# Mod-04 Lec-02 Tubular Joint Design for Static and Cyclic Loads – 2 So, today we will continue to look at the tubular joint design You can see from the picture left side You see here, the welding is made in multiple passes You know, it might look so small in this diagram, but actually this width depends on the thickness of the plate Whatever the thickness of the plate, say it is 50 mm, you will see that basically from here to here may be 70 mm and another 70 mm So it is a quiet large size area where you need to do the welding When you try to do this, you normally do it using multi pass Means every time use a 6 mm or 8 mm welding rod, you weld around first pass, second pass, and third pass So, you will see that several passes have to go through in order to make sure that you get the complete fillet And the reason why we need to know this, the particular purpose is the profile of the welding You see at the surface, If you actually have… I might show in one of the class the real photograph of welded surfaces, you will see a lot of changes in the curvature So, when it is getting adjoined to this connection between the base metal and the weld, you may not get a very nice clean surface That is where most of the time we see the stresses increasing because of the notch effect We will see from one of the finite element picture later on I think you might seeing here You can see the change in stress at that location could be substantially larger and that is the reason why we need to know So, we will come back to this picture later Basically, the reason why we need to know how it is welded, is just to understand how the distribution of stresses at the location of the welding That makes a difference because that stress is larger than stresses applied at the plate elsewhere You know, basically that is the reason why we want to know Now, if you look at total process of application of load from brace to chord, you could see here in these two diagrams that any one of them can happen So, the first point is basically local bending of a shell Imagine if you have the brace wall thickness is substantially larger, good, strong And you apply the load, what will happen is basically just poking at a thin shell You know, if that chord diameter is large, wall thickness is smaller, what will happen? It is just going to go down This is something very similar to a local bending of plate Probably, if the shear capacity is not adequate, what will happen? Simply shear through and the brace can enter into the chord member So, that is basically a starting with the local shell bending It may actually end up punching through, piercing through the chord if the chord thickness is very small So, now you can see, one parameter we have identified The thickness of the chord is going to play a major role whether it will fail or not fail, isn’t it? And association with the diameter See, you cannot isolate a thickness and say whether it is too small or too big, all depends on what slenderness of the section itself So, larger the diameter, bigger thickness also becomes slender Smaller the diameter, smaller thickness also can become very stiff So, the D by T ratio is an important parameter rather than just the wall thickness, the diameter to the thickness If you look at the right side, because we made the wall thickness may be better, thicker, you can see instead of locally failing, overall pipe is getting ovalized So something similar to ellipse So, that also can happen depending on a relative stiffness of the brace and the chord So, what we need to understand now is the total problem may be not isolated only to the chord or only to the brace, it depends on the relative stiffness of the brace member and the chord member And that is what we are going to just look at one by one When you do this kind of bending, for example, you have a load here, you have a bending like this So you will see that the bending moment will develop locally and you may have a local bending stress, which can actually substantially be larger than the actual stress produced by this load itself Because we made the plate thickness so small, so it is basically bending here And that is the kind of information we are actually looking at Now, if you look at this, yesterday we discussed about, you know, the design approach is from three dimension to planar information, we are trying to for plane by plane And in each plane, you can look at any connection, they will fall any one of these characteristics Either it can look like T junction, it can look like a Y junction or it can look like a two Y junction in opposite direction or can be direction which is perpendicular to each other or can be any angle between them which is similar like an X joint So, what we are trying to understand? Anyone of this will be fitting into your actual design Only thing is that the parameter may change, for example, when it is 90 degrees, we call it a T junction When it is less than 90 degrees, it can be from any angle from lowermost as like say 30 degree, 40 degrees up to 90 degrees So, if it is within this, you will call it Y junction because it looks almost like a shape of a Y Whereas, when it becomes 90 degrees, it is T junction And if you have two or three members coming in… For example, in this case, I have drawn only a two members coming in, which we call it double Y or we can call it K junction Now, there is a primary criteria for a K junction, which we will see little later Because just a look at it, we are just classifying based on geometry, whereas it is not going to behave similar like a K. K means what, it is only shape, but the behaviour, we have to look at the load transfer So, you can see here, you go and do your design or anybody does the design, almost every one of them will fall into any one of this category, which we will see one by one Now, what is called a K junction or K connection? What is defined as is basically a balancing of loads For any joint to be in equilibrium, like this, then you have two members, one member is having a tensile load, another member is compression load then, it is called a balanced K junction So, as long as you have this balancing, if whatever the load comes here and takes in by the other brace, angle of this and angle of this is same, then there is no load applied on the chord across the section So, there is no shear load because member load coming in, member load goes out So, that means it is balanced So, this balanced junction is always better because the local stresses will be counterbalanced One is compressive and the other one is tensile So, that is why we have a special case where the loads are balanced, then it is called balanced K junction Or you have T or Y, there is no balancing here Whatever the load is coming from the brace have be taken as a beam shear by the chord member So, here there will be substantial increase in stresses compared to the K junction So, when we do practice using design, we will compare Use the case of balanced K equation and use the Y junction and find out The result will be more for this compared to K So, that is the idea that we want to show When you are trying to classify, you need to see not only the shape but also whether the load is balancing or not For example, you have both equal loads You can classify as a K joint, but if one of them is getting more load and another one is getting lesser load, so you can see that there will be fraction of K joint plus fraction of unbalanced Y joint, isn’t it? So, that is what the classification, we call it load path dependent classification Not only the geometry how it looks, but also you should look at whether the load is balanced or unbalanced So, for classifying into K junction, we need to have the loads are balanced For T and Y, you do not need to have the load balancing X connection, anyway you can have any type of combination But of course, you can have both braces carrying compression or both carrying tension whichever, you will have to have two different design equations And many of the times, we have these types of connections So, now you can see You just carefully watch these three diagrams The first diagram is the diameter of the braces smaller Quite smaller, comparatively smaller to the chord diameter I think most of you understand now the chord and the brace no? So, basically the receiving member versus the member transferring the load So, the blue color is the chord member receiving load from this brace member Now, you see the diameters, I purposely made it to just indicate how things will go wrong or how complicated things could be You could see here, it is smaller So, basically the ratio becomes less than half or equal to half or whatever When you make the brace bigger and bigger, see here, the D by d ratio is… Oh! This must be the other way Basically d by D and this also So, when you have the d by D ratio close to 0.8, you can see almost, they look almost similar, isn’t it? When you come to the right side, when they become equal, you can see the brace correction is coming all the way up to the middle of the chord member So, you need to realize how this will be done, because this will be a singular point Both diameters are same and welding here becomes actually impossible And that is why we do not want to have any brace member as big as the chord member We try to limit less than 0.9, 0.8 When you have such a situation, you will actually have the stress concentration here, will be very, very large because of the welding singularity So, you need to understand the configuration when before designing whether you should go this way or the other way, the results could be different Just to indicate what the increased stress at the junction is I just wanted to show you basically just a flat plate, 50 mm by 200 mm welded to another 50 mm by Just a plane plate is not a plate, it is not a three dimensional plate So, load it applied in terms of pressure at the top above 100 mega pascal So, all the plate, around all the way up to this point, you can see, it stressed equally because there is no change in direction, there is no change in dimension, there is no change in any local pattern So, you can see uniformly applied axial stress on the plate from top all the up to here But when it comes to a junction, you can see here, the local change in direction from a vertical plate to horizontal plate, you can see a notch stress Basically, we call it a notch effect and that becomes a highly stressed point Now, if you look at the stress difference between, this I applied a 100 mega pascal and when you apply to this location, you could see almost 250, something around So, one location here, the dimension of this area is about, say may be 5 mm maximum to 10 mm, in that vicinity you can see the stresses to 250, two and a half time applied stress But can we conclude based on this, this assembly will fail? Definitely it will not fail Because it is only a… If you see everywhere the whole area throughout the neck section here, if it is 250 mega pascal, probably we can conclude the section is highly stressed trying to overstress and failed But, fortunately only to junctions, left side junction and the right side junction, it is only a local 10 mm plus 10 mm But still substantial cross-section is under-stressed because, you see here, the stress at this location is around probably 110 and 112, because this blue and green mixed So still it will take larger stress before the failure takes place and that is what we need to understand This local hot spot stresses or local stresses are only isolated for one location, not throughout If you understand that concept, that means this junction or this connection is not going to fail right now until you increase this stress in such a way that the whole neck will become 250 or 300 mega pascal So, yielding will start and that is the idea behind We need to worry about hot spot, but actually we should not be unduly worried because the hot spot is not going to be are throughout the section And that is why it is called hot spot, it is a basically isolated points on the connection A similar exercise can be looked at on a pipe to pipe connection by just looking at it You can see a typical pattern Because in this case, it is not a flat plate, it is a hollow circular section welded with another hollow circuit section So, you could see here, on that particular location, it is very high stress of 200 plus, but same 100 mega pascal only I have applied at the top Most part of it is green Basically, there is no change, no deviation in the load, no change in the cross-section, and it comes But when it comes to the connection at this point, it is reflected on two sides, reflected on the brace and reflected on the chord So, if you go back to this picture also, you can see here this junction, some portion of the vertical plate is stressed, some portion of the horizontal plate also stressed So it has got effect on both sides and that is why we need to know, what the pattern of stress in the chord side and what a pattern of the… So, if you go actually, if you zoom this area very, very large zoom, you will find that there is the plate horizontal and plate vertical coming and joining, you will see that the stress on the vertical and the stress on the horizontal, there will be different magnitude, but they will be matching at the intersection If it is not matching, it has probably failed That means that they have separated So, in order to see that, you need to go to the software I purposely could not put it here, but you can see that there will be a connected plate stressed in a different manner So, what we understand from here? When I apply 100 mega pascal at the top of the brace which is basically nothing but load divided by your area, because you know the load on the remember, you divide it by the area, you got 100 mega pascal which has become 200 something mega pascal at the junction, purely because of the change in geometry for a vertical pipe it becomes a horizontal pipe carrying the load So, that is called a hotspot stress or stress concentration Several terms, we can use It is basically nothing but the stress produced here, that 207 is not uniform throughout, it is going to be maximum at one place and lesser elsewhere This is what we were discussing about the methodology, I think the idea is clear We could not do the design in three-dimensional multi planar joints So, what we are going to see is, develop a parametric equation, empirical method for each of the plane frame and basically looking similar to either T, Y, K or X. Analyses will be done plane by plane Of course, the three-dimensional effect is taken into account in terms of empirical multiplications So, you do the design of one side, but that effect of other side is already taken into account So, that is the idea behind all those empirical equations And basically, you repeat the procedure for all frames in one junction and look at whichever is producing maximum requirement and that will be the design For example, if I have one jacket leg One member is coming in this direction and another member is coming in the perpendicular direction You will do the design of one member first, find out what is the thickness required, keep it one side Go to the next frame plane, do the design, find out thickness Whichever is asking for highest thickness, that will be the design requirement It is not that you will take thickness from here and thickness from other, add it together It is not like this The cross-reference effect is taken into the design itself So, you do not need to worry, which it is going to be So, that is that methodology adopted in the tubular joint design Now, you see here, this is what we were trying to discuss earlier also If you look at this picture, the first yield is the most important If you look at the load-deflection diagram of a typical tubular joint, either T junction of Y junction, the first time when you keep on increasing the load, when you see hotspot, that hotspot is one location maybe two locations, the joint is not going to fail And you further increase the load until such time cracks develops at one point Very similar to the discussion we had on the plastic collapse analysis You know, basically you keep on increasing the load until such time the hotpots will start increasing from one location to multiple locations Basically, one location, yielding load is transferred to the next point and next point, next point So, you will see that basically cracking will happen after a sufficient amount of load have been applied But one small crack does not fail So, you need, for a failure to happen, you need to have dislocation of the brace and chord for a sufficient length One millimeter is not going to fail So, if it is 20, 30, 50, all around the circumference, so that means the failure will occur when the load is substantially larger So, from the time that we saw first yield or so-called the hot spot at one location to a failure you will see that the amount of load that you have to increase to fail that junction is typically 6 to 8 times or even 10 times sometimes That means that if you have 100 kilo newton applied on this, it will only fail at 800 kilo newton That means the redundancy exists in this type of connections Now, we have to decide whether we want to do the design as per 0.6 or 60 percent of yield, like normally we have designed the members no? 0.6 as our allowable stress factors, which I think most of you remember for bending, axial and shear and so on We need a design whether you want to use that kind of concept or we want to go beyond Now, nobody will accept a design when the design itself says “I will have a crack”, isn’t it? I think no one will accept So, you can actually have a condition – ‘not acceptable if there is a crack’ – in the design calculation So, what we are trying to find out whether we want to go below yield or slightly higher than yield The concept adopted by API is basically between the yield and the crack Because the first crack may happen at, say 500 kilo newton instead of first yield at 100 kilo newton So, there is a substantial margin between 100 and 500 So, let me use 200 maybe Still crack is not there, but other points have yielding, which is acceptable But still a lot of redundancy is there So, the idea behind the tubular joint design, we are not using the elastic concept, we are going to use the elasto-plastic or so-called ultimate strength concept The ultimate strength – basically just below first crack We do not want to have crack, but we want to have higher strength than the first yield So, that is the idea behind, divided by factor of safety Basically, that is the idea of almost all the codes behind tubular connections So, we need to find out what is that ultimate strength You look at this picture here, in this picture Under the elastic stress… What is the meaning of elastic stress? If you remove the load, what will happen? The shape should come back to original circular shape You look at just beyond yield, there may be a permanent deformation It could be larger, it could be smaller depending on where you are If you are very close to the yield, maybe you would not see this distorted shape But if you are close to somewhere here, you will see that this distorted shape will become permanently, which is also not good But if you go beyond a first crack, you may see that the connection becomes disjointed That means the brace will come separately and the chord will become damaged So, basically we want to go between this and this and with a proper factor safety we want to… We do not want to have permanent deformation, we do not want to have a crack, but we also do not want to design below yield limit because the capacity is very small and that is exactly the idea We go beyond yield, yield means one location, hotspot, not yield everywhere Whereas, if you actually take a piece of plate like this, you apply tensile stress, yielding will be uniform across, isn’t it? This is because when you apply 300 mega pascal on either side, this stress along the section everywhere will be 300 So, basically that is not permitted Whereas why we are permitting here, beyond yield is because it is only one location is yielded We have so many other connections less than, far less than the yield point and that you must remember Because you cannot get an idea that ‘we will allow yielding in joint design, but not allow in member design’ The reason why we are allowing is because of non-uniform state of stress along the periphery of the connection and one point is higher The other points are very low stress So, you want to utilize the reserve strength available so that we can optimize the connections Typically back in 1990s, early 80s or 90s, many, many research were carried out on these types of joints by doing experimental tests So, you fabricate a T-joint, go to the testing machine I think most of you might have seen the universal testing machine So, you can put it there, apply load, keep increasing in increments and just find out what is the load at which the junction has failed either by collapse or by pull-out So, both tests you can carry out And basically you see this diagram, what you see here is, horizontal axis is gamma See gamma is a ratio of D by T of the chord, very important parameter Too slender you make, it is going to fail definitely The vertical axis is the failure… the relative punching shear stress at which the failure occurs Quite a lot of experiment were done as usual You can see that they have driven They have drawn a line just at the bottom of the whole experiments and described by this curve, basically you can write the equation using a regression analysis and find out what will be the equations for future use So, this is how almost until 90s, quite a number of experiments were done, but after 90s, what happened? The experiments have become quite expensive So, what was done during 90s to 2005, quite a lot of finite element studies, like what you have seen, this kind of analysis provided your tool is validated That means you will do one experiment, compare with your finite element analysis, make sure your parameters are right and then you go for several finite element analysis instead of spending lot of money and time on doing experiment So, that is the idea behind Over a period of time, lots and lots of such publications have come So, API had a committee in 2001 to 2004 A committee of researches was put together and collected all the study work from 1970s until 2000 They come up with a new design code This is actually old design code, which I am not going to speak about it, because it is becoming obsolete Until 2002, we were using this method, but they found that this is not really conservative So, that is why the committee was set up to make sure that they collect all the information from the recent past and they come up with new design equations That is what we are going to see Basically parametric equation, you should understand nothing but the equations are simple polynomials I think most of you also can do experiment in our laboratory You can fit a polynomial equation to describe the behavior between the result and a parent variable The parent variable could be diameter, wall thickness, angle, length, any; more than one or one itself So, basically the result will be your response of the structure in terms of deflection, in terms of capacity to failure So, that will be your goal So, if you relate the response versus the parent variable by some means, some relationship, not necessary that you should derive it Basically, you know in mechanics, you normally derive For example, a bending capacity of beam, you do not write yourself You actually derive from first principle of simple bending theory If it is axially loaded, you derive Whereas in this particular case, we cannot derive because the behavior is so complex So, it is purely based on experimental studies And the relationship between the capacity and the parent variable is by, I would say, simple interpolation You do two experiments, so in between, maybe it might behave in a similar manner So, that is called a parametric equation which is nothing but a semi-empirical idea So, what will be the failure criteria? We do not want to have a situation where you have a local chord failure, something like this You see here, this chord is not just a limited length It is continuous, connected to other parts of the structure So, you could actually have a failure like this, because the chord is having sufficient stiffness, but locally failing Something similar like a beam You can see here, it is actually both a supported and the middle is going down just like a small span beam So, reaching elastic limit of the material is one of the goal that we want to see, but we want to go slightly higher than that And material yield and then the first cracking and the load at which, which is what we saw in that… So, we need to have test or simulated until this So, you cannot do finite element analysis in an elastic state and take the result and use it, which is not correct We need to do a finite element analysis until the failure occurs and then note down the capacity until first crack So, it is a substantial, you know computational power required Normally if you do a static analysis, it may be faster But when you want to do this kind of elasto-plastic stage analysis, it may take a longer time So, what are the failure modes we are expecting? We think it may be happening in this way There are four discrete probability that any one of them will be causing the problem One is the general collapse Second one is the local failure which we saw earlier Then, the third one is unzipping Basically, one location is failing and at that location, there is no contact, load is going to the next two locations around and that locations get over-stressed and opening up So if you have a one location opening or a crack or a separation, the load from that part will go to the next part and subsequently the opening becomes larger and larger and becomes, you know, disconnected or disjointed The last one is the material problem which we discussed about it during the earlier few days You know, basically during welding, you heat the material and you make a fusion bonding And that may actually give up because of the irregularities there So, we need to see what exactly is the remedy that we can make Because this, we can prevent definitely by selecting suitable material, whereas for the first three, we have to design for it in such a way that that does not happen So, general collapse is something like this One of the members is getting compression load, the other member is getting tension load So you can see a rotational behavior about the common point, which actually can ovalize, as well bulge and buckling effect at the location there The local failure of the chord is basically because of the pull-out because the D by T is so small, just coming out When it is just coming out, it is actually taking part of the chord itself It is actually a punching pull-out The third one is the unzipping It is nothing but a very simple idea Smaller yielding, smaller crack The cracked portion load is transferred to the next point and continuously progressive unzipping happens This may happen if you have one particular location not welded properly or defective welding That is a location the load cannot take, whereas you have actually taken full area for your load calculation, whereas actually some locations are not possible to transfer And this progressive failure can easily happen in any type of connection Last one is basically the material problem Now, the material is one important aspect we have to see in this connection Always remember that when you try to weld plate perpendicular to the plate surface, when you try to pull out, what will happen? You know, across the thickness, the load is applied Normally, the plate is very strong, when the load is applied along the length or width direction, the plate has got grain direction aligned in the plate length or width Now you applied load across, that means the skin is trying to come out That means the plate characteristics should be such that you should have enough strength in your crystalline structure that they are not going to come out So, that means we have to go back to the parent material Whether the material characteristics are able to transfer the load across the thickness or not Otherwise what will happen is something similar to your plywood It will start coming out You imagine, you take one plywood, layers of material and try to apply the loading across the thickness It will straightaway, the first layer will come out, isn’t it? So, that is exactly the bonding required between the grain structure And this can actually happen in any material Specifically for steel, it may actually happen when the thickness is larger and larger For example, 10 mm, less susceptibility to come out For a 50 mm, the chance of peeling off is more And that we call it lamellar tearing, basically, the plate comes out Instead of coming out together, something similar If it comes out like this This is not any more a material problem, it is actually a local wall thickness problem Not enough so it is coming out Whereas here, you see this picture Wall thickness is still adequate, but unfortunately, the material is degraded for several reasons One of the reasons could be the heat affected zone Basically, at that location, when you are welding, you are increasing the temperature to 1000 degrees So, at that time material characteristics deform and get weakened and basically cooling it faster than what the necessity For example, whenever you are doing welding, 1000 degrees and you should not cool it very quick It should be slow cooling If it is quicker then, you will have a brittleness formed and can actually crack even immediately of the welding So, the heat affected zone is one of the potential problems where we have a worry about And also the failure may happen due to fatigue I think that is what we normally do if we want to break something, you apply the load or you apply the similar thing several times repeatedly, so it may come out or break So, in order to avoid this, we need to select a suitable material Number one – it should be homogenous across the thickness I think you understand the word homogeneous That means there is no impurity or voids or crack within the thickness across So, when the load is applied, it should not come out So that special material, we need to buy Because only for that location, not for everywhere because at the connection we will buy a special material which we call it through thickness property That means the property across the thickness is same And when the loading is applied, the grind bonding is such that the lamellar tearing will not happen So, that material sometime is noted as Z35 or we call it Z property Because across the thickness, it is called Z property Length and width direction anyway you will have That means the notation what we normally give is that 35 that means 35 percent of elongation across thickness So, how do we do it? Actually, most of we might have seen a UTM machine You have seen or not seen? OK So, you might have seen the tensile testing specimen It will be a small rod with the attachment pieces at… and you just do a tensile testing So, you take the same tensile specimen testing and cut the specimen into a half at the middle, you cut a plate For example, this is the plate You cut one circular plate of 10 mm diameter Basically, in the tensile specimen, you fit it in between and again pull it So, you are pulling actually across the thickness When you pull it, before failure if 35 percent elongation happens For example, I took only 10 mm thick plate So, it should become 135 percent or basically 13.5 mm it is elongated Then, it has got 35 percent elongation before the neck form and failure Because you keep on pulling, then there will be a neck formation and just breakout So, that means the more percentage like this is, it is better because if it failed in a 5 percent deformation, that means this is not very good So, we need to see that when you apply the loading across, it should take ductile failure rather than brittle failure Suppose if you have some kind of voids inside the thickness, when you pull it, it may actually come out straightaway There is no deformation and that is what we were trying to prevent So, that notation is called Z material because it got a Z property thickness property which makes the load transfer without failure You will see that in that this kind of picture I have given you some kind of… You see here, that there is a special color, green color there Basically, only at the junctions, we provide such material so that the connections become safe So, what are the codes available? Basically, about this compact connection, we will discuss later What the codes available are, basically, nowadays ISO, API and also DNV codes But the originator of this whole business is actually coming from American Welding Society Actually, even before API was set up, this American Welding Society has come up with the design requirements in an informal way because that society is not meant for offshore business, but they have been using non-circular tubes For example, like box sections, rectangular box sections, hollow sections used for various building industries That is why they wanted to develop such a connection Basically that, from there it originated and subsequent editions of AWS, they have introduced circular sections In case, some places you can see in many of the airports, circular hollow sections are also used And then, later it was adopted by, this was adopted by the API codes and copied and modified Almost all the work is coming from this P.W Marshall He one of the pioneer He has done extensive work on tubular connections He is still alive and has been doing some more… more and more publications He is the member of the API sub-committee for structures Most of his work was adopted in the earlier revision But what happened is, unfortunately his work was based on the early part of some small-scale experiment plus some finite element analysis proved to be not conservative and rather… Right now, we are not using his proposals or his equations because they were found to be not very good Over a period of time, more and more data was collected, more and more experiments were conducted and the new equations will be not looking like what he proposed earlier So, basically he has done some work Now, we will just look at the classification of joints based on loads I think this is very interesting We should understand that it may become Y joint or it may become K joint depending on whether the load is coming balanced or not balanced So, if you look at, that we call it load path dependent classification So, you should not just believe that the joint looks like a Y joint, I will go for Y It should not be that way We look at geometry plus the loads coming in The only simple idea is, if it is balanced, then it will automatically go to K joint If it is unbalanced, it will either go to T or Y joint So, simple classification idea, you see here, I have got a brace one and brace two One is carrying compression load, brace one The other one is carrying tension load Different magnitude, but then, we just find out what is a vertical component or component normal to the chord We should not call it vertical or horizontal, normal to the chord So, this is basically 90 degrees So, it is normal to the chord and this is basically an angle I will find out what is the normal component Now, if this P1 and P2V are equal, then I can call it K joint because this load is balanced Even though they do not look like… they do not look like K geometry because there is one member which is vertical, the other member is slightly inclined, doesn’t So, you may not classify as K joint, but fortunately, the loads are balanced Now, you may not get exactly same load Nobody is able to control the load So, you make it different magnitude So, if you look at this vertical component or normal component equal to P1, then both members, this member and this member will come under the classification of K joint Now, if they are unequal, that is where the problem Because even after finding out the normal component, if P2V is larger or P1 may be larger, so we have got two classes In first one P1 is greater than P2V P1 is larger P2V is smaller So, what we will do is we will find out what is the amount it is balanced For example, if this is 200 kilo newton, this is 300 kilo newton 200 kilo newton is balanced Only the reminder 100 kilo newton is not balanced or unbalanced So, we would say out of 300, 200 is balanced That means we can find out 200 by 300, 66 percent behavior as K joint for both the braces, but for P1, because it is slightly larger, 100 kilo newton, so 33 percent is T joint You understand the idea no? So, we just simply split the problem into two different ideas Vice versa can also happen You see here, P1 is less than P2V So, automatically what will happen? Whichever is satisfying that much portion is balanced, reminder portion is unbalanced So, this is how the joints have to be classified depending on whether the loads are balanced or not balanced We will have some few cases, if you have understood If you have not understood, then let us stop now Because you will have to classify a joint and design yourself in the exam Basically, first idea, normal components of braces if they are balanced each other, then it is called a balanced If anyone of them is larger, the larger one you take it, split in to two halves, balancing part and non-balancing part Balancing part, the ratio is so many percentage of balanced K joint The reminder part divided by the overall load or bigger load will be unbalanced part It can be T or it can be Y In this first case, it became balanced part is T joint The second one balanced part is Y joint So, you should do this one before going and designing So, you cannot get just fooled by how the joint looks like It can be looking not like K, but we will classify into K joint So, you need to do some practice Probably, I will give you one of the examples, one of the days So, we have got some nine cases just to illustrate how things are done So, I will just explain one or two Then, you can just follow the notes So, if you look at the first one, very similar to what we described just now The brace one is carrying 1000 kilo newton The brace two is carrying 1400 opposite So, basically in this one, if you just look at it, I have just taken as 46 degrees which will be basically 1400 If you find out the normal component, what will happen? You will get around 1002, 1003 So, 1000 and 1000 get cancelled each other So, this can be classified as 100 percent K. You understand the idea no? If I have this angle instead of 46 degrees, I have 25 degrees or 30 degrees, then you would not get 100 percent K joint You need to find out what is the load amount here and that amount only will be K joint The reminder here, there will be a T joint of certain percentage So, you should know how to calculate So, same thing here, if you come to the second I have 1400 applied only on this brace This brace does not carry any load So here, I do not have a balancing load, it is unbalanced load fully So, this will be 100 percent Y joint There is no K behavior because there is… This number is carrying no-load So, that means that I cannot go to K Coming to the last one, you see here, exactly that is what we were trying to talk about 500 there, but I will get 1000 from there So, we get basically 50 percent K joint for this because that is the one higher, isn’t it? Because that 1000 is going out, 500 will be balanced by this So, this and this 50 percent K, whereas the Y joint additional 50 percent will come because that is carrying more load So very simple algebraic comparison So, like this there are quite a few examples I was just given from API So, you should understand, try to I will ask the girl to give that notes today Try to practice So, the next one, I do not think we need to go through because you can easily read it Just to get an idea The next one is the parametric equations are developed based on three parameters One is the diameter ratio As I think I have explained to you the importance of diameter ratio If the diameter is very close to 1, you see a problem there Similarly, this is slenderness ratio of the chord, diameter to wall thickness The third one is the wall thickness ratio of brace and a chord These three parameters plus you will have the angle as one of the major parameter to differentiate between K, Y and a T joint Basically, with these parameters if somebody can come up with the equation to describe this is the capacity, that will be the best So, the basic idea is, what are the parameter’s range is permitted is just summarized I mentioned it in the last class You cannot go beyond these limits Basically, if it is going beyond, the equations are not valid because most of the tests and finite elements studies are done within these ranges For example, beta Beta is basically between 0.2 and 1 Gamma is between 10 and 50 Theta is between 30 and 90 The yield stress would be less than 500 The gap basically should be greater than minus 0.6 That means you do not have overlap So, these are the parameters they have used to study the experiments and the finite elements and come up with the empirical equation So if you are outside here, there are some guidelines given here Calculation using actual geometric parameters Do that exercise Calculate based on the limiting For example, if the angle is 28 degrees, you have to do two calculations You to do the calculation using 30 degrees and do the calculation using 28 degrees and whichever gives you the lowest capacity, you use that capacity as the design capacity So that is the practice It is not that if you go outside, you will not be able to design You will be able to design, but with the lower capacity I think we will see this tomorrow