$($For Problems $1-2)$ Please provide detailed solution and answer to the following section properties. Determine the properties of the combined sections shown below $"$C$"$ Wide Flange Section$=$ W$18$x$192$ ; $"$B$"$ Channel Section$=$C$12$x$30$ ; $"$A$"$ Angle Section$=$ L$65$x$50$x$10$

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 $($Smaxi$)$

g$.$ Radius of gyration at an axis of min moment of inertia $($ r$\_("$minI $"))$

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 $25$ mm $.$

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

Determine the following:

a$.$ Maximum moment of inertia in mm$4.$

b$.$ Minimum moment of inertia in mm$^(4).$

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

rotated counterclockwise $55^($@$)$ from the x$-$axis.

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

e$.$ Maximum product moment of inertia in mm$^(4).$

f$.$ Minimum product moment of inertia in mm$^(4).$