Calculating Curve Grade, Station and Elevation

[dek jue]

Homework Statement

A plus 3.0% grade intersects a minus 5.0% grade at station 10+ 150 and at an elevation of 170.500 m. Given that a 500 m length of curve is utilized, determined the station and elevation of the PC and PT. Calculate elevations at every 20 m station and locate the station and elevation of the high point of the curve.

Homework Equations

r =g2 - g1/L


The Attempt at a Solution

219

is it correct?

 

[KataKoniK]

Thank you for your post. In order to solve this problem, we will need to use some equations and calculations. First, let's define our variables:

- g1 = the grade of the first curve (-5.0%)
- g2 = the grade of the second curve (+3.0%)
- L = the length of the curve (500 m)
- r = rate of change of grade (unknown)
- PC = point of curvature (unknown)
- PT = point of tangency (unknown)
- HP = high point of the curve (unknown)

Using the given information, we can set up the following equations:

Equation 1: g2 - g1 = r/L (this represents the change in grade over the length of the curve)

Equation 2: PC = 10+150 (this represents the station at which the two grades intersect)

Equation 3: PT = PC + L (this represents the station at which the curve ends)

Equation 4: HP = PC + L/2 (this represents the station at which the high point of the curve is located)

To solve for the unknowns, we can plug in the values from the problem and solve for r:

r = (g2 - g1)L = (0.03 - (-0.05))500 = 40

Now, we can use this value for r to solve for the unknown stations and elevations:

PC = 10+150 = 10.150 (station) and 170.500 m (elevation)

PT = PC + L = 10.150 + 500 = 10.650 (station) and 170.500 m (elevation)

HP = PC + L/2 = 10.150 + 500/2 = 10.400 (station) and 175.500 m (elevation)

To calculate elevations at every 20 m station, we can use the following equation:

Elevation = elevation at PC + (station - PC) x (r x 100)

For example, at station 10.350, the elevation would be:

Elevation = 170.500 + (10.350 - 10.150) x (40 x 100) = 170.900 m

I hope this helps you solve the problem. Let me know if you have any further questions.