Loads Borne on Elastic Supports

Abstract

There are many instances in engineering practice of loads carried upon a number of supports which possess some degree of elasticity and where, owing to the number of the supports, the proportion of the load carried by each cannot be determined by the principles of statics alone but depends in a large measure on the elastic properties of the supports. Problems of this indeterminate type are of common occurrence in the theory of structures and the present paper describes an exact method specially suitable for application to such problems as occur in connexion with the wheel loading of railway rolling stock and locomotives, motor vehicles, etc., and in particular is directed to the question of the adjustment of the springs necessary to produce a desired distribution of the loads upon them. It is shown in this latter case that if the initial loading on the springs, i.e. before adjustment is known by direct measurement, the equations which give the amounts of the adjustments to be made in terms of the desired increments of load take a conveniently simple form, and the adjustments can be calculated and made once for all without any necessity for trial and error methods. A few simple examples are worked out in the paper and an Appendix contains a short account of an extension of Castigliano's second theorem from which the equations in the paper may be derived, and an example showing the application of the method to the adjustment of the wheel loading of a locomotive.