When constructing buildings, why do we always use beams which have a cross-sectional shape of I? Let's explore this intuitively in this video. Created by Mahesh Shenoy.
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- why in the centre there is no stress ? why is it taken zero ?(4 votes)
- because at the ends the tensile and compressive strength are maximum at centre they will act at half magnitude so these two will cancel out and the total stress would come out to be almost zero(1 vote)
- Why we don't use beams of 'X' shape with two flat surfaces on the top?(4 votes)
- well i am not sure but in x shape with flat surface not maximum area would be removed from the centre and our main is to remove it from centre not from sides(1 vote)
- Can we use "Z" as a beam with two thick layers at the top and bottom? Will there be any effect produced by the slanting middle part instead of a straight one?(1 vote)
what is the most common shape of beams that you see in all these structures it's the famous eye beam as you can see over here it's called as the eye beam because it the cross-section spells out the capital letter I but why do engineers prefer this particular shape why I why not any other alphabet suppose we want to build a bridge which is supported at its ends and let's say we start out with a bridge having a rectangular cross section due to various forces which are acting on the bridge like gravity is pulling down on it so its own weight is pulling down on it and there are other things on top of this maybe there comes there could be some vehicles moving around all these things push down on this bridge and as a result of this force this bridge could deform now the exaggerated this bending over here but it does we've already studied that materials deform under external forces all right and when they deform they try to snap back and do that there are restoring forces generated inside and as a result this whole bridge now is under a lot of stress and we've also studied that if the stress goes beyond a particular value if you deform it too much then the whole thing can even break and the whole question now is how do we resist this bending that's the that's the big question we don't want this bridge to break we want to resist the bending so how do we do that well we can start with our intuition we already know that if you have a thin stick like this then it's quite easy to bend and break it but on the other hand if we had a very thick stick then it's more difficult to bend it it's more difficult to break so a very simple thought that we could have is we just make this bridge thicker right so you take this bridge and make it thicker just make it thicker and we are done well but there's one problem with this if you make this if you make the bridge thicker then you're using more material and you're increasing the weight of the whole thing and if the weight increases the bending force further increases that's a problem and not just that and our support has to be strong and then if you want to carry this from one place to another so if you're manufacturing it in one place and then you're transporting it to another place then again that becomes more difficult so there are a lot more problems that are introduced when you make this bridge thicker so you're creating more problems than solving it so you know what we the great were we great thing to do we would we want to find a way to make the bridge thicker without increasing its weight without adding more material to it and at first you were like what how do we even do that all right so engineer switch we're faced with this problem and initially it feels like it's not possible but if we if we dig into the physics of it then we can come up with a solution so the key is to understand exactly what kind of stress is generated inside such a bent beam we've learned a couple of kinds of stresses we learned about tensile stress compressive stress shearing bulk stresses we learned about those in previous videos and if these things sound new to you then maybe maybe it will be a great thing to go back watch those videos especially tension tensile stress and compressive stresses those are going to be important over here watch those videos and then come back over here you'll be able to appreciate this much better but anyways in all any of those videos we never spoke about bending like this so it might seem like bending is a little bit more complicated it is but we if we look at it carefully you can actually understand what kind of stress is generated over here to do that we look at this bridge one more time but this time let's imagine some hypothetical imaginary sticks that we have put imaginary rods that we are put inside these are going to help us understand how the stresses and now again due to the force when the bridge deforms notice that the sticks come closer to each other on the top and they go farther away from each other on the bottom which means on the top the molecules must have come very close to each other that's what these sticks are doing they're helping us understand what happens to the molecules the molecules must be coming closer to each other on the top and the molecules must be going farther away from each other at the bottom so at the topmost point the molecules are the closest just like how the stick are the closest at the topmost point the molecules over here are the closest and remember when the molecules come close to each other we are talking about compression can you see that the the sticks over here since they have come close to each other this top part is actually under compression so this this part over here is under compression and there is maximum compression at the topmost part over here so there's a lot of stress there's a lot of compressive stress maximum compressive stress on the top but notice just like how the stick goes far away at the bottom at the bottom most point molecules have also gone very far away from each other and therefore at the bottom most point we have maximum tensile stress the molecules are going farther away from each other so there's tension going on over here so there is maximum tensile stress maximum tension we would say so again a lot of stress is over here and notice as you come closer and closer to the centre the the compression decreases and similarly as you come closer with your tension decreases so the closer you go towards the centre the compression and the tension decreases and pretty much at the centre pretty much at the centre there is no compression or tension and so we could say there is no stress over here no stress at all now we'll go back to our intuition why is it that when we make that stick thicker it'd be difficult to break well that's because when you make it more thick you're adding more material you're adding more resistance to bending because there will be more restoring forces and that's why it becomes it becomes more difficult to bend it but guess what if you want to resist bending over here you only require more material on the top because that's where compression is going on and you also require a lot of material on the bottom but you don't require a lot of material in the center because there is no stress there is no resistance going resisting resisting forces and set up in the centre so why waste material by putting it in the centre and that was the idea that engineers came up with and so engineers said well we can make the whole thing thicker like this but not by adding more material all we have to do is remove the material in between because they're not going to provide any they're not going to be pro any resisting forces so that's not let's not waste our material over there so let's remove all the material from this Center let's get rid of all the materials over here let's remove them let's keep it very thin at the center and let's put all that material at the top and notice as a result the shape that you end up with is the eye shape and this is the famous eye beam so what we have done is we have made it thicker in the regions where the stress is maximum thereby making it very hard to bend but we have not used any more material than we are using before so the weight of this is pretty much the same as before and that's why engineers say that this is the most efficient shape to withstand bending and therefore I beams are awesome