7 .B6 The angle of rotation at either end (the docking port or the window) would be l.64xl0-S radians. Thus, the assumption of a 10% alternating stress is conservative because it requires a large perturbation force to cause a 5% deviation and the resulting angular rotation would be too small to be perceived by the inhabitants. The applied torque required to load the hull beyond its designed stress limits sets the maximum permissible torque for spin-up or spin corrections. The following equation relating mass moment of inertia Ix to the applied torque L will lead to a solution for the spin-up rate. I a = L X For our system [Ix and Las previously calculated] the maximum angular acceleration a= 7.872xlo4 rad/sec 2 . If this angular acceleration was continuously applied to the colony, the hull would reach the design rotational rate of 3 RPM in approximately 6.65 minutes . This is extremely fast and shows that the spin-up rate or·the spin corrections are not limited by structural considerations, but by the maximum torque that can be applied. VII.B.4: BENDING Vibrations due to bending could be an important factor in determining the operational envelope of the space colony. As a first order approximation, the tension in the hull due to the pressure loading of the endcaps will be neglected. This leads to the following homogenous equation for bending. To make the solution of this problem easier and more interpretable, the equation will first be nondimensionalized. w = w/1 X = x/1
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