 Dr. Patil Snellkumaris, Professor and Head Surveying Department, Valchin Historic Technology, Solapur. So today I'm going to discuss about the analysis of multi-span continuous RCC beam, learning outcomes. At the end of this session, the viewers will be able to analyze a multi-span RCC continuous beam. That is, they will be able to determine the bending moment and shear force at critical sections for a RCC continuous beam introduction. Multi-span continuous beam, a multi-span continuous beam is a part of a framed structure which is continuous over four or more number of supports as shown in figure. Here there are four number of supports, whereas it can be even more than four number, five, six, anything. So four or more number of supports are required, which is shown in below. It will be having a sagging bending moment in mid-span. That means for every span, the sagging bending moment is there at the mid-span, here also. And this is for the third span. And hogging bending moment over the middle supports. Here this is one of the middle support. This is another middle support wherein you will be having a hogging bending moment over here. So it is a statically indeterminate structure, because here you are having unknowns more than three. Therefore it is a statically indeterminate structure. Hence, we are supposed to determine the bending moment at critical sections. So one has to refer table number 12 of IS 456-2000 for bending moment coefficients. So this is table number 12 for bending moment coefficients from IS 456-2000. So here we find the span moments and the support moments given separately. Now for the span moments, we are having near middle of end span and at the middle of interior spans. And for the support moment, we are having at the support next to the end support. And at over interior supports. So here we find the coefficients given for dead load and live load separately. So the dead load and imposed fixed load. So both together, the coefficient for the span moment, it is 1 by 12. And for live load, which is changing, it is 1 by 10. So near middle of the end span. So that means if you just see the figure, you will find. So this is m1 will be the first one near the middle of end span. Even m2 is also near the middle of the end span. And next, at the middle of interior support, it is 1 upon 16 and 1 upon 12. So that is at the locations here. This is m2. And next will be the support moments. If we go to the support moments, the let us discuss span moment, which is sagging, which is taken from the, which is at the near of the middle of end span. It is 1 12th of Wd into L square plus 1 10th of Wl into L square. So at the middle of interior span, it is 1 16th of Wd into L square and 1 12th plus 1 12th of Wl into L square, where Wd is the dead load and Wl is the live load given. Now the support moments. The support moments that is hogging moment at the support next to the end support. That means at the support next to the end support, we will be having the highest support moment that is 1 10th of Wd into L square plus 1 9th of Wl into L square. Next, at the other interior support, it is 1 12th of Wd into L square and 1 9th of Wl into L square. So here, the support moment is more than the span moment. That is hogging moment is more. So identify the location of maximum bending moment and write the equation. So compare both using both sagging as well as hogging, you are supposed to identify the maximum bending moment where it is and what is the equation for it. The maximum bending moment is at the support next to the end support, which is given by 1 10th of Wd into L square plus 1 9th of Wl into L square. Shear force at critical sections. As we have seen for the shear force variation for multi span RCC continuous beam is as shown in figure below. Here this is the shear force variation. For determining the shear force at critical section, one has to refer table number 13 of IS 456 2000 for shear force coefficients. So now, here you will find the, this is table number 13. So shear force coefficients as per IS 456 2000. So, which will be having a type of load is given here in the first column that is dead load or imposed fixed load also. That is your floor finish, et cetera, it comes under imposed fixed load. And the live load that is moving load, it is taken separately. And here you will find a second column at end supports. That means at the last support. So at the end supports it is obviously very lesser value. It is 0.4 coefficient and the for live load it is 0.45. Next they have given another column wherein you are having at support next to the end support. At the support next to the end support we have again outer side and inner side. So there are two things. One is outer side and another is inner side. So that means if I want to show you on the figure, so this is this V1 and this one, it V4 both are end supports. And this is the support next to end support. Similarly from this side, this is also support next to end support. So here you will find this is the outer side and this is the inner side. So for both the values are different. So at the support next to the end support for the outer side the coefficient is 0.6 for the dead load and 0.6 for the live load also. For the inner side it is 0.55 for the dead load and 0.6 for the live load. So at other interior supports we find it is 0.5 for the dead load and 0.6 for the live load. So now we will write the equations for shear force at critical section. At the end support the shear force equation is given by 0.4 WD into L plus 0.45 WL into L. At the support next to the end support the outer side you'll find 0.6 into WD into L plus 0.6 WL into L. So for the inner side it is 0.55 WD into L plus 0.6 WL into L. At all other interior supports it is 0.5 WD into L plus 0.6 WL into L. So here you will find the highest value is this one. This is outer side. So at the support next to the end support the shear force is maximum at the outer side that is 0.6 into WD into L plus 0.6 into WL into L. So that is 0.6 times both WD plus as well as WL into span. So here so this is the location where we find the highest value that is here you will find on the outer side the highest value and here also on the outer side the highest value. So these are the supports which are next to end support. At the support extra end support on the outer side you get the maximum value of the shear force. Now identify the location of maximum shear force and write its equation. So you are supposed to identify the location of maximum shear force as well as you are supposed to write the equation for it. Answer will be at the support next to the end support on the outer side you get 0.6 times WD into L plus 0.6 times WL into L. So that is the highest shear force we get. So that means in all what we can conclude in this particular session is that a continuous beam which is continuous over more than four supports is having the maximum bending moment at the support next to the hogging bending moment it is at the support next to the end support and the maximum sagging moment will be a span moment. So which is the at the first span itself that is first inner span span moment that will be you the maximum span moment whereas the hogging moment will be over the support next to the end support. And whereas the shear force is maximum at the outer side of the support which is next to the end support. So these are the references used for the today's session. Thank you and you all.