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 l / k where l is the length of the column and k is the radius of gyration, the latter defined by k 2 = I / A where A is the area of the cross-section of the column and 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 E .

Structural engineers generally consider slender those skyscrapers with a ratio minimum of 1:10 or 1:12. Slim towers require to adopt specific measures to counter the high strengths of the wind in the vertical cantilever, like including additional structure to endow greater rigidity to the building or diverse types of tuned mass dampers to avoid unwanted swinging.

The most slender residential skyscraper in the world is the Highcliff of Hong Kong which, with 72 floors and a height of 252 metres (827 ft), possesses one of the highest slenderness ratios,1:20. The extreme slenderness is something characteristic in Hong Kong, where there are more pencil-shaped buildings that in any other place in the world.