If a curve is designated as a $4^{o}$ curve on a 30 m arc. The mid ordinate of the curve will be _________ if the deflection angle is $36^{o}$

17.18 m

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21.03 m

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22.11 m

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139.62 m

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Solution

The correct option is B 21.03 m

$Mid ordinate, M_{c} = R - O M$

$Radius of the curve, R = \frac{30 \times 180}{4 π} = 429.718 m$

$Mid ordinate, M_{c} = R - R c o s \frac{Δ}{2}$

$= R (1 - c o s \frac{Δ}{2})$
$= 429.718 (1 - c o s \frac{36}{2}) = 21.03 m$

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If a curve is designated as a 4o curve on a 30 m arc. The mid ordinate of the curve will be _________ if the deflection angle is 36o

The correct option is B 21.03 m Mid ordinate, Mc=R−OM Radius of the curve, R=30×1804π=429.718m Mid ordinate, Mc=R−RcosΔ2 =R(1−cosΔ2) =429.718(1−cos362)=21.03m

If a curve is designated as a $4^{o}$ curve on a 30 m arc. The mid ordinate of the curve will be _________ if the deflection angle is $36^{o}$

The correct option is B 21.03 m

$Mid ordinate, M_{c} = R - O M$

$Radius of the curve, R = \frac{30 \times 180}{4 π} = 429.718 m$

$Mid ordinate, M_{c} = R - R c o s \frac{Δ}{2}$

$= R (1 - c o s \frac{Δ}{2})$
$= 429.718 (1 - c o s \frac{36}{2}) = 21.03 m$