$1\mathrm{.}6\mathrm{.}5$ Problem $5$

$(10$ pts$)$ Use SolidWorks to model the L$-$section shown in problem $4($extrude back $6^n),$ setting the origin at

the bottom left corner of the L$.$ Use the Section Properties tool to determine the following $($make sure you

extrude back and select the front surface of the part so that your output coordinate system is in the same

plane as your selected surface$)$:

$($a$)$ The moments inertia, $I_x$ and $I_y,$ for a set of $x$ and $y$ axes passing through the centroid.

$($b$)$ The moments inertia, $I_{x^{\text{'}}}$ and $I_{y^{\text{'}}},$ for a set of $x^{\text{'}}$ and $y^{\text{'}}$ axes passing through the output axes ori$-$

gin.

$($c$)$ Use the parallel axis theorem to hand$-$calculate $I_{x^{\text{'}}}$ and $I_{y^{\text{'}}}$ given the values for $I_x$ and $I_y$ determined in

part $($a$),$ the location of the centroid $($from SolidWorks$),$ and the area of the cross section $($from SolidWorks$).$

$($d$)$ What are the values of the maximum and minimum moments of inertia about any set of $x$ and $y$

axes passing through the centroid? Where is the location of this set of axes relative to the standard $x$ and

$y$ axes that passes through the centroid?

$($e$)$ Sketch the L$-$section below and draw and label the axis that passes through the centroid $n$ which that

L$-$shaped bar would most easily bend about.