Dear learners, in this class, we shall learn about few types of fields. Now money used in construction and mechanical design, I just open the subject, This is lesson 0506 under bracket five that is, we are started from 06062345 all coming under the same category that is we are dealing with beams, bending moment, moment of inertia and also your suction cup. And in this chapter, we will briefly go over types of booms in construction. Okay, now everything has been prepared by me and I will just open the Google Sheet and we have here the sheet number one We will first determine, we will understand two types of statically determinate and another one statically indeterminate. So, in this statically determinate beams the all the forces, bending moment shear force and all values can be calculated by three equations, sigma hatch equal to zero sigma v equal to zero, sigma M equal to zero, you must be knowing about what is sigma what is V and what is M. However, I will explain once again see, whenever a force acts on a body, it is determined by the direction, sense and magnitude.

So, when number of forces acting in your body then it will be resolved into two components, that is one vertical and one horizontal, more about it The test the same effect today on the particular force you have one you apply a force in a vertical direction and the component in your horizontal direction together will have the same effect. Because since you force each record quantity and if you draw a line that is also a quantity of course is always proportional to the lines drawn. Suppose, you have a triangle of forces, then the triangle forces the proposal proportional to the content triangle and to set on scale okay that is all gone we hedge our calculated vertical and horizontal columns raw result that is, suppose you have one easy person, then one cos theta is equal to x value that he divorces in granted the horizontal direction at an angle teeka then each component to the design production is Phone cost data and its component to what it actually needs, you have one sine theta like that F one f two f three all forces are dissolved into h direction and y v direction, you have four h f one f two hitch f th your forehead etc.

And since they are in the same direction, you can add them together in the horizontal and vertical and then one single pose acting in a horizontal direction in a vertical direction. And once we will combine that the square root of sigma x square plus square root of sigma v squared, you do this acting course, when the forces are acting not at a single point, then it forces a barrel, then, we have to take the moment the buyer means, we take moments or two points a sigma m one plus m m one equal to W one you Do excellent was w two on WC of one plus f two t x two, etc You can find all the moments and we will get another equation that is another equation. So, we can have three things can be determined, which is a simultaneous equation. So, we can find out this is in the case of statically determinate beam, then we call that statically determinate beam, because we can come in to find out the values by applying these rules and now, you come to statically indeterminate what is that means statically indeterminate means that we cannot solve the other various other forces or resultant forces and anger for Second pose and resultant moment or angle opposite and moment, just having these three equations and then we need to have something else more that is the case of statically indeterminate the quantities are known quantity will not be three more than three.

So, that is how we will arrive at tactical indeterminant big files that are being said to be statically indeterminate then we have some work condition imposed on it, no doubt sigma x sigma is zero at the same time with the forces acting on second beam then, we will either vertical deflection or deformation when it goes undergoes deflection it has settled at any point and it has certain deflection also vertical movement. Moment Have you been okay this week constraints drop support at a position when was at a body and you have scope at applying the angle theta, then we will constrain the angle theta zero by applying some actual force, okay. And actual force applied to reduce the drop to zero, that is the actual force upgrade will be set that we apply a force in a direction of positive theta and magnitude equal to minus theta.

Similarly, deflection also suppose the deflection at the point is wide and we want to make it zero, then we apply a course equal to in such a way that that pose which causes a deflection of minus y and its direction is opposite to that, let's indicate remains why and it will be zero and that force will be another unknown and that is We have more unknowns more than three and is called statically statically indeterminate. With this in mind will now define various types of beams, I will open to to have already drawn everything. See here has shown two types of beings, one is called simply supported statically determinate that means, the forces acting on just beams can be obtained by having sigma hit. By these equations, we can determine the reactions and direction of the reaction. here since all the forces are vertical direction is also vertical.

So, you went by calculation you get vertical directions only by by general knowledge of engineering we can always own 10 vertical forces to be balanced. we'll work our forces together Since a baby is in equilibrium to reaction forces will be so not on vertical. So, in the case of simply protect statically determinate there will be two supports here, it may be a war it will be a column or anything in the steel section, I section is actually whatever section or a concrete beam you just placed on it without tightening or without grouting without doing anything, simply press run so, that you can rest on it the length of the entity anything so, that the beam and when a force is applied on it, then the reaction will be on this rest surface with a uniform reaction on the length to talk the length of the rest of this.

Okay. And that reaction, we can find out by knowing before all these causes and their distances and by taking the moment I can get So, this is called simply supporting that here, you have just kept the beam or the support, nothing is fixed here. In this case, you cannot play an angle pose just like this, we cannot apply an angle post, because, if the angle post is more than the frictional force between the support and the beam the beam strike to one side and it will follow. So, hence in these circumstances, the upgrade forces should always be vertical it should not be inclined or horizontal. And even if you apply a vertical inclined force it may be very small quantity so that the frictional force resists the movement of the key. Now, we'll come to the another type of digital source practical determining, here we are so we can find out the values of moments by controlling the questions with my work See unknown says one unknown here one unknown yeah and the direction is either working moment to three or taking resultant of all these forces and finding the force, horizontal and vertical forces.

Yeah, I have shown you like this is simple. Here what we have done this is a hinge point this is also called as pin. That means, it is only sort of a sled. So, it can take the reaction in any direction and it refix the point is we cannot move out of the point unlike this year ago if you can crank for second move away, but you're not moving, the beam is firmly secured in position, your spine will not change. Okay, it may sink. It may slightly incline upward Ukraine downward but but it will not move From this point where the differences access was existent, cannot move from x distances here to here rejects you can move, but here it will not fix implosion This is called a hinge point hinge acquire can always take reaction, any damage, not mystery in particular.

So, if you can apply Of course, in the inclined direction, so, that this will take you know, we have put a wall here and so, this is a vertical is supposed to always vertical because the roller indicate was has to be always vertical, it cannot be in That's the meaning in Grand Forks knives then we roll Learn these words out in this incredible sadness tilt right roller rolls off, so that always the reaction will always be what cannot be change direction. So, we have three parameters to be fun rock, in case you have several roles acting that is also sector 1234. And we know all the forces magnitude and also the forces of vertical forces in play. So, then what we take will resolve into horizontal and vertical direction, and you can the horizontal component is equal to or isn't true copper and just thought because we've been equally.

So, beam has to be in equilibrium reaction, forces should be or magnitude and direction. But, whereas, when you resolve this for a reason to push here is always vertical session will continue and then vertical forces to consider a component is vertical and this vertical force directly because it cannot have any horizontal movement because it is supported on words and I want to force the role of walls out on the cushion and makes new course are these vertical. Now, let us know how we will find out the deflection deflection in the last class, that is 0603 I have already explained how to find your deflection to rows between two reaction roads are in Britain's reaction. And we have calculated the deflection that we found with all the forces pulling a human and then we use the quantum law to find a reflection In that case, there was only one row deflection one deflection.

Earlier I have shown you here the probable deflection is just because all the forces acting causes sagging the meaning sag like a row, but you cannot see very many new facts. Suppose the length is one meter depending upon the port and moment dependency I have everything shrank maybe find minimum one mm. Okay. So, the curve is shown like this. It is something like a arc, but actually, it is a parabola. It looks like an OG we call the T's and inflection is where it's more see quarter quarter proper depression in case grants support and now, the role is appointed also we can find it by taking vertical will write too much Who's that we are not bothered about it now, we will take the component of this vertical component of this vertical and find the moment component of this vertical that is all vertical forces equated with component of this vertical and this vertical pose vertical, this component vertical some of these vertical forces on this vertical forces equated the value of v and with another equation horizontal component we can get you know how to solve on the piano curries similar to one also acting between two supports these are all statically determinate we can we can find out the forces by three zeros.

Now let us come this is two types of we'll come to this is here has been to other types. In this case, we will consider this listing all of them all we can say except cantilever, these two are, we can call it as statically indeterminate In fact, can do and also can be continuous Can you tell me but we can just get by without any difficulty we can always find out the moment and deflection getting raises determinate. So, here just see what that means, there will not be any anger that means, I will explain to work here what we have gone into the curb support our deep at this point of the curve v drive tangent inclined to the horizontal at certain angle and whatever may be magnitude very small question in crime similar here also it isn't right. Here also whereas, in this case the beam in traffic said it is not inclined, the beam is not supposed to deflect at the end to get an angle so, it is always horizontal.

So, it will try a tangent here. Slowly with zero to many at this point and anger occur somewhere here. So, this is called voting fixture in this case what we are doing the action First we will assume you can simply say I just simply supported you fine. And we get the slope awesome. We have our equation deflection equation equation because she knows. So, in that equation what we do in order to make this integration minus theta if it is inclined in anti clockwise, you can just lift it up to the point in the opposite direction.

What is the angle that needs to be great the slope here yeah Responding the question of stroke in the depression so that we get the Judo Judo stroke that we run wicked, we will take a moment what is required restrain the beam horizontally. Similarly, here the angles force of the year what happened the reflection and the center will be then robots are centered on the center at that particular point which is zero at the end rope is always zero any angle slightly more than that is to strengthen and one on. This is called as both in pictures views. Now, we'll call the other type of being one of the first unit statically indeterminate another type your work we have done yet one in districts as array we are not fixed, we have supported by Aurora, Aurora have been what have you supported in such a way that deflection at that becomes zero means, we consider an example I explained to you cantilever, okay, what I do in first explain cantilever and then come back to you.

So, we'll continue continue but you forget about what I explained now. So we'll come back to later on first plank cantilever, the cantilever one and this fixed beam is rigid enough and other entities cannot be fixed. forces will react in any direction and then your current opposite momentum created. Horsley beam in connection with the beam is not fixed with the spring between The sooner it will rotate. So and you will be displaced just like this rested then also if there is no real support on the other side, the moon will fall down and if the beam is pinned here and no support here, it will swing downward and the door will swing. Okay.

That's very what we have done it is fiction, it cannot also rigidly just you hold a pencil or any thing like that was the dream. It means there will be a moment which is the opposite. You have to keep in mind that change will not take any supports will not take any moment See, yet there is no moment bending moments bending moment, it will not take any bending. So there's no deflection in this moment there will be deflection vandeman the deflection at the end of this movement. Similarly, here also your wrench will not take the payment he will not bring you whereas tactically return in return will be group take bending, this is critical to take moment. So, that moment will be resistant by difficulty and so, we may not see it as swinging to an angle.

So, except a beams will have moment at the end, whereas, in the statically determinate beam from nothing Halloween candy candy one kicks in and depression zero and slope is often this is the most maximum deflection occurs on the end, depending upon your load. Suppose we the no load here, maximum deflection even damage occurs. At this point the deflection in the beam will be a straight line from here to here if there's no other it will be complete clear. It is just a curve. So that slope is maximum. cantilever stroke is maximum friction depending upon the rotor in both of the engines and now we'll determine tactically This is another type of one sided fix.

So that is it is like a cantilever. Suppose we can deliver, we lift it up so that you can lift it up. We have apply some force. So, that force is applied here when you rip it up. So, deflection is zero here and hence, this will be a curve like this and he ends up with some stroke on here. deflection at this point zero, deflection on this point is maximum, whereas we support the end that is called nominee Pro.

Which is in this case also you can apply anger to more types of beings. Now, I think it is clear to you know these, these three types of leaves that are statically indeterminate, technically indeterminate, this is can't be statically determinate even though extend is applied when we're applying an external moment. We can find out the moment entities, we can call, technically, you can be called by T question you can find out momentum equation was written by a friend and a positive concrete man it is. The probable deflection is already shown here. Now we'll move to another two types of beams. There are two more types of beams.

We can categorize number of ways of categorizing but we can, for time being we can consider effects of beam which normally we come across. He said we're hanging we're hanging beam. This is also a statically determinate decking. It has only two reactions, which which we'll find out by the equations. The only thing is, the supports will be in between beam on either side it winds for such beam is called walling. There'll be two reaction here and a number of forces post maybe more anger action also and here also falls into GCP GCP supported this type of grant she grabbed a vertical role in the war and VMs Also, you can have one green jazzer and roller Okay, then it becomes green and orange icon green which I like this, but one of the things he supports is not at the end, it is in between this we can call this you can call it a spin, then we can apply the force in the inclined direction.

If you just support the beam is more lengthy supported here. Moreland support area, then we cannot operate vertical for angle force, vertical force will need to be applied. If we make the beam pin and roll support, then we can apply angle. If we make it simply support this type of support, then you can upgrade one D which in this case, the simplest of all being With war angling, if only vertical forces operate and only supported the reaction just the beam is kept on the support here one more year and more and be more anxious on both ends. But the force upgrade is also limited because no war can it more. So, it should be at the end of course should be limited to the extent the moment that moment will view how much is the reaction in this case, should we be upward or downward then need to be rigidly to the bottom support reaction will be downloaded and it should be.

Now we'll come to another type of which is called continuous beam. See here what we have seen is to enter friction as you have seen here. Entropy she will be here Go into, but beam is very long. So, we want to restrict the flexion it should not deflect more than 150 of the length of the Why don't you say that some court practice the beam deflection should be and actually what we do is you just deflection we deflect you will lift the beam to force, so, that the deflection we do that is by lifting by applying your force here, maximum deflection also will reduce in reflection at this point we suppose, there is no support like just the flexion will be like this something like this. So, it could be more so, by lifting it, if you find that this is a statically indeterminate in this case, we have to find out the forces For these two courses, what is upgrade cost to reduce it to zero deflection and here there are two supports, we have to read the slopes of you to gain slopes of the route and accrue points to 12344 parameters have to make slope at the end zero and deflection are just 2.0 margin that is, this is what to be simply supported we then we apply at the moment to reduce the stroke zero and apply force begin to reduce deflections you know that these two forces that use for more unknowns are added to the summer loads to find out.

So what we do is we calculate the normal deflection and then we create we'll find out what is the deflection in the spine and equation we get a defined equation in terms of its return value and then you could get to em or R and deflection if it were to be in the upward direction by applying only or then we equated we get on that message calculation, you will know I don't explain, that you can Denton conjugate beam with and how the production can be bad and this also follows is the continuous beam must calculate the beam parameter to this length and then when we calculate parameter on this one and then move it, you know this, then this and this one we can go to like that you'd continue being used by step by step. You can use it on we can also use stainless steel In both various types of depression, etc thank you the next class let us see what we can study arguably we can study the conjugate conjugate, we were to the best method of biographically finding by using the conjugate and other type of finding deflection that is also one other method and also we can find out the fixed moments also we can find theorems to be adopted.

And I will explain a little bit of all those things, because this is basically how to use the Google Sheet and if you want to follow all those things here, and I will explain some extreme aspects of this. These teams by now Thank you very much