THE STORAGE OF GAS 633
and the section modulus must be made of such dimensions as to withstand this bending moment.
The sectional dimensions of the columns are calculated from the well-known formula'—
Bending moment = /max Z, where /max is the maximum allowable stress in the steel, i.e. 6 tons per square inch for ordinary steelwork,
and Z = the section modulus, or = .
Y
Where I = the total moment of inertia of the structure, and Y = half the depth of the section.
It must here be borne in mind that we are dealing with a cantilever composed of the structure as a whole, and not with an isolated column. Therefore, in arriving at the value for Z,
Y = half the total diameter of the holder = —.
2
The moment of inertia I can be found by the summation of the elements, using the ordinary formula—
Ix = lo + AD2.
Where Ix = the moment of inertia of each element about the true neutral axis of the section.
lo = the moment of inertia of each element about its own neutral axis.
A = the area of the element.
D = the distance of its neutral axis from the true neutral axis.
This formula is, however, somewhat tedious ; and, althoughnot strictly accurate, Rankine’s formula is very much more easily håndled.
The formula says—
Z = 0-25 NÅD.
Where N = number of the columns.
A == cross-sectional area of each column in square inches.
D = diameter of holder in feet.
Then, ha ving found the value of Z, it is possible to equate this to the bending moment in the ordinary way :—
Bending moment = /max Z.
(It must be noticed that the wind pressure P was taken in Ibs., and the allowable stress /mav is in tons. The two must therefore be reduced to equivalent units.)
From above—
D3
8DD 1= 6 X 2240 X 0-25 NAD,
3
D3
8 L2D + -. 3 or A —------->---------------
6 X 2240 X 0-25 ND
24 L2 + D2
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