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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. In structural engineering , slenderness is used to calculate the propensity of a column to buckle .
Fig. 1: Critical stress vs slenderness ratio for steel, for E = 200 GPa, yield strength = 240 MPa. Euler's critical load or Euler's buckling load is the compressive load at which a slender column will suddenly bend or buckle. It is given by the formula: [1] = where
A short steel column is one whose slenderness ratio does not exceed 50; an intermediate length steel column has a slenderness ratio ranging from about 50 to 200, and its behavior is dominated by the strength limit of the material, while a long steel column may be assumed to have a slenderness ratio greater than 200 and its behavior is dominated ...
The slenderness ratio is an indicator of the specimen's resistance to bending and buckling, due to its length and cross section. If the slenderness ratio is less than the critical slenderness ratio, the column is considered to be a short column. In these cases, the Johnson parabola is more applicable than the Euler formula. [5]
The slenderness ratio of a wall is defined as a function of the effective height divided by either the effective thickness or the radius of the gyration of the wall section. It is highly related to the slenderness limit that is the cut-off between elements being classed "slender" or "stocky".
As detailed in the article on buckling, the slenderness of a compression member, which is defined as the ratio of its effective length to its radius of gyration (= /), has a critical role in determining its strength and behavior with axial loading: [2]
432 Park Avenue (middle), a pencil tower in New York City. A pencil tower (also known as a skinny skyscraper, [1] pencil-thin tower, super-slender tower, or super-slim tower) is a high-rise building or skyscraper with a very high slenderness ratio, meaning it is very tall while being very thin.
For thin beams (beam length to thickness ratios of the order 20 or more) these effects are of minor importance. For thick beams, however, these effects can be significant. More advanced beam theories such as the Timoshenko beam theory (developed by the Russian-born scientist Stephen Timoshenko ) have been developed to account for these effects.