Problem $3$

For the beam shown in Figure P$3,$ the loads w $=14\mathrm{.}2$ kN$/$m and P$=11\mathrm{.}4$ kN$,$ and the fixed support reactions, shown in their correct directions on the Figure are equal to;

$A_x=0$;$A_y=68\mathrm{.}2kN$ and $A_m=199\mathrm{.}0kNm$

Figure P$3$

Use the following positive sign convention for the internal forces in a beam:

a$)$ What is the value $($including the sign$)$ of the internal shear force at point $B$ in the beam? $[1$ mark$]$

Provide your answer in units of $kN$ to at least $2$ decimal places using the positive sign convention noted above.

Internal Shear force at $B[kN]=|$

b$)$ What is the value $($including the sign$)$ of the internal bending moment at point $B$ in the beam? $[1$ mark$]$

Provide your answer in units of $kNm$ to at least $2$ decimal places.

Internal Moment at $B[kNm]=$

c$)$ What is the value $($including the sign$)$ of the internal bending moment at point A in the beam? $[0\mathrm{.}5$ mark$]$

Provide your answer in units of $kNm$ to at least $2$ decimal places.

Internal Moment at

$M(x)=c^{***}(x-3{)}^2+d^{***}(x)+e^{***}(x-1)+f$

where $c,d,e$ and $f$ are numerical coefficients and $x=0$ at the fixed support $A.$

Work in units of $kN$ and $m$ and find the value of the four coefficients $c,d,e$ and $f.[2$ marks$]$

To be awarded full marks here the sign of every coefficient must be correct so it is important your use the positive moment sign convention as shown in the question.

$c=$

d :