a$)$ Explain the difference between a curved beam and an arch.

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 $\backslash ($ D $\backslash )$ subjected to a uniformly distributed load and an inclined concentrated load at $\backslash ($ F $\backslash ).$ 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 $\backslash ($ A$,$ D$,$ F $\backslash )$ and $\backslash ($ B $\backslash ).$

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