Engineer and a mathematician standing at the beginning of a long hallway, on the other side is their significant other/love of their lives.
They can advance in turns, but there’s a condition: for any step, each can move only half of what each did the previous step.
The mathematician gives up immediately – "It’s impossible, I'll never get there".
The engineer proceeds to the other end – "I’ll get close enough for any practical purposes".
There are two takeaways:

 It’s way better to be an engineer.
 FEM is an approximation, AND it's good enough for “any practical purpose”.
Following is an overview of FEM, and why you should try it.
FEM  Finite Element Method
This is the leading way in industry, hobby, or anywhere really, to calculate stresses, displacements and other stuff related to structures.
During the last decade it became so accessible and easy to use that everyone uses it, even if they know nothing about stresses, displacements and other stuff related to structures.
You've probably used it yourself.
With FEM, no matter how complicated your structure is, everything goes. No more looking for rectangles and circles...
On the other hand, you can't do anything without a CAD model, simply no way around it.
The transition is seamless though, since it's integrated into the CAD software.
How It Works?
Let's go over it one time, I promise you won't need it for everyday use:

 Divide your model into tiny elements (mesh).
This is the approximation part. We assume a certain behavior of the elements and later combine for the whole structure.  Define constraints and apply loads
Remember clamped and simply supported? These are constraints to define in your problem.
Only external loads are applied, you don't need to calculate them in every point like we did here.  In the background
The program creates thousands of equations for every node (of every element).  Solution
Displacements are calculated for each node. Later, these can be translated into stresses and other structures related stuff.
 Divide your model into tiny elements (mesh).
The user (you and me) isn't concerned with the last two steps, the program does it (how cool is that?).
Binding Example
The YoBis bindings were designed to hold loads of a heavy board. Also it's a nice example to show the general procedure.
*I'll be using Fusion360 for the show.
Mesh
Take your designed part and divide it into elements (click of a mouse).
You don’t want the elements to be very big (ugly results) or too small (will take too long to solve).
Although an automatic mesh is a good start, don't stop there, play with it a little and see how the results change.
Elements shouldn't be too big (ugly results) or too small (will take too long time to solve).
Constraints and Loads
Constarints are the places where your structure doesn't move (or move in a limited way). In our case these are the 4 bolt holes at the base:
Define only the external loads.
Let's assume a heavy board of 30kg, meaning 15kg per binding (or ~150N) vertically up.
Solve, Look at Your Colors
Hit solve.
(You can appreciate the thousands of equations which are solved in the background)
Assuming everything went well, you'll get several options to show colors.
Colors being the distribution of whatever you want to see.
Displacements for example:
Or stresses:
7.4 MPa=0.75 kg/mm²
Obviously nowhere near the 3 kg/mm² which is the failure stress for PLA.
Conclusion
Finite elements is a simple way to calculate stresses and understand how your structure holds the loads.
With FEM the results are shown for the whole structure (rather than for certain points) and in bright colors.
Go ahead, try it. It helps you make better decisions about your design.
Enjoy,
Dani
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PS
I’m doing something new here.
A short series of posts dedicated to designing your own, as strong as you want, structures.
I’ll cover the basics, so you can do the rest.
Let me know what you think: dani@dosimplecarbon.com