# Understanding Buckling | Summary and Q&A

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August 17, 2021
by
The Efficient Engineer
Understanding Buckling

## TL;DR

Learn about buckling, a failure mode in structures caused by compressive loads exceeding critical limits, and how it can be accounted for in engineering design.

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### Q: How does buckling differ from yielding or fracturing in structures?

Buckling is a failure mode that occurs when compressive loads cause a change in the shape of a structure, leading to instability and the inability to support loads as designed. Unlike yielding or fracturing, buckling does not necessarily result in material failure but renders the structure incapable of carrying a load effectively.

### Q: What are some examples of structures at risk of buckling?

Columns in trusses and frames, railway tracks on hot days, and subsea pipelines carrying hot product are all examples of structures that can be at risk of buckling when subjected to compressive loads.

### Q: How does Euler's formula determine the critical buckling load of a column?

Euler's formula, developed by Leonhard Euler, relates the critical buckling load of a column to three parameters: the Young's modulus of the material, the area moment of inertia of the cross-section, and the length of the column. It does not depend on the strength of the material.

### Q: How do different end conditions affect the critical buckling load of a column?

The end conditions of a column, such as being pinned at both ends or fixed at one end, significantly influence the critical buckling load. An effective length is introduced to account for different end conditions, and design codes provide guidance on selecting appropriate effective lengths.

### Q: What is the slenderness ratio, and how does it affect the critical buckling stress of a column?

The slenderness ratio, calculated as the column length divided by the radius of gyration, determines a column's susceptibility to buckling. Very slender columns, with high slenderness ratios, have low critical buckling stresses, while stocky columns, with low slenderness ratios, have high critical buckling stresses.

### Q: How does eccentric loading or the presence of imperfections affect Euler's formula for buckling?

Eccentric loading, where the applied load is offset from the centroid of the cross-section, and the presence of imperfections can both reduce the critical buckling load of a column and change how buckling occurs. These effects are modeled using the Secant formula and can introduce additional bending moments.

### Q: Are there other types of buckling beyond flexural buckling of columns?

Yes, thin-walled open cross-sections can buckle by twisting (torsional buckling) or a combination of twisting and bending (torsional-flexural buckling). Thin plates and shells can also buckle, but predicting their behavior is more complex and often requires non-linear analysis using methods like the finite element method.

## Summary & Key Takeaways

• Buckling is a failure mode that occurs when compressive loads cause a change in the shape of a structure, leading to instability and the inability to support loads as designed.

• Euler's formula, developed in the 18th century, provides a simple equation for calculating the critical buckling load of columns and other compression-loaded members.

• Slender columns are more prone to buckling, and the slenderness ratio, defined as the length divided by the radius of gyration, determines a column's susceptibility to buckling.