Structural rigidity explained!
Structural rigidity is a very underrated concept I'm afraid. You see, usually which part is more rigid than other does not directly influence the code-driven design methods. "Magic" happens when you do static design, and this process is far less regulated that dimensioning itself. I often meet engineers who completely do not understand this concept. I think that this hinders their possibility to find the best solutions (or even good ones sometimes!).
If you are using FEA to analyze stresses and displacements of the structure, it is really important to understand what rigidity is all about. If I would have to ask my potential new employee one question to check their skill it would definitely be "what is structural rigidity and where it influence the design?". Let's find an answer to that question - shall we?
Structural rigidity = gummy bears!
I love talking about complex problems in a simplistic, caricatural way. I think this way it is easier to explain something (and in style!). But what is most important it will be far easier for you to actually memorize and recall what you learn this way! This is why many examples here (like my favorite wet sweater or guys carrying a rock) are so weird.
After more than 10 years of teaching at University I strongly believe that we have developed far too many long complex words to describe things. Sure it make us sound smart, but this is getting us nowhere. The best specialists I know can easily explain almost any concepts using simple examples without any "uncommon" words, why beginners often hide their uncertainty behind complex definitions... This is why I always refer to structural rigidity as Gummy Bears (I mean in all honesty... science without gummy bears?).
Let's roll!
Normal version: Imagine a table with 4 legs.
University version: Imagine a table with 4 legs that have an infinitely rigid table top that can move only in vertical direction.
When I stand on a table my weight (100kg - yea... I know) is evenly distributed between 4 legs meaning that each "get" 25kg. We got used to think that stress "appears" in the table legs, but let's look a tiny bit closer. What really happens is that the leg shortens a bit (and becomes a bit wider according to Hooke's law). This shortening means that particles of material that forms each leg got a bit closer to each other
Since they are closer, they start to repel each other - this repealing is stress. This is also why legs became a tiny bit shorter. It is a very small movement (let's say 1nm) so it is easy to forget about this nuance (it will be critical in a second!). Also let's assume that 25kg is the maximal capacity of the table legs. If the "leg shortening" is higher than 1nm the legs are destroyed. Reason for that is simple - higher shortening means that the higher force than 25kg was applied.
Gummy bears in action
Now imagine we have the same table, but legs are made from gummy bears. The cross section stays the same, we just used another material. What will that change?
For one, let's assume that those are really "strong" gummy bears and that they can actually withstand 25kg each.
If that is the case, you can easily imagine that the only difference is the fact that the table top will move downward, as gummy bears deform under load. It is quite obvious, that gummy bears will "compress" far more than normal wooden legs (but we did the gummy math correctly and there will be no buckling!). The difference here is the Young Modulus (just so you know, this is not a story about Young).
Assuming that gummy bears follow Hooke's law if the leg "shortens" 10cm under full 25kg of load, then it will shorten 5cm under half of the load (this is linear). How much force will "appear" in gummy bear column with only 1nm of shortening? Literally nothing, or at least nothing worth considering.
Let's summarize what we know:
- "Normal" wooden legs deform very little under the load of 25kg each - we "guessed" it will be 1nm
- If the leg is loaded beyond 25kg (leading to deformation higher than 1nm) it is destroyed
- Gummy bear legs deflect far more - 10cm under 25kg
- Force in gummy bear column that appears when shortening is 1nm is practically equal to zero
How this all influence design and what to learn from it?
Read a full article here!
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