$(1)$ Consider a long slender beam with a length of $18$ m $,$ a constant Young's Modulus $E=200$ GPa $,$ Poisson Ratio of $0\mathrm{.}3,$ and constant square cross$-$sectional area of $25cm25cm.$ The beam is clamped at its right edge and subject to a distributed downward loading which varies linearly from $0k\frac{N}{m}$ at its left edge to $1k\frac{N}{m}$ at $6$ m from its the left edge as well as an upward point force of $7$ kN at $6$ m from its right clamped edge.

$($a$)$ Determine the distribution of the internal bending moment in this beam.

$($b$)$ Determine the maximum shear strain ${}_{xz}$ in the cross$-$section at $2$ m from the right edge.