Optimal space between anchor points on a long piece of material

[freeelectron]

TL;DR

Placement of anchor points for even force

Let's say I want to fix a 4x4 lumber against a flat board, or any other material against any other.

Depending on the situation, I may use 3, 4 or 5 screws or even more.

Regarding the last and first screws, what distance should there be between them and the end of the lumber to ensure an even force?

Should it be half the distance as between 2 screws or some other distance?

Thanks

 

[Baluncore]

Use the Bessel points to minimise the sag of points along a beam.

Use a total of n fasteners.
Space n-2 fasteners, equally along the beam, using the ends as reference.

Place the two remaining fasteners closer to the ends. The end fasteners should be about 28% of the way from the end of the material towards the first regularly spaced fastener.

 

[Lnewqban]

Regarding the last and first screws, what distance should there be between them and the end of the lumber to ensure an even force?

What do you mean by even force in this case?
In what direction is that force acting?
Each anchor will produce similar clamping force between both members of the assembly.

 

[freeelectron]

What do you mean by even force in this case?
In what direction is that force acting?
Each anchor will produce similar clamping force between both members of the assembly.

I mean an even pressure by the lumber on the board all along the length, but you could also call it an even pull by the screws on the board.
Basically, the idea is to spread the screws evenly, even though the lumber has ends.

Baluncore's answer sounds perfect. If someone has an explanation for the 28%, feel free to go ahead.

 

[berkeman]

Are you just putting the screws down the centerline of the 4x4? That seems like it would be weak for some loads on the system. I'd either use two screws at each anchor point (spaced across the width of the 4x4), or consider alternating the width-wise position of the screws along the length of the 4x4.

 

[freeelectron]

Are you just putting the screws down the centerline of the 4x4? That seems like it would be weak for some loads on the system. I'd either use two screws at each anchor point (spaced across the width of the 4x4), or consider alternating the width-wise position of the screws along the length of the 4x4.

That would be a good idea indeed.

My question is more at a "mathematical" level. I'm mostly curious about the optimal way to place the last/first anchor points on a finite length.

 

[Baluncore]

https://en.wikipedia.org/wiki/Airy_points
https://en.wikipedia.org/wiki/Airy_points#Bessel_points