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

382 Chapter Thirteen
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FIGURE 13-1 Geometry of a circle.
The plans will give the values of H and L, and possibly R. If the
value of R is not given, it will be necessary to calculate it. Considering
the triangle ODC,
sin a = l/R
cos a = (R-H)/R
sin 2 a + cos 2 a = 1
(a)
(b)
(c)
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Substituting the values of sin a and cos a in Eq. (c) gives:
l 2 /R 2 + (R-H) 2 /R 2 = 1
l 2 + (R-H) 2 = R 2
l 2 + R 2 – 2RH + H 2 = R 2
l 2 – 2RH + H 2 = 0
2RH = l 2 + H 2
R = (l 2 + H 2 )/2H (13-1)
If l is replaced with L/2, Eq. (13-1) gives:
R = L 2 /8H + H/2 (13-2)
Example 13-1
Determine the radius of a curve for which the span is 60 ft and the rise
is 10 ft. Applying Eq. (13-2) gives:
R = L 2 /8H + H/2
= (60 ft) 2 /8(10 ft) + (10 ft)/2
= 45 ft + 5 ft
= 50 ft
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