Last Updated on June 2, 2025 by Maged kamel
Buckling for columns-effective length factors
What is buckling?
Buckling is identified as a failure limit state, the shape of failure 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 from both sides, the actual distance will be from the inflection point to another inflection point.
First, what is the cause of buckling? Buckling occurs when a straight column acted upon by compression force is converted to another form having a bending moment, as shown in Figure 1b; it was plumbed later 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, etc. All use the effective length factor) buckles.
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, then the structure is braced (the structure has a greater ability to deal with any lateral forces). If the structure is above 1.0, then the structure is unbraced (the structure has a lesser ability to deal with any 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 set to be=0.65.
2-Case:2- Column is hinged from one side and hinged from the other. The effective length factor k value is 0.70, but the recommended value is set to 0.80.
3-Case:3- Column is fixed from one side, rotation fixed, and translation free from the other side. The effective length factor k value =1.0, but the recommended value is set to be=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 included 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 in front of us that general Buckling occurs when a column is under compressive force from both ends is a general Buckling for the whole column.
Local buckling, from its name, occurs for a portion of the column, as in the right figure, under a compression load.
The following image shows the k factor is based on the distance between the inflection points.
The definition is essential for 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 for the three cases is the same; the root of curvature changes at a point. That is why it is called the point of inflection. Due to inflection, the distance becomes smaller as K*L=0.5 L.
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 have to buckle about the major axis, then our pointed arrow direction is perpendicular to the major axis in the x-direction. That major axis has a bigger value of inertia, on the contrary.
If we have to buckle about the minor axis, with a smaller value of inertia, then our arrow points in the direction that is perpendicular to the y-direction.
The next post: Buckling for columns-part 2.
For a good reference from Prof. T. Bart Quimby, P.E., Ph.D., F.ASCE, refer to this link for public concepts.