Consider the beam ABCDEF shown in Figure P$5,$ which has roller support at B and a pin support at D$.$

Please note that point $C($located $xm$ from point $A)$ indicates the point of maximum bending moment along span $BD.$

Given:

$w=24k\frac{N}{m},P=14kN,y=1\mathrm{.}3m$

$B_y=107\mathrm{.}3333kN,D_y=80\mathrm{.}6667kN$

a$)$ Determine the moment in the beam at $B,M_B($in $kNm).[1$ mark$]$

$M_B=$

$kNm$

b$)$ Determine the location $\text{'}x\text{'}$ where the maximum positive moment occurs under the uniformly distributed load $($i$.$e$.$ the maximum moment along span $BD$ occurs at point $C).$

Note: $\text{'}x\text{'}$ as shown, is the distance measured from point $A.$ Provide your answer in units of $m$ to at least $4$ decimal places. $[2$ marks$]$

$($Drawing a shear force diagram may assist you with this question.$)$

$x=$

$m$

If you are unsure as to how to find the value of $x,$ proceed with part c$)$ assuming a value of $x$ such that $M_c=kNmym{M}_E=|kNm2\mathrm{.}1.$

$c$