Hyperbolic Paraboloid Structures on Four Supports

by Roy R. Russell,
Kurt H. Gerstle,

Serial Information: Journal of the Structural Division, 1968, Vol. 94, Issue 4, Pg. 995-1010

Document Type: Journal Paper


It is generally recognized that actual loading and construction details of hyperbolic paraboloid structures are far from ideal, and therefore incompatible with the membrane state of stress, leading to bending and twisting of shells and edge members. The magnitude of deformations and internal forces in the edge members of square hyperbolic paraboloid structures supported on four corners is discussed. The governing equations of the bending theory of shallow hyperbolic paraboloids are used for the shell, the classical relations of technical beam and torsion theory are used for the edge members, and continuity between shell and edge members and external support conditions are accounted for by appropriate boundary conditions. The resulting equations are nondimensionalized in terms of suitable structural parameters, converted to finite difference form, and solved by means of a high-speed computer. Results are plotted in the form of dimensional design curves suitable for the design of such structures.

Subject Headings: Paraboloid | Bending (structural) | Shell structures | Load factors | Construction management | Membranes | Deformation (mechanics) | Beams

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