Formwork for Concrete Structures by R.L.Peurifoy and G.D- By EasyEngineering.net

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CHAPTER 13
Forms for
Thin-Shell
Roof Slabs
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Introduction
Thin-shell slabs of cylindrical or barrel shapes, with the axes perpendicular
to the spans, are frequently used as roofs for structures. For
slabs of this kind, the form designer has at least two problems:
1. He or she must determine the elevations of sufficient points
along an arc on top of the decking to ensure that the decking
will be constructed to the required shape and elevation.
2. He or she must design the members that support the decking,
commonly referred to as centering.
The plans furnished by the architect or engineer specify the span, the
rise at the center, and the thickness of the concrete shell. This information
is required by the designer to determine the geometry of the formwork.
Geometry of a Circle
Because a vertical section through a cylindrical shell is an arc of a circle, the
elevation of points along the surface under the shell can be obtained by
using the equations that define the geometry of a circle. Figure 13-1 illustrates
an arc of a circle, which corresponds to the underside of a thin-shell
roof. Although several methods can be used to obtain the desired information,
the method developed in this chapter uses the basic algebraic and
trigonometric equations to determine the geometry of circular slabs.
Let R = radius of circle
L = span of roof
H = height of rise at center of span
l= one-half the span of the roof
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