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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
Vertical
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.
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.
N=g1−g2 — deviation angle or algebraic difference in grades
L=N×C — length of vertical curve based on rate of change of grade
y=cx2 — standard equation of a simple parabolic vertical curve
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.
Vertical curves are introduced in the vertical plane at intersections of different gradients.
They are classified into Summit Curves (Crest) and Valley Curves (Sag).
Parabolic curves are preferred because the rate of change of grade is uniform throughout the curve.
Provides a smooth, comfortable transition between different grade slopes.
Ensures required safe stopping sight distance (SSD) and passing sight distance (PSD).
Minimizes impact forces on vehicle suspension caused by sudden slope changes.
Requires larger earthwork quantities (cutting and filling) during construction.
Summit curves can restrict sight distance if designed with insufficient length.
Joining upgrading and downgrading sections of highways and expressways.
Rail tracks transition between gradients to prevent excessive coupler stresses.
Flyover and underpass ramp transitions.
| Feature | Horizontal 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 |
Option A (Circular) and Option B (Transition) are horizontal curves used to change the direction of alignment in the horizontal plane.
Square parabola is standard for vertical curves in highways because the vertical offset is proportional to the square of horizontal distance (y∝x2).
C is correct — Vertical curves are designed in the vertical plane specifically to join sections of a road or railway having different gradients.
Remember that horizontal curves handle centrifugal force during direction changes, whereas vertical curves handle sight distance requirements and passenger comfort during grade transitions.