# Column buckling checks with SDC Verifier

Last Updated on April 12th, 2024

Column buckling checks are important in structural engineering to ensure the safety and stability of structures. Buckling is a sudden and catastrophic failure mode that can occur in slender columns when subjected to compressive loads. It is characterized by lateral deflection of the column, which can lead to collapse.

## What is Column buckling

Buckling occurs in columns when a compressive load is applied to a column that exceeds the column’s critical load. The critical load is the maximum load a column can carry before it loses stability and begins to buckle or bend. This can happen due to various factors, such as column size, material, and the type of loading applied to the column. The critical load is influenced by the column’s slenderness ratio and length ratio to its least gyration radius. Columns with a high slenderness ratio are more likely to buckle than those with a low slenderness ratio.

The mathematics of buckling was first explored by Leonard Euler and is presented in the following formula:

$$P_{cr}=\frac{\pi^{2}EI}{L^{2}}$$

where E is the modulus of elasticity in (force/length2), I is the moment of inertia (length4), L is the length of the column.

Long columns can be analyzed with the Euler column formula

$$F=n\pi^{2}EI/L^{2}$$

where

• F = allowable load (lb, N)
• n = factor accounting for the end conditions
• E = modulus of elasticity (lb/in2, Pa (N/m2))
• L = length of column (in, m)
• I = Moment of inertia (in4, m4)

The formula helps to understand how the critical load is affected by column length, cross-sectional properties, and material properties, choose appropriate materials for columns based on their modulus of elasticity and other relevant properties, perform preliminary stability checks, optimize column designs to use materials and resources efficiently while meeting safety requirements.
Columns transfer loads vertically while beams transfer loads horizontally into columns, and they often coexist in a structure. Learn more about the essentials of beam buckling in detail in this video:

## Types of Column buckling

The different types of column buckling are primarily categorized based on the boundary conditions and buckling modes. Here are the main types of column buckling:

• Euler buckling (perfectly pinned-pinned) – is the simplest form of column buckling, assuming the column is perfectly pinned at both ends. The buckling mode involves a single half-wave, and the critical load is determined by the column’s length, material properties, and cross-sectional area.
• Column with fixed ends (perfectly fixed-fixed) – in this case, the column is assumed to have fixed ends, which means it cannot rotate or translate at those points. The buckling mode involves two half-waves.
• Column with one end pinned, one end free (pinned-free) – one end of the column is pinned while the other end is free to move laterally. The buckling mode involves a quarter-wave.
• Column with one end fixed, one end pinned (fixed-pinned) – one end is fixed against rotation and translation, and the other end pinned. The buckling mode involves three-quarters of a wave.
• Column with fixed-fixed ends and intermediate lateral support – the column is fixed at both ends but has additional lateral support or bracing along its length. This type of column buckling involves intermediate lateral-torsional buckling.
• Column with eccentric loading – when an axial load is applied to the column’s centroid but does not pass through its centroidal axis, it introduces bending and axial compression. This can lead to combined bending and buckling behavior, known as flexural-torsional buckling.
• Non-uniform columns – columns with varying cross-sections along their length are more complex to analyze. The buckling behavior can be influenced by the changes in cross-sectional properties, leading to multiple modes of buckling.
• Slender strut buckling – refers to the buckling behavior of very slender columns where the effects of imperfections and material nonlinearity become significant. The analysis of such columns often requires considering the effects of geometric imperfections and material behavior.

Considering different column buckling types helps ensure structures’ safety, reliability, and compliance with established engineering standards. By analyzing different buckling modes, engineers can determine the critical loads at which buckling becomes a concern and design structures to resist such failures.

## How to avoid Column buckling

In general, buckling can be prevented using a larger cross-section or stiffer material. Additionally, it can be seen in the critical load calculation that the buckling load is inversely proportional to the length of the structural member squared, so if required, reducing the length of the structural member or bracing the member can be used to increase the critical buckling load.

## Column buckling checks with SDC Verifier case study

With the help of Beam member finder, torsional length was obtained, and length torsional and torsional-flexular buckling were calculated.

Based on the beam member check results according to Eurocode 3 standard, several beam members with utilization factor above 1 were found. All members that showed a Utilization factor above 1 and did not satisfy requirements according to Eurocode 3 standard required reinforcement.

Moreover, additional checks according to standards such as tubular joint check, deflection check, serviceability check, or Eurocode3 beam member check show how the structural elements will behave at different conditions and help engineers conclude if the columns are safe to operate or their parameters should be changed, reinforcements added, connections modified and so on to ensure the structure safety.

The automatic Model Setup Report created by SDC Verifier contains the entire model descriptions and explanations of all calculation details for the supporting structure and all its components separately. The stakeholder can easily extract the essential results from the report and repeat the structure’s analysis in the future to compare the changes in the state of the structure with time.

SDC Verifier automates column buckling checks by extracting critical load factors and modes, streamlining the evaluation process. It also provides a library of industry-standard design codes, enabling engineers to assess column stability and meet regulatory requirements quickly.