b$)$ The three hinged tied arch AEB shown in Figure $3$ is supported with a pin at $\backslash ($ A $\backslash ),$ a roller at B and a cable CB$.$ The arch supports one end of a $10$ m beam at point D subjected to a uniformly distributed load and an inclined concentrated load at F $.$ The arch follows a parabolic shape with equation $\backslash ($ y$=-\backslash$frac$\{10$ x$^\{2\}\}\{20^\{2\}\}\backslash ).$

i$)$ Use the equation of the parabola to determine the $\backslash ($ y $\backslash )$ distance from the top

of the arch to points A$,$ D$,$ F and B$.$

ii$)$ Determine the external applied load that acts on the arch at point D$.$

iii$)$ Evaluate the components of the reactions at $\backslash (\backslash$mathrm$\{$A$\},\backslash$mathrm$\{$B$\}\backslash )$ and the tension in the

cable CB$.$

iv$)$ Assess the components of the internal forces at the hinge E

Figure $3$

$($Not drawn to scale$)$