Slenderness ratio

In architecture, the slenderness ratio, or simply slenderness is the quotient between the width of a building and its height.

In structural engineering, slenderness is a measure of the propensity of a column to buckle. It is defined as ${\displaystyle l/k}$ where ${\displaystyle l}$ is the length of the column and ${\displaystyle k}$ is the radius of gyration, the latter defined by ${\displaystyle k^{2}=I/A}$ where ${\displaystyle A}$ is the area of the cross-section of the column and ${\displaystyle I}$ is the second moment of area of the cross-section. Slenderness captures the influence on buckling of all the geometric aspects of the column, namely its length, area, and second moment of area. The influence of the material is represented separately by the material's modulus of elasticity ${\displaystyle E}$.

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