ABSTRACT
The calculation of displacements in elastic structures by the method of virtual work represents probably the most general approach to the problem. All the equations developed in this chapter can be applied with a slight modification to a beam on an elastic foundation, that is, to a beam which, in addition to the forces already mentioned, receives transverse reaction forces proportional at every point to the deflection of the beam. Several methods can be used to find the deflection due to bending of beams. The moment–area or the elastic-weight methods can be used when the variation of the bending moment along the beam is known. Both these methods are based upon relations between the area under the bending moment diagram and deflection. In the method of elastic weights, the calculation of angular rotation and deflection is similar to the routine calculation of shear and bending moment, except that the applied load and support conditions of the beam are generally altered.
