The Form-Finding Analysis Research Of Plane Beam String Structure

With the rapid development of Chinese economy and technology, high requirements aredemanded for the long span structure. More longer, lighter, lower cost and more stablestructures are popular among designers. Such as Beam string structure (abbrev. BSS), whosedevelopment is significantly fast as the new kind of representative.BSS belongs to the inner equilibrium system of semi-rigid, its bending resistancemembers and tension members are combined by brace strut. It includes unidirectional BSS,bi-directional BSS and multi-directional BSS, etc. It is crucial to understand the performanceof single BSS. Although BSS is widely applied in the practical engineering, there are stillmany sturcture’s problems haven’t been solved well in the design and calculation aspects ofBSS. Such as, the prestress distribution of initial equilibrium state, the determination of initialgeometry in zero state, the form optimization in loading equilibrium state, etc.This paper’s main work is about the theory of form-finding calculation for single BSS.Firstly, from the angle of the construction process of BSS, the paper introduces the method ofthe prestress’ exerting in cable and some traditional theories of form-finding for single BSS;secondly, it introduces the deducing progress of the beam element’s tangent stiffness matrixand the theory of answering geometric equilibrium equation by Newton-Raphson iteration,that establish the theoretical foundation for form-finding of single BSS; thirdly, the paperuses its own form-finding method of single BSS called tangent stiffness matrix inverseiteration method; finally, according ideas above, develops BSS Form-Finding program,and proves the program is correct and feasible through an example.Tangent stiffness matrix inverse iteration method is a new kind of form-finding methodabout single BSS from the initial state to the zero state. It’s different from the traditionalmethod, because it has a firm theoretical foundation, a simple and rapid calculationprogress. What’s more, the method avoids some disadvantages that appeared in those oldmethods. It’s helpful for researcher who Engaged in the practical engineering of long spanbeam string structure.