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
In the first workshop for students in WrUT organized by Enterfea and Dlubal, a problem of rigidity of the connections in steel structures was presented and discussed. I had the pleasure to teach there with Ola Kociołek (CEO of Dlubal Poland).
Have you ever wondered how to be sure that your connection is a hinge? Perhaps you are interested in the influence of connections rigidity on the outcomes of static calculation or how to incorporate this rigidity in the design. Maybe you want to know when connection rigidity is actually important and cannot be omitted… you are in the right place!
The topic of connections rigidity in steel structures became popular several years ago with the publication of code EN 1993-1-8. Chapter 5 of this code classified connections between steel members not only as hinges and rigid connections but also as semi-rigid. This alone was nothing new, but the fact that the code actually gave information on how to calculate this semi-rigid approach meant that this will be a “thing”. I won’t go to the procedure of calculation given in the code (I’m not a fan), but I will gladly discuss the phenomenon and give my advice, so everything here is not code-related and can simply be used regardless of codes you are using.
This is a very broad topic, so I decided to break it down into several posts. Today I will discuss verification if the connection is a hinge or not, but in upcoming weeks following topics will be discussed:
Main issues with connection rigidity:
There is a misconception that a hinge is a connection that has no capacity to carry any significant bending moment. Unfortunately, that is not true. Imagine a cantilever made of glass (that cannot carry any tension, and thus cannot carry any bending). If you would load such a cantilever then it would break (since it cannot carry any bending moment)… I wouldn’t call that a hinge.
To move examples to more “structural” areas, let’s take a beam like the one above. Assuming someone wished to treat this connection as a hinge, screws are placed wrongly. Since they weren’t designed for it, let’s say those screws don’t have any significant capacity to carry tension. Notice that uplift deformations at the end of the beam will cause a high tensile force in screws – this is nothing else than the beam trying to “fix itself” into the support using the pair of forces (tension in screws, compression in bearing). Screws do not have sufficient tensile capacity, so they break (and hence “allow” for rotation in the support).
This leads to a very important conclusion:
Hinges are connections that allow for free rotation.
It doesn’t matter if the connection capacity due to bending is high or low – if it allows for free rotation you simply cannot apply to bend to it! Deformation of the structure increases (and other elements have to deal with the strain) but the connection did not take any bending, so its capacity to it is irrelevant.
In the beam example above the screws prohibited rotation, so the connection took in the bending moment, and since screws capacity was small, they broke. If you would place screws like on the drawing below, those would not prohibit rotation. Such a solution is a true hinge. Of course, there is a “price” – since we do not carry bending “elsewhere”, the analyzed beam will get a much higher bending moment (but elements that are connected to the beam won’t get any, and that is the point!)
So let’s think about how to analyze if our connection allows for free rotation. Let’s use one of the most common shear connections as an example.
First of all, we can notice, that with more than one screw the “free rotation” of our connection will be somehow limited. Since 2 screws can generate a pair of forces they can “try” to stop the rotation (by shear action). If any significant bending moment will be applied to this connection, it is obvious that the screws will break. It’s because the distance between them is small, so the forces in the pair of forces will be very big.
However one can realize that the holes in all screwed connections have holes diameter higher than the diameter of the screw. Taking this into account shows that in order to carry shear (in a non-preloaded connection) screws have to “travel” to the edge of the hole first (see below). This distance is relatively small (usually 0.5-1.5mm depending on the screw size and its location in the hole), but with a distance between screws being small as well, this actually produces a quite significant rotation possibility (especially since rotations in typical beams are quite small).
So the easiest method to verify if the connection is a real hinge is to check what is the allowable free rotation, and then apply the hinge in static design and see if the rotation in that connection is smaller than the allowable free rotation. If it is – the connection is a hinge.
When the rotation is actually higher (which in most cases means you are calculation something interesting), then this will be a bit more tricky. I will get to this in the next post (using the numerical model shown above). If you are interested in it, be sure to subscribe so you won’t miss it 🙂
Also, not all cases allow estimating the free rotation in hand calculations. Sometimes you have to do a simple numerical study to see what the allowable rotation is – eventually I will get to this as well.
I’m very happy that you have read so far! In fact, I have a surprise for you : ) If you are interested you can subscribe below to get my free FEA essentials course.
I must admit that we completely overslept the information campaign about this event. Ola and I both had so much work lately that we simply forgot to tell anyone… I realized this 2 days before the event and at that stage, all I could do is to send an informational email (which of course I did). Ola posted information on the Dlubal blog… and we hoped for the best.
To make it even worse I haven’t realized that I set up the date of the event on Friday afternoon… before a long weekend (there were some holidays on Tuesday and students had Monday free as well). It was obvious everyone will travel home… (self-note: check if the event is before a long weekend next time).
Still, 50 people actually came to the workshop, which is a great success (and taking the above into account a small miracle 🙂 ). Thank you all for being there – I hope you enjoyed it!
As always have a good one 🙂
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