Web under local loads – Hand calculations
It’s very hard to calculate the capacity of small sections of any structure under concentrated loads. Luckily EN 1993-1-5 gives us a decent solution for webs under concentrated loads!11 January 2021
Slippage in connections is often neglected in the design of steel structures. I have seen its importance when I was working in the team investigating the structural failure. Just as easily I could learn about it when it was my design under investigation! It is incredible how easy it is to discard slippage from calculations, and how terrible outcomes this may bring!
Slippage is a possibility of the connection to deform, before it starts to transmit forces. It has nothing to do with capacity of the connection, only with its rigidity. This makes omitting this phenomenon easy, as engineers tend to think that if capacity is ok, everything will be fine.
Screwed connections with long holes (without pre-tensioning) are the best example of slippage:
This connection will not carry any force at the beginning. First, the movement (slippage) has to happen in order for the screw to reach the sides of holes in both elements. Then the shear force will be transmitted as can be seen below:
After the screws are in contact with the sides of the holes, forces are transmitted as normal. So what is the problem you might ask… the problem is with the movement itself!
In the above example connection can easily slip more than 30mm (depending on the long hole length of course) – it is obvious that the designer’s intention was to allow such movement. But in a “normal” screwed connection this movement is usually restricted to around 2mm (holes tend to have a diameter 2mm higher than bolts). Seems like very little right… I will show you the effect of such 2mm slippage on 2 examples below.
Please note, that as Peter pointed out below you should never use slotted holes on both sides of the connection. The above example looks like this, as I was afraid that on small screens (like your smartphone) people won’t be able to see the movement otherwise. Thank you, Peter, for pointing this out!
Sometimes slippage only causes additional deformations – i.e. if a table has 4 legs screwed with slippage it will end up being shorter than originally assumed. Such shortening in itself does not have to be critical. If the structure is not overrigid this will only cause additional deformations. If those deformations are acceptable, then everything is fine.
Most structures, however, are overrigid, and in those structures, additional deformation actually causes force redistribution. This means that some parts of the structure will take less load than they “should” and other elements will be overloaded.
Let’s try with a simple truss first – I will compare the outcomes from a truss with no slippage connections, and the one with 2 slippage connections in the middle:
I have defined the slippage in the nonlinear tab of connection properties with the following chart. You can see that at the beginning deformation (u) rises without any force (P) appearing, and then after a certain value of slippage (here 2mm) connection start to rigidly transmit normal forces:
Outcomes for both trusses, of course, are quite different. Take a look at the deformation below:
You can easily see that the truss with the slippage has much higher deformations (4 times higher to be precise). Notice that the model with slippage software actually shows slippage (bottom chords are drawn as “not continuous” while the top chord is overlapping). I should also mention that those additional deformations are almost 10 times higher than the slippage value – slippage is in the horizontal direction, while we measure the vertical deflection.
In truss with slippage, some additional forces appeared, but overall the biggest change is in the deflection. Let’s see now how many additional deformations can drastically influence some structures.
In overrigid structures, additional deformations of certain elements can greatly influence the force distribution in the structure. As long as everything deforms together, things tend to be better than if some elements move more than others (this is why uneven foundation settlements are considered far worse than even settlements).
I will use a relatively small model to show you how incredible this influence can be. The model consists of 6 trusses (with circumferential truss) intersecting each other as shown in the picture below (it actually uses the same trusses as the one in the first example):
The intention of the designer of this structure is clear – trusses in both directions should carry the load evenly. This allows the structure to carry a relatively high load (when compared to trusses in one or the other direction working “alone”). However, there is a problem with structures like this one. While in one direction trusses can be “continuous” (the red ones below) in the other direction (the green ones) they will have a connection on both sides of perpendicular trusses (black rectangles). This means that the top view will look like this:
If the rigidity of the marked connections will be sufficient, nothing wrong will happen. Trusses in both directions will work evenly resulting in capacity usage shown below:
However if the connections will have slippage (for instance shear screwed connections without pre-stressing), force distribution changes greatly.
Let’s get back to the simple truss in the first example for a moment. The one without slippage was able to take a lot of load without much deformation, but the one with the slippage had to deform in order to carry the same load. Both could safely carry the load, but since here they will cooperate they will deform together…
Since a continuous truss will deform only “a little”, the truss with the slippage will never reach the deformation needed for it to carry the load. It may “close” the gaps in the connections (there are far more here than in the first example) but even then continuous trusses will be greatly overloaded. This effect called redistribution of forces can be seen in the drawing below, showing capacity ratios in the model with slippages:
As you can see above the continuous trusses are clearly overloaded (the capacity ratio is twice as high as in the first example). Such redistribution is why slippage is so dangerous. If the connections would be evenly spaced in both directions (not a very practical solution to be honest), then such effect will be smaller. Sure, deformations would be higher, and some additional forces would appear, but the redistribution of forces wouldn’t be as drastic.
Some ideas I have described today, you might want to remember:
Thank you for reading! I hope you will find it useful : ) Also I have a surprise for you : ) If you are interested you can subscribe below to get my free FEA essentials course. If you have any questions you can always leave them in the comments!
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