A FAST ANALYTICAL SOLUTION FOR MULTI-STORY FRAMES UNDER COMPLICATED LOADS

For multi-story frames under complicated loads, it is unable to obtain an analytical solution by common methods. A continuous subsection independent systematic integral method (CSISIM) is presented for fast determination of analytical solutions of multi-story frames. In CSISIM, a frame is separated into a series of segments firstly. The general mechanical model is established for solutions of frames under complicated loads. A forth-order differential deflection equation of any cross section is derived from the model. Then the general solutions of deflection are obtained independently by forth-fold integration. Integral constants are determined by boundary conditions, force conditions and continuity conditions. The solution procedure is developed with MAPLE language to determine the corresponding analytical solution. It enables analytical solution by computer for multi-story frames under complicated loads. It is not necessary to simplify loads or frames during establishing the model of multi-story frames and its process of derivation. Engineering examples show that CSISIM is suitable for computer programming and it can get systematic analytical solutions. It is not only suitable for statically determinate frames, but also suitable for statically indeterminate ones.