 Hello friends, in today's session, we are going to discuss on a topic analysis of a support reaction by myself, Mr. Bipin Patil, Assistant Professor, Department of Civil Engineering, Walsh and Institute of Technology, Solapur. So dear friends, these are the learning outcomes for today's session. Basically, we are going to focus on two points. First one, what do we mean by uniformly distributed load? The function of this particular uniformly distributed load. And next, how to identify the support reactions? This is very important. Let's focus on this particular figure. Here, the definition of uniformly distributed load we are going to discuss. First of all, the abbreviation is present here, UDL, uniformly distributed load. So you observe this particular figure. For example, you consider this is a horizontal structural member with UDL. So sometimes we are considering here the symbol for UDL just like, or some arrows are present here, or half semicircle is present here. This is the symbol to identify a uniformly distributed load. Here it indicates uniformly distributed load is a load that is distributed or spread. This particular load is spread across the whole region of the element, such as it may be beam, it may be your slab. Consider here, this is two supports, simple supports are there and this is the span. The width of this particular beam here, it indicates uniformly distributed load is distributed uniformly surrounding this particular surface. Whenever we are going to solve any problems or support reactions, you must know the signed inventions. Upward force, positive sign, right hand side forces consider positive one and clockwise rotary fact you consider positive sign. Similarly, left hand side forces negative sign, downward forces negative sign and anticlockwise rotary fact you consider negative sign. These are the basic steps to identify the beam means support reactions, three steps are there common for all. Step one, draw the free body diagram for your given structure, showing the loadings, which types of loadings are there, so UDL, UVL, point load by considering your support condition means simple support, roller support, in support, fixed support, etc. Second step, apply the equation, three static equations are there, summation f of x is equal to 0, means all horizontal forces, all vertical forces that is summation f of y is equal to 0 and consider movement at any one point. Here you also assume the directions. Step three, find the unknown reactions. Let us discuss one problem. In this particular problem, you have to determine the reactions at support A and support B for the loading shown. So support A, it indicates roller support, support B, it indicates hinge support. Different loading patterns are there, simple support, you consider here point load, second one UDL, third one inclined point load having 45 degree with respect to horizontal surface. So first this particular 20 kiloton attacks 2 meter distance from support A, 30 kiloton per meter attacks, 6 meter distance from support A and similarly 60 kiloton inclined load attacks near about 2 plus 4, 6 plus 1, 7 meter from support A. So your first step is, you remove this particular UDL and convert into point load. Let us see, this is your problem statement, you are removing the supports of a beam. So here you remove the roller support, you remove the hinge support, also you mention the point load for this particular UDL and 2 components of this particular inclined point load. Similarly for roller support, only one vertical reaction is there or for hinge support there are 2 reactions are there, one is in horizontal direction, second one it is in a vertical direction. So we cannot say RB, we consider here HB and VB, so reactions. Convert this particular UDL into point load, so for that you consider this particular, so you observe here 30 attacks in a downward direction. So how to convert the UDL into point load? So this particular load means 30 kiloton per meter attacks this particular 4 meter span. So whenever you are converting this particular UDL into point load, you must consider this particular load into the distance and it acts always midway between the span of this particular UDL. So 30 into 4 and it acts 2 meter from this particular 20 kiloton point load. So 2 meter from here, 2 meter from here it acts here. Similarly mention the 2 components by considering this 45 degree inclined point load. So 60 cos 45 and 60 sin 45, let us will solve, first you apply summation f of x is equal to 0 that is horizontal, so all right hand side forces, so here only 2 forces are present. One is 60 cos 45, right hand side remember the sin convention positive minus HB is equal to 0, now we require the value of HB, so how to calculate it? Do the calculations and try to identify the value of HB, so HB it comes 42.43 kiloton. Similarly you apply second condition that is summation of movement at point B is equal to 0. So here HB and BB both are 0, 60 cos 45 right hand side and it acts on a same lamina. So this particular 60 cos 45 is equal to 0, further you consider vertical force, so it acts in a downward direction and according to this particular point B it creates anticlockwise rotor effect, so you consider negative sign. So minus 60 sin 45 and this particular 60 sin 45 acts from this particular nodal point, so the distance is 2 meter, so that is why I am consider here 2 meter. Similarly you consider next point that is this particular udl, so 13 to 4 that is 120 acts in a downward direction, so from this particular point to here the total distance is 5, 2 plus 1 plus 2 and it also create anticlockwise rotor effect, so consider negative sign, so 120 into 5, next 20 point load and this whole distance 2 plus 2 4 plus 1 5 plus 2 7, so 20 into 7 it is also create anticlockwise consider negative sign, last one that is your RA, so RA upward direction and it creates clockwise rotor effect, so consider positive sign. So positive sign means RA plus this whole distance, so this whole distance 9 meter, the value of RA is equal to 91.65 kilonewton, next you apply summation f of y is equal to 0, so we consider here all vertical upward forces that is RA plus VB all vertical downward forces consider negative sign minus 20 minus 120 minus 60 sin 45 is equal to 0, means RA plus VB is equal to 20 plus 120 plus sin 60 sin 45, so the value of VB is 90.78 kilonewton this is according to the equation number 1, so how to calculate the value of RB, so for that HB is known, RA is known, VB is known, so use this particular formula and find out the value of RB. Similarly find out the angle with respect to horizontal, so alpha comes 64.94 degree, according to that easily you can identify the remaining values, let us we will solve quickly one other one problem, same simple supports overhang beam is there 30 kilonewton downward UDL is 24 kilonewton per meter and one point load that is 40 kilonewton, same steps is in a simple support remove the UDL mention it is in a point load, so let us see remove the UDL mention it is in a point load 30 kilonewton simple supports RA and RB all simple supports are present, because already we have converted UDL into point load, now we apply moment at point A is equal to 0, so 30 into 1, 24 into 3 that is 72 into 1 plus 1 plus 1.5 that is 3.5 plus 40 into this whole distance 6.5 minus RB into this remaining 1.5, 1.5, 3 and plus 2 5, let us calculate the value of RB, so we have converted UDL into point load and then you calculate, similarly summation f of y is equal to 0 all vertical upward forces equate into all vertical downward forces RA plus RB is equal to 30 plus 24 into 30 that is 72 plus 40, so the value you just try to calculate RA is equal to 33.6 kilonewton, so according to that easily you can calculate the support reactions, so my dear friends you just try to pause the video try to identify the answer of this particular question, these are the answers for this particular questions, to prepare this particular video I refer these particular references books, thank you.