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Stationing of pvi = 11+700 and the length of the curve is 200m find the stationing of the pvc and pvi

Mathematics

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Answer

11+600\text{11+600}

11+800\text{11+800}

Step-by-step solution

4 steps

This problem involves calculating the stationing of the Point of Vertical Curvature (PVC) and the Point of Vertical Tangency (PVT) given the stationing of the Point of Vertical Intersection (PVI) and the length of the vertical curve.

  1. Understand the given information.

    • Stationing of PVI (Point of Vertical Intersection) = 11+70011+700. This means 11700 m11700\, \text{m} from the starting reference point.
    • Length of the curve (LL) = 200 m200\, \text{m}.
  2. Determine the distance from PVI to PVC and from PVI to PVT.

    For a symmetrical vertical curve, the PVI is located at the midpoint of the curve. Therefore, the distance from PVI to PVC is half the curve length, and the distance from PVI to PVT is also half the curve length.
    Distance = L2=200 m2=100 m\frac{L}{2} = \frac{200\, \text{m}}{2} = 100\, \text{m}.

  3. Calculate the Stationing of PVC.

    The PVC (Point of Vertical Curvature) is located before the PVI. To find its stationing, subtract the distance calculated in Step 2 from the PVI stationing.
    Stationing of PVC = Stationing of PVI - L2\frac{L}{2}
    Stationing of PVC = 11700 m−100 m11700\, \text{m} - 100\, \text{m}
    Stationing of PVC = 11600 m11600\, \text{m}
    In stationing notation, this is 11+60011+600.

  4. Calculate the Stationing of PVT.

    The PVT (Point of Vertical Tangency) is located after the PVI. To find its stationing, add the distance calculated in Step 2 to the PVI stationing.
    Stationing of PVT = Stationing of PVI + L2\frac{L}{2}
    Stationing of PVT = 11700 m+100 m11700\, \text{m} + 100\, \text{m}
    Stationing of PVT = 11800 m11800\, \text{m}
    In stationing notation, this is 11+80011+800.

    The Stationing of PVC is 11+600\boxed{\text{11+600}}.
    The Stationing of PVT is 11+800\boxed{\text{11+800}}.

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