28.10
Exemplo de design: Definindo uma curva usando dados de design
Projetar e plotar uma curva usando dados de campo requer cálculos e execução precisos. Uma curva horizontal com um raio de 200 metros e um ângulo de i…
Consider that a civil engineer has to plot a simple horizontal curve with a 200-meter radius and a 20-degree intersection angle in the field.
The engineer uses the method of perpendicular offsets from the long chord to plot the curve.
First, the long chord length is calculated as 69.46 meters, and the intervals for perpendicular offsets are set at 3 meters.
Next, the offset expression at the midpoint is used to determine the ordinate of the long chord’s center, and to ensure accuracy, this value is verified against the middle ordinate of the curve.
The engineer marks the long chord of the curve on the ground, and the points at 3-meter intervals along both sides of the midpoint are marked.
Then, the expression for the offset distance is used to calculate the perpendicular offsets, which are marked along the long chord at the corresponding points.
Finally, the engineer connects the top ends of the perpendicular offsets to form the curve.
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Q1: What is the perpendicular offsets method for plotting horizontal curves?
The perpendicular offsets method plots a horizontal curve by measuring perpendicular distances from a long chord at regular intervals. The engineer marks the long chord on the ground, identifies points at equal intervals along it, calculates perpendicular offset distances using a formula, and marks these offsets at right angles to the chord. Connecting the offset endpoints creates the curve.
Q2: How is the long chord length calculated for a horizontal curve?
The long chord length is calculated using the curve's radius and intersection angle. For a 200-meter radius curve with a 20-degree intersection angle, the long chord measures 69.46 meters. This chord spans between the curve's endpoints and serves as the reference line for plotting perpendicular offsets.
Q3: Why is the middle ordinate validated against the offset expression?
The middle ordinate is validated to ensure the curve's design adheres to precise geometric standards. The engineer calculates the ordinate value at the chord's midpoint using the offset expression and verifies it against the middle ordinate formula. This validation confirms accuracy before marking perpendicular offsets on the ground.
Q4: What interval spacing is used when marking points along the long chord?
Points are marked at 3-meter intervals along the long chord on both sides of the midpoint. This interval spacing maintains accuracy in plotting while keeping the number of calculations manageable. Each interval point receives a corresponding perpendicular offset distance calculated using the offset formula.
Q5: How are perpendicular offsets measured and marked in the field?
For each marked point along the long chord, the engineer calculates the perpendicular offset distance using the offset formula. The offset is then measured and marked on the ground at a right angle to the chord. The top ends of these perpendicular offsets represent the curve's position at specific intervals.
Q6: What is the final step in completing the curve plot?
After all perpendicular offsets are marked, the engineer connects the upper ends of the offset points smoothly to form the curve on the ground. This creates a continuous curve that adheres to the design specifications, providing a reliable framework for the project.
Q7: Why is selecting appropriate interval spacing important for curve plotting?
Appropriate interval spacing balances accuracy with practicality. The 3-meter intervals chosen for this example ensure the plotted curve closely matches the design specifications without requiring excessive calculations. Smaller intervals increase accuracy but demand more field work, while larger intervals reduce effort but may compromise precision.