Unformatted text preview: Course: TTE 4804/5805--Highway Geometric Design Homework No.: Two Due Date: Tuesday, January 25, 2011 Problem #1 Given the following data for a vertical curve of a road: Gl = 2.5%, G2 = +5.5% and station of PVI = 250+50. At station 252+50, the vertical curve must intersect an existing road at elevation 48.48 ft. The elevation on the tangent section at station 256+50 is 67.55. (a) Draw a good sketch of the vertical profile indicating all major points. (b) What is the length of the vertical curve that satisfies the above geometrics? (c) What is the elevation of the road at station 244+50? Problem #2 The grades on a vertical curve intersect at Sta. 105 + 00, elevation 350 ft. A drain grating exists at elevation 358.30 ft. (a) What is the minimum continuous curve length such that no point on the curve will be lower than the drain grating? (b) If a length of 1,900 ft is used, what are the stations of BVC and EVC? (c) If a length of 1,900 ft is used, what is the elevation of the lowest point on the curve? (d) If a length of 1,900 ft is used, what is the elevation at Sta. 106 + 40.00? Problem.#3 A vertical curve with BVC point at station 43+00 and elevation of 426.00 ft is on a grade 4.2% that intersect a +2.6% grade. The length of vertical curve connecting the two grades is 850 ft. Find: (a) the curve elevation at Station 48+60.00, (b) the station at which the slope of line to the vertical curve is 2.7%, and (c) the station beyond the PVI at which the elevation of the curve is 417.75. Problem #4 A vertical curve is to pass through a railroad at grade. The crossing must be at station 37+40.00 and at an elevation 574.00. The initial grade of the highway is +1.8% and it meets a 3.4% grade at station 38+00 at an elevation of 577.73 ft. The rate of change along the vertical curve must not exceed 1.0% per station. (a) What length of curve (to the nearest foot) will meet these conditions? (b) What is the station and elevation of the high point of the curve? Problem #5 A culvert is to be placed at the low point of a vertical curve used in the design of a rural highway. BVC is at station 30+60.00 with G1= 2.5% and G2 = +1.6%. The length of vertical curve is 900 ft. (a) What is the station of the culvert location? (b) If the elevation of station 30+60.00 is 438.00 and the culvert is to be 18.0 ft below the finished roadway, compute the elevation of the culvert invert. Problem #6 A new vertical curve of length 1,200 ft is to pass through point D, which is located at the high point of the curve. Find the percent grade for g2 that satisfies the design constraints as shown. BVC EVC Problem #7 Two tangents with G1= +4.5% and G2 = +1.5% intersect at the PVI with station of 57+50 and elevation of 620.00. At station 55+70.00 it is desired to pass a vertical curve through point B at elevation 611.40. Find the length of vertical curve (to the nearest 5 ft) that will satisfy this constraint. Problem #8 A 500 ft long sag vertical curve passes under a bridge at station 82+45.00. The beginning of vertical curve (BVC) is at station 81+00.00. A 3.6% curve meets a +4.4% curve at the point of vertical intersection (PVI), which is at elevation 425.38 ft. What is the elevation of the point on the curve under the bridge? Problem #9 A vertical curve is to be placed through station 81+50.00 at an elevation of 638.42 ft. The grade into the curve is 3.6% and the grade out of the curve is +3.8%. The beginning of vertical curve (BVC) is at station 76+00.00 and elevation 646.12 ft. What length of curve is required? Problem #10 The grade into a vertical sag curve is 2%. The curve length is 1,400 ft. The grade out of the curve is +4%. The elevation and station of the grade intersection are 226.88 ft and 7+20.00, respectively. The curve goes through a flood plain where the 50year flood elevation is 240 ft. (a) Find the stations where the curve drops below and emerges from the 50year flood plain. (b) What length of curve will be submerged in a 50year flood? (c) How will increasing the length of curve change the length of the curve that will be submerged? (d) How will decreasing the length of the curve change the length of the curve that will be submerged? (e) What can be done to the pavement so that flooding will not degrade it? Additional problems for graduate students only Problem #11 The tangent vertical alignment of a section of a proposed highway is shown in a figure below. Assume the river valley in the vicinity of Curve 2 floods to an elevation of 350.00 feet. Find the following: (a) the vertical curve elevation (feet) at Sta. 38 + 0.00, (b) the station of the highest point on Curve 1, and (c) the vertical curve elevation (feet) at the highest point on Curve 1. Problem.#12 A road contains a vertical curve starting at station 60+00.00 and ending at station 68+00.00. The elevation at the beginning of the curve (BVC) is 562 ft. The grade prior to the BVC is 1.5%. Just after the end of the curve (EVC) the grade is +2.5%. (a) Determine and show on a drawing the centerline elevations of the road every 50 ft from BVC to the EVC? (b) The road is constructed in the marshy ground subjected to flooding. At station 63+00.00, the road becomes elevated and is supported by five piles bents every 50ft. The piles are separated from each other by 10 ft (perpendicular to the road centerline) and are cut 3 ft below the finished road grade. A 4 horizontal circular curve to the right starts at station 64+50.00 and finishes at station 66+00.00. Superelevation on the curve is 12% and is fully developed around the curve. What are the cutoff elevations for each of the five piles in the four bents in horizontal curve? Problem.#13 A vertical curve connects a 1.3% tangent and a +1.8% tangent. The tangents intersect at station 74+00.00 and elevation 310 ft. A railroad line at grade crosses the curve at station 75+20.00 and elevation 314 ft. (a) What is the length of the vertical curve? (b) If the curve length is changed to exactly 1300 ft, what will be the difference in elevation between the railroad line and the roadway? (c) The road is curbed and guttered. If the curve length is exactly 1300 ft, at what station and elevation would a single grate inlet be placed on the curve? Problem.#14 A 2.9% street grade and +2.1% street grades intersect at station 18+40 at elevation 1140.40. It is necessary to pass an overhead structure at station 19+10 with a 14.5 ft clearance requirement. The lowest steel girder support is at an elevation of 1160.00. Compute the maximum length of parabolic curve required to meet the given conditions. Problem.#15 Two intersecting profile grade lines consist of a +5% grade meeting a 4.2% grade at station 29+30.00 and elevation 840.00. For a vertical curve length of 850 ft: (a) determine the elevation for the BVC, (b) determine the elevation of EVC, (c) determine the curve elevation at station 26+85.00, (d) determine the curve elevation at station 31+10.00, (e) determine the elevation of highest point, and (f) determine the station of the highest point. ...
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- Spring '11
- Slope, Road, vertical curve, Grade separation, Curve 2