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

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Forms for Thin-Shell Roof Slabs 383
It is necessary to calculate the slope of the tangent to the circle at
point C in order to determine whether forms are needed on top of the
concrete slab for a portion of the shell.
sin a = l/R
= (30 ft)/(50 ft)
= 0.60
Using the arcsin function on a handheld calculator, the angle a
can be determined as follows:
arcsin a = 0.60
a = 36 ° 52′
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Locating Points on a Circle
Let the curve ABC in Figure 13-1 represent the underside of a shell
roof and thus the top of the decking. Assume that the elevations of
points A, B, and C are given. It is necessary to determine the elevations
of points along the curve ABC, which may be done by determining
the distances down from the x axis. Let P be a point on the
curve a distance x from the y axis and a distance y below the x axis.
The equation for a circle whose center is at the origin of the x axis
and the y axis is
x 2 + y 2 = R 2
(d)
where x and y are the distances from the y axis and the x axis, respectively,
to any given point on the circle. Where the circle passes through
the origin of the x axis and the y axis, with the center on the y axis and a
distance R below the origin, the equation for the circle will be:
x 2 + z 2 = R 2 where z = R – y
(e)
Substituting this value for z in Eq. (e) gives:
x 2 + (R – y) 2 = R 2
(R – y) 2 = R 2 – x 2
2 2
R= y = + / − R −x
2 2
y = R− R −x
(13-3)
This equation can be used to determine the distance down from
point B of Figure 13-1 to any point P on the curve. Assume that it is
desired to determine the distances down from a horizontal line
through B to each of 10 points, equally spaced horizontally along the
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