# Slenderness ratio

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The Highcliff is one example of an extremely slender skyscraper.

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 effective length of the column and ${\displaystyle k}$ is the least 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. The effective length is calculated from the actual length of the member considering the rotational and relative translational boundary conditions at the ends. 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 ${\displaystyle E}$.

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

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 most extreme slenderness ratios, 1:20. Its extreme slenderness is characteristic of Hong Kong, where there are more pencil-shaped buildings than in any other place in the world.[2]

## Examples

Building Location Floors Height (m) Slenderness Year
111 West 57th Street New York, NY 82 438 1:24 2018
Highcliff Happy Valley, Hong Kong 73 252 1:20 2003
150 North Riverside Chicago, Illinois 54 228 1:20 at base 2017
Collins House (Melbourne) Melbourne, Australia 61 190 1:16.25 2019 (under construction)
432 Park Avenue New York, NY 85 425.5 1:15 2015
One Madison Park New York, NY 50 188 1:12 2016
Sky Hous 55 179 Between 1:12 and 1:17 Proposed
785 Eight Avenue 42 158 Between 1:18 and 1:15 Proposed

## References

1. ^ Willis, Carol. "The Skyscraper Museum: SKY HIGH & the logic of luxury WALKTHROUGH". Retrieved 2016-01-24.
2. ^ Willis, Carol. "Presented by The Skyscraper Museum". Retrieved 2016-01-24.