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.
Tall buildings with high slenderness ratio are sometimes referred to as pencil towers.
Examples
BuildingLocationFloorsHeight (m)SlendernessYear111 West 57th StreetNew York, NY8243824:12018HighcliffHappy Valley, Hong Kong7325220:12003150 North RiversideChicago, Illinois5422820:1 at base2017220 Central Park SouthNew York, NY7029018:12019Collins House (Melbourne)Melbourne, Australia6119016.25:12019432 Park AvenueNew York, NY8542615:12015One Madison ParkNew York, NY5018812:12016Sky HouseNew York, NY55179Between 12:1 and 20:12008IconNew York, NY42158Between 15:1 and 18:12009
References
External links The Super Slender Revolution