Problem $3$

The cantilever beam shown in Fig. $3\mathrm{.}1$ has a rectangular cross$-$section with h $=120$ mm and b $=$

$80$ mm$.$ The $12$ kN and $10$ kN forces act parallel to the x and z axis, respectively, and pass through

the centroid of the beam cross$-$section at the locations they act. The $10$ kN force acts at the free

end of the cantilever, whereas the $12$ kN force acts $250$ mm away from the free end. The cross$-$

section ABCD is $750$ mm away from the free end.

a$)$ Determine the magnitude and location of the maximum tensile and compressive bending stress

at the cross$-$section ABCD and indicate the neutral axis on it$.$

b$)$ If an additional force, F$,$ is applied on the beam parallel to the z axis at a point $500$ mm away

from the free end, what should be its magnitude and direction to make the bending stress at point

B zero?