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
This is the third post about the rigidity of the connections in steel structures. Since we already have discussed what a hinge actually is, and how to calculate the connection rigidity, it is time to discuss how this all fits into the static design. It is also important to discuss the impact of connection rigidity on the outcomes from static design which is today’s topic.
Knowing how to calculate connection rigidity is one thing, but today I want to show you how that rigidity impacts the outcomes from static calculations. I know for a fact, that connection rigidity is frown upon by many engineers (let’s face it, it is additional work, and there is no additional time!). I hope that this post will show how important this topic may be in your design.
To begin the discussion we should consider one simple idea:
If we are talking about rotational rigidity of the connection we expect the outcomes from the static design to be somewhere between those for a hinge and those for a rigid connection
If we are talking about translational rigidity of the connection the outcomes will be somewhere between those for a rigid connection and those with no connection at all!
If we would think about it for a second we can get to a point where we realize this is not only the issue for moment and force distribution in the model (which is what I want to discuss today). This will also have an impact on element or structure stability (and I will discuss it in the future)!
The simplest example is, of course, a simply supported beam. For this example, we are using an HEB 300 cross-section between 2 concrete walls. Since we have assumed in our design that the connections will be rigid (and we have designed the beam that way) we want to make an end-plate connection with sufficient rigidity. Let’s go through possible options:
Presented models are very simple (only one plate, cross-section outline with rigid elements, and rigid cantilever). There is always a temptation to add several elements for them to look “nicer”. Here, for instance, we could add a few centimeters of the cantilever length as shells, simply for a better looks at the outcomes. I would advise against it however as it significantly impacts the results when deformations are so small (0.054mm as maximal deformation!).
As you can see above a certain length of the beam was modeled with surface elements (100mm length to be precise). Note that maximal deformation increased greatly – this is due to deformation of the added cross-section (that replaced rigid element). Since in our final model that cross-section will be there, we shouldn’t take its deformation into account as we discussed previously.
The rigidity of the connections was calculated in the same way I have presented in the previous post – this time, however, there will be no slippage. Outcomes for different geometries and plate thickness are given below:
As I wrote above we will expect the outcomes to be somewhere between the hinge connections and the rigid ones, so let’s try it out. For the first solution A all rigidities were added into the following model: 5 different 10m long HEB 300 beams were implemented with the different stiffness of the supports. Starting from the hinged connection (on the bottom left) and going through all the rigidities up to a completely rigid connection (on the top right).
As can be seen, a model with the plate t=10mm has the bending moment in the middle of the span 50% higher than that for the completely rigid solution. Even plate t=20mm has a difference of 13%. Sometimes such difference is huge, sometimes it is negligible – I will address such considerations in the post summarizing the connection rigidity segment. For now, let’s keep in mind that the differences can be quite high.
Of course, a similar comparison can be done for solution B:
Here differences are smaller, but still quite high in certain cases (up to 142% for plate t=10mm).
Of course, at this point, we could discuss that it is easy to stiffen solution B with additional plates on web extension, etc. This is all true, however, I do not wish to optimize a simple connection, but to show you how big influence the rigidity of the connection may have on the outcomes from static design. I completely understand that such influence is not always important and that in several cases it won’t produce as dire effects – I will discuss such topics in the summary post of the connection rigidity segment.
However, since we are all here, let’s take a look at one more example. The same beam but from a different perspective. Let us assume that we want to have a hinged connection to that concrete wall. Of course, I would pick an end-plate solution as below – for future reference let’s call it Solution C:
With such geometry actual rigidity of the connection is:
Of course, rigidity is significantly smaller than in the case of solutions A and B (that was the point after all), but let’s see how this influence the static design outcomes in a similar way than before:
You can easily see that regardless of the plate thickness bending moment in the middle of the span drastically decreases (even by 50%). This alone is not a problem of course, but:
in static design it is always like this: if conditions for some element improved, surly some other element have worse conditions that before! Nothing is free in static design!
In this example, the “better conditions” element is clearly the beam (less moment in the span), but the connection has it “worse”! There is a bending moment on the support that we haven’t foreseen with assumed hinged connection… and experience shows that if an unexpected moment “appears” in the connection we are in for some trouble!
As I have shown here rigidity of connections is not only a problem when you try to transfer bending moment… it is also a problem when you try NOT to transfer it. This fact is greatly overlooked in my opinion (well the entire topic of connection rigidity is, I think). We have to be aware that “nothing is free” in static design – if something decreased somewhere, there is a cost: something else must have increased somewhere else!
There is no way to convince a steel connection to act as a hinge or a rigid one, and we so often assume one or the other out of habit. In many cases, this is completely understood and accepted, but in others, this may lead to serious problems.
Thank you for reading, I’m very happy that you decided to take some time to reach this point. In fact, I have a surprise for you : ) If you are interested you can subscribe below to get my free FEA essentials course.
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