Question

Question 1. Find the moment of inertia of the following with respect to centroidal x and yaxes. [15 marks) 60 mm 120 mm – 120 mm –ի

Answer 1

X It can be considered as composition Of Mercee sech' end, la 22 3 are removed from 1 to obtain this ((ช, y ) 1 140,120) ..M. I about lentroida niso Sum of M. I of each section about centroid anis M. I about Centroid nais (x-x) 6 For 1) ਤ, X Inna bh3 Igy = hb? h 7 3 =) Inn = 160x240) 12 Tyy= 240 x11803 12 5184 3 2X104 mmt = 8192 x 100 mm for 2) Home) 19.40 mm 110 NE By parallel any's theorem Inn - Int A 912 ران In = 6oxladº = 2888104 mma 36 A=4X60X120 Similarly I gg = Ikt A 112 Ik= 120X1600C 72x107mm r = somm 36 Inus 268810f 30x120x180 1² A=304120 2592x108 mm 92=40 . Igy = 924104+ 30x120 + (4032 = 648X104 mm

Rox 3) 1 мм = ок(120) 1. 2 08 J2 ords o) = 2592xo'я ) 2 Тя у = 648xo 4 mm 4 - -Т =) M. I about tomposition of area ) Inne Inne Тий, -ии , =(1% 4 3 2 2542 -2592 x 104 - 13 248 УТо+ mmt 그 В = 18 19 2.- 64% 698 ) х 4 всяко mma