The elasticity and resistance of the materials of engineering . I = -~ + bt6 , {d + ij , (^ 4- /) d^ . -|- ^ {s. â a) {d â 2df \- a {d â 2sY â (I) If the dotted Ls are not omitted : j^bjj ^ ^^, {d + tY ^ {2s -V f) d^62 6 \s â a) {d â 2ay -V aid â 2sY â â (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 â a) (zv + 2/4- 2ay^--6^ 6 ^ 6 ⢠(d â 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 â {w â 2sy\^^^ + 6 {sâd)\{w + 2t + 2df
The elasticity and resistance of the materials of engineering . I = -~ + bt6 , {d + ij , (^ 4- /) d^ . -|- ^ {s. â a) {d â 2df \- a {d â 2sY â (I) If the dotted Ls are not omitted : j^bjj ^ ^^, {d + tY ^ {2s -V f) d^62 6 \s â a) {d â 2ay -V aid â 2sY â â (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 â a) (zv + 2/4- 2ay^--6^ 6 ^ 6 ⢠(d â 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 â {w â 2sy\^^^ + 6 {sâd)\{w + 2t + 2dfâ{wâ2df\ {dâ2s) \{w + 2ifâuf\ . 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 ^. Box Column of Plates and Channels. Fig. 2 shows a normal cross sec-tion of this column. FB and CDâB intersect in the centre of gravity of, ^ the cross section. As in the pre-ceding Fig., these lines are lines ofsymmetry. The moment of inertiaabout FB is: I=^J1 + bt (^ + ^y -i- {s â \- t)d^-s{d- 2ay ^ ^^^ The moment of inertia about CD is : J. _ fb^ 2a (w 4- 2/ 4- 2^)3 4- (^ â 2a) {w + 2/)^ - dW^ , . Art. 49.] COLUMN OF PLATES AND ANGLES. 4^5 If latticing takes the place of the two plates bt\ all termsin the second members of Eqs. (6) and (7) involving / will dis-appear. The moment of inertia about FB then becomes : 1 ^ ; . . \p) and that about CD : T â ^^ ^^ + 2/ + 2^)3 + (d â 2a) {w + 2/)3 â dw^ , ^ ~ 12 / C {Radius of gyratioiif ~ r^ = â ; in which A A -f^ is the area of whole section. Eqs. (7) and (9) may also take the forms Igiven in Eqs. (15) and (16). j Built Colunm of Plates and A^igles. -1. F r B < \ fI Fig. 3 shows a normal cross section of this k^ât-^â
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