User:Wigwamscarlos/Slenderness ratio

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In architecture, the slenderness ratio, or simply slenderness, is an aspect ratio, the quotient between the height and the width of a building. 150 North Riverside in Chicago, the most top heaviest skyscraper with a taper at the bottom vs setbacks. 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.

Supertall buildings are often constructed with a slenderness ratio of between 7:1 and 8.6:1, while megatall buildings are often constructed with a slenderness ratio of between 10:1 and 15:1.

Tall buildings with high slenderness ratio are sometime referred to as pencil towers.