What's the best way to design a joint with two fasteners?

Question

When you're trying to design a relatively long joint with only two fasteners, what's the best way to arrange them? Since fasteners effectively radiate a circle of clamping force around them, what's the best way to evenly distribute this force?

I originally thought of this question while thinking of the best positions for the binder clips holding my 3D printer's build plate on, but the core concept is surely applicable in larger applications too.

Some ideas off the top of my mind:

• 1 fastener at 25% and the other at 75%. This is flawed in my mind because the 50% mark will receive far less clamping force than the rest of the joint.
• 1 fastener at 33% and the other at 67%. This is also not great because the middle section of the joint is receiving a double dose of clamping force, which is obviously not very evenly distributed.

From these two examples, I can see that the ideal position is somewhere between 1/4 and 1/3 of the joint length for each fastener. What would this position exactly be?

What about a joint with more than two fasteners?

Answer 1

I think you might have a misconception regarding to how far the pressure from the fasteners extends. One subject you might want to have a look into is "bolt joint stiffness".

The most popular is the "Rotscher’s pressure-cone method". Essentially there is a pressure cone which radiates outwards with an pressure cone angle a.

According to Shigley using an $a= 30^\circ$ is usually suitable. The pressure cone angle is determined by the material properties, design of the fastener etc. However, the angle is less than $45^\circ$. This means that it will be impossible for a long (>5 bolt diameters) and thin plate (less that 3 diameters) to be clamped uniformly with only two fasteners.

Having said the above, the clamping force and the friction should (more or less) remain the same irrespective of the position of the clamp. IMHO, what you should be more worried is where should I place the fasteners so that the whole system exhibits better strength.

For the strength, you can go the analytical way (see Shigley, Norton or other mechanical design textbook), or follow some rules of thumb (see 1, 2, ... etc).