Destabilizing effect of additional restraint on elastic bar structures

Abstract This paper revises the well-known theorem; “The addition of restraint to a structure cannot decrease its elastic critical load”. It is pointed out by theoretical arguments and simple examples that this theorem is valid only if the displacement components in the buckling direction are additionally restrained. But additional restraints on pre-buckling displacements, which are orthogonal to the direction of buckling, can decrease the elastic critical load factor of the structure. In the case of additional restraints on prebuckling displacements, by the Dunkerley theorem, a bracketing formula is presented which gives lower and upper bounds to the minimum positive critical load factor of the modified structure with the help of minimum positive critical load factors of different loading patterns on the original structure.