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To quickly determine structural integrity, we can perform a buckling calculation, assuming long vertical cuts are made (or a similar, equivalent cut):

Given some amount of aluminum from the cup on both ends of the column, this scenario is best approximated as a double-wall-mount buckling problem. Only first order buckling is possible, because the mission package tube constrains the cup in one direction. Thus the critical buckling load is:

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From Matweb, the Young's Modulus of aluminum is 68.9 GPa = 1.00e+7 psi. The area moment of inertia for a rectangle under buckling is

Mathinline
body \frac{bh^3}{12}

. Given a 0.1" cup thickness, bh, we can solve for the minimum width of each column, b. We apply a 2x factor of safety on the piston load (360 lbs) and generalize the number of columns as n_c. Assuming evenly spaced columns, each column will endure an equal amount of load. An additional factor of safety is applied when we set L = 14", the total height of the cup:

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Mathinline
body b = \frac{4.3 in}{n_{c}}

So if, for example, if 8 evenly-spaced columns are used, the minimum necessary width of each column is 0.54 inches.

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