Bending of an axially constrained beam

In the elementary theory of bending of beams, the neutral surface is assumed to be inextensible and free relative longitudinal motion of the ends of the beam is permitted. In the present analysis, the bending of a pin-connected beam due to lateral loads is considered under conditions that no such relative end displacements are permitted to occur, thereby giving rise to a stretching of the neutral surface under induced axial constraint forces. The problem then becomes essentially non-linear since the forces of constraint themselves depend on the lateral deflection of the beam. Resulting axial constraint forces, lateral displacements and moments in the beam are determined in terms of a single parameter depending on both the applied load intensity and slenderness of the beam.