A vertical symmetrical sag curve has a descending grade of - 4.2% and an ascending grade of +3% intersecting at station 10 +020, whose elevation is 100 m. The two grade lines are connected by a 260 m vertical parabolic sag curve. (a) At what distance from the P.C. is the lowest point of the curve located in m? (b) What is the vertical offset of the parabolic curve to the point of intersection of the tangent grades in m. (c) If a 1 m. diameter culvert is placed at the lowest point of the curve with the top of the culvert buried 0.60 m. below the subgrade, what will be the elevation of the invert of the culvert?

7. A -3% grade meets a +5% grade near an underpass. In order to maintain the minimum clearance allowed under the bridge and at the same time introduce a vertical transitioning curve in the grade line, it is necessary to use a curve that lies 200-m on one side of the vertex of the straight grade and 100-m on the other. The stationing of the beginning of the curve (200-m side) is 10+000 and elevation is 228m. a.) Determine the stationing of the lowest point of the curve. b.) Determine the elevation at STA 10+040. c.) If the uphill edge of the underside of the bridge is at station 10+220 and at elevation 229.206m, what is the vertical clearance under the bridge at this point?

Q- A vertical summit curve is formed at the intersection of two gradients. +5% and −5%. The length of summit curve needed to provide a stopping sight distance of 100 m will be