# Mod-04 Lec-02 Tubular Joint Design for Static and Cyclic Loads – 2

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

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