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There were three failure modes that were taken into account when modifying the design of the Staging Cone.
1) Exceeding the shear strength of the bolts
To run calculations on the shear strength of the bolts, it was assumed that all of the sustainer's weight would be on on the cone section and reacting against the bolts. This would yield the most conservative estimate. The forces accounted for on the cone were the weight of the sustainer under a maximum acceleration of 20 G's and drag force at Max-Q (from RASAero). To find the shear stress, this total force is this divided by the minor area of a bolt multiplied by the number of bolts to be used. To find the equivalent or von mises stress, this stress is then multiplied by the square root of 3. This comes from the equation of von mises stress under the condition of shear only. This von mises stress allows us to compare against the tensile strength of the bolt which is easier to find.
2) Exceeding the bolt tear out strength of the aluminum
To calculate the tear out stress from the bolts reacting against the aluminum of the base (smaller thickness), that same derived total sustainer force is then divided by the projected area of the bolt onto the walls of the hole. This is A = minor diameter * wall thickness. This area calculation was used knowing that there are more correct and conservative estimation methods but it was felt that this was sufficient and simple. After finding this stress, a stress concentration factor of Kt = 3 was multiplied. Without this, stress calculations will be severe underestimates.
3) Exceeding the maximum moment the cone could impart on the sustainer
To calculate the pure moment that would be imparted by the cone section onto the sustainer in the event of non-zero angle attack, a maximum angle of attack is specified. In the case of my calculations, it was 5 degrees. Flight conditions including velocity and dynamic pressure are specified at their maximum values (these values are coupled). Experimental data on the drag coefficient of a cylinder based on the Reynolds number of the flight was then used with a compressibility factor given that the rocket will be supersonic to find the drag on the projected area of the rocket. This force is then assumed to be concentrated at half the length of the rocket and a moment is calculated from there.
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