Find the value of offsets from long chord at 10 m distance, fo... | Civil MCQ | Examoogle

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Find the value of offsets from long chord at 10 m distance, for a curve having radius 200 m and mid ordinate 15m.

14.749 m

15.749 m

12.749 m

16.749 m

Correct Answer

⚙️ TE • Technical Concept & PrincipleCivilAdvanced Survey

Option A

14.749 m

Quick Summary:

The offset from the long chord at any distance $x$ from the mid-point for a circular curve can be calculated using the exact standard relation $O_x = \sqrt{R^2 - x^2} - (R - O_0)$ , where $R$ is the radius, $O_0$ is the mid-ordinate, and $x$ is the distance from the midpoint.

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⚙️TETechnical SolutionConcept & Principle

💡 Explanation

🔢 Key Formulas

$O_x = \sqrt{R^2 - x^2} - (R - O_0)$ — Exact offset from long chord at distance $x$

$O_x \approx O_0 - \frac{x^2}{2R}$ — Approximate offset formula when $R$ is very large compared to $L$

⚙️ Working Principle

In a circular curve, offsets are vertical ordinates drawn from the long chord to the curve. By setting up a right-angled triangle from the center of the curve to a point at horizontal distance $x$ from the midpoint, the ordinate at distance $x$ is derived geometrically by subtracting the distance from the long chord to the center from the radial distance to the curve at $x$ .

📌 Key Points

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Given values: $R = 200\text{ m}$ , $O_0 = 15\text{ m}$ , and $x = 10\text{ m}$ .
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Substitute into formula: $O_{10} = \sqrt{200^2 - 10^2} - (200 - 15) = \sqrt{40000 - 100} - 185 = \sqrt{39900} - 185$ .
▸
Calculation: $\sqrt{39900} \approx 199.7498\text{ m}$ .
▸
Hence, $O_{10} = 199.7498 - 185 = 14.7498\text{ m} \approx 14.749\text{ m}$ .

✅ Advantages

▸
Simple method for setting out simple circular curves of short lengths.
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Does not require angular instruments like theodolites; can be done with a chain/tape.

❌ Disadvantages / Limitations

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Not suitable for long curves or large radii due to cumulative measurement errors.
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Errors increase near the ends of the chord.

🛠️ Applications / Uses

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Setting out simple circular curves in field surveying for roads and railways.
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Laying out small radius curves using basic linear measurements.

📄 Additional Information

▸
Option A (14.749 m) is the exact calculated offset.
▸
Option B (15.749 m), Option C (12.749 m), and Option D (16.749 m) represent incorrect mathematical evaluations.

📊 Diagram / Illustration

✅

A is correct — Using $O_x = \sqrt{R^2 - x^2} - (R - O_0)$ , substituting $R=200$ , $O_0=15$ , and $x=10$ gives $14.749\text{ m}$ .

Core Concepts Used

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Long Chord Mid-Ordinate Offsets from Long Chord

💡 EXAM TIP

Remember that if the question asks for an approximate value or if $R \gg x$ , you can use $O_x \approx O_0 - \frac{x^2}{2R} = 15 - \frac{100}{400} = 14.75\text{ m}$ , which yields a nearly identical answer very quickly in exams!

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