Substituting for a, 7 .B9 ul = 22.37 ,/IT 4 ml The values of the above material constants and colony geometry were derived in Section VII.B.3: E 2.069xlo 11 N/m 2 for steel 5.662xl0 5 m 4 m = 3. 966xl0 6 Kg/m 300m Substituting into the above· equation: w = 42.72 radians/second ~ = 6.80 Hertz This bending frequency becomes very important during the construction of the colony. Assuming a working stress at l.738xl0 7 N/m 2 for the inner hull and using a 5% allowance (plus or minus) for vibration induced stress, the omax which sets a limit on the bending torque applied to the habitat is: a max = 8.69xl0 5 N/m 2 Using the following equation and the allowable stress variation, the maximum allowable torque can be obtained: Mz 0 max Ip M 4.92xl0 9 N-m This moment implies a force couple at each end of the colony equal to 3.28xl0 9 N. This value is extremely large for a sustained torque and it seems unlikely that the above value will be exceeded during construction or operation.
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