# Determine force distribution from a bolt pattern

Need some help designing a bolt pattern for a pressure tight enclosure.

How do i determine the force applied at a distance from a bolt location so that I meet the minimum force to compress the gasket along the entire length of the enclosure but while using the minimum number of bolts?

And if anyone know how to model this on solidworks that would be very useful as well!

I remember learning about this in design class. Each bolt has two components to it's shear force. One is equal to a fraction of the applied load directly, and the other is the shear force needed to create an equipollent moment at the center of the bolt pattern.

Specifically, with $n$ bolts, and $\mathbf{r}$ the location of the load from the bolt pattern center, the equipollent moment is

$$M =\| \mathbf{r} \times \mathbf{F} \| = r_x F_y - r_y F_x$$

If the position of the i-th bolt is $\mathbf{b}_i = R_i \mathbf{e}_i$ where $R_i$ is the radial distance and $\mathbf{e}_i$ the radial direction vector.

Consider also the perpendicular direction $\mathbf{n}_i$. This points tangentially from each bolt.

The total shear force for the i-th bolt is

$$\mathbf{S}_i = \frac{1}{n} \left( \mathbf{F} + \frac{M}{R_i} \mathbf{n}_i \right)$$

You can show that this satisfies the equilibrium equations

$$\begin{cases} \sum \limits_{i=1}^n \mathbf{S}_i = \mathbf{F} \\ \sum \limits_{i=1}^n \| \mathbf{b}_i \times \mathbf{S}_i \| = M \end{cases}$$

This assumes that the connecting parts are compliant enough to give an equal load distribution to the bolts and that the bolt holes are a loose fit and don't push against the bolts when not loaded.

I found these documents relating to my question. However i suspect they're all for circular gasket designs with the bolt pattern being circular.

Journal Paper: International Journal of Pressure Vessels and Piping 120-121 (2014) Comparative study of bolt spacing formulas used in bolted joint designs Abdel-Hakim Bouzid