 Hello viewers. I welcome you all for the today's session on analysis of super elevation. I'm Ashok Kumar, Assistant Professor, Department of Civil Engineering, Valchan Institute of Technology, Solapur. The learning outcome of the today's session, at the end of the lecture, students will be able to design the super elevation for mixed traffic condition. Before we go for designing the super elevation, let us understand what is the maximum super elevation and minimum super elevation. So considering these slow vehicles and the slow vehicle with heavy loaded vehicle, so considering these slow vehicle, the maximum super elevation is restricted as per the IRC guidelines. In the plane and rolling terrain, it is fixed as 7%. And in hilly terrain, we go up to maximum 10%. And in urban section, we design the intersections and all maximum super elevation of 4%. Considering the drainage aspect, so whenever we know that when the radius increases, like 2,000 meter or 4,000 meter, when the radius increases, there might be not requirement of any super elevation. But whenever the super elevation comes lesser than the camber value, but it is suggested that you have to provide the super elevation equal to the your camber value. For bituminous roads, we know that it is 2.5%. So for bituminous roads, it is taken as 2.5% super elevation, even though there is not requirement of any super elevation, but we have to provide the minimum super elevation of 2.5% that is equal to camber value. In the previous session, we have derived this equation of E plus F equal to V square by 127 R, where V in kmph. Now can you think this equation holds good for mixed traffic condition? What is mixed traffic condition? What I'm trying to expect here, the mixed traffic condition where this equation should meet the requirement of fast moving vehicle as well as the slow moving vehicle. Let us take an example over here. If I derive the equation, if I calculate the super elevation required for fast moving vehicle, taking the speed of 100 kmph, the super elevation might be in the range of 6% or 5%. Now that the super elevation is suitable for high speed vehicle. That higher super elevation is suitable for slow moving vehicle, that is the question arises here. So this super elevation, which you have considered for higher speed, it is suitable for high speed vehicle, but may not be suitable for slow moving vehicle. In other case, if I take the speed as low speed, that is say 40 kmph or 30 kmph, and design the super elevation using this equation, now you will get the lower super elevation. Now whatever the value which you have obtained, whether that suits for fast moving vehicle, no. It is suitable for slow moving vehicle. So here question arises, the whatever we, but whenever you providing the super elevation, there is no separate super elevation for slow moving, no super elevation for fast moving. So one super elevation where I should take care of both fast moving and slow moving. So here this warrants the designing of a super elevation for mixed traffic condition, considering slow moving as well as fast moving vehicles. Now how to design that the super elevation for considering the both fast moving and slow moving. As we know that the for mixed traffic condition, it is a very complex problem to design both slow moving and fast moving vehicle. So taking the lower E and rely on the completely on lateral friction would be unsafe for a fast moving vehicle. So yes, we are taking the lateral coefficient of friction help to contract the centrifugal force, but this may suits for the slow speed vehicle. But what about the high speed vehicle? Entirely depending on the lateral coefficient of friction for high speed vehicle is completely unsafe. So again, providing higher E incanonent for slow moving vehicle. So rather again you thinking on to increase the E value for take care to fast moving vehicle, but this may affect on the slow moving vehicle. So now we have to compromise between the fast and slow moving. How I'm going to compromise here, we are compromising in the speed of the design speed of the vehicle. So what we are compromising here, we are taking the 75% of the design speed neglecting the lateral friction. So here where we are trying to reduce the 25% of the design speed and taking the 75% of the design speed and that the speed is suitable for both slow moving and fast moving vehicle. So whatever you are trying to calculate the E value, it is for 75% of the design speed. Whatever the given value, you have to multiply the 75% and take that speed for designing the super elevation. Here the sentence holds good only whenever the maximum super elevation is allowed up to 7%. So beyond that, again, we have to redesign the, either we have to increase the radius or we have to decrease the, your speed of the vehicle. Now how we are going to design this super elevation considering the 75% design speed. So let us understand the different steps here. You can see the first steps, I'm calculating the 75% of the design speed where we in meter per second RK MPH. Here whatever the, here we are neglecting the lateral coefficient of friction here. So 0.75V square by 127R where V is in KMPH. So now you simplify this, taking the 0.75 in the denominator that is 127 divided by 0.75 square, that gives me approximately the value of 225R. Now here we in KMPH. Now calculate the E value using this 75% of the design speed. See that the E should not exceed the maximum given value of 7%. So if it is not exceeding, you can stop the design and provide whatever the obtained value here. If the E value exceeds the 7%, that is the maximum super elevation of 7%. We have to go for step two. What we are trying to do in the step two. So if it is exceed 7%, take the maximum super elevation of 7% and check your the lateral coefficient of friction in the third step. So assume the maximum super elevation of 7% and now you have to check the coefficient of friction that is F value here. Again you use the basic equation that is E plus F equal to V square by 127R. Here the E value is exceeded. So we are assumed that it is a maximum value of 7%. Put the E value as 0.07 and calculate the what is the lateral coefficient of friction. Suppose here the lateral coefficient of friction comes lesser than 0.15, then you can stop the design here and provide the maximum super elevation of 7% over here. In case if the F value exceeds the 0.15, we have to restrict the speed in the step four. Now we will go to the step four because both E value is also exceeding the maximum value of 7% and F is also exceeding the 0.15. Now we have left out with the restricting this your design speed. Again using your basic equation of E plus F equal to V square by 127R and you put the maximum value of E as 0.07 and F as 0.15 and you cross multiply this, the addition. So you're going to calculate the allowable speed that is VA equal to square root of 27.94R where R is in the radius of the curve in meter and V in kmph. So this is how you calculate the allowable speed. But the check that this allowable speed is more than the design speed. That is the we are expecting that. And here if the allowable speed calculate above is higher than the design speed then the design speed is adequate and provide a superlation of 0.07. In case this allowable speed is lesser than the design speed, then we have to limit your speed lesser than the allowable speed and put the warning sign, sign, the speed regulation sign. So either if you have tried to avoid this kind of the alignment because your allowable speed is coming lesser than the design speed. So it means that the curve radius if there is a chance of increasing the curve radius you go for increasing the radius otherwise you have to put the warning signs and the speed regulation sign. Let us understand this whole process of designing the superlation with this example. The speed is given as 80 kmph and radius is 200 meter and F is 0.15. So calculate your design the superlation and there is one constraint given here. Due to the side constraint we are not able to increase the radius. So in case we have a restriction of the radius so you can calculate the allowable speed on this horizontal curve of 200 meter because we are unable to increase the radius due to the side constraint. So let us see how we are going to solve this one. So as the first equation step one I will be taking the superlation for 75% of the design speed that is V square by 225R. Now you see that the value which we obtained here it is 0.142 it is more than 0.07 it is approximately coming 10.42 it is more than 7%. Now as per the steps we have studied we have to assume that the E value is given as 0.07 and check your lateral coefficient of friction in the step three here. So take E value as 0.07 and check the what is F value here. Again using the E plus F equal to V square by 127R and put the E value as 0.07 and calculate the F value here. The F value I got it is 0.18 again it is more than 0.15. So again it is exceeding 0.15 and as per the step process we know that we have to calculate the allowable speed for this particular design speed. So in the step four we will calculate the allowable speed using the this equation square root of 27.94 into R here R is given as 200 meter. Now it is again we are expecting that VA should be more than design speed. Here in this case you see that VA is coming less than 80 kmph. In this case we have to provide the allowable speed is lesser than this. So say 70 kmph is the allowable speed and we are not allowing the 80 kmph here. We have to restrict the allowable speed to 70 kmph and put this the warning signs and regulation sign because here we are unable to increase the radius and due to that and we don't have option to go for real element also. So in this case you have to put the warning signs and speed regulation sign saying that this curve is designed for lower design speed. So this is how we calculate the this super elevation for a given radius and speed. These are the references I have used for preparing this presentation. Thank you.