# 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