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CivilAdvanced Survey
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In which is following curve used for Different grades are joined together?

A

Circular

B

Transition

C

Vertical

D

Both A and B

Correct Answer

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

Vertical

Quick Summary:

A vertical curve is used to connect two intersecting gradients or grades of a roadway or railway alignment. It provides a smooth and gradual transition between different slopes, ensuring driver safety, comfort, and adequate sight distance. Parabolic curves are most commonly chosen for vertical curves due to their constant rate of change of grade.

тЪЩя╕ПTETechnical SolutionConcept & Principle
ЁЯТб Explanation

A vertical curve is used to connect two intersecting gradients or grades of a roadway or railway alignment. It provides a smooth and gradual transition between different slopes, ensuring driver safety, comfort, and adequate sight distance. Parabolic curves are most commonly chosen for vertical curves due to their constant rate of change of grade.

ЁЯФв Key Formulas

N=g1тИТg2N = g_1 - g_2N=g1тАЛтИТg2тАЛ тАФ deviation angle or algebraic difference in grades

L=N├ЧCL = N \times CL=N├ЧC тАФ length of vertical curve based on rate of change of grade

y=cx2y = cx┬▓y=cx2 тАФ standard equation of a simple parabolic vertical curve

тЪЩя╕П Working Principle

When two different gradients meet, an abrupt angle change would create severe impact loads, poor visibility, and discomfort for passengers. Vertical curves smooth out this transition by providing a continuous, gradual change in slope along the length of the curve.

ЁЯУМ Key Points
  • тЦ╕

    Vertical curves are introduced in the vertical plane at intersections of different gradients.

  • тЦ╕

    They are classified into Summit Curves (Crest) and Valley Curves (Sag).

  • тЦ╕

    Parabolic curves are preferred because the rate of change of grade is uniform throughout the curve.

тЬЕ Advantages
  • тЦ╕

    Provides a smooth, comfortable transition between different grade slopes.

  • тЦ╕

    Ensures required safe stopping sight distance (SSD) and passing sight distance (PSD).

  • тЦ╕

    Minimizes impact forces on vehicle suspension caused by sudden slope changes.

тЭМ Disadvantages / Limitations
  • тЦ╕

    Requires larger earthwork quantities (cutting and filling) during construction.

  • тЦ╕

    Summit curves can restrict sight distance if designed with insufficient length.

ЁЯЫая╕П Applications / Uses
  • тЦ╕

    Joining upgrading and downgrading sections of highways and expressways.

  • тЦ╕

    Rail tracks transition between gradients to prevent excessive coupler stresses.

  • тЦ╕

    Flyover and underpass ramp transitions.

ЁЯФД Comparison Table
FeatureHorizontal Curve (Circular/Transition)Vertical Curve

Alignment Plane

Horizontal plane

Vertical plane

Primary Purpose

Change direction of alignment

Join different gradients smoothy

Ideal Shape

Circular arc with spiral transitions

Parabolic curve

ЁЯУД Additional Information
  • тЦ╕

    Option A (Circular) and Option B (Transition) are horizontal curves used to change the direction of alignment in the horizontal plane.

  • тЦ╕

    Square parabola is standard for vertical curves in highways because the vertical offset is proportional to the square of horizontal distance (yтИЭx2y \propto x┬▓yтИЭx2).

ЁЯУК Diagram / Illustration
Vertical Curve (Joining Different Grades)+gтВБ% (Upgrade)-gтВВ% (Downgrade)Parabolic Vertical CurveLength of Vertical Curve (L)
тЬЕ

C is correct тАФ Vertical curves are designed in the vertical plane specifically to join sections of a road or railway having different gradients.

Core Concepts Used
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Vertical Alignment Summit and Valley Curves Grade Deviation Angle
ЁЯТб EXAM TIP

Remember that horizontal curves handle centrifugal force during direction changes, whereas vertical curves handle sight distance requirements and passenger comfort during grade transitions.

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