الفهرس 
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Abstract
The analysis of beams on elastic foundation is well established in literature.Hetenyi extensively developed the clasical differential equation approach. Miranda and nair adopted the method of initial parameter to express the solution of the differential equation of the beam column on elastic foundation, in terms of four special functions that are associated with deflection, slope, moment and shear, respectively. These special functions prossess an intersting property. The derivates of the functions can be related back to the original functions, leading to substantial simpification in the solution of the boundary value problem.
Bowles formulates a stiffness matrix combining a conventional beam element with discrete soil springs at the ends of the beam. Te degree of accuracy using the element is highly dependent on the number of element models.
In this thesis, it is aimed to find the design moments for te laterally loaded beam column on elastic foundation, and also to find the buckling loads (or Eigenvalues) for the unloaded vibrating beam on elasti foundation. The first chapter comprises a review of the previous work especially that of Timoshenko, Fertis, Ting, Mockry, West Mafi. The second chapter deals with the elastics of elastic beams on elastic foundation. The study is limited to two hinged beams carring uniformly distributed load and also simple beams carring the same load. Chapter three deals with the free undamped vibration of elastic beam column on elastic foundation. The study comprises simple and continuous beams. In the fourth chapter, a new method is suggested. The research is divided into two parts, the first part is the determinated of the bending moments for simple and contiouous beam columns on elastic foundation, carrying lateral loads.The second part is the determination of the critical axial loads (taking stability into consideration) for the simple and continuous vibrating beams on elastic foundation. Acheck for each of the two parts is presented.Application is given in the fifth chapter. Acheck example for the case of acontinuous beam carrying lateral load is solved by the new method and the moment distribution method for the sake of comparison. Other examples are given and the results obtained by the new method compared reasonably with those given by other investigators.