Question

Justify the reasons for saving the materials during the construction of vertical curves in highway ,with the
component elements of vertical curves . Also Give the necsssity of providing the component parts of vertical
curve

Answer 1

NECESSITY:Vertical curves are the second of the two important transition elements in geeometric design for highways,the first being horizontal curves.

Two types of vertical curves exist:*)Sag curves and *)Crest curves.

*1)Sag curves are used where the change in grade is positive,such as valleys,while crest curves are used when the change in grade is negative,such as hills.

2)These are the vertical curves with convexity downwards.

3)when a descending gradient meets another descending gradient .

4)W hen a descending gradient meets a flat gradient.

5)When an ascending gradient meets another ascending gradient.

* 1)Crest curves are the correct equation is dependent on the design speed.If the sight distance is found to be less than the curve length,the first formula blow is used.

2)When a psitive gradient meets another positive gradient.

3)When positive gradient meets a flat gradient.

4)When an ascending gradient meets another descending gradient.

S<L:Lm=AS^2/200(SQRT h1+SQRT h2)^2

S>L:Lm=2S-200(SQRT h1+SQRT h2)^2 /A

Where:

Lm:Minimum curve length(m)

A:The absolute difference between g2 and g1,multiplied by 100 to translate to a percentage.

S:Sight Distance(m)

h1:Height of drivers eye above roadway surface(m)

h2:Height of objective above roadway surface(m)

Both types of curves are in parabolic form.Parabolic functions have found suitable for this case because they provide a constant rate of change of slope and imply equal curve tanjents,which will be discussed shortly.

The general form of the parabolic equation is defined below,where y is the eevation for the parabola.

y=ax^2 +bx+c

REASONS FOR SAVING THE MATERIALS