$($For Problems $1-2)$ C$=$W$24$x$162$

Determine the properties of the combined sections shown below

a$.$ Area

b$.$ Centroid

c$.$ Moment of inertia $($Ix and Iy$)$

d$.$ Section Modulus $($Sx and Sy$)$

e$.$ Radius of gyration $($rx and ry$)$

f$.$ Section modulus at an axis of max moment of inertia $(S_{\text{m}\text{a}\text{x}\text{i}})$

g$.$ Radius of gyration at an axis of min moment of inertia $(r_{\text{m}\text{i}\text{n}\text{I}})$

Use the Steel Manual for the properties of the above sections.

Channel section and angular section with longer leg vertical

Two identical Channel Sections placed back to back with a clear

distance of $25mm.$

Given a Wide Flange section, $($see above table for your WF section$)$

Determine the following:

a$.$ Maximum moment of inertia in $m{m}^4.$

b$.$ Minimum moment of inertia in $m{m}^4.$

c$.$ Moment of inertia in $m{m}^4$ with respect to the $x^{\text{'}}-$axis,

rotated counterclockwise $55$ from the $x-$axis.

d$.$ Product moment of inertia in $m{m}^4$ with respect to the $x^{\text{'}}-$axis.

e$.$ Maximum product moment of inertia in $m{m}^4.$

f$.$ Minimum product moment of inertia in $m{m}^4.$