A Buckling Problem: The Case of an Elastically Supported Beam

LET us consider a continuous beam with an even number of spans. The spans are each of length l, a constant cross‐section of area A with a constant moment of inertia I about the axis of buckling and are subjected to the compressive force P. The elastic stiffnesses of all intermediate supports are equal and the elastic stiffnesses of the two end supports are also equal but generally different from those of the other supports. We set out to determine the buckling condition for the beam and the relationship between the critical load and the elastic stiffness of the supports. E is Young's Modulus of the material of the beam or the momentary modulus corresponding to the stress at the buckling load.