CEG8403 DoTI 2023-24
Reminder: Use a diagram and show your method of calculating.
All answers should be correct to the nearest millimetre.
1 Horizontal Alignment
Two straight sections of road are to be linked by a circular arc with symmetrical clothoid transition curves between the straight and curved sections.
|
Deflection angle between the two straight sections
|
Φ
|
|
Radius of the circular arc
|
R
|
|
Rate of gain of radial acceleration
|
q
|
|
Design speed of the road
|
100kph
|
a) What is the length of the circular arc?
b) What is the minimum distance between the intersection point of the tangents and the alignment?
[16 marks]
2 Vertical Alignment
A parabolic vertical summit curve between two gradients has been designed in accordance with desirable minimum standards given in CD109 – Highway Link Design.
Approach gradient g1
Departure gradient g2
Summit level hsum
Chainage of the vertical intersection point 2513.615 m
Design speed 120kph
a) What is the chainage and level at each end of the curve?
b) Between what chainages is the level greater than 42m?
[20 marks]
3 Horizontal Alignment
An existing road with a design speed of 85 km/h passes from one tangent through a right hand circular arc onto a second tangent, and then through a left hand circular arc onto a third tangent which is parallel to
the first. The circular arcs are joined to the straights by clothoid transition curves.
|
Radius of both circular arcs
|
R
|
|
Rate of gain of radial acceleration on all transitions
|
q
|
|
Length of straight between the two curves
|
Lstr
|
|
Length of both circular arcs
|
250 m
|
a) What is the perpendicular distance between the parallel straight sections?
b) Using the same tangents and Intersection Points, the arc radii are increased to 2500m and the transition curves upgraded to a design speed of 120 km/h. How long is the straight section
between the two curves after this redesign?
[20 marks]
4 Vertical Alignment Design
A road must be designed to cross some railway tracks. The approaches are both flat, with no horizontal
curvature and are at the same level. The vertical alignment comprises a level approach at ground level, a sag curve, a single crest curve over the railway, and a sag curve returning to ground level. The maximum permitted gradient is 6%, and lengths of this gradient may be used between the crest and sag curves if
required. The railway tracks are at ground level, and are [W] metres wide. The road alignment must be at least [h] metres above ground level over this entire width.
|
Width of the railway tracks
|
W
|
|
Clearance (height) between rail tracks and alignment
|
h
|
a) Design the shortest combination of vertical curves using the desirable minimum standards from CD109 – Highway Link Design for a design speed of 60kph. Give your answers in a table with the following headings:
|
Element description (hog, sag or gradient)
|
Length (m)
|
K value or
Gradient (%)
|
Start Level (m)
|
End Level (m)
|
|
Sag curve
|
|
|
0
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
b) Show how much shorter the alignment could be made if the crest curve is redesigned to one step below desirable minimum K value, but all the other constraints remain the same. Tabulate your answer as in section (a), and state the change in length due to the redesign.
[24 marks]
5 Horizontal Alignment
Two straight sections of road are to be linked by a wholly transitional curve comprising two clothoid spiral curves with differing rates of gain of radial acceleration.
Deflection angle between the two straight sections of road Φ
Design Speed V
Rate of gain of radial acceleration for entry transition curve q1
Rate of gain of radial acceleration for exit transition curve q2
Answers required:
a) What is the value of the point radius where the two transition curves meet?
b) What is the distance between the horizontal intersection point where the two straight sections of road intersect, and the centre of the circle of which the point radius mentioned in part (a) above is a part?
[20 marks]