a simplify analytic approach for converting airplane and cantilever beams distributed loads to equivalent concentrated loads

The equations for converting distributed load to concentrated load at the arbitrary acting point with equal resulted deflections are specified. these equations are developed for cantilever simple and tapered beams and the same structural that are under various distributed loads on their different parts longitudinally. the equations are established via analytical process by using the resulted formulations from integration methods for beam bending and the principal of superposition. having obtained enough confidence in the accuracy and validity of the derived equations, the simple and tapered beams are assigned typically. the beams are divided to different parts with applied arbitrary and various distributed loads on each part. the equivalent point loads are calculated for all sections through the suggested equations. the finite element models of the beams are prepared. by applying the distributed and obtained equivalent concentrated loads of each part at the assigned places, the deflections are determined for both loading conditions through the numerical solutions, separately. finally, the resulted deflections from distributed and equivalent concentrated loading are compared and developed equations are validated.