Ch3 Examples and Solutions PDF

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Chapter 3 Geometric Design of Highways (Exercise)

Vertical Curve Alignment QUESTIONS Q1

A vertical parabolic curve is to be used under a grade-separation structure. The curve is 775ft long and the minus grade of 3.8 percent intersects the plus grade of 6.3 percent at station 250+75. Calculate the low point of the curve if the intersection at station 250+75 is at elevation 426.83 ft.

Q2

Calculate the stopping sight distance over a crest of a 1500-ft vertical curve with a plus grade of 4.4 percent and a minus grade of 2.3 percent.

Q3

A 500-ft-long, equal tangent crest vertical curve connects tangents that intersect at station 340+00 and elevation 1322 ft. The initial grade is +4.0 percent and the final grade is -2.5 percent. Determine the elevation and stationing of the high point, PVC and PVT.

Q4

An equal tangent sag vertical curve is designed to provide desirable SSD. The PVC of the curve is at station 109+00 (elevation 950 ft), the PVI at station 110+92.5 (elevation 947.11 ft), and the low point is at station 110+65. Determine the design speed of the curve.

Q5

An equal tangent vertical curve was designed in 1988 (to 1984 AASHTO standards) for desirable SSD at a design speed of 70 mph to connect grades G1  1.0 percent and G2  2.0 percent. The curve is to be redesigned for a 70-mph design speed in the year 2020. Vertical braking technology has advanced such that coefficients of stopping friction, f  s, have increased by 40 percent relative to 1984 standards given in Table 3.1, but, due to the higher percentage of older people in the driving population, design reaction times have increased by 20 percent. Also, vehicles have become smaller such that the driver’s eye height is assumed to be 2.75 ft above the pavement and roadway objects are assumed to be 0.25 ft above th pavement. Compute the difference in design curve lengths for 1988 and 2020 designs.

Q6

A highway reconstruction project is being undertaken to reduce accident rates. The reconstruction involves a major realignment of the highway such that a 60-mph design speed is attained. At one point on the highway, an 800-ft equal tangent crest vertical curve exists. Measurements show that, at 3+52 stations from the PVC, the vertical curve offset is 3 ft. Assess the adequacy of the existing curve in light of the reconstruction design speed of 60 mph and, if the existing curve is inadequate, compute a satisfactory curve length. (Consider both minimum and desirable SSDs.)

Chapter 3 Geometric Design of Highways (Exercise)

SOLUTIONS Q1

By equation (3.11), distance to low point from PVC: .  775 38 LG 1   29158 x  k G1  . ft or 2.9158 sta G1  G2 . 101 775 PVC Sta  25, 075   246  87.5 2 PVC Elevation  42683 .  3875 . ( 38 . )  44156 . The equation of the parabolic curve is given by, G A x 2  1 x  c where c is the elevation of PVC y 200 L 100 .) .  6.3  (  38  38 So the elevation of low point y   29158 . 2   .  44156 .   29158  100  200  775 =436.02

Q2

By equation (3.16)

S (or SSD)  1329  1500 6 .7  546 ft Since S...