Short Calculations $-10$ points each

$11.$ Calculate the maximum bending moment that a W $1490$ steel cross section will be permitted to carry to ensure a factor of safety of $1\mathrm{.}67$ against yielding if $F_y=50$ksi.

$12.$ A W$14$x$74$ hot$-$rolled structural steel wide$-$flange shape is used as a simply supported beam. Calculate the maximum bending stress. $($Answer nust include correct units, include self weight. Hint: Use the Appendix in the text for help$)$:

$13.$ For the steel wide flange beam, calculate the maximum shear stress on the cross section at a point on the beam where the value of the shear diagram is $150$ kips $.$ Use the simplified formula for shear stress:

$14.$ Calculate the value of the internal shear and bending moment just to the right of the $30$ kN load. Indicate positive or negative.