Question

how to solve 9.38

the moments of inertia and the radli of gyration of the section with respect to the centroidal axes shown. C250 x 2.8 C 200 171 8 mm W 160x113 -300 mm Fig. P9.37 Fig. P9.39 9.37 Two channels and two plates are used to form the column section shown. For b = 160 mm, determine the moments of inertia and the radit of gyra. tion of the corabined section with respect to the centroidal axes, 9.38 In Prob. 9.37, determine the distance b for which the centroidal moments of inertia 1, and 7 of the column section are equal

Answer 1

Since, In combined = fy combined 80.45x106 2x18x10° + 2x 6 Disusxio 응 +2170 40-23 = (271.56 2104( *10.5/2y - 18 + o. sngt2.178100 wird III =91 <= b= 170mm , In In and and ty of the Colums are equal

203 101.5 mm 101.5 + 8 105.5mm -) 1203 mm for each chennet section b x = 14.5mm 6 18mm 4 Im = 13.5x 10° mm' 6 fyt 0.545x10 Area - 2170 mm त्र mm 300mm T 14.5mm 9.37 moment of exestia of plates about their controidal anais Ipe 3 3 bd 12 4 300 x 8 12 12800 mm on applying pesellel assis theorem to get mos about t-aramies Ipa 300 * 3 * (105-5) - Ipc ta Ay? 1280ot 300 x 8 x - 26725400 26.725 x106 4 about naamin combined moment of ešertia ti . 6 2 * 13.5*10'+ 2 * 26.725 x 10° 80.45 x10 mods about to axis combined moment of enerhia 6 [- = 80145 x 100 mm

mm" Combined area = 2x300x8+2x 2170 - nm² 9140 mm ke T 6 80.45 x 10 Combined relies of gysebion Combined radius of guestion А gino 93.82 mm about y-aris Ichannel こ 0.545 iO sus x10° moment of biertia about their centroidal line of plates Ipe = 8x300 12 = 18x106 moos + A A ? applying pasolled annis theorem for channels to get more about y-aris Try = Ichommel Icy 0.545x100 + 2170 x ( 160 + a)" 0.545X10 + 2170 (20 + 1.50€ 19.924x10 mm 4 Combined moment of inertia about yo asis 2*18X106 + 2x 19.924x106 - 6 - 75.8 5x10 mmh

radius of gydation ka s A 75.85 10 2170 91.1 mm 09.38 Combined Centrordal moment of enestica In, combined suing x 106 mm about K-ara's Combined Centroidal moment of enestia calculation about y amis moment of exertia of each each of the plates about h-anis + 300 x 8 x 1105-5) Lpx - Geneline 26.725 8106 mms 1280o about n-anis combined moment of exertia I = 2*26.725 x 106 + 2 * 13.5 /06 = 80.450100 mm about y-ara's moment of ejesha of plates 18x10 r101 6 mm about y comis, mos of channel Sayt orsasalo+ 270 ( + m.51 6