Circular Curves MCQ with answer and solution

Concept

Linear methods like offsets from tangents suit short curves, where both the deflection angle and the radius are small.

Formula

Perpendicular offset O_x = R - √(R² - x²) ≈ x²/(2R); Tangent length T = R tan(Δ/2)

Step-by-step solution

1. Offsets from tangents is a linear method. It uses only a chain or tape, with no theodolite. 2. Tangent length T = R tan(Δ/2). If both Δ and R are small, T and the curve length are short. 3. On a short curve, offsets are measured over short distances, so the work is easy and accurate. 4. If Δ is large or the curve is long, the offsets and distances become long and errors build up. 5. So the method fits when both the deflection angle and the radius are small. Answer: B.

Explanation

Offsets from tangents is a simple tape method. It is used for short curves. A curve is short when both the deflection angle and the radius are small, so option B is the standard textbook answer.

Why the other options are wrong

A: a large radius gives a long curve, where linear methods are less suitable. C: a large angle and a large radius give a very long curve, which needs the theodolite (Rankine) method. D: a large deflection angle gives a long curve and very big offsets.

Shortcut

Linear methods (offsets from tangents or long chord) = short curve = small Δ and small R.

Common mistake

Choosing A by thinking that a large R gives small offsets, while forgetting that a large R makes the curve long.