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Motor Case Bolt Shear Stress Calculation

When building a motor with a radially bolted case, you must make sure that your bolts will be able to stand up to the forces applied to them. To demonstrate this, we will look at the Phoenix booster as an example. 

Calculated Booster Max Booster Pressure = 826 psi

Forward Closure Inner Area = 10 in^2

Number of Bolts = 24

First, we must calculate the force on the forward closure due to this pressure.

F = P*A

F = 826*10 = 8260 lbs

This force is assumed to be perfectly distributed among each bolt, so the force on each bolt is:

8260/24 = 344.16 lbs

Our bolt is under a single shear, which looks like the reference diagram below. In order to evaluate the shear stress, we need to use the equation on the right. Our bolts have a diameter of 1/4 of an inch. 

Image Added

F = 344.16 lbs

D = 0.25 in

T = (4*344.16)/(pi*0.25^2) = 7,011.17 psi

That is the tensile load that each bolt experiences, so now we must compare it to the max shear rating of the bolt. The bolts we use are here: https://www.mcmaster.com/91253A537/. Using the specs here, we can calculate:

Actual Shear = 7011.17 psi

Max Shear =  120000 psi

Factor of Safety  = 120000/7011.17 = 17.12