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111 West 57th Street in Midtown Manhattan is the world's most slender skyscraper. 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.
Eulers formula for buckling of a slender column gives the critical stress level to cause buckling but doesn't consider material failure modes such as yield which has been shown to lower the critical buckling stress. Johnson's formula interpolates between the yield stress of the column material and the critical stress given by Euler's formula.
A reinforced concrete column is a structural member designed to carry compressive loads, composed of concrete with an embedded steel frame to provide reinforcement. For design purposes, the columns are separated into two categories: short columns and slender columns.
If the ratio is greater than 10, it is considered a long column (sometimes referred to as a slender column). Timber columns may be classified as short columns if the ratio of the length to least dimension of the cross section is equal to or less than 10. The dividing line between intermediate and long timber columns cannot be readily evaluated.
Thus in the temple of Apollo Branchidae, where the columns are slender and over 10 diameters in height, the intercolumniation is 1 3 / 4 , notwithstanding its late date, and in the Temple of Apollo Smintheus in Asia Minor, in which the peristyle is pseudodipteral, or double width, the intercolumniation is just over 1 1 / 2 .
The Ionic column is always more slender than the Doric; therefore, it always has a base: [5] Ionic columns are eight and nine column-diameters tall, and even more in the Antebellum colonnades of late American Greek Revival plantation houses. [citation needed] Ionic columns are most often fluted. After a little early experimentation, the number ...
The shaft is wider at the bottom than at the top, because its entasis, beginning a third of the way up, imperceptibly makes the column slightly more slender at the top, although some Doric columns, especially early Greek ones, are visibly "flared", with straight profiles that narrow going up the shaft. The capital rests on the shaft.