# Problem 02 - Symmetrical Parabolic Curve

# Problem 01 - Symmetrical Parabolic Curve

**Problem**

A grade of -4.2% grade intersects a grade of +3.0% at Station 11 + 488.00 of elevations 20.80 meters. These two center gradelines are to be connected by a 260 meter vertical parabolic curve.

- At what station is the cross-drainage pipes be situated?
- If the overall outside dimensions of the reinforced concrete pipe to be installed is 95 cm, and the top of the culvert is 30 cm below the subgrade, what will be the invert elevation at the center?

# Problem 03 - Simple Curve

# Problem 02 - Simple Curve

# Problem 01 - Simple Curve

# Parabolic Curve

**Vertical Parabolic Curve**

Vertical curves are used to provide gradual change between two adjacent vertical grade lines. The curve used to connect the two adjacent grades is parabola. Parabola offers smooth transition because its second derivative is constant. For a downward parabola with vertex at the origin, the standard equation is

# Spiral Curve

# Compound and Reversed Curves

**Compound Curves**

A compound curve consists of two (or more) circular curves between two main tangents joined at point of compound curve (*PCC*). Curve at *PC* is designated as 1 (*R*_{1}, *L*_{1}, *T*_{1}, etc) and curve at *PT* is designated as 2 (*R*_{2}, *L*_{2}, *T*_{2}, etc).

# Simple Curves

**Formulas for Circular Curves**

The formulas we are about to present need not be memorized. All we need is geometry plus names of all elements in simple curve. Note that we are only dealing with circular arc, it is in our great advantage if we deal it at geometry level rather than memorize these formulas.