As shown in Fig. $02($a$),$ it has a length of $L=13m,$ a uniform loading of $q=5k\frac{N}{m},$ a concentrated loading of $P=30kN$ and there is a simple supported beam with a T cross$-$section shown in Fig. $2($b$).$

Determine the following $($The modulus of elasticity of steel is $E=210$GPa.$)$

$(1)$ Reaction forces at both ends A and $B,(2)$ shear force diagram, $(3)$ bending moment diagram, $(4)$ maximum shear force, $(5)$ maximum bending moment, $(6)$ maximum bending stress and position, $(7)$ maximum shear stress and position, $(8)$ sketch the stress state at point E as shown in Fig. $02($c$),(9)$ draw Mohr' s circle for the stress state at point $E$ and the principal stresses$({}_1$ and ${}_2).$