For the beam shown,

$(1)$ derive equations for the shear force $V$ and the bending moment $M$ for any location in the beam. $($Place the origin at point A$.)$

$(2)$ use the derived functions to plot the shear$-$force and bending$-$moment diagrams for the beam. Specify the values for key points on

the diagrams.

Let $a=2\mathrm{.}1m,b=5\mathrm{.}9m,c=1\mathrm{.}7m,P=62kN$ and $Q=17kN.$ Derive the equations and construct the shear$-$force and bending$-$

moment diagrams on paper and use the results to answer the questions. For all answers, use the sign conventions for shear force and

bending moment as detailed in Section $7\mathrm{.}2$

$($a$)$ at $x=2\mathrm{.}0m$

$V=$

$kN$

$($b$)$ at $x=2\mathrm{.}2m$

$M=$

$kN*m$

$V=$

i

$kN$

$($c$)$ at $x=8\mathrm{.}1m$

$V=$

$i$

$kN$

$M=$

$kN*m$

$($d$)$ Maximum positive bending moment $,M_{\text{m}\text{a}\text{x}}=$

$kN*m$

$($e$)$ Maximum negative bending moment $,M_{\text{m}\text{a}\text{x}}=$

$kN*m$