The elasticity and resistance of the materials of engineering . tangles to each other, its moment of inertia is the same about allaxes passing tJirough its ce7itre of gravity and lying in it. Eqs. (\a) and the two preceding it also show that the samecondition obtains, if the moments of inertia about fo2ir axes atright angles to each other, in pairs, are equal. In the case of such a surface, therefore, it will only be nec-essary to compute the moment of inertia about such an axisas will make the simplest operation. Since a column fails partly by flexure, it is manifest that themoment of inertia
The elasticity and resistance of the materials of engineering . tangles to each other, its moment of inertia is the same about allaxes passing tJirough its ce7itre of gravity and lying in it. Eqs. (\a) and the two preceding it also show that the samecondition obtains, if the moments of inertia about fo2ir axes atright angles to each other, in pairs, are equal. In the case of such a surface, therefore, it will only be nec-essary to compute the moment of inertia about such an axisas will make the simplest operation. Since a column fails partly by flexure, it is manifest that themoment of inertia of its cross section should be the largest possibleabotit an axis passing through its centre of gravity, and normalto the plane of flexure. Art. 49-] BOX COLUMN. 413 Box Column of Plates and Angles. Fig. I shows the cross section of Ta box column composed of 4 platesand 4 or 8 equal legged Ls. FB and CD intersect at the centre of ^f lt~1 J1 ^ gravity of the cross section. If the 4 Ls shown in dotted lines Jare omitted, the moment of inertiaabout FB will be :. I = -~ + bt6 , {d + ij , (^ 4- /) d^ . -|- ^ {s. — a) {d — 2df \- a {d — 2sY ? (I) If the dotted Ls are not omitted : j^bjj ^ ^^, {d + tY ^ {2s -V f) d^62 6 \s — a) {d — 2ay -V aid — 2sY ? ? (2) If the 4 Ls shown in dotted lines are omitted, the momentof inertia about CB> will be : J- __ /^3 a {w + 21 + 2sy (s — a) (zv + 2/4- 2ay^--6^ 6 ^ 6 • (d — 2s) (w 4- 2/y _ dw^ . * 12 U • • • • ^^^ 414 MOMENTS OF INERTIA. [Art. 49. If the dotted angles are not omitted : J. _ tb^ a\{w -V 2t ^ 2sy — {w — 2sy\^^^ + 6 {s—d)\{w + 2t + 2df—{w—2df\ {d—2s) \{w + 2if—uf\ . 12 If latticing is used instead of the two plates bt\ f becomesequal to zero, and the first term in the second member of eachof the above equations disappears. If A represents the area of the cross section, and r theradius of gyration: -i (5) L 1 1 ^
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