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Fundamentals of Stress and Vibration 1. Mathematics for Structural mechanics
[A Practical guide for aspiring Designers / Analysts]

dθ dy 2
Further simplifying, we get: R = 1 + - - - - (1.7)
dx dx

2
dy d y dθ
2
We know that = tanθ , differentiating again we get: = sec θ - - - - (1.8)
dx dx 2 dx
dy 2
2
2
We also know that, sec θ = 1 + tan θ = 1 +
dx
2
d y dy 2 dθ
Therefore, equation . could be rewritten as: = 1 + - - - - (1.9)
dx 2 dx dx

1 2
2 2
2
d y 2 1 + dy ∗ 1 + dy
dx 2 dy dx dx
R 2 = 1 + dx = R = d y
2

1 + dy 2
dx dx

3
dy 2 2
1 + dx
Simplifying the above expression, we get: R = - - - - (1.10)
2
d y
dx 2

1
Expression . is that of radius of curvature R and curvature is given by .
R

2
d y
is positive for a concave curve and negative for a convex curve.
dx 2

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3
dy 2 2
1 + dx
Radius of Curvature R = - - - - (1.11)
2
d y
dx 2

“—ƒ–‹‘ ȋͳǤ͹Ȍ ƒ ‘™ „‡ ”‡™”‹––‡ ƒ•ǣ

QP No. SSC/Q4401, Version 1.0, NSQF Level 7, Compliant with Aero and Auto Industries, Page 13