# What is the importance of the slenderness ratio

## What is the aspect ratio?

The aspect ratio is the ratio of the length of a column and the smallest gyro radius of its cross section. Often referred to as lambda.

It is widely used to find the design load, as well as to classify different columns into short / medium / long.

Example - Short steel column - Lambda is less than 50. Intermediate - 50-250 long - 250 above.

Why is that important? - Long columns under pressure can fail both by kinking (bending sideways) and by crushing. Various formulas for calculating such error properties make extensive use of this ratio.

I hope it helps.

Column Failure Types: A short column crushes when the direct compressive stress due to the load exceeds the yield point of the material. Long column failure is caused by the combined effect of buckling stress and direct stress. When the column kinks, the induced bending stress is of much higher value compared to the direct stress. This is why a long column will fail at much less stress, even if the direct stress due to the stress is less than the yield strength of the material.

Slenderness ratio: In order to demarcate the difference between short and long gaps, a generally defined parameter is called the slenderness ratio. In general, we understand slenderness to be the ratio of length to lateral dimensions. To some extent, this is true to distinguish between short and long gaps. In the mechanics of materials, however, the aspect ratio is defined as the ratio of the effective length of the column to the smallest gyro radius of the column cross-section.

Aspect Ratio Critical Value: As mentioned earlier, the columns are classified based on the aspect ratio value. Each material has a different value for this classification. This is known as the critical value or limit of aspect ratio. This critical value of the aspect ratio, which is used to distinguish between short and long columns, is generally a material property. It is obtained by equating the Eulers Buckling Load and the breaking load for a short column. This is given by the following equation

(\) given frac {L} {k}) \ _ {krit} = \ sqrt {\ frac {\ pi ^ 2 E} {\ sigma \ _ {c}}}. Where E is Young's modulus of elasticity and \ sigma \ _ {c} is the yield point of the material.

The aspect ratio of a given column depends only on the geometry (length and cross-section) of the column and its end conditions, while the critical value of the aspect ratio depends only on the material properties, the elastic modulus and the material yield stress.

Aspect Ratio Meaning: If the aspect ratio value for the given column is less than this critical aspect ratio value given by the above equation, the column is considered a short column. If the value is above the critical value, the column is long. The Euler formula for the buckling load only applies to long columns.

In general, steel columns with an aspect ratio of less than 50 are considered to be short columns, and if they are larger than 200, they are considered to be long columns. For a slenderness ratio between 50 and 200, the column is treated as an intermediate column

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