# thin shell structures

A structural membrane or thin shell structures is a curved surface structure. Usually, it is capable of transmitting loads in more than two directions to supports. It is highly efﬁcient structurally when it is so shaped, proportioned, and supported that it transmits the loads without bending or twisting.
A membrane or a shell is deﬁned by its middle surface, halfway between its extrados, or outer surface and intrados, or inner surface. Thus, depending on the geometry of the middle surface, it might be a type of dome, barrel arch, cone, or hyperbolic paraboloid. Its thickness is the distance, normal to the middle surface, between extrados and intrados.

Thin-Shell Analysis

A thin shell structures are a shell with a thickness relatively small compared with its other dimensions. But it should not be so thin that deformations would be large compared with the thickness.
The shell should also satisfy the following conditions: Shearing stresses normal to the middle surface are negligible. Points on a normal to the middle surfacebefore it is deformed lie on a straight line after deformation. And this line is normal to the deformed middle surface.
Calculation of the stresses in a thin shell generally is carried out in two major steps, both usually involving the solution of differential equations. In the ﬁrst,bending and torsion are neglected ). In the second step, corrections are made to the previous solution by superimposing the bending and hear stresses that are necessary to satisfy boundary conditions .
Ribbed Shells. For long-span construction, thin shells often are stiffened at intervals by 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. Stress and strain distributions in shells and ribs consequently are complicated by the interaction between shells and ribs. The shells restrain the ribs, and the ribs restrain the shells. Hence, ribbed shells usually are analyzed by approximate methods based on reasonable assumptions.
For example, for a cylindrical shell with circumferential ribs, the ribs act like arches. For an approximate analysis, the ribbed shell therefore may be assumed to be composed of a set of arched ribs with the thin shell between the ribs acting in the circumferential direction as ﬂanges of the arches. In the longitudinal direction, it may be assumed that the shell transfers load to the ribs in ﬂexure. Designers may adjust the results of a computation based on such assumptions to correct for a variety of conditions, such as the effects of free edges of the shell, long distances between ribs, relative ﬂexibility of ribsand shell,and character istics of the structural materials.

References:

• BUILDING DESIGN AND CONSTRUCTION HANDBOOK for Frederick S. Merritt & Jonathan T. Ricketts

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