Civil Engineering - Highway Engineering - Discussion

@Azanaw.

You will find a clear explanation in IRC 38 codebook. However, I will try to briefly summarise it to you.

Basically superelevation is provided to counteract the centrifugal force experienced by a vehicle when it's negotiating a curve. Now counteracting the full centrifugal force developed for a given design speed would require us to provide superelevation of more than 7%. But IRC restricts the maximum value of e= 7%.

So in practice for mixed traffic, most vehicles travel at less than design speed (where we have both slow and fast-moving vehicles) so as a compromise since we can\'t provide the actual value we design superelevation to resist the full centrifugal force developed at 75% design speed.

Eg: If the design speed of a National Highway is 80kmph. We design the superelevation to fully resist the centrifugal force developed due to 75% of 80kmph = 60 kmph.

This method of giving superelevation will not be inconvenient to fast-moving vehicles but would be of aid to slow-moving vehicles.

Given data,

Speed = 75 kmp = 75*5/18 m/s = 20.83333333 m/s.
75% speed is the designed speed. So, 75% speed=20.83333333*0.75 m/s =15.625 m/s
Radius of curvature = 1000m.

Here 'g' is the gravitational acceleration and the value of 'g' is 9.8 m/s.

Formula of super elevation is (V2/gR) =(15.625*15.625/(9.8*1000)) =0.024912309%
0.024912309% of Super elevation means 1 in 40.1408.
So, the answer is 1 in 40 is correct.

Superelevation is always.

e+f=v^2/127R.

But for the design of the superelevation we take,

e=V^2/225R.

So, Here velocity 75 kmph and horizontal curve 1000 meter given.

That means it is the radius of the horizontal curve.

Note:- Horizontal curve always given in the form of the radius.

Put these values to find the horizontal curve,

e = 75^2 / (225*1000).

e = 1/40.

Thank you.

The actual formula of super elevation is;

We know the super elevation is calculated for 75% of design speed.

So,
E = (.75V)^2/GR.
V = Desing speed.
G = Gravity.
R = Radios.

Now,
E = (.75 * 20.83)^2/9.81 * 1000,
V = 75 * 1000/60 *60,
V = 20.83m,
E = .2488,
E = .25 approx,
E = 1/40 answer.

This will as per the design steps given by IRC for heterogeneous traffic. Step one is, you have to find the value of e (superelevation) neglecting friction for 75% of design speed.

If the value so obtained is less than 0.07, the design is over and that value is taken as the designed value of superelevation.

Let's clear something out first,

e+f=v^2/127r (When V is in kmph) and
e+f=v^2/225r (When V is in mph)

For initial design, we assume mix traffic and hence the velocity reduces to 75% and f is taken as 0.

So, the equation will be e=(0.75v)^2/127r.
Now, the answer will be 0.0249 or 1 in 40.

To determine super elevation we need only f- value, design speed and radius of the curve. So, if it is not mentioned then directly take the value with the unit of distance i.e meter.
the formula for mix traffic.

e + f = V^2/225R
HERE
f = 0 R=1000m and V =75kmph
so
e= 0.025 (1/40).

Concept:

The superelevation is given by:

e = (V ^ 2)/(225R) Where,
V = speed (in kmph), and R = Radius (in m).

Calculation:

Given: V = 75 kmph, and R = 1000m,
e = ((75) ^ 2)/(225 * 1000) = 1/40.

So, the super elevation is 1/40.

I think the formula of superelevation e= v^2/225R.

So we put all values as given in the question e = 75 * 75/225 * 1000.
e = 1/40.

The question stated that 75km/hr is design speed, thus simply we can calculate e=(75^2)/225R. b/c 'f' is not given.

There fore, 1:40 is the correct answer.
If 'f' were given, we use (e+f) = (75^2)/127R.