Abstract: The bending problems of nonuniform beams with variable cross-section can be approximated by that of a step beam under sectionally uniform load (including both concentrated forces and couples). In this paper, the concept of Heaviside function {x-a}⁰ will be generalized, and a new function {x-a}⁰, n=0,1,2…,will be defined, which may be named as a generalized step function. The rules of operation will also be given to {x-a}ⁿ{x-b}⁰. The reciprocal of the flexural of rigidity 1/EJ and the bending moment M(x) can all be expressed in terms of {x-a}ⁿ,and substituted into the differential equation of the elastic curve of the beam respectively. Thus we may establish a set of unified method to solve various types of bending problems of straight beams. The general solution of the deflection equation will be given.

Key words: reliability growth, Duane model, AMSAA model, AMSAA-BISE model