Question

GTETTU You are logged in as Humaid Al Aamri Fing2020 4 Determine the moment of inertia about the neutral axis in mm The centroid of the section is 46 mm from the top ered 120 mm 20 mm 12.00 stion 10 mm 160 mm T Cross-Section Answer Next page

Answer 1

-120 mm 20 mm -XB 46 pm |(160 + A 10 =) 170 mm *ro 160 mm 30 mm y x . cosider the The cross section with proper dimensions us shown below. - The centroid of the whole system is at point A and the centroid of individual upper and lower (180-46) beam is =134 at B and respecticely let's I tomne the ground to lee Y=0 line. Thus all the distances distances from J= 0 and relatie distances are 4640. พง- the figure. Let I, and I be the moment of entre inertia of individual learns. Let Al and Az be the area of the individual luams (uppre and loove) let dy, and dy be the distances of the individual centre of of gravity 아 apper and loneve mam respectively from centroid of the systems de dy 2 dy 2 = Ae A,= 120X20 mm Aza 160x10 mm that moinent of Now 90 inertia of rectangular beam height h and weeth in is 2x1 wh3 2 = AB and . 9 with of

with of inertia the 2 X120 x 20 mm IL 3 1 mm moment Now formula of imeritia of I = { different elements of the where Inn is the moment respect to asus parallel the neutral anes) to height (here • I (face cepper beam) 16x105 mmt 4 simularely 22 (fore tone mam) = 1 x 10 x (1603 mm => 22 = 54.6 X10 of know from a cross section + { Aidy 2 who wu i covesponds to total system. RoIF I + I + I + Iz + Andy + Az dy ? (i=2 hare for = (16 x103) +(3416 X10*) + (120 X20X A8%) + (160x10x4cm) =(16*109) + (54.610+)+(2400x{170-1343) +(1600x1200) (2 A = (BAL= (170-134) mm and Inel= (134-80) mm → ſ = 55.1X107 Thus the total moment of inseritia about the neutral anes is I = 55.4 x107 mmy upper and loweve mm