Optimal space between anchor points on a long piece of material

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Discussion Overview

The discussion revolves around the optimal spacing of anchor points (screws) when fixing a piece of lumber against a flat board. Participants explore how to ensure even force distribution along the length of the lumber, considering various configurations and mathematical principles.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant inquires about the appropriate distance between the first and last screws and the ends of the lumber to achieve even force distribution.
  • Another participant suggests using Bessel points to minimize sag along a beam, proposing that the end fasteners be placed about 28% from the ends towards the first regularly spaced fastener.
  • There is a clarification request regarding the meaning of "even force," with emphasis on the direction of the force acting on the assembly.
  • A participant expresses a concern that placing screws down the centerline of the lumber may be weak for certain loads, recommending the use of two screws at each anchor point or alternating their positions across the width of the lumber.
  • One participant indicates a focus on the mathematical aspect of determining optimal placement for the first and last anchor points on a finite length of lumber.
  • Links to external resources on Airy points and Bessel points are provided for further reference.

Areas of Agreement / Disagreement

Participants express differing views on the optimal placement of screws, with some supporting the use of Bessel points while others raise concerns about structural integrity based on screw placement. The discussion remains unresolved regarding the best approach to achieve even force distribution.

Contextual Notes

There are assumptions regarding the load conditions and material properties that are not fully articulated. The discussion also lacks a consensus on the definitions of "even force" and the implications of different screw placements.

freeelectron
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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
 
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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.
 
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freeelectron said:
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.
 
Lnewqban said:
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.
 
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.
 
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berkeman said:
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.
 
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