Gabled Hyperbolic Paraboloid Roofs without Edge Beams

Abstract

Finite-element analyses have shown that the membrane theory assumption for the behavior of gabled hyperbolic paraboloids is incorrect. The form of the structure was originally conceived using this erroneous assumption of membrane behavior, which assumes equal compressive and tensile arches, requiring an edge member that carries large axial forces. Finite-element models have shown that the tensile arches do not exist and that the edge member carries much smaller forces than those predicted by the membrane theory. This paper proposes a design based on these observations in which the edge beam is removed from the hypar. Material is added near the support to reduce the high stresses that result due to the removal of the beam material at this corner. The resulting form has no edge beams, and it has a thickened corner region.