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Simply schematics of what i think of.I have a question about the distribution of forces on bolts in mechanical connections. Suppose we have a flat bar bolted to a flat surface with three bolts along the longer edge. An equally distributed force perpendicular to the plane acts on the flat bar, trying to stretch it along the shorter edge.

Theoretically, this force should be evenly distributed among the three bolts, which means that each bolt carries F/3 of the total force. Why is this the case?

It's funny, because for a long time I didn't even question it, but recently someone asked me if we should change the design because the front bolt in a similar case transmits too much force. I couldn't find a good answer to this question

Some additional questions that stuck in my mind.

  1. Why do we assume that the force is distributed evenly across all bolts? What are the basic assumptions and principles that lead to this conclusion?
  2. In reality, is the force distribution exactly uniform? What factors can influence one of the bolts to carry most of the load?
  3. How can the proportion of force distribution on the bolts be changed? What design or material changes can affect a more or less uniform distribution of forces?
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  • $\begingroup$ The problem is statically indeterminate; [F/3 F/3 F/3], [F 0 0], [0 F 0], and [0 0 F] are all possible and acceptable outcomes (as are their linear combinations) depending on the details of the connections and deformability of the constituent parts. There are many related discussions on this site (1, 2, 3, 4). $\endgroup$
    – Chemomechanics
    Commented Jun 10 at 17:36
  • $\begingroup$ The [F/3 F/3 F/3] result is appealing because of symmetry but can't be depended on in practice because the connections aren't truly identical and because the slightest give in two of the bolts would lead to a load of up to F on the third. See also practical discussions at Engineering Stack Exchange. $\endgroup$
    – Chemomechanics
    Commented Jun 10 at 17:44
  • $\begingroup$ Try to have a look at this approach physics.stackexchange.com/questions/256965/… $\endgroup$
    – basics
    Commented Jun 10 at 17:48
  • $\begingroup$ Great, thank you. I will certainly dig dipper into that. To this day I thought this F/3 on all of three supports is obvious answer. Couldn't be more wrong. btw Thank You for the link :) $\endgroup$
    – Adam Dutkiewicz
    Commented Jun 10 at 17:48
  • $\begingroup$ Some assumptions are made there. Here you could assume that the structural element can be modeled as a linear elastic beam and that the bolts transit forces that are proportional to the displacement of the point. This is just to have some qualitative results. For more detailed results (especially when assumptions made here don't hold), it's likely you need some FEM simulations $\endgroup$
    – basics
    Commented Jun 10 at 17:50

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