Homework 4 Solutions: Vertical Curve Calculations in Highway Engineering

Homework 4 February , 2021 CE 392 Introduction to Highway Engineering Chapter 3 Mannering and Washburn (Due Friday 8 th ) Problems Select Answers 3-6 Sta Highpoint = 113+36 Elev Highpoint 245.45ft 3-8 3-9 y= 1201.86 ft 3-13 8.9 ft 3-16 3-21 3-24

Homework 4 February , 2021 3.6 A vertical curve is designed for 55 mi/h and has an initial grade of +2.5% and a final grade of −1.0%. The PVT is at station 114 + 50. It is known that a point on the curve at station 112 + 35 is at elevation 245 ft. What is the stationing and elevation of the PVC ? What is the stationing and elevation of the high point on the curve? GIVEN: K = 114 (@ 55 mi/h), G 1 =2.5, G 2 = -1.0, A= 3.5, PVT = 114+50 Point Station = 112+35, elev point = 245’ Calculate Curve Length L = K*A = 399’ Calculate PVC PVC = PVT-L = 115+51 x:= point-PVC = 184’ Calculate offset of point above curve Y point := (A/200*L)*x 2 = 1.485’ x*(G 1 /100) – Y point = 3.115’ from offset of point calculate elevation of PVC elev PVC := elev point -3.115 = 241.885’ Calculate location of high point x h := KG 1 = 285’ Y h := (A/200*L)*x h 2 = 3.562’ Calculate station of high point elev hp := elev PVC + Y h = 245.45’ STA hp = PVC+x h = 113+36

Homework 4 February , 2021 3.8 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 + 40.76 and the PVT is at station 37 + 24.66 . What is the elevation difference between the high point and the PVT ?

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Homework 4 February , 2021 3.9 An equal-tangent crest curve connects a +2% initial grade with a −1% final grade, and is designed for 55 mi/h. The station of the PVI is 233 + 40 with elevation 1203 ft. What is the elevation of the curve at station 234 + 00?

Homework 4 February , 2021 3.13 A 1200-ft equal-tangent crest vertical curve is currently designed for 50 mi/h. A civil engineering student contends that 60 mi/h is safe in a van because of the higher driver's eye height. If all other design inputs are standard, what must the driver's eye height (in the van) be for the student's claim to be valid?

Homework 4 February , 2021 3.16 An equal-tangent crest vertical curve connects an initial grade of +2.5% and a final grade of –0.5%. The curve is designed for 70 mi/h and the station of the PVT is 132+62 and is at elevation 833 ft. What is the station and elevation of the curve's high point?

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Homework 4 February , 2021 3.21 An equal-tangent sag vertical curve is designed with the PVC at station 109 + 00 and elevation 950 ft, the PVI at station 110 + 77 and elevation 947.34 ft, and the low point at station 110 + 50 . Determine the design speed of the curve.

Homework 4 February , 2021 3.24 An equal-tangent vertical curve connects an initial grade of -3% and a final grade of +1% and is designed for 60 mi/h. The PVI is at station 250+50 and elevation 732 ft. What is the station and elevation of the lowest point on the curve?

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