Johnson's parabolic formula

In structural engineering, Johnson's parabolic formula is an empirically based equation for calculating the critical buckling stress of a column. The formula was developed by John Butler Johnson in 1893 as an alternative to Euler's critical load formula under low slenderness ratio (the ratio of radius of gyration to effective length) conditions. The equation interpolates between the yield stress of the material to the critical buckling stress given by Euler's formula relating the slenderness ratio to the stress required to buckle a column.

Buckling refers to a mode of failure in which the structure loses stability. It is caused by a lack of structural stiffness. Placing a load on a long slender bar may cause a buckling failure before the specimen can fail by compression.

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