A FAST ANALYTICAL SOLUTION FOR STATICALLY INDETERMINATE BEAM OF VARIABLE STIFFNESS UNDER COMPLICATED LOAD

For statically indeterminate beams of variable stiffness under complicated load, a continuous subsection independently systematic integral method (CSISIM) is presented for fast determination of the analytical solutions of deformation. In CSISIM, the beam is first separated into segments series. The general mechanical model is established for variable stiffness beams under complicated 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 forth-fold integration. Integral constants are determined by boundary conditions and continuity conditions. The solution procedure is developed for the corresponding mathematical model. It does not need to simplify loads and beam structure during establishing the model of the continuous curve shaped variable stiffness beam and its process of derivation. This method is used to give the analytic solutions of three engineering examples of statically indeterminate beams including beams of stepped cross sections, beams of inertia moment varied quadratically and beams of inertia moment varied by the fourth power. The results show that the CSISIM is suitable for computer programming. Compared with the finite element method, the advantage of the method is that it can quickly get the analytical solution of bending deformation.