Hello. In this class we shall learn about conjugate v diffusion and also reflection replicability. The beam, one beam by example is a big arbitrary class of techniques. one centimeter in one dish are the deep and wide so it is immaterial because you can change it up and you played binders are new. This is a being we have on this big one in kg between one will not work at all just poking each other and distinctive moment and Western in kg from our reaction to a 10 meter apart these are all variables we can always be taught Monica bending moment of the week But, as you you have to find the bending you know in the last class up here to find out the action, taking the moment and also taking the action taking the mental armor and to somebody located on you'll get ready before start I will make some calculation and explain to you the knee bending john and bending moment here and just playing under 44.4 and load 10 kg it is to know that I am not going to Last class this is the Guardian rendering and the same as a beam the load will be the bending moment itself and they'll be two reaction r one and r two lash as I shown the same position as an r1.

So, we are considering this as a beam know that this load will be the bending moment diagram and reaction to V and j shaming as r1. So, I will tell you what is this load this bending moment diagram represents a load that is the load as we discuss some form you can use of acting so, but here you have Seems that the law does not constantly indicate slope as uniformly very low varies by kilometer per meter distance. Last class we know that we have seen that uniform roll the roll up meaning the constant rate yeah it is not. So, it is varying from zero to a maximum of 4.4 changing square g meter that is here roadies, not GG is G meter, because bending moment v kg meter. Similarly bending moment here I see F is 22.4 kg meter. Occasionally director we consider considered as a load that is lower Here you will find four Did you meter per meter that is variation or at this point is small length suppose you continue a dx a very infinitely small length your new load is uniform or the shock length at 4.4 kg meter by meter a short distance which is 20.1 meter.

That means, the law once again I will explain you at the at jido increases 4.4 kg you call it as dg meter. Similarly, here instead of gauges because they call you meter rated change applauded GG meter game fun meter, okay, which means this small triangle that is v v represent a local road And the Lord is acting at the center of the center of gravity of the triangle our sense of the triangle role the FCC is a trapezoidal rule that means we're role varies from V to C that is from qualifying for GG meter, supine four kg meter, that is the starting point v 4.4 kg kg meter roll and for short distance is constant and then the load volume meter coupon living and Regis value are continually paying for another watch the area be FC whatever you get, which represent the total load kg meter roll.

So, it is just similar to this beam back roll will not be concentrated. It is uniformly varying row region Not uniform rule if it is uniform load, then you know it will be a rectangle from here to here, this is uniform no more triangle added to that it was uniform revealing this triangle, it is uniformly varying, if it becomes a rectangle that is 4.4 kg from here itself then remains the same, the rate change or the same at this point, then the rectangular or your uniform road your keys uniformly varying road by meter road will be very just like x over here, acceleration is feet per second per second like that 30 kilometer per meter. Such a beam, we really consider the bending moment diagram picture as a node. And the same point we continue the reactions eunbi he's called junie B, I am not going to prove you how easy it will be able to draw the flower, but I will just use the tvpa This will support you further find out the deflection, I mean sorry the minimum income this beam, as you find from here to here you've got bending moment from here if you find out the bending moment diagram, then that Ben Newman diagram represent that deflection curve, but it will not represent exactly the value of deflection you in order to get the value of deflection at every point, we have to divide by UI.

To see you know to follow the square white divided by dx square equal to my bending moment divided by yea elastic modulus and moment of inertia the class action Key. So, such a beam is called as economy beam, where the bending moment diagram represents the load. And now not to find out the deflection, we have to find out the bending moment diagram of this. But what we have to do is, first we have to find out the reaction, I have already finding the action. It's already calculated here. I will explain you how to do it because I don't want to get a question in front of you.

And I have already done it, but we should do it very carefully because the very chance of being Miss Jang, which is basically do the computation of our addition subtraction calculations and all that even though we can the Google Sheet putting up the formula should be correct otherwise, we will get wrong results. First what we have to do the procedure. First we have to find out the area AB V 4.4 that means, up into B into half ye v that means that you're up half into base into height, you know the triangle, that is this third point how we got to find it to be thick meeseeks Alderney represented here. You should see the length from regret from your distance, the stitches are the same only this will vary. And when the moment interest gauges we put it when the moment value and define distances and reaction point will remain the same.

This is 4.4 that is half your base This is too good to be 14 the 14 is we have no idea This actually is the total roll. This is total 4.4 kg meter square meter meter square that is unit tempting because we have to multiply the unit uniformly varying bending moment with the base up to what it is you uniformly varying. Then we get a meter multiplied by base that is also in meter. So can you meter into meters two meters squared that's dimensionally 4.4 kg. Similarly, the F g b of t is a rectangle, we just multiply v 14 v 14 is F Once again v 14 that is this point qualifying for each remove this attendance, it remains the same up to F 4.4 into base this distance between these two that you see up here is V eight v eight your fight is fighting to get one like the bank that is 62 then VGC VGC is once again that triangle and roadies half into V 15 minus b 14, this length is V 15 into minus v 14 v eight v 15 is the value here 3.4 minus V 14 is the value here.

That means gf is V 15 to multiply by the ways we ate this year. In fact, we could have taken the entire trapezoid in the area, but it becomes more complicated and cumbersome. So, we have broken into a rectangle, triangle. Next we come to the area c f c f d up here, this is also a triangle find five v 15 minutes before p. BGP upon versus VCF D this is going to be 9.4 multiplied by b 15 inches, length 15 length is I have written here, b 14. The reason is length. So, this is to see, so, now we have converged the total area, total area ABCD A, B C D covered by this one 234 sided figured quadrilateral you realize that some deputies 137 is 137 meters square.

So much of local road acting on the beam you meter a product you need to spoil the load acting. That's the top row This is an actual kg meter per meter. This is a total is can you sum up on this top row overall this triangle Coco, Coco district train so you just click on uniform English 4.4 you know we have a red geese and you know, we'll find out the rate of increase how much and then finally we any road increases parameter that is we have Congo Beautiful angle this bird plank will vary from zero to 4.4 values be 1414 divided by length six six point this is rating, but a very weaker that the minimum six point I suppose it is 6.2 here, zero here, one way to language is 6.2 and then second then we go to this 4.4 kilometer per meter variation, the 6.2 kilometers per meter, we are at 4.4 kilometers per meter variation.

So, if you have a meter it is 3.1 kilometer per meter vantage point she will rate of increase here we have one For GC rate of increase, different b 14 into B eight, V eight is flanked by a meter, five meter by meter. He's from unity 4.4 2.4. In other words, here it is zero here and too late in QC of V is once again zero here, and here it is 22.4. The length is key. So we have divided by v 1550s. That's when you do it by yourself all these triangles and rectangles, we now are finding the action how to find your final reaction is straightforward.

Just like we did find when you find onto the net assuming this ABCD as a load acting on that a to be uniform earring for a coupon for buying for D to sequence to find For this we'll find out the goal multiplied by distance take a moment at any point in our mesh on day two. That is what I have done, what we want to do r1 took on that, but it is part one r1 r1 to find a new element r1 that is b 19. On actually had to find note on latches meaning you could go into length, that length is 10 meters. This should be equal to momentum on the area. I've taken off One back then then use a bat because these are very good measures that are going to be 10 equal to this young up you bees. Yeah.

Yeah this is this is how we can find this area up up here consider the distance, this is one time one third of crew plus this distance five, three. So exactly monitor this area similarly Other area we can deep into V eight VA to find out here what is the VA v five v nine point b v nine plus 21 v 22 b at 2.5% v nine v nine is that since we don't have taken v 20 this area momentum this area is rectangular linear momentum. As I just mentioned gravity is rectangle acting, so v eight into half V at the length, five meter, five meter into half return to this 16 into really into point five Press been in this region to multiply to get the momentum that plus v 21 v 21 or the B 21 this 27 area this small area okay. This one is multiplied by 100 into B A plus B and I will tell you the central gravity of this triangle or central this triangle is one third from the base from our example from to one third to left okay that is what they have taken vag length five meter length bat length into one that is from year to year 138 plus v nine this distance that might be 20 the area okay.

Similarly, consider the neck DS this area beat on T two Be 20 to 35 find one that multiplied right now, it is from this sharp point is to be 22 two times two to be nine is one a triangle. So, it will be say from here to grantees to touch from the effects the triangle. So, this is good. So, from here I wanted for you to measure the distance into distance from here, this is something to tie up here to 33 and we know that distance, this entire thing is the moment of the entire board that is once again is playing the role v v that is area v one third of the distance plus five plus three will make up this Yeah, let's go Melinda This is a rectangle 4.0 into half of five. Let's see, let's do just one area. Usually, they have this one turn from here, one third of five, press three, and then this triangle CFD in the eyes off area I'm going to multiply by one third not half one third from Region One into three.

So, all this together the moment the moment we get into this entire this conjugate be that divided by that is should be equal to on dash one into distance 10 meter, just like taking a bigger 10 meter we bring to the side, the right side of that one intubated, equal to this to bring two sided become belatedly began and calculating all the marketing all you think comes to mind. Similarly submitted to Iran we can find the gold from 137 you can deduct this value are, you take the moment have taken a moment and just point to this distance, you have this triangle, multiplied by one third of one third of each year did not 230 haunter from here plus five plus two. And similarly, rectangle five into 4.4 multiply by half of this group and disability this area, this area v two thirds Don't come here who touched on five plus two and then this is two thirds of this area in this area, moment or two can bring back this into their eye I sent you because you're very well written and this you get certified.

So, now we have money r one r two both are available for the reaction on the conjugate know what we do is we once again we have to find the moment of this bending moment of this that is the deflection venom of this beam conjugate which is called conjugate dream that will be like how we get bending moment good moment every time here what we are doing now, because the question is not continuous. So, we have to control the bending moment, this area will take about three values because we have to draw a curve we have to go through that people values to get a smooth curve. So, up here suppose we take moment from identifying within you. So at zero at year zero At any point, this is a point five to five of basics that is to use basics to use basics here trying to find a basics that each find five registers up from here to find one somewhere here find one.

Now, we are covering this small area find the distance height will be in proportion 4.4 and we know the rate of increasing node, that is rate of increase in road use we explained to you too spine to the rate of increase for the length of Fine Fine, fine, fine, fine, fine. How we can we can do so in creates a TA To return your van conjugate beam loaders r1 minus this is once again convention you can do sagging upward, the renewal and yakking sagging and this is Auggie order two minus V 24 in two years t v 246 point two 830 8.5 so I just want to find five we can do for you for the rate of 2.5 what is increased up to 2.2 that is the role here I just blanked is about the height will be 2428 psyche that 3.1 see pine cones that is what we like to call it return before we continue to find that one Again we had to multiply by 32.5.

That if you had to find a union, the small triangle area and that is point four use the length. That is, it is V 24. In two years again because increasing growth and the rate of 6.2 multiplied by base 838 38 we have already taken 38 which is 1.6 38. And multiplied by point five, that is the area, this small variable triangle, at a distance of point five from that area of the triangle is that multiplied by one third the moment we know where it comes from the moment from here it is from you forget moment yet central of this area is from this punch is unique based on that idea and this point will be somewhere one Third from this point to one third, one third of that, it's actually the distance is point five, which one that's what was that moment we had to do that and the next activity 3.1 similarly, now, you should have find all you are controlling one after one point, triangle remote area that is 6.2 into one that is the rate of increase in doing done that is your artitude on this G 6.2.

And the base is one meter and it is one third of one meter that you get subtracted from the VA 39. Like that we had to completely calculate 1.5 when you get up to here is 3.2 have considered the banking at the point now, Boom, we get into who also we can compare contrast and just add into one basic one, you will get 121 point this bringing the random woman at V 166 point wagyu arguing This is approximate is not the correct values an arbitrary value for the future to have shown you here is actual calculate value get r1. So that you need to assume this is the correct figure and familiar here so it's 1.1 that is not equal to 72.3. You assume that he's already just African, roughly my actual register have calculated yet. That is our last one is 64.7 72 point. Just do that he just brought up our values on you in here.

Not correct values are calculated is to be considered as correct use also you just for my own purpose calculation Don't worry about how I have done one we can we can see the basic principle of geometry and we are no here just one country and that's why the VM is a variable within two European European region Nigel nice to see ya. Five and one and 1.5 no arbitrary point is revealing points we find out next week on 43.5 tobacco playing independent movie when you consider any point comedians that you meet once again on an x one x 164 megabyte gems and the Nakia in distance minus render momentum add up I mean one third plus this will create a new directory one group that we complete or have taken at least two that we have to add file to file to be at the point that means, I keep trying to find it point to point in the area like to play that one title Let's just jump 1.1 point two five, this is the bending moment here okay that's the wrong one let you study peacefully, you will get your water taken bending moment on this I just point to point to find a conservative bending moment on this area and this rectangle B is this rectangle small time the bending moment of a disappointing bending moment r two r one dash n minus bending moment on this at this point let me this year line 231 depresses guests that will act 3.2 point one When you get into 2.3 point 2.25 or controller 3.2 forget this one and two this 1.2 that is the value I just value all these calculations are done, you see this minus b 19 into one third the basic will be 19 A to be 640 to be six, V six is two and acting on the blank like this triangle district design this tender, this is a rectangle to have added a to b into pi by 42 minus b 642.

This is the uniformly varying or benign thing 4.4 Find the destructor 2.2 point two detective or 3.1 point two v d into your pocket to the basics into Python into the 16 total length of this rectangle and the center of the load will be half of the distance that is point one. So, this is how we calculate. And then the third figure will be the small triangle, small triangle trying to find a to b six B six point prove the rate of microcredit multiplied by eight you have to multiply by To multiply by 6.25 minus b six, you start from crude. So it is 1.25 did you roll to roll that is vertical height of this triangle up to 3.25 to two there's a triangle formation, this triangle formation that is called multiplied by bass you tune in to find by half baked into the I guess unique rate of roll into you in particular and then we have to multiply by 0.22 minus V six.

That is One Two times two times two to 42 u minus v g. Similarly the last 10 meter portion we start from chapter seven the tokens