A channel and a plate are welded together as shown below to

A channel and a plate are welded together, as shown below, to form a section that is symmetrical with respect to the y axis. Determine the moments of inertia of the combined section with respect to its centroidal x and y axes. look online for properties of channel C8 x 11.5

Solution

in this link i found the dimesion of the channel c8x11.8

http://www.engineersedge.com/standard_material/Steel_channel_properties.htm

so the inertia of x and y is

Ixx=32.6 in^4

Iyy=1.32 in^4

A=3.38 in^2

the intertia of the other part is given by

Ix=(1/12)bh^3 =(1/12)15*0.3^3 =0.03375 in^4

Iy=(1/12)b^3 h = (1/12)(15^3)(0.3) =84.375 in^4

A=15*0.3= 4.5 in^2

using the parallel method to know the complex inertia

Ix= 32.6 + 0.03375= 32.6034 in^4

Iy= 1.32 + + 3.38*(2.26-0.571)^2   + 0.03375 + 4.5*(0.3)^2 = 11.4009 in^4