Last Updated on September 17, 2026 by Maged kamel
Buckling for columns: effective length factors
This is a brief overview of the content of this Post and the following Post, as shown on the next slide.
What is buckling?
Buckling is identified as the failure limit state for that column. We recall our equation as Pcr =π^2 EI/(KL)^2; the coefficient k Value is given as per the shown Table based on the AISC code.
Here are the different shapes. If it is fixed at both ends, the actual distance will be from one inflection point to the next.
First, what causes buckling? Buckling occurs when a straight column under compression deforms into a bent shape with a bending Moment, as shown in Figure 1b; it was later plumbed to the deformed shape.
Recall the buckling for beams about the major axis x. Deflection is a lateral movement in the Y direction.
Effective Length for columns.
Effective Length (K) Factor Explained:
The K factor approximates the Length of columns for concrete, aluminum, and other materials. All use the effective-length-factor buckling.
The effective Length can be longer, shorter, or precisely the actual Length, depending on the rigidity of the supports. In practice, if the K factor is below 1.0, the structure is braced (it has a greater ability to resist lateral forces). If the structure exceeds 1.0, it is unbraced (it has a lower ability to resist lateral forces).
The effective length method is included in Appendix 7-Alternative Methods of Design for Stability. The effective Length of the member is termed Lc; Lcx is the effective Length of the member for buckling about the x-axis, while Lcy is the effective Length of the member for buckling about the y-axis.
AISC code provision for the effective length Table.
The AISC code, as referenced in the C-A-7.1 Table, specifies 6 cases for the effective Length of columns, as shown in the next slide.
1-Case:1- Column is fixed from both sides. The effective length factor k Value = 0.50, but the recommended Value for K is 0.65.
2-Case: 2- Column is hinged on one side and hinged on the other. The effective length factor k is 0.70, but the recommended Value is 0.80.
3-Case:3- The column is fixed from one side, rotation fixed, and translation free from the other side. The effective length factor k is 1.0, but the recommended Value is 1.20.
4-Case:4—The column is hinged from two sides. The effective length factor k Value is 1.0, but the recommended Value is 1.00.
5-Case:5—The Column is fixed from one side and free from the other side. The effective length factor k Value is 1.0, and the recommended Value is 1.00.
6-Case:6—The Column is hinged from one side, with rotation fixed and translation free from the other side. The effective length factor k Value is 2.0, and the recommended Value is 2.10.
The equation for Euler elastic stress is shown in the following slide image (As E3-4).
The difference between local buckling and general buckling.
To differentiate between local and general buckling, the figures show that general buckling occurs when a column is under compressive force from both ends, affecting the whole column.
Local buckling, as the name suggests, occurs in a portion of the column, as in the right figure, under compression.
The following image shows that the k factor is based on the distance between the inflection points.
This definition applies to both the strong and weak axes; for a W section, the Moment of Inertia about the x-axis is much higher than the Inertia in the y-direction.
The x-axis is the strong axis, while the y-axis is the weak axis; the figures on the left express this. The distance between the inflection points is the same in all three cases; the curvature changes sign at that point. That is why it is called the point of inflection. Due to the inflection, the distance decreases, with K*L = 0.5L.
The next image shows the difference between buckling about the major axis and buckling about the minor axis.
Imagine that you have a curved bow and an arrow. If we buckle about the major axis, the arrow points perpendicular to the major axis in the x-direction. The major axis has greater Inertia
If we buckle about the minor axis, with smaller Inertia, our arrow points perpendicular to the y-direction.
You can view or download the PDF for this Post and the following Post from the following Link.
The next Post, Post 2a: Buckling for columns-part 2.
For a good A Beginner’s Guide to the Steel Construction Manual, 14th ed. Chapter 7 – Concentrically Loaded Compression Members.
For a good A Beginner’s Guide to the Steel Construction Manual, 15th ed. Chapter 7 – Concentrically Loaded Compression Members.
For a good A Beginner’s Guide to the Steel Construction Manual, 16th ed. Chapter 7 – Concentrically Loaded Compression Members