Derive the relation between slope deflection and radius of curvature
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A small portion PQ of the beam, bent into an arc is considered .
Let ds be the elemental length PQ of the beam
R be the radius of the arc
C be the centre of the arc (into which the beam has been bent)
ψ be the angle which the tangent at P makes with x − x axis and
(ψ + dψ) be the angle which the tangent at Q makes with x − x axis
From the geometry of Figure 8.3,
∠PCQ = dψ and
ds = R. dψ
Let ds be the elemental length PQ of the beam
R be the radius of the arc
C be the centre of the arc (into which the beam has been bent)
ψ be the angle which the tangent at P makes with x − x axis and
(ψ + dψ) be the angle which the tangent at Q makes with x − x axis
From the geometry of Figure 8.3,
∠PCQ = dψ and
ds = R. dψ
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