The beam section shown in the Figure has dimensions $H1=24,H2=12,W1=12,W2=30,$ and $R4=6.$ Determine the location of the centroid.

Use the table below to organize your calculations. For regions that are holes, the area is negative.

Calculate the product of the area and tilde$(x)1$ for region $1.$

Calculate the product of the area and tilde$(x2)$ for region $2.$

Calculate the product of the area and tilde$(x3)$ for region $3.$

Calculate the product of the area and tilde$(x)4$ for region $4.$

What is the $x-$coordinate of the centroid?

What is the $y-$coordinate of the centroid? remember you need to find tilde$(y)$ for all regions. Then find the product of the area and it's tilde$(y).$

Separate your answers with commas.

tilde$(x)1A_1,$tilde$(x)2A_2,$tilde$(x)3A_3,$tilde$(x)4A_4,x,y=$ 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 $9).$

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$).I_x($MOI for the beam about $x-$axis. $I_{\stackrel{}{x}}($MOI for the

beam about it's centroid$).$

$I_{cbf},I_{\text{c}\text{u}\text{f}},I_{cw},I_x,I_{\stackrel{}{x}}=,c{m}^4$