The elasticity and resistance of the materials of engineering . FB is: ^ ^ bx,^ + t{d + t - x:f -(b- t) {x, - ty 3The moment of inertia about CD is: tb^ + dt^ 1 = (29) 12 (30) {Radius of gyrationf = r^ z= — . As in the other cases, FB may be located by balancing on aknife edge. Art. 49.] FALSE EYE SECTION. 421 False Eye Section. If the area is not taken from the weight per yard, it may be written : • (c A=bd-{b- t) {d - 2t) , . (31)The moment of inertia about CD is: r &t ?»! ^_ 2/^3 -^ [d — 2t)0?? • • • 12 (32) About FB it has the value: J ^ bd^ - {b - f) (d - 2ty12 I « D . • . (33) {Ra
The elasticity and resistance of the materials of engineering . FB is: ^ ^ bx,^ + t{d + t - x:f -(b- t) {x, - ty 3The moment of inertia about CD is: tb^ + dt^ 1 = (29) 12 (30) {Radius of gyrationf = r^ z= — . As in the other cases, FB may be located by balancing on aknife edge. Art. 49.] FALSE EYE SECTION. 421 False Eye Section. If the area is not taken from the weight per yard, it may be written : • (c A=bd-{b- t) {d - 2t) , . (31)The moment of inertia about CD is: r &t ?»! ^_ 2/^3 -^ [d — 2t)0?? • • • 12 (32) About FB it has the value: J ^ bd^ - {b - f) (d - 2ty12 I « D . • . (33) {Radius of gyratiorif = r^ = — , Star Section. Fig. II shows this section with the different dimensions. The area of cross section is: II >1 I 1 F- + -f -i— A = bt -\- bt - tt . . (34) -5 *i I The moment of inertia about FB is: -B /=+!t - ^ . . (35) About CD the moment of iner-tia has the value: 422 MOMENTS OF INERTIA. [Art. 49. ~ 12 (36) Ordinarily, ^ = /. / (Radius of gyratiorif = r^ = — . Solid Rectangular In Fig. 12 ^ = moment of inertia aboutFB\s\ /-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 — 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 Solid and Hollow Circular Sections. First consider a solid cylindrical column whose cross section has the radius r^^ as shown in Fig. moment of inertia ab
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Keywords: ., book, bookcentury1800, booksubjectbuildingmaterials, bookyear1883
