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CivilAdvanced Survey
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Which of the following methods is used when curve to be designed is short?

A

A) Linear method

B

B) Angular method

C

C) Tangent method

D

D) Curvature method

Correct Answer

тЪЩя╕П TE тАв Technical Concept & PrincipleCivilAdvanced Survey
Option A

Linear method

Quick Summary:

Linear methods (or chain and tape methods) are used for setting out simple circular curves when the length of the curve is short and high precision is not required. These methods rely solely on linear measurements made with a chain or tape, without using angle-measuring instruments like a theodolite.

тЪЩя╕ПTETechnical SolutionConcept & Principle
ЁЯТб Explanation

Linear methods (or chain and tape methods) are used for setting out simple circular curves when the length of the curve is short and high precision is not required. These methods rely solely on linear measurements made with a chain or tape, without using angle-measuring instruments like a theodolite.

ЁЯФв Key Formulas

O0=RтИТR2тИТ(L2)2O_0 = R - \sqrt{R^2 - \left(\frac{L}{2}\right)^2}O0тАЛ=RтИТR2тИТ(2LтАЛ)2тАЛ тАФ Mid-ordinate formula in linear setting out

Ox=R2тИТx2тИТ(RтИТO0)O_x = \sqrt{R^2 - x^2} - (R - O_0)OxтАЛ=R2тИТx2тАЛтИТ(RтИТO0тАЛ) тАФ Offset at distance xxx from the mid-point of the long chord

тЪЩя╕П Working Principle

Linear methods use geometric properties of circles, chords, and tangents to locate points along the curve using chain or tape measurements. Offsets are measured either perpendicular or radial to a tangent or long chord to mark points along the curve.

ЁЯУМ Key Points
  • тЦ╕

    Linear methods are suitable for short curves, sharp curves, and where low accuracy is acceptable.

  • тЦ╕

    Instruments required for linear methods are simple: chain, tape, arrows, and optical square.

  • тЦ╕

    Common linear methods include: Offsets from Long Chord, Successive Bisection of Chords, Offsets from Tangents, and Offsets from Produced Chords.

тЬЕ Advantages
  • тЦ╕

    No angular measuring instruments (like theodolites) are needed.

  • тЦ╕

    Simple to execute in the field with basic surveying equipment.

тЭМ Disadvantages / Limitations
  • тЦ╕

    Errors accumulate over longer distances, limiting use to short curves.

  • тЦ╕

    Low precision compared to angular setting out methods.

ЁЯЫая╕П Applications / Uses
  • тЦ╕

    Setting out sharp circular curves in minor road intersections or street corners.

  • тЦ╕

    Short curves in canal alignments and minor railway tracks.

ЁЯФД Comparison Table
FeatureLinear MethodAngular Method

Equipment Used

Chain, Tape, Arrows, Optical Square

Theodolite, Total Station, Tape

Suitability

Short curves, low precision work

Long curves, high precision work

Cumulative Error

High (increases with curve length)

Low (independently measured angles)

ЁЯУД Additional Information
  • тЦ╕

    Angular methods (such as Rankine's method of deflection angles or Two-Theodolite method) are used when curves are long and require higher accuracy.

  • тЦ╕

    Option B (Angular method) is preferred for long curves with high precision.

  • тЦ╕

    Option C (Tangent method) is a subtype of linear/angular setting out, not a primary classification based on length.

  • тЦ╕

    Option D (Curvature method) is not a standard surveying classification for setting out curves.

ЁЯУК Diagram / Illustration
Linear Method: Offsets from Long ChordTтВБTтВВLong Chord (L)OтВА (Mid-ordinate)Used for short curves where high accuracy is not required
тЬЕ

A is correct тАФ Linear methods use simple chain and tape measurements, making them ideal for setting out short curves where high precision is not mandatory.

Core Concepts Used
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Linear Method of Curve Setting Offsets from Long Chord Rankine's Deflection Angle Method
ЁЯТб EXAM TIP

In competitive exams like GATE and SSC JE, remember: Linear methods = Short curves (Chain/Tape), Angular methods = Long/Precise curves (Rankine's Deflection Angle method using Theodolite).

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