Capstone Design Topic: Transportation
Date 11/06/2020
DESIGN PROJECT 2
Capstone Design Topic: Transportation
Capstone Design Topic: Transportation Topic 1; After Graduation, you started an
engineering firm, and the first project is to design a two-lane highway in a rural area in
California. The Highway descends a hill, crosses under a bridge, and must shift to a parallel
alignment on level terrain. You will design in the paper the vertical alignment and the horizontal
alignment to meet design standards and minimize earthworks. Diagrams and other specifics are
appended to the next page.
Section to work on:
1. Designed section defined by The natural terrain is flat until station 100 + 00, where a
downhill begins, as shown in the second diagram. Between station 100 + 00 and 120
+ 00, the soil elevation could be approximated by a cosine curve as and x is the
distance (measured horizontally) from station 100 + 00. This leads to an elevation of
7,100 ft before the hill and an elevation of 7,000 ft at station 120 + 00 and onward.
Date Complete by:
2. The design section defined by The highway crosses a bridge at a right angle at station
120 + 00; the bottom of the bridge is 20 ft above the soil.
Date Complete by:
3. Design Section defined by Because of right-of-way reasons, the horizontal alignment
must be straight until station 140 + 00. The transition to the new alignment must be
completed within 3,000 ft, as shown in the plain view.
Some calculations to fulfill this requirement:
DESIGN PROJECT 3
Solution
The Cosine Function is given as:
In this case, it is assumed that the soil cannot be moved within the site. Therefore, the
total cut and fill are computed by taking the integral of the absolute value of the difference
between the natural terrain and the proposed alignment. Therefore, using the parabola for vertical
curves:
y = 7050 + 50cos (πx /2000) ………(i)
120+00
140+00
3,000 ft.
Highway centerline
Bridge
1,000 ft.
Natural terrain
Cross-section of the bridge
DESIGN PROJECT 4
Station = 100 + 00; Elevation = 7,100 ft.
100 + 00
Plan View N
Natural Terrain
Station = 120 + 00; Elevation = 7,000 ft.
Elevation = 7050 + 50cos(πx/2000)
x 20 ft.
A
A’
BB’
C
C’
The cosine function in this case can be formulated in terms of the sine function as either:
y = A sin (Bx) ……………(ii)
y = A cos (Bx)……………. (iii)
Sin �=
!
!
�== angle theta
a= length of the opposite side a
h=
DESIGN PROJECT 5
DESIGN PROJECT 6
DESIGN PROJECT 7
References
National Research Council. Transportation Research Board. (, 2003). Transportation
management and public policy of 2003.