Question

Two L4X4 in angles are welded to a steel plate as shown in the figure, where h = 16 in. Determine the moments of inertia of the combined section with respect to centroidal axes, parallel and perpendicular to the plate. in. in The moment of inertia of the combined section with respect to centroidal axis parallel to the plate is The moment of inertia of the combined section with respect to centroidal axis perpendicular to the plate is in4

Answer 1

in the centroid G of the section must lie on this aris. Let the distance of the centroid G de: YY is an aris of symmetry 0.5 in 11:306 To Locate the centroid G IG 16 in 15,75 from the top edge of the section =ų ing = 116 x 4 x 147 2[4 x1y)x14+ 35K! (0.5X16) + 2 [Luxge)+ 3.5x3] K 14x 4x1. 2 150 0 Itp 12 64 + 111.25 8 + 7.5 -) I j = 11.306 in To determine the M. I of the whole section about the top edge of the plate, 15X16)*8 420.5x 43 +(4x0.5)x142 + 3.5x 0.5°+ (3.5x015) * 15.75 Ivp = 2048 + 1657.625 3 Let Inn = M.I of the whole section about an anis upassing through the centreid and beefendicular to the flate. Inn = Itp- Aga Iren = 56167 12 s) Itp = = 56167.4 in 24 [(15 x 16) + 2 (42015) + 2 (3.520.s)]* 1.306 24 Inau = 359 in Ang, CS Scanned with CamScanner

bet M. I Igy = of the whole section about an anis passing through the centroid and parallel to the plate 3 3 iS + 12 3 Iyy = 16X0.5 2 4x0.5 +(4x0.5)x0,52 + 12 0.5x3.53 +(0.5*3.5)*2.5 12 2) Tyy = 26.698 in Ams: 4 Igy = 16 + | 6 249 32 CS Scanned with CamScanner