Analysis of bending curve and critical load of a variable cross-section beam by means of influence function method

In this paper the method of influence function is applied to solving of the problem of deflection curve and critical load finding in a variable cross-section beam. The function describing the deflection curve of an elastic supported beam with variable flexular rigidity is obtained in terms of the Cauchy function in a power series form. A general form of a characteristic equation is obtained which made it possible to calculate the estimators of critical Euler load. Some examples of different beams being used frequently in practice are given in details. The results are compared with the well-known theoretical results and show a good agreement.