The critical load of a column member is determined by factors including the column's length, cross-section, material, and boundary conditions. Two formulas are used to calculate column buckling in the buckling calculator depending on the slenderness ratios of the column:

• Euler's Formula for Column Buckling is used when the Slenderness Ratio of the column member is greater than the Critical Slenderness Ratio.
• Johnson's Parabolic Formula for Column Buckling is used when the Slenderness Ratio of the column member is less than the Critical Slenderness Ratio.

The column buckling formula used in this buckling load calculator is Euler's formula for buckling when the column's slenderness ratio exceeds its critical slenderness ratio. For cases where the slenderness ratio is lower, Johnson's parabolic formula is used as an alternative.

Leonhard Euler was a Swiss mathematician who derived a formula that determines the load at which a column will buckle. The formula is relatively simple:

It is important to note that Euler’s formula is used in the buckling calculator when the column the slenderness ratio of the column member is greater than its critical slenderness ratio.

J. B. Johnson developed the parabolic formula for column buckling for columns with a low slenderness ratio. Johnson's Parabolic Formula is as follows:

The effective length value (K) used in the SkyCiv Column Buckling Calculator is based on the recommended design value found in Table C-A-7.1 Approximate Values of Effective Length Factor, K of the ANSI/AISC 360-22 Specification for Structural Steel Buildings.

If in the analysis stage of an engineering project, a column is found to be buckling then an engineer can try a couple of methods to ensure structural integrity. This first method includes increasing the cross-sectional dimensions of the column to enable improved column load capacity. Material changes are also possible, such as using higher strength/stiffness steel will again improve the columns load capacity. Finally if required the column can be braced, laterally supported, or reinforced to help it resist buckling. You can simulate these approaches in the SkyCiv buckling load calculator above.

• Column Buckling is the general structural phenomenon used to describe when a column (vertical member) deflect sideways due to axial loads leading to a reduced compressive capacity in the column.
• Critical Buckling is a term used by engineers to design the specific point at which a column reaches it's critical or maximum load a column can resist in it's elastic range before buckling occurs.

If you want to gain a deeper understanding of column buckling and understand the calculations provided in this buckling load calculator then SkyCiv has a detailed tutorial on Column Buckling to get you started.

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As well as our column buckling calculator SkyCiv offers a wide range of Cloud Structural Analysis and Design Software for engineers. As a constantly evolving tech company, we're committed to innovating and challenging existing workflows to save engineers time in their work processes and designs.

Using the SkyCiv Column Buckling Calculator is simple. First, enter the length and support conditions for your column. Once this is done the next step is to enter the details of the Cross Section of the column including the Cross Section Area and Second Moment of Area. Finally, you need to enter Young's Modulus and Yield Strength of the material that makes up the column cross-section. Once you are satisfied with this click run to get your results.

Column buckling occurs when a vertical member fails by laterally deflecting (bending) due to axial compressive loads. This can lead to sudden and catastrophic structural failure. Column bowing, however, is the lateral deformation of a structural element due to multiple factors (uneven loads, temperature changes). Generally, this is a gradual change and does not necessarily lead to failure. If you have concerns about column buckling or bowing, then a registered structural engineer should be consulted to check columns for buckling or bowing.

The slenderness ratio of a column is the property of a vertical member that can be used to determine the stability of a column when subjected to axial loads. It is determined by the ratio of the effective length of the column over its radius of gyration. The slenderness ratio gives an indication of the column’s susceptibility to buckling or lateral deflection-based failure modes.

The buckling of a column is a failure mode generally found in column members due to high axial compressive loads. When a column buckles it experiences high lateral deflection and can suddenly daily by collapsing, unpredictably deforming, or crumpling. The ability of a column to resist buckling can depend on the factors of the column including the cross-section, material, supports, length, and slenderness ratio.

The critical load of a column can be calculated with either the Parabolic Johnson Formula or Euler's Formula for Column Buckling. Several factors can affect the critical load of a column member including the support conditions, length (and subsequent effective length), cross-section, material, and shape. Use the above calculator to determine the critical load using the most relevant formula based on these factors.

The effective length factor, often called the k factor, is used by engineers to determine to account for the reduction in the critical buckling load of the column due to its boundary conditions. Based on table C-A-7.1 ANSI/AISC 360-22 the following common effective length factors can be used:

• Columns Fixed at Both Ends: 0.65
• Columns Fixed at One End and Pinned at the Other: 0.8
• Columns Pinned at Both Ends: 1

The full table of all support conditions used in the buckling load calculator and related effective length factors can be found below: