance for columns, specifically for plumbness (verticality).
It dictates that the variation of a column’s working line from a plumb line should not exceed 1/500th of the distance between its working points. This tolerance is defined in AISC Code Section 7.13.1.1.
Camber and sweep are terms used to describe slight curves in steel columns, but they occur in different planes: camber is a curve in the vertical plane (strong axis), and sweep is a curve in the horizontal plane (weak axis).
Why are they used?
- Structural Performance: Camber and sweep can be intentionally introduced into steel columns to enhance their structural performance, particularly when subjected to uniform loads. For example, cambering a beam can help counteract the sag or deflection it might experience under a uniform load.
- Members with both compression and moment can be referred to as beam-columns.
This is a link to the next post-1a-Steel columns and Euler’s formula-part 2.
This is a link to an external resource: Chapter 7 – Concentrically Loaded Compression, Members.