7. G2 area of the plate section. By placing columns every five meters, we obtain a design area of 5 x Sm. Returning to the original Rayleigh-Ritz analysis, we obtain a quartic equation fort expressed as follows: 2.449xl0 4 t 3 + 9.366xl0 3 t 4 - 1 = 0 = M Figure 7.Gl is a graph of M versus t as given by the above equation. At the point where M = 0, the correct thickness is obtained which is 3.375 cm for these plates. Since the hull plates are 4 cm thick, the floor plates for the buildings could be 4 cm also, or they could be the same thickness as the bulkheads (3 cm). For a 3 cm thick floor plate, a Wmax of .75 cm is obtained under the maximum design loading,which is an acceptable deflection. By making the floor plates the same thickness as the bulkheads, a weight and a cost savings is realized since retooling is unnce~sary during the manufacturing process. Each column must now support the load on one complete 5 x Sm plate section that is three levels high. The total load on the column (including the weight of each floor itself) is 7.216xlo 5 N. The standard equation describing the buckling of a thin column is given by: where: nP p load (N) n = factor of safety 1 column length (m) E Young's modulus of elasticity (N/m 2 ) Moment of inertia (m 4 ) Letting n 2, the value of I becomes l.767xl0-S m 4 . For a square section, I equals h, where bis the length of one side. Thus, the column necessary to support the floor has a 12 x 12 cm rectangular cross section.
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