A-3% grade meets a +5% grade at a vertex (El. 146.24m) directly under an overpass bridge having underside elevation of 155.74m. A 6 meters clearance under the bridge and the center of the curve was observed. Determine the horizontal length of curve in meters.

A 800ft vertical curve has its PVI at elevation 232.25ft. The initial and final grades are 3.7% and -5% respectively. Determine the elevation of a point 349ft from PVC.

Sag Curve: A grade from the PVC to the PVI is -6% and from PVI to PVT is +2%. It is required to connect these grade lines with a vertical parabolic curve will pass 3.0 m. directly above the PVI. 11. Determine the length of this curve. a) 420 m b) 380 m c) 400 m d) 300 m 12. Determine the location of the lowest point measured from the PVT. a) 100m b) 75m c) 100m d) 225m 13. Compute the vertical offset at a point on the curve 100m from the PVC. a) 2.45m b) 2.33m c) 1.56m d) 1.33m

b) A 400 m vertical curve connects a -2% grade with a +4% grade. The P.I. is located at chainage 150 meters with an altitude of 29 meters above sea level. Calculate the elevation of the lowest point on the vertical curve.

1.) A -2.6% grade meets a +4.8% grade near an underpass. To maintain the minimum clearance allowed under the bridge and at the same time introduce a vertical transition curve in the grade line, it is necessary to use a curve that lies 240m on one side of the vertex of the straight grade and 115m on the other. The station of the beginning of the curve, PC, is 18 + 612 and its elevation is 415.81m. a. Determine the elevation at station 18 + 672. b. Determine the stationing of the lowest point of the curve.

2. There is a Vertical Curve with a length of 300 feet, a g1 of -3.2%, a g2 of 1.8%, a PVI at station 20+50.00, at an elevation of 365.92. Determine the HP/LP and elevate all even 100 foot stations and the HP / LP.

Note: Solve and draw

A sag Vertical curve has a profile elevations @ BC and at distance L/2 are 206 and 202.5 m respectively and the PI elevation is 200 m. Find the following elevation at. a) 0.25L b) 0.75L c) EC   Find the Station and elevation of the lowest point.