Stresses and Deformations in Umbrella Shells

by Jehangir F. Mirza,


Serial Information: Journal of the Structural Division, 1967, Vol. 93, Issue 2, Pg. 271-286


Document Type: Journal Paper

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Abstract: Governing equations in the form of two, coupled, fourth-order partial differential equations are obtained from shallow shell theory. The equations are specialized for the hyperbolic paraboloid shell known as the umbrella and solved by the method of finite differences. Results are presented in chart form and compare deformations, bending moments, and normal forces in three umbrella shells, with respective functions in an equivalent flat plate. They indicate that (1) the umbrella shell deflects seven to eight times less than an equivalent flat plate, (2) small magnitude bending moments are present, and (3) middle surface forces are approximately 20% higher than the predictions of the membrane theory.

Subject Headings: Deformation (mechanics) | Bending (structural) | Moment (mechanics) | Plates | Coupling | Differential equations | Paraboloid | Displacement (mechanics)

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