 Hello friends, I am Prashant Danshati, Assistant Professor, Department of Civil Engineering from Walsh and Institute of Technology, Solapur. Today I am here to explain you about the influence line diagram for calculating the reaction at the supports. The learning outcome of today's lecture will be the student will be able to study the effect of moving load on structural members, apply Muller-Bruslaw's principle for qualitative influence line and able to construct influence line diagram. Definition of ILD, so ILD means influence line diagram, a curve or a graph that represents the function like reaction at the support, shear force at the section, bending moment at the section of a structure for various position of unit load on the span of a structure is called as influence line diagram. So ILD is used for in the design of structures that resist very large live loads or moving or rolling loads. So due to this ILD, it will be able to detect the location of the live load which will cause the greatest influence on the structure. Moving or live load, loads applied to a structure with points of application including their magnitude can vary as a function of position on the structure. So including the magnitude means the rolling load or a moving load will having different magnitudes and with different positions. Now can you give me an example of moving or a live load? Here pause a video and try to write an answer on a paper. So the example of moving load includes live load on the buildings, then traffic or vehicle loads that move along the bridge. So here you can consider a truck moving over a bridgepan. So this is a truck which is moving over a bridgepan and the load is applied due to these wheel loads. In the analysis the moving loads can be modeled as distributed loads, series of concentrated loads or a combination of distributed load and concentrated loads. A moving unit load, it is a concentrated load of a unit magnitude with its point of application varies as a function of position on the structure. This when a unit load passes from one end to another end, so the value of function varies means reactions are varying, then shear force at sections are varying, then bending moment is varying. So due to this moving unit load or the response due to the moving unit load, the quantity of interest that indicate the effect of moving load on the structure is to be studied. So they are the internal forces, support reactions, displacement and rotation, deformation, etc. The response functions are termed as influence function and the graphical representation is known as influence line diagram, Mueller-Bruslaw's principle. So these principles state that if a unit deformation is created in the structure in the direction of function like reaction, bending moment, shear force, the deflected shape of the structure gives the influence line diagram for that particular function. The methods of constructing influence line diagrams are tabulate values using influence line equation and using Mueller-Bruslaw's principle. Now tabulate values according to this, so here a unit load is applied on this beam A to B. So for varying position a static using static the reaction or the function which have to be determined is calculated and a table is prepared for various load position and the corresponding value of function that is reaction. And after that we have to plot that points and connecting that points will give you ILD. So here I have taken a unit load which is passing from A to B. So I have taken a load interval of 0.25. So when a unit load is exactly at point A, so using static I have found the reaction at A is 1, reaction at B is 0. When the unit load is placed at 0.25 L, so the reaction at A is 0.75, reaction at B is 0.25. When this unit load is at 0.5 L, the reaction A is 0.5, reaction B is also 0.5. When the unit load is placed at 0.75 L, the reaction A is 0.25, reaction B is 0.75. When the unit load is exactly at point B, so the reaction at A is 0 and reaction at B is 1. Now using these values we have to plot a points corresponding to this span and joining these points you will get the ILD. So this is the ILD for reaction RA and this is the ILD for reaction RB. Now using influence line equation, so here a equation equilibrium equation is developed and again the points are for a specified interval you have to take the values of function and plot that function. So here for reaction RA, so here reaction RA what I have to consider is x distance from B. Now for reaction RA we have to take moment about B. So taking moment about B or I have considered this unit load at a distance of x from B. So RA into L is equals to 1 into x. Therefore RA is equals to x by L. So now again I have taken a interval of 0.25 L and from this I have calculated RA and I have just plotted that points and connected it that will give you ILD for RA reaction. Similarly now for ILD for RB I have to consider a distance x from point A as I have to take the moment about A. So RB into L is equals to 1 into x. Therefore RB is equals to x by L and again I have taken a load interval of 0.25 L and calculated RB and I have joined this point that will give you ILD for reaction RB. Now using Muller-Bruslaw's principle, so it states that to find out the reaction RA you have to remove that support and give a displacement positive displacement of unit in the direction of that reaction. So here I have removed this support and I have given a displacement of one unit to this RA. Then the deflected shape of that beam or structure is the influence line diagram for that function. Therefore again to find out the ILD for RB I have to remove this reaction and give a unit displacement to B and the deflected shape will give you the reaction RB that is ILD for RB. Now this ILD can be used for single concentrated load to a concentrated load that is a wheel load having a fixed distance between them. Multiple concentrated loads that is a truck of more than 6 wheel vehicle than a uniformly distributed load or combination of load system. Now we will try to determine the reaction for a given system of load using ILD. So first of all you have to find out the ILD for reaction B. So we know the procedure as explained earlier. So here I am giving a unit displacement to this B according to Muller-Bruslaw's principle and I have connected this that will give you the ILD. So now to find out the reaction RB, so what we have to do is so reaction can be found out by multiplying load into ordinate of the influence line corresponding to the position of the load. So now I have to find this ordinate corresponding to the position of load. So for 10 kilo Newton I have to find this ordinate of the ILD for 5 kilo Newton load I have to find this corresponding position ILD and for 20 kilo Newton I have to find this ordinate. So the load into this corresponding ordinate will give you the reaction. So RB is equals to 10 into 0.2 then plus 5 into 0.4 plus 20 into 0.7 this will give you RB reaction 18 kilo Newton. For RA reaction we have to draw the ILD for RA and similar way we have to find out this ordinate using similar electric triangle then again this load into this ordinate value will get the reaction RA. Now to determine the reaction for uniformly distributed load system, so reaction can be found out by multiplying the intensity of load with the area of influence line diagram between the UDL. So for this again we have to find out draw the first ILD. So here ILD for RB is drawn and this starting value of this ordinate is taken for UDL and end value of this ordinate is taken for UDL. So we have to calculate this area covered by this UDL as it is a triposaddle you can easily find out the area one half sum of parallel side into height. So this is the area and multiplying by the intensity of load that is 10 kilo Newton. So you will get the reaction RB. Similar way you can find out the reaction RA. So again area into intensity will give you RA reaction. So these are my references which I have referred. Thank you. Thank you very much for watching my video.