The columns are rigid and relatively slender structural members designed primarily to support axial compressive loads applied at the ends of the members. The relatively short and thick columns are subject to failure by crushing rather than buckling. Failure occurs when the direct stress from an axial load exceeds the compressive strength of the material available in the cross section. However, an eccentric load can produce bending and leads to an unequal stress distribution in the section.
The central core is the main area of any horizontal section of a column or wall in which the resultant of all compression loads must be located if only compression efforts are to be present in the section. A compression load applied outside this area will
Long slender columns are subject to buckling failure rather than crushing. Buckling is the sudden lateral or torsional instability of a slender structural member induced by the action of an axial load before reaching the yield stress of the material. Under a buckling load, a column begins to deform laterally and cannot generate the internal forces necessary to restore its initial linear condition. Any additional load would cause the column to deform further until the collapse occurs. The greater the slenderness ratio of a column, the less critical the stress that causes its buckling. A primary objective in the design of a column is to reduce its slenderness ratio by shortening its effective length or maximizing the turning radius of the cross section.
The slenderness ratio of a column is the quotient of its effective length (L) between the smallest tilt radius (r). Therefore, in asymmetric column sections, buckling will tend to occur around the weaker axis or in the direction of the minimum dimension.
The effective length is the distance between the inflection points of a column subject to buckling. When this part of the column is buckled, the entire column fails.
The effective length factor (k) is a coefficient to modify the true length of a column according to the conditions of its ends and thus determine its effective length. For example, fixing both ends of a long column reduces its effective length by half and increases its load capacity by a factor of 4.
The tipping radius (r) is the distance from an axis for which it can be assumed that the mass of a body is concentrated. For the section of a column, the tipping radius is equal to the square root of the ratio of the moment of inertia between the areas.