Consider the exact same loading and exact same beam as above except we are now going to remove the lower flange. This completely changes the beam cross$-$section properties because we now have a T$-$beam. Do the following: a$)$ Show that the centroid is $6\mathrm{.}25$ inches up from the bottom and that I is $124\mathrm{.}33i{n}^4.$ I strongly recommend that you try the method we outlined in class to find the centroid and moment of inertia to see if you like this approach. b$)$ Show that the maximum tensile stress is $2\mathrm{.}654$ksi and the maximum compressive stress is $6\mathrm{.}03$ksi. c$)$ Use both our analytic method to show that the total axial force in the upper flange $($the only one we have remaining$)$ is now $17\mathrm{.}37$ kips in tension. You might want to check using the graphical approach.

We paid a pretty heavy price $($our max stress is $3\mathrm{.}5$ times greater than that for the I$-$beam$)$ for removing $\frac{1}{3}$ of our beam area.