 Hello friends. In today's session, we are going to discuss or a topic analysis of a support reactions by considering uniformly varying load. Myself, Deepin Patil, Assistant Professor, Department of Civil Engineering, Vulture Institute of Technology, Sulapur. Let us we discuss some learning outcomes. You will be able to explain the function of uniformly varying load. What do you mean by uniformly varying load? Second, how to identify the support reactions for uniformly varying load? The definition for this particular beam consider a horizontal structural member having a simple support span L with B. What are the indicates? A beam is a horizontal structural member. It carries transverse load and supported at ends. Means it is a horizontal structural member. It carries different types of loads, may be point load, may be UDL, may be UVL, may be inclined load, different types of loads are there. There are different support conditions are there. May be simple support, may be your roller support, in support, etc. It has one dimension length. Means one dimension that is you consider your length considerably larger than other two dimensions. Other two lengths thickness and width is there. What it indicates? A little bit difference. Horizontal structural member with UVL. With UVL means uniformly varying load. What it indicates? So let us we discuss the definition of uniformly varying load. If the intensity of load increases linearly, if the intensity of load increases linearly along the length, along the length is called varying load or vice versa. If the intensity of load decreases along the length means at one end it is 0 and at another end it is a maximum. It indicates a uniformly varying load. The nature is just like one type of right angle triangle. The load whose magnitude worries along the loading length with a constant rate, with a constant rate that is nothing but your uniformly varying load. Next, you observe here the sign conventions. To solve any type of beam problems that support reactions, we need these particular sign conventions. Let us you observe here positive and negative sign. So the green color arrows it indicates. Right hand side force you consider positive sign. Left hand side forces you consider negative sign. Similarly, focus on this particular red color arrows. One is moves in upward direction, second one it is moves in a downward direction. So upward force consider positive sign, downward negative. This is very important. Clockwise rotary effects. So clockwise rotary effect you consider positive sign, anticlockwise rotary effect you consider negative sign. Sign convention plays a very important role. These are the basic steps how to identify the support reactions. Draw the free body diagram first of your given problem statement. Mention the loads, whatever the loading pattern they are mentioned over the problem statement. Similarly, the reaction at the supports with respect to which type of support is there. Second, apply the equations that is three standard equations are there considering the sign conventions. One is horizontal force that is f of x, second one is vertical force you may consider f of y and last one that is the movement. All these particular three cases, three equations you created to zero and find out the unknown reactions. How to identify the support reactions? So for that we will discuss one problem. Determine the reactions at support A and support B for given loading. I am consider here a single triangular load that is single span uniformly varying load. Span is 2 meter. First thing is very important that is you convert this particular UVL into point load. So, at one end it is zero and another end it is maximum that is 30 kilo ton per meter. Let us we convert this UVL into point load. So, first remove the supports mentioned at support A or A, support B or B and convert this particular UVL into point load. So, how to convert it? That maximum loading pattern at maximum load it is present at nodal B. So, from that particular end here 90 degrees present to easily identify. So, it acts one-third of your this particular span means this particular point load it acts one-third of this particular total UVL span from support B it acts one-third from support A it acts two-third of your span. So, two-third of your span means two by three into two one-third of your span means one by three into two and how to identify the intensity of this particular UVL whenever you are identifying the point load. So, the area of this particular triangle means one half into base two into height that is the load 30. So, let us you apply the moment at any one point either A or B. So, I am considering here A so point five into two into 30 means this one and I am considering support A. So, it creates clockwise rotary facts. So, positive sign and the distance is two-third of the span into two two-third into two minus means we consider first this one minus R B into this whole distance two why we are consider minus because it creates anticlockwise rotary effects. So, the answer you calculate it it comes 20 kilonewtons. Let us find out the remaining reactions apply second static equilibrium equations that is your equations summation f of y is equal to 0. So, here you equate all vertical upward forces and downward. So, vertical upward forces R A plus R B is equal to vertical downward only single force that is 0.5 into 2 into 30. So, R A already you have calculated here 20 put the value of R A here plus R A. So, next one you mention 0.5 into 2 into 30. So, R A is equal to 10 kiloton. Next one you observe one more problem here determine the reactions at A and B for the loading shown one is 2 meter your uniformly varying load second one exactly at a node you consider here one end is fixed or there is free from support 60 kiloton one point load is present. So, for that you just try to identify the support reactions let us see how to calculate it. So, one end is fixed means here total three reactions are present one is in a vertical direction that is V A second one in horizontal direction that is H A and third one that is the movement you may consider positive negative M A convert this particular UVL into point load that is 1 half base 45 sorry height and the base is 2 meter. So, it acts from the maximum loading pattern and the lowest point is present here lowest force gradually increasing. So, from here it acts one third of your span and from another one point load another one support it acts 2 third of your span. So, movement at point A is equal to 0 minus M A plus 1 half base into height into the distance is one third of your span. So, next one 16 into this whole distance 2.5. So, easily you can calculate the movement present at point A. So, it comes 180 kiloton per meter. Similarly, how to calculate the V A and H A? So, we apply remaining 2 equations that is f of y is equal to 0. So, V A upward positive minus this particular one half base into height plus 60 is equal to 0. So, V A it comes 105 upon 00 kiloton and next one that is you consider all horizontal forces. So, you observe here only one horizontal force is present that is H E. So, there is no horizontal force you consider the 0 you pause the video and try to identify the answer of this particular question. This is the answer to prepare this particular session refer this particular reference. Thank you.