 Hello everyone, I welcome you all for this today's session on design of transition curves and routes. I am Mr. Ashok Kumar, Assistant Professor, Department of Civil Engineering, Vulture and the Institute of Technology, Solapur. Learning outcomes, at the end of the session, students will be able to design the length of transition curve. In the previous class, we have learnt about the transition curve, the requirement of transition curve, objective of transition curves and ideal shape of a transition curve. We know that to design the length of transition curve, it has to fulfill the three conditions. The first condition is rate of change of centrifugal acceleration to be developed gradually. We know that the centrifugal acceleration to be gradually introduced in the transition curve uniformly, hence the length of transition curve should be sufficient to introduce the centrifugal acceleration. Second condition is we are introducing the super elevation gradually from a normal camber to the designed super elevation, hence the length of the transition curve should accommodate this design super elevation from normal camber to the design super elevation. And IRC has given some empirical equations, we have to calculate the length using these empirical equations and compare all these three conditions and adopt the length of transition higher of the all three. Let us go by one this one by one to find out the length of transition curve. First one is rate of change of centrifugal acceleration, we know that the this V square upon R that is centrifugal acceleration is 0 at this straight point or that tangent and it starts it is infinity at that point and it starts decreasing, the radius is starts decreasing and centrifugal acceleration starts gaining some value that is increasing. So, centrifugal acceleration is increasing gradually and radius decreasing gradually. So, now this V square upon R we have to introduce in the transition uniformly and gradually. Now for that we have to design the length of transition. So, at the end of the transition the radius R has the minimum value Rm and hence the centrifugal acceleration is distributed over length of Ls that is Ls is the length of the transition curve. Of that if the t is a time taken to travel this Ls, so t is given by Ls upon V that is speed equal to distance upon time. So, time equal to Ls upon V where V is in meter per second. This maximum centrifugal acceleration that is V square upon R is introduced in time t through the Ls and hence the this change of centrifugal acceleration C is given by V square upon RT where C is the centrifugal acceleration and put this t value as Ls upon V. So, that comes to Vq upon Ls into R. So, length of transition Ls to meet the condition of centrifugal acceleration that is Ls equal to Vq upon Cr where V is in meter per second. So, as is suggested to find this C value that is centrifugal acceleration given by 80 upon 75 plus V where V is in kmph. Now this value comes in meter per second cube and the value of the C is suggested the minimum of 0.5 and maximum of 0.8. So, 0.5 to 0.8 we have to design the the C value. Here the previous equation is in meter per second to convert that into kmph we need to multiply 1000 and divided by 16 to 60 to convert into seconds into hours. So, the final equation for in V in kmph is Ls equal to 0.0215 Vq upon Cr where C is the centrifugal acceleration 0.5 to 0.8 meter per second cube and R is the radius in meter and Ls is the length of transition in meter. With the previous class understanding I hope you are able to select the correct answer over here. Now you pass the video and give me the correct answer for these two questions. First one is the radius of transition curve decreases and becomes maximum at the beginning of a circular curve is it true or false or in the dash curve the radius is inversely proportional to the length and rate of change of centrifugal acceleration is uniform throughout the curve which curve it is fulfills that whether lemniscate spiral or cubic parabola. I hope you are able to select the correct answer the correct answers are first one is false because the transition curves decreases the radius decreases at the transition curve at the state point and maximum at the beginning of the circular curve it is not maximum it is minimum hence the correct answer is false. In spiral has that the transition properties where radius is inversely proportional to the length and rate of centrifugal acceleration is uniform throughout the curve. So, that is spiral fulfills the ideal shape of the transition curve. Going to the second condition that is rate of introduction of super elevation again here we are introducing this super elevation in the transition from normal chamber to the design value by rotating in a two ways in a through with respect to the centerline and with respect to the inner edge. Here in open country we know that we need to provide some higher super elevation higher super elevation we cannot raise it suddenly we have to raise it uniformly and the sudden rate is not more than 1 in 150. So, we will not go beyond 1 in 150 this e 7 percent from 2.5 percent to 7 percent we have to raise it at a rate of 1 in 150. Now, the length of transition curve is this n is the rate of change of super elevation that is the raising rate is 1 in n. So, n multiply by the total raising. So, suppose if you are rotating with respect to the center line the total raising at outer edge is e by 2 and at the same time it is lowered by e by 2. So, the e by 2 multiplied by the rate of raising that becomes the transition length that is ls equal to e upon 2 that is e upon 2 at the outer edge multiplied by the rate of raising that is n value. If I put the e value what is the e how to calculate the total e e equal to b into e e is the rate of super elevation and b is the width of the pavement. If you are adding extra widening add extra widening to calculate the total b. So, here you can see here the total is from here to here it is b and adding. So, w plus w total width is w and w e is the extra widening. So, adding together w plus w e becomes a total b that is capital b. So, b into rate of super elevation gives the capital e that is total raising with respect to the inner edge or total raising with respect to the center line. Now, when you are rotating with respect to the inner edge. So, e multiplied by n that is rate of raising. So, again e is equal to b into e. So, where b is w plus w e and e is the super elevation. Now, let us understand what is this the rate of raising that is n value here the n we can able to decrease in a built up area we can able to decrease the length of transition curve providing 1 in 100 and in hilly area because of the space constraint we can still we can decrease the rate of raising 1 in 60. So, there where the length of transition curve will be minimum in the built up area as well as in the hilly area. Let us understand little bit more about the value of n. From here you can see here at the state point r is infinity we know that the state that is the radius is infinity and let us assume that we are providing a chamber of 2.5 percent. From 2.5 percent to we have to increase it for 7 percent here from here to here it is a transition curve from here to here it is a circular curve again here it is a transition curve. Now, we are not able to suddenly increase this 2.5 to 7 percent it is very undesirable and it is not safe we have to increase this 2.5 percent gradually. So, 2.5 will become 3 4 4.5 5 and 5.5 6 and 7 percent. Now, at what rate we have to increase here that is the value of n. So, for every 150 meter 1 meter is a vertical like that you calculate at a particular intervals what is the raising of outer edge with respect to the center line. Now, x 1 1 unit is raised x 2 length again another 1 unit is raised for x 3 another 1 unit is raised like that the slowly gradually we have to raise the outer edge. From here we we get one more clarification from this image also here you can see here the outer edge is slowly gradually raised. So, here it is 2 percent and 2 percent. Now, here the point is little bit from here to here that is some distance they calculated 1 in 150 are having the n value calculate the what is the amount of raising to be done on the outer edge from here little bit more and here more and here the start of the circular curve you can see here the rate of raising they are maintained that is 1 in 150 are the designed n value. So, this I was telling you the n value we have to adopt it and slowly we have to increase the outer edge at a rate of 1 in 150 by empirical formula as per the ISA standard depending upon the terrain condition the plane and rolling terrain it is given by 2.7 v square upon r where v is in Kmph for mountainous and steep terrain it is given by v square upon r where v in Kmph. Now, adopt this we have to compare all these three rate of change centrifugal acceleration length of transition curve and length of transition curve depending upon the introduction of super elevation and by empirical formula. So, adopt the LS that is length of transition curve higher among all these three. So, that is the final length we have to calculate it comparing all these three conditions. This is the readymade table given by ISA 38, 1988 where we can directly get the transition curve length here in this one there is a speed is given 180, 40 and all speeds. Now, radius is also given on this side. So, depending upon the speed and terrain condition here p is nothing but your plane terrain h is nothing but hilly terrain. So, depending upon the terrain condition speed and radius you can directly choose the radius of the curve. Here you can see here suppose for example, I will be going for 100 Kmph and the radius is something like 350. So, for 350 and for 100 Kmph you can see the 130 meter is the transition curve. So, 130 meter before the starting of the circular curve again at the end of this circular curve. So, two transition curve we have to provide before and after. These are the references I have used for representing this presentation. Thank you.