The beam section shown in composed of two horizontal flanges and a vertical web with dimensions $H=16cm,W1=19cm,$ and $W2=9cm$ and the plates all have thickness of $t$

$=3cm.$ 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 $9).$

from step $4.$

Enter your answers for the following, separated with commas:

centroid$).$

$I_{cbf},I_{\text{c}\text{u}\text{f}},I_{cu},I_x,I_{\stackrel{}{x}}=42\mathrm{.}75,20\mathrm{.}25,1024,19504,9147\mathrm{.}64c{m}^4$

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