Problem $1$:

A beam is subjected to a distributed load and a concentrated load and the cross of the beam as shown.

Draw shear and moment diagrams;

Determine the maximum bending moment and maximum shear force, and their locations;

Determine the centroid and moment of inertia about the neutral axis $($or centroid axis$)$ of the cross$-$sectional area;

Determine the bending stresses at point $a,b,$ and $c$ on the cross$-$section, where the maximum bending moment $(M_{\text{m}\text{a}\text{x}})$ occurs in the beam.

Determine the transverse shear stresses at point $a,b,$ and $c$ at the cross$-$section Bright in the beam.

$*$Note: For point b$,$ you need to calculate shear stresses at b$\_$above and b$\_$below at b$.$

Partial Ans: $B_y=58kN($up$),C_y=26kN($up$),M_{\text{m}\text{a}\text{x}}=33\mathrm{.}8kN-m(+)$ at $3\mathrm{.}4m$ from B and shear stresses should be the same direction as the shear force $V_{\text{B}\text{r}\text{i}\text{g}\text{h}\text{t}}.$