L'élasticité et la résistance des matériaux de l'ingénierie . Dans la Fig. ^ 12  = M.le moment d'inertie / aboutFBs^-Y ; . (37) et sur CD : /  = 12 (38) / /j'^^{b de rayon r  = gyrationf^  =z -  = - ou - jrL 1212 si la section est rectangulaire, carré b  = h. Les sections rectangulaires creux, le domaine de la section de la Fig. 13 est : ^4 r = bh - b/t.l'instant d'inertiaabout est FB : bk3 ^ ^7/3 =-Y-^- ; . (39) ^ c 111 h1 -hB 1111 et que sur CD est : ^ . ^- Fig. 13. Article 49-] SECTIONS circulaires. 423 /  = hb^^ - hb 12 (40) / 3 K-f J (rayon d'gyratioiif^  = r  = Toutes les équations de ce cas (e

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The elasticity and resistance of the materials of engineering . In Fig. 12 ^ = M.The moment of inertia aboutFBs /-Y^; . (37) and about CD : / = 12 (38) / /i^ b^{Radius of gyrationf = r^ =z — = — or — jrL 12 12 If the rectangular section is square, b = h. Hollow Rectangular Sections, The area of the section shown in Fig. 13 is: ^4 r= bh — b/t.The moment of inertiaabout FB is: bk3 _ ^7/3 ^=—Y-^—; . (39) ^ c 1 1 1 h1 -hB 11 1 1 and that about CD is : ^ .__^- Fig. 13. Art. 49-] CIRCULAR SECTIONS. 423 / = hb^ - hb^ 12 (40) / 3 K-f J (Radius of gyratioiif = r^ = All the equations of this case (except Eq. (40)), just as theystand, apply directly to the rect-angular cellular section of Fig. 14, considered in reference to the axisFB. If there were n cells insteadof 3, the space between any adja-cent two would have the width n 3 Fig.H Solid and Hollow Circular Sections. First consider a solid cylindrical column whose cross section has the radius r^^ as shown in Fig. 15.The moment of inertia about any di-ameter is : 7rr/. / = {Radius of gyrationf = (41) Ttr^*47rr, Fig. 15. 4 Next consider a hollow circular column whose interior andexterior radii are r^ and r^ respectively. The moment of iner-tia about any diameter is: / = -^-^— -^ = ^ J -; {A = area) . (42) (Radius of gyratiorif = I 7r(r/ - r, ) + r. = r 424 MOMENTS OF INERTIA. [Art. 49. As tables of circular areas are very accessible, it may beconvenient to write: 7^ = ^^2^ . or r^ =r ^(^/ -f- ^i)12.566 12.566 Phcenix Section. Fig. 16 shows the section of a 4 segment Phoenix column. Let CD represent any axistaken through the centre of thecolumn. The moments of iner-tia of the rectangles bl aboutaxes through their centres ofgravity and parallel to CD willbe very small indeed comparedwith the moment of inertia ofthe whole section. The mo-ment of inertia of any oneof these rectangles, therefore, about CD^ will be taken asequal to the product of its areaby the square of the normaldistance from its centre of gravit

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