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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
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]
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 .
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 Perry–Robertson formula is a mathematical formula which is able to produce a good approximation of buckling loads in long slender columns or struts, and is the basis for the buckling formulation adopted in EN 1993. The formula in question can be expressed in the following form:
Accounting for the additional stiffness of the steel, the nominal loading capacity P n for the column in terms of the maximum compressive stress of the concrete f c ', the yield stress of the steel f y, the gross cross section area of the column A g, and the total cross section area of the steel rebar A st
If the ratio of the length to the effective radius of the material loaded in compression (Slenderness ratio) is too high, it is likely that the material will fail under buckling. Otherwise, if the material is ductile yielding usually occurs which displaying the barreling effect discussed above.
Columns at the Airavatesvara Temple, India A compression member is a structural element that primarily resists forces, which act to shorten or compress the member along its length. Commonly found in engineering and architectural structures, such as columns , struts , and braces, compression members are designed to withstand loads that push or ...