The Mathematical Model of the Reinforcement Layout of the Making of Hyperbolic Paraboloid Thin Shell Roofs

Abstract

The key to the making is the arrangement of prestressed reinforceds. According that a hyperbolic paraboloid is a ruled surface and the methods of spatial analytic geometry and vector algebra, obtain the distributed model of prestressed reinforceds in two situations: one is that the reinforceds are imagined as one-dimensional straight lines; the other is the reinforceds prestressed are cylindrical steel pipes whose diameters are needed to be considered. In the second case, by applying the feature that the central axis of the reinforceds have no intersections when they are arranged, establishing the center straight generatrix model based on the coordinate translation, the position of center straight generatrix for each reinforced is solved. Thus, the mathematical model provides a concise reasonable operational guidance for workers’ construction.