Form Finding and Principal Curvature Analysis of Double Ruled Surface with Non-Coplanar Quadrangle As Boundary
Curved surface structures with non-coplanar quadrangle boundary have been widely used in building structures because of their beautiful shape and clear force transmission path.The main structure of the roof of the New City Stadium in Luliang is steel structure,and more than 800 square units with a plane projection side length of 4352mm are formed between the bidirectional ribbed steel beams on the roof,each unit is a precast concrete shell with non-coplanar quadrilateral boundary.Combining with the design,fabrication and installation of the concrete shell of the roof unit of the new City Stadium in Luliang,the paper studies the form finding and surface curvature of the curved surface with the boundary of non-coplanar quadrangle.The parameters-1 ≤ u ≤ 1 and-1 ≤ v ≤ 1 are taken as local coordinates,line connected the equal proportion points of opposite sides is taken as generatrix,the curved surface equations of two families of straight generatrices are established.According to the relation between global coordinates and local parameters,the quadratic coefficients of the first and second basic forms of hyperboloids are obtained by differential geometry theory,and the formulas of principal curvature and its direction are derived.Through the form finding.calculation of the precast concrete roof slab of Luliang Stadium,not only the correctness of the form finding method and the calculation formula of curvature,but also the independence of the form finding method and the principal curvature and the selection of coordinates are verified.The paper can provide theoretical basis for architectural space design,curved surface roof structure design and construction.
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