I'm trying to create an Excel spreadsheet that takes a 3D bolt group with x y and z coordinates, applied loading, and determines the distribution of forces into each bolt based on weighting by the distances from the centroid and bolt diameter. By "3D bolt group" I mean a pattern of bolts existing in 3 dimensions, not just in 2. I know this complicates the calculation because now there are 3 dimensions to consider. And I've seen quite a few spreadsheets that only take into account a 2D bolt group.

I found the following program (http://www.chestnutpens.co.uk/misc/boltgroup.html) that does exactly what I'm trying to do, but I'm having trouble replicating the results in my spreadsheet. I'm able to replicate almost the entire program, up until the last step that adds the forces due to direct loading and rotation. And I'm not sure why I'm getting the results I'm getting. Note: I've created in FEM the bolt group and matched the results of the program.

Has anyone ever tried to create something like this, or can help me understand where I'm going wrong? I know its a complicated method and its difficult to understand without seeing my spreadsheet. Actually, am I able to share my spreadsheet here? I'm not entire sure on all the rules here.


  • $\begingroup$ I would start with 1D then expand with all conditions to 2D and then include all conditions for 3D. Trying to do 3d straight off usually means missing something. $\endgroup$
    – Solar Mike
    Oct 17, 2020 at 7:34
  • $\begingroup$ Pretty sure the diagram would just involve coordinates and not bolt sizes. Putting in a bigger bolt doesn't mean it takes up more load. But beyond that, turning each bolt load and moment vector into x,y,z components should do what you want. To be clear, you are starting with 3 force vectors that are balanced, right? $\endgroup$
    – Tiger Guy
    Oct 21, 2020 at 2:42
  • $\begingroup$ The distance method is applicable for bot group subjected to in-plan (V & T) loads only, it does not work for out-plan moment, since the bolt is effective in resisting shear and tension, not compression. For example, consider a cantilever beam is connected to the concrete wall through end plate and 4 anchor bolts (one each corner). The beam is subjected to a load P, with a moment arm L, resulting in R = P, M = PL. Assume the bolt spacing are known, can you calculate the forces in the anchor bolts using the method you proposed? How, if you can. Why not, if you can't? $\endgroup$
    – r13
    Mar 17, 2021 at 0:32
  • $\begingroup$ Take a look at how axial loads are distributed to pile groups. Similar concept can be used to distribute load to bolt groups. The key is the base plate cannot be in contact with the support surface. When the base plate is in contact with the support surface things get more complicated and you need to figure out how much of that contact surface is in compression. $\endgroup$
    – Forward Ed
    Nov 12, 2021 at 18:39
  • $\begingroup$ It is tedious but the same as the 2D case. First, you need to find the geometry center of the bolt group, then calculate the forces in 3 dimensions and distribute them based on the geometric properties of the bolt group with respect to its geometry center. $\endgroup$
    – r13
    Nov 7, 2022 at 17:50

2 Answers 2


After the emergence of software design programs, we all have become too nonchalant about the basics. I take a stab at it here.

Let's annotate the center of the bolt system, C. And call the bolts B_1 through B_n and assume there are differences between the bolt sizes areas hence their strength varies, but they are all set in fully and are not cantilever so they can either have direct compression, tension or shear only.

Then $$C_i=\frac{\Sigma Area B_n*i_n}{\Sigma Area B_n} $$

i is the indices for x,y,z, the distance of the bolt from our reference in respected direction.

If we apply load P at the distance Di from C, and call its projection passing through C, Pc the forces and shear reaction each bolt carry is:

Direct tension or compression loads tributary to each bolt,

$FB_n=Pc*Area B_n / \Sigma Area B_n$

And additional torque shear,

First, we define I of the bolt group as

$ \Sigma Area B_n*(d_in^2) $

$ Shear:\ \tau_i B_n= Pi*Di\frac{Area B_n*di_n}{\Sigma Area B_n*(d_in^2)}$

i is x, y, or z components, and d is the distance of the bolt to the centroid of the bolt group calculated above. I think these are easy to write to an excel sheet.

These algorithms do not apply to bolts applied in a cantilever configuration, More complication arises when dealing with cantilever bolts and their type of connection.


Many years back, I constructed a 3D bolt group analysis template using Mathcad. The approach I took was to input the x,y,z coordinates for the bolts but also include a stiffness (N/mm) for each bolt in the three axis directions. This permitted me to derive equations for forces and moments. As an example, a fastener force in the x direction includes components based on rotations about the y and z axes, and a moment about the x incorporates forces in the z and y directions. This method gives you a 3x3 matrix equation for the moments about each axis, allowing the rotations about each axis to be solved.


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