Reinforced Concrete Hyperbolic Paraboloid Shells

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Abstract
An experimental study is presented of the behavior of reinforced concrete inverted umbrella hypar shell models loaded with uniform load to failure. Reinforced microconcrete model shells with three different edge member geometries were tested. The shell strength was controlled by the tensile edge members around the periphery of the shell, and was independent of position of edge members with respect to shell midthickness. Ultimate load capacity was about l50 psf (7,l80 N/m2). Shells without compressive ribs had the same strength and only slightly more flexibility than similar shells with compressive ribs. The edge members and a substantial portion of adjacent shell act together in resisting the accumulated membrane shears from the shell. This interaction is defined with an effective width concept based on PVC model results. Direct stresses in the shell differ substantially from membrane theory predictions; the tensile principal stress exceeds the compressive principal stress in all cases. The ratio of bending stress to direct stress is on the order of 1 in the edge members and considerably higher in the shell.

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