A FAST ANALYTICAL METHOD FOR THE DEFORMATION OF BEAMS WITH VARYING CROSS-SECTIONS

For beams with varying stiffness and complex loads, the common method is unable to obtain analytic solutions. A continuous subsection independently systematic integral method(CSISIM for short) is presented for fast determination of analytical solutions of the deformation of beams with varying sections. In CSISIM, the beam is first separated into segments. A general mechanical model is established for solution of beams with varying stiffness under complex load. The forth-order differential deflection equation of any cross section is derived from the model. Then the general solutions of beam deflection are obtained independently by four-fold integration. Integral constants are determined from the boundary conditions and continuity conditions. It is not necessary to simplify loading and beam structure when establishing a model of continuous curved variable cross-section beam and processing the derivation. The beam deformation analytical solution procedure is programed directly by using symbolic computation software. It realizes an analytic solution by computer for beams with varying stiffness under complex loads. In this paper, there are three engineering examples-a stepped beam, a uniform depth variable width cross-section beam, and a uniform width variable height cross-section beam. Their analytical solutions are obtained by CSISIM. The engineering examples show that it is simple to establish mathematical models using this method. Calculation programming is systematic. Analytical solution can be quickly obtained.