PRIN.OF HIGHWAY ENGINEERING&TRAFFIC ANA.
7th Edition
ISBN: 9781119610526
Author: Mannering
Publisher: WILEY
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Chapter 3, Problem 38P
To determine
The common grade between sag and crest curves and the elevation difference between
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A horizontal curve on Texas Highway 83 (Tx83) comprises of a two-lane rural highway with a lane width of 12 ft. and superelevation of 8%. The posted speed limit is 50 mph. along a 0.5-mile section of highway, both a horizontal and vertical curve exists. The vertical curve has an initial grade of -2.00% and a final grade of +4.00%. The PVI is at station 156+40. A driver traveling eastbound strikes a stationary roadway object. The daytime crash results in a fatality and is being investigated for safe design speed. Evaluate and comment on the roadway design.
You are designing a vertical sag curve joining a -3% grade to a + 2% grade. The design speed is 60 mph.
For the design of the curve, the stopping sight distance is based on a 0% grade.
1. Is the shape of the vertical curve circular, elliptic, or parabolic?
A 500-m long equal tangent vertical curve has a point of vertical curvature at station 2 + 600 and elevation 450 m. The initial grade is -1% and final grade is +1%
b) determine the highest and the lowest points on this vertical curve by using the K-value.
Chapter 3 Solutions
PRIN.OF HIGHWAY ENGINEERING&TRAFFIC ANA.
Ch. 3 - Prob. 1PCh. 3 - Prob. 2PCh. 3 - Prob. 3PCh. 3 - Prob. 4PCh. 3 - Prob. 5PCh. 3 - Prob. 6PCh. 3 - Prob. 7PCh. 3 - Prob. 8PCh. 3 - Prob. 9PCh. 3 - Prob. 10P
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- A sag curve and crest curve connect -2.75% tangent section of highway (to the west) with -1.25% tangent section of highway (to be the east). The -1.25% tangent section is at higher elevation than the -2.75% tangent section. The two tangent section are separated by 450m of horizontal distance. If the design speed of the curve is 70KPH. Which of the following most nearly gives the common grade in percent between the sag and crest curvearrow_forward3.7 An equal-tangent crest vertical curve is designed for 65 mi/h. The initial grade is +3.4% and the final grade is negative. What is the elevation difference between the PVC and the high point of the curve?arrow_forwardA symmetrical sag curve has a descending grade of -4.2% and an ascending grade of +3.6% intersecting at Station 10+130, whose elevation is 121.55 m. The rate of change of grade is restricted to 0.60%. a. What is the vertical offset of the parabolic curve to the point of intersection of the tangent grades? b. At what distance from PC is the lowest point of the curve located?arrow_forward
- A horizontal curve on Texas Highway 83 (Tx83) comprises of a two-lane rural highway with a lane width of 12 ft. and a super elevation of 8%. The posted speed limit is 50 mph. along a 0.5-mile section of highway, both a horizontal and vertical curve exists. The vertical curve has an initial grade of -2.00% and a final grade of +4.00%. The PVI is at station 156+40. A driver traveling eastbound strikes a stationary roadway object. The daytime crash results in a fatality and is being investigated for safe design speed. Evaluate and comment on the roadway design.arrow_forwardA 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?arrow_forwardA sag vertical curve is to be designed to join a -5% grade to a +2% grade. If the design speed is 65 km/h, determine the minimum length of the curve that will satisfy all criteria. Assume a=3m/squared and perception-reaction time = 2.5 sec.arrow_forward
- A crest and sag curve connect a 0% west highway segment (left) with a +1.80% east highway segment (right). The 0% west highway segment is at a higher elevation than the start of the +1.80% east highway segment. The two vertical curves connect with each other (PVŤ = PVCG) and share a 2.2% (use -2.2% for calculation) common grade. If the design speed of the curves is 60 mi/h. What the elevation difference (ft, use format 0.00, range is +/-0.02) between the two road segments?arrow_forwardThe design speed of a sag parabolic curve is 100 kph. The downward tangent grade is 2%. The length of the curve is 126 m. What is the numerical value of the upward tangent grade in (%) of the parabolic sag curve?arrow_forwardAn equal-tangent crest vertical curve is designed for 70 mi/h. The high point is at elevation 1011.4 ft. The initial grade is +2% and the final grade is -1%. What is the elevation of the PVT?arrow_forward
- A symmetrical sag curve has a descending grade of -4.2% and an ascending grade of +3% intersecting at station 10 + 200, whose elevation is 100 m. The rate of change of grade is restricted to 0.55385% per station. a. What is the vertical offset of the parabolic curve to the point of intersection of the tangent grades? b. At what distance from PC is the lowest point of the curve located? 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?arrow_forwardAn equal-tangent vertical curve is to be constructed between grades of -2.0% (initial) and +1.0% (final). The PVI is at station 110 + 00 and at elevation 420 ft. Due to a street crossing the roadway, the elevation of the roadway at station 112 + 00 must be at 424.5 ft. Design the curve.arrow_forward1) An equal-tangent crest vertical curve has a 50 mi/h design speed. The initial grade is +3%. The high point is at station 33+37.43 and the PVT is at station 37+18.26. What is the elevation difference between the high point and the PVT? 2) A 1400-ft-long sag vertical curve (equal tangent) has a PVC at stateion 115+00 and elevation 750ft. The intial grade is -3.5% and the final grade is +6.5%. Determine the elevation and stationing of the low point, PVI, and PVT. If you could show as many steps taken as possible that would be helpful in me actually understanding how to do the problem. Thanksarrow_forward
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