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GATE 2017 CE (CE1) – Question 26

Transportation Infrastructure · Geometric design of roadways: cross-section, sight distance, alignments · 1 mark · Multiple choice

Superelevation $e$ is provided on a circular horizontal curve so that a vehicle can stop on the curve without sliding. With design speed $v$ and maximum side-friction coefficient $f_{max}$, what must hold?

  1. $e\leq f_{max}$
  2. $e>f_{max}$
  3. No limit can be set on e.
  4. $e=\frac{1-f_{max}^2}{f_{max}}$

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Correct answer: (A) $e\leq f_{max}$

Explanation

For a stationary vehicle on the bank, the downslope gravity component is $mg\sin\theta$. Available friction is at most $f_{max}mg\cos\theta$. Avoiding sliding requires $\tan\theta\leq f_{max}$. Since road superelevation is $e=\tan\theta$, the criterion is $e\leq f_{max}$, A; the stationary check does not depend on design speed.

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