Jessica Mandrick E90 Project Proposal Swarthmore College Department of Engineering
Thin Shell Concrete Structure Design and Construction
The ACI code defines a thin shell as a: “Three-dimensional spatial structure made
up of one or more curved slabs or folded plates whose thicknesses are small compared to their other dimensions. Thin shells are characterized by their three-dimensional loadcarrying behavior, which is determined by the geometry of their forms, by the manner in which they are supported, and by the nature of the applied load.” Concrete shell structures are able to span large distances with a minimal amount of material. An arch, spanning tens of feet, can be mere inches thick. In maintaining this economy of material, these forms have a light, aesthetic, sculptural appeal. I am planning on designing and constructing a thin shell concrete structure for my senior design project. The structure constructed would be at a maximum size, ten feet by ten feet, which may be scaled down if necessary during the design phase. I will be working on this project with Rebecca Burrow who is assisting as part of a directed reading arranged through Professor Siddiqui. Rebecca is currently abroad. Thin shell concrete structures are pure compression structures formed from inverse catenary shapes. Catenary shapes are those taken by string or fabric when allowed to hang freely under their own weight. As string can bear no compression, the free hanging form is in pure tension. The inverse of this form is a pure compression structure. Pure compression is ideal for concrete as concrete has high compressive strength and very low tensile strength. These shapes maximize the effectiveness of concrete, allowing it to form thin light spans.
Structural Design and Analysis of Thin Shell Structures A structural design of the thin-shelled concrete structure will be computed using
catenary and geometrical shape equations. The design will be anticlastic meaning that its main curvatures run in opposite directions, like the hyperbolic saddle. It may be formed out of a combination of two intersecting hyperbolic paraboloids, forming a hyperbolic groined vault (Figure 1) or a similar complex shape. The hyperbolic paraboloid (Figure 2
2) could be formed as a curved surface or from straight boards, and is the only warped surface whose stresses can be calculated using elementary mathematics (Faber 1963). The analysis becomes more complicated when multiple shapes are combined and the resulting equations will need to be derived or computed via numerical analysis. The resulting shape will be modeled by ANSYS software. A variety of forms and dimensions will be modeled until both aesthetics and strength of shape are maximized. AutoCAD software will be used to produce engineering drawings of the final design.
Figure 1: La Concha Motel Lobby Las Vegas (Save La Concha)
Figure 2: Diagram of a Hyperbolic Paraboloid (Billington 1982)
y2 x2 − z= h2 h1 w h ere a2 h1 = c1 b2 h2 = c2
Equation One Surface of a Hyperbolic Paraboloid
The shell will be subject to analysis of stress and deflection using ANSYS finite element software. This software will reveal critical areas and may lead to modifications in the design if the strength of the concrete shell is surpassed at any point. The structure will most likely be modeled using plates. A sufficient number of plates will be chosen such that the curvature of the shell is approximated. In “An Introduction to Shell Structures”, Michele Melaragno presents a chapter on computer analysis of shells and domes. For a 360 degree circular domes structure she breaks the shell into 36 radial lines each with 11 circumferential divisions. These divisions may be used to approximate the number of plates needed to model the hyperbolic paraboloid. Melaragno also suggests that thin shell structures could be modeled using tension and compression members in a...
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