Slenderness ratio
In architecture, the slenderness ratio, or simply slenderness, is an aspect ratio, the quotient between the height and the width of a building.
In structural engineering, slenderness is used to calculate the propensity of a column to buckle. It is defined as where is the effective length of the column and is the least radius of gyration, the latter defined by where is the area of the cross-section of the column and 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 .
Structural engineers generally consider a skyscraper as slender if the height:width ratio exceeds 10:1 or 12:1. Slim towers require the adoption of specific measures to counter the high strengths of 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]
Tall buildings with high slenderness ratio are sometime referred to as pencil towers.[2]
Examples
[edit]
| Building | Location | Floors | Height (m) | Slenderness | Year |
|---|---|---|---|---|---|
| 111 West 57th Street | New York, NY | 82 | 438 | 24:1 | 2018 |
| Highcliff | Happy Valley, Hong Kong | 73 | 252 | 20:1 | 2003 |
| 150 North Riverside | Chicago, Illinois | 54 | 228 | 20:1 at base | 2017 |
| 220 Central Park South | New York, NY | 70 | 290 | 18:1 | 2019 |
| Collins House (Melbourne) | Melbourne, Australia | 61 | 190 | 16.25:1 | 2019 |
| 432 Park Avenue | New York, NY | 85 | 426 | 15:1 | 2015 |
| One Madison Park | New York, NY | 50 | 188 | 12:1 | 2016 |
| Sky House | New York, NY | 55 | 179 | Between 12:1 and 20:1[3] | 2008 |
| Icon | New York, NY | 42 | 158 | Between 15:1 and 18:1[4] | 2009 |
References
[edit]- ^ Willis, Carol. "The Skyscraper Museum: SKY HIGH & the logic of luxury WALKTHROUGH". Retrieved 2016-01-24.
- ^ Wainwright, Oliver (5 February 2019). "Super-tall, super-skinny, super-expensive: the 'pencil towers' of New York's super-rich". The Guardian. Retrieved 1 December 2020.
- ^ "Sky House". CTBUH Skyscraper Center.
- ^ "Icon". CTBUH Skyscraper Center.