Stress and strain distributions in shells and ribs consequently are complicated by the interaction between shells and ribs. Usually, the construction is such that the shells transmit some of the load imposed on them to the ribs, which then perform structurally as more than just stiffeners. For long-span construction, thin shells often are stiffened at intervals by ribs. In the second step, corrections are made to the previous solution by superimposing the bending and shear stresses that are necessary to satisfy boundary conditions (bending theory, Art. In the first, bending and torsion are neglected (membrane theory, Art.
And this line is normal to the deformed middle surface.Ĭalculation of the stresses in a thin shell generally is carried out in two major steps, both usually involving the solution of differential equations. Points on a normal to the middle surface before it is deformed lie on a straight line after deformation. The shell should also satisfy the following conditions: Shearing stresses normal to the middle surface are negligible. But it should not be so thin that deformations would be large compared with the thickness. Thin-Shell AnalysisĪ thin shell is a shell with a thickness relatively small compared with its other dimensions. Its thickness is the distance, normal to the middle surface, between extrados and intrados. Thus, depending on the geometry of the middle surface, it might be a type of dome, barrel arch, cone, or hyperbolic paraboloid. It is highly efficient structurally when it is so shaped, proportioned, and supported that it transmits the loads without bending or twisting.Ī membrane or a shell is defined by its middle surface, halfway between its extrados, or outer surface and intrados, or inner surface. Usually, it is capable of transmitting loads in more than two directions to supports.
A structural membrane or shell is a curved surface structure.
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