Column end fixity and effective length
The restraint at the ends of a column has a significant influence on the effective length and therefore the buckling strength.
Because of the significance of the effective length, the way a column buckles under load will depend on how the column is constructed. If one end of a slender column is fixed at its base and the other end is totally free of any restraint, the column will be extremely prone to lateral buckling under load. In contrast, a column which is fixed at both ends will be much more stable.
End conditions can be idealised as free, pinned or fixed.
Idealised end conditions for a column are described as free, pinned or fixed. Each of these conditions is described below.
Pinned ends allow free rotation.
When a column end is connected in such a way that the joint allows the column to rotate freely but restrains it from translation (horizontal movement), the connection could be described as being pinned. Such a joint could be produced in practice in several ways. For example the figure below shows a typical arrangement where the column is free to rotate in the xx direction, but it is secured in position at point A.
Fixed ends do not allow any rotation.
A fixed end does not allow the column end to move in any manner, ie. to translate or to rotate. Such a joint could be bolted or welded.
Free ends allow both lateral movement and rotation.
Such a condition can apply to only one end of a column and the other end must be fixed to ensure stability of the column. A free end is totally unrestrained and both translation and rotation may take place.
The end conditions influence the shape of the buckled form; the effective length corresponds to that part of the column which deforms as a single curve in the shape of a pin ended buckle.
The type of end condition will dictate how much restraint to lateral buckling is offered to the column. The pin ended column can buckle more freely than a fixed ended column and is therefore less strong.
The effective length describes the part of the column which is free to buckle laterally. For pinned ends, the effective length LE and the actual length L are the same. For partial or nominally full rotational end restraint, the effective length LE = 0.85 L and 0.7 L respectively. These figures are established by laboratory experiment. For a cantilever column the effective length can be deduced by comparing with a column which has both the ends pinned. When the deflection configuration is completed, it becomes clear that the effective length LE is 2L.Table 24 of BS 5950 lists a number of end conditions for columns and the related factors for the effective lengths.
