Chapter 7, Problem 36P

The area moment of inertia $I_{x_e}$ of a rectangle about the axis x₀passing through its centroid is $I_{x_e}=\frac{1}{12}b{h}^3$. The moment of inertia about an axis x that is parallel to x₀is given by I_x= $I_{x_e}+A{d}_x^2$, where A is the area of the rectangle, and d_xis the distance between the two axes. Write a MATLAB user-defined function that determines the area moment of inertia $I_{x_e}$ of a I-beam about the axis that passes through its centroid (see drawing). For the function name and arguments use Ixc=IxcBeam(w, h, d, t), where the input arguments w, h, d, and t are the dimensions shown in the figure and the output argument Ixc is $I_{x_e}$. For finding the coordinate y of the centroid, use the user-defined function centroidI from the previous problem as a subfunction inside IxcBeam. (The moment of inertia of a composite area is obtained by dividing the area into parts and adding the moments of inertia of the parts.)

Use the function to determine the moment of inertia for a beam with w=10 in., h=8 in., d=6 in., and t=0.5 in.