Part B $-$ Tutorial shows step by step how to calculate the moment of inertia for each segmental area.

The beam section shown in composed of two horizontal flanges and a vertical web with dimensions $H=16cm,W1=20cm,$ and $W2=12cm$ and the plates all have thickness of $t=1cm.$ Calculate the moment of inertia of the section about the $x-$axis. Calculate the moment of inertia of the section about the centroid axis parallel to the $x-$axis.

Solution steps:

Calculate the moment of inertia of all segments about their own centroid. $($Note: This member will be divided into $3$ segments, Upper flange, lower flange, and the web$).$ use the table at the end of the textbook.

Calculate the moment of inertia of each segment about the $x-$axis $($since the first question asked to calculate the moment of inertia about the $x-$axis$)$ by using the parallel axis theorem. $I_x=I_{ci}+A_i^{**}{d}_i^2,$ where $I_{ci}$ is the MOI about the centroid of the segment, $A_i$ is the area of the segment, and $d_i^2$ is the perpendicular distance between the segment centroid and the $x-$axis.

Add all the moments calculated for each segment together to get the moment of inertia for the section about the $x-$axis.

Find the centroid of the section $($see chapter $9).$

Re$-$do steps $1$ through $3$ to calculate the moment of inertia about the centroid of the section. the difference will be $d_i^2$ is the perpendicular distance between the segment centroid and the section centroid from step $4.$

Enter your answers for the following, separated with commas:

$I_{cbf}($MOI for bottom flange about it's centroid$),I_{\text{c}\text{u}\text{f}}($MOI for top flange about it's centroid$),I_{cw}($MOI for the web about it's centroid$).I_{\stackrel{}{x}}($MOI for the beam about $x-$axis. $I_{\stackrel{}{x}}($MOI for the beam about it$\text{'}$; centroid$).$