Question $2$: Energy Methods

A two$-$dimensional beam structure or frame $($ABCDE$,$ shown below$)$ has a concentrated moment, $M,$ acting at Point $C.$ You can assume that the connections at $B$ and $D$ have sufficient strength to react the applied load and that loads and moments are transferred between the beams. You can assume that the members have a constant cross$-$section and that El$=$constant. Use centreline dimensions when making calculations.

When answering this question ensure that you sketch all relevant bending moment diagrams, the equations that relate to these diagrams, your assumed coordinate system, and the range for each of the equations $($i$.$e$.0x_{2}2\mathrm{.}0m)$

In order to evaluate the design you must:

$($a$)$ Use energy methods to determine the horizontal deflection at Point $E,$hat$(o{)}_x.$ Ensure that you clearly explain your approach and show your final answer. Clearly state any assumptions made.

$(2\mathrm{.}5$ marks$)$

$($b$)$ Use energy methods to determine the vertical deflection at Point C$,y.$ Ensure that you clearly explain your approach and show your final answer. Clearly state any assumptions made.

$(2\mathrm{.}5$ marks$)$