Consider the truss in Figure P$4,$ which is supported on a pin at point A and a rocker$/$roller at point G$.$ It is loaded with two horizontal forces P$=\{53\}$ kN and Q$=\{18\}$ kN$,$ and a vertical force R$=\{38\}$ kN$.$ The support reaction forces and their assumed directions are illustrated in the figure and their values are A$\_$x$=\{-71\mathrm{.}0\}$ kN$,$ A$\_$y$=\{-123\mathrm{.}05\}$ kN$,$ and G$\_$y$=\{161\mathrm{.}05\}$ kN$.$ Here, H$=\{2\mathrm{.}3\}$ m$.$

a$)$ Determine the force in member BE using the method of sections. Use a positive value to indicate tension and a negative value to indicate compression. Provide your answer in kN to $4$ decimal places. $[1$ mark$]$

Force in member BE $[$kN$]=$

b$)$ Determine the force in member BC using the method of sections. Use a positive value to indicate tension and a negative value to indicate compression. Provide your answer in kN to $4$ decimal places. $[2$ marks$]$

Force in member BC $[$kN$]=$

c$)$ Determine the force in member FE using the method of sections. Use a positive value to indicate tension and a negative value to indicate compression. Provide your answer in kN to $4$ decimal places. $[2$ marks$]$

Force in member FE $[$kN$]=$

d$)$ Consider the case where the vertical load R remains pointing downwards but its magnitude can change. All other loads $($P and Q$)$ are unchanged. Determine the maximum allowable magnitude of R if support G only manages a force of $\{293\}$ kN upwards. Provide your answer in kN to $4$ decimal places. $[2$ marks$]$

Maximum allowable magnitude of R $[$kN$]=$