 In today's session, we are going to discuss on topic support reaction. Basically, we focus on compound beam, micelle, Bipin party, assistant professor, department of civil engineering, Vulture Institute of Technology, SolarPool. So my dear friends, these are the learning outcomes for today's session. At the end of this particular session, student will be able to explain the function of compound beam, what do you mean by compound beam? Second, analyze and calculate the support reactions for compound beam. So my dear friends, we just focus on this particular figure. First point is present, the definition of compound beam. Basically, there are four types of supports, simple support, fixed support, one in each, other on roller. Just like you just consider here, different types of loads are also present, point load, inclined load, uniformly distributed load, uniformly varying load. If we consider two supports and only one member is present, we call that simply supported beam. If one end fix and another end, there is no support, we call that fixed beam. At one end, in support, other on roller support, we call that one in hinge and other on roller support. Just like compound beam is present here now. Now you just observe this particular figure. A, B, C, these are nothing but your nodal points. A and C, simple support is there. And B, here we have just connected two members by using one internal beam or roller. On this particular first segment, A, B, second one, B, C is there. On A, B segment, we are consider here one additional external load is there, that is P. Sometimes we called as point load. MBC, there is no support or there is no external load is present there. The span of your first segment is L1, span of second segment is L2. Now what do you mean by compound beam? So, you just observe here. When beam consists of two or more than two members. So, here we are consider two members or more than two members. It is connected by internal beam or roller. So, internal beam is present here, roller. Such beam is called as compound beam. Now you just observe here. These two particular beams are connected by using this particular beam or roller we called as compound beam is there. So, how to analyze this particular beam means how to calculate the reactions for this particular beam. Now basically, the sign conventions are very important before solving any problems. So, two parts we have just consider here. One is positive sign, second one is negative sign. How to bifurget it? All vertical or poor forces consider positive sign. All vertical downward forces consider negative sign. All right hand side forces you just consider positive sign. All left hand side forces you just consider negative sign. Clockwise rotary effects consider positive sign. Anti-clockwise rotary effects consider negative sign. Now these are the steps to identify the reactions. So, determination of beam reactions. First step, now you just observe or remember previous slide two members are present, two segments are present AB and BC is there. So, first one you just consider second segment draw the free body diagram of the structure showing the given loading and the reactions at the supports. Means you just remove this particular supports mention only simple support and by considering that particular simple support you just mention the external loads. It may be point load, maybe your UDL, maybe your UVM. Basically, second step consider the topmost beam that is nothing but the second segment and analysis done by considering this particular topmost beam and find the reactions. Third step apply the static equilibrium equation that is the three equations are present summation f of x is equal to 0, summation f of y is equal to 0 and summation m is equal to 0. So, here you just consider some directions that is nothing but the sign conventions already were discussed. By referring this particular sign conventions you just identify the reactions. The last one step is there by using this particular equation you just identify the unknown reactions. Let us we discuss one problem, determine the reactions at support A, support C and D in the compound beam I have shown here. B is nothing but the internal pin or roller is there. So, as we discuss here in our strips AB is a topmost beam. So, first you just identify the reaction present over this particular beam. Then whatever reactions are present on this particular beam it acts in a downward direction as a point load to this particular second segment. So, our first step is by considering this particular geometry, this particular figure just remove the supports, mention the simple support and try to drop free body diagram for this particular given figure. Similarly, mention external loads. So, this is the solution first one consider first segment AB. That is you just consider one movement center A and you just apply first equilibrium equation that is summation m at point A is equal to 0. Now, on this particular segment AB only one external load is there that is 180 kiloton and this is your movement center. So, this force into lateral distance or horizontal distance that is nothing but the movement. So, 180 into 3 that is it creates clockwise. So, you just consider positive sign second one minus RB into this total distance that is 4 and it creates anticlockwise rotor effects. So, we consider negative sign. Now, by solving this particular equation we get the answer RB is equal to 135 into 2nd you just apply static equilibrium equation summation f of V is equal to 0. Now, here we are considering all vertical upward forces and left hand side all vertical downward forces on right hand side. So, here RA plus RB is equal to 180 already we have calculated the value that is this particular equation number one RB put this particular value in this particular equation calculate the value of RA and its counts 45 kiloton. Similarly, consider segment CD. Now, whatever the value you have calculated here that is RB 135 kiloton attacks in a downward direction or this particular segment and this particular distance they are mentioned in 0.5 meter. So, now you just consider C as your movement center summation of movement at point C is equal to 0. So, C first one RB it creates here anticlockwise all right. So, RB into this 0.5 it creates anticlockwise rotor effects on negative sign minus there is no any external load present over this particular segment CD. So, you just consider only this particular support reactions minus RD into this 4. Now, put the value of RB here. Now, you just consider this part here in right hand side do the arrangement and calculate the value of RD. So, the value of RD is 16.875 kiloton. So, this is for segment C to D. So, just like you just calculate the support reaction present at support A, C and D for components. Similarly, apply second static equilibrium equation summation f of v is equal to 0. So, all vertical upward forces on left hand side all vertical downward forces and right hand side RC plus RD is equal to RB that is 135. From equation number 2 here we already calculated put the value in this particular equation calculate the value of RC. So, it comes 151.275 kiloton just like you just calculate the support reactions present at A, C and D supports. Now, my dear friends you just pause the video and try to give the answer of this particular question. This is the answer of this particular question. To prepare this particular session I have referred these particular references. Thank you.