A simply supported horizontal beam is $1\mathrm{.}5$ m long and has a cross$-$sectional size of b $=50\backslash ,\backslash$text$\{$mm$\}$ and h $=100\backslash ,\backslash$text$\{$mm$\}.$ The beam is loaded with vertical point loads P $=5\backslash ,\backslash$text$\{$kN$\}$ at $0\mathrm{.}5$ m and $1\mathrm{.}0$ m from the supports. The beam is also subjected to an axial tensile load of $40$ kN$,$ acting at both ends, $25$ mm above the cross$-$sections centroid.

$($a$)$ Determine and draw the normal stress distribution over the cross$-$sectional surface at the midpoint.

$($b$)$ At what eccentricity $($measured from the centroid$)$ does the compressive stress at the top of the

beam vanish for the axial load?

Answers: and I want to know why

$6-13($a$)$k: $=-10$MPa

$,$ uk: $=26$MPa $($:$I_z=4\mathrm{.}17*{10}^{-6}{m}^4$