Last Updated on September 4, 2026 by Maged kamel
Steel columns, 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, defined as the ratio of height to 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, and E is the modulus of elasticity.
Using KL instead of L accounts for the actual column length and support conditions. Here 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. hat is the definition of compression members?
The second point will illustrate the different modes of failure.
The third point illustrates where to use the different steel sections for compression members.
The fourth point is how to derive 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 failure modes for short columns? The last point is torsional buckling.
Definition of the compression member.
From Prof. Alan Williams’ book Steel Structure Design LRFD-ASD, for the definition of a compression member.
What is a compression member? 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 supported truss are compression members.
The failure of a compression member can cause structural collapse, making the design of compression members a crucial subject.
In Professor Varma’s lectures, he shows the formula for computing stress.l He defined compression members as the structural elements that are subjected to axial compressive forces loaded through the centroid.
Stress can be evaluated as the compressive load divided by the Area. But in reality, the situation might vary. It is also possible to have a concentric load.
Causes of additional stress in compression members.
1 -The accidental eccentricity of loading concerning the centroid.
2-Residual stresses in the member due to the fabrication process; these can cause both tensile and compressive stresses.
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 performance, particularly under uniform loads. For example, cambering a beam can help counteract the sag or deflection it might experience under a uniform load.
- Members that carry both compression and Moment are referred to as beam-columns.
The PDFs for this post and the next can be viewed or downloaded from the following link.
This is a link to the next post:1a-Steel columns and Euler’s formula-part 2.
For a good Beginner’s Guide to the Steel Construction Manual, 14th ed., Chapter 7 – Concentrically Loaded Compression Members.
For a good Beginner’s Guide to the Steel Construction Manual, 15th ed., Chapter 7 – Concentrically Loaded Compression Members.
For a good Beginner’s Guide to the Steel Construction Manual, 16th ed., hapter 7 – Concentrically Loaded Compression Members