As shown in Fig. $01,$ there is a simply supported beam with $B$ and $C$ overhanging. The span length of the beam is $8$ m $,$ and the overhang length is $2$m$.$ A uniformly distributed load acts over the entire length of the beam, and a concentrated load acts at a point $3$ m away from A$.$ Given that the material used for the beam has a modulus of elasticity $E,$ calculate the following:

$(1)$ Reactions at points A and $B.(2)$ Shear force diagram. $(3)$ Bending moment diagram. $(4)$ Maximum shear force. $(5)$ Maximum bending moment. $(6)$ Maximum bending stress and its location. $(7)$ Shear stress distribution across the cross$-$section. $(8)$ Maximum shear stress and its location. $(9)$ Centroid of the cross$-$section. $(10)$ Moment of inertia of the cross$-$section.

Fig. $01$