Q$1$

$[k]=EI\left[\begin{array}{cc}2\mathrm{.}333& 0\mathrm{.}666\\ 0\mathrm{.}666& 3\mathrm{.}333\end{array}\right]$

ii$)$

$[P]=\left[\begin{array}{c}+26\mathrm{.}67\\ +54\mathrm{.}17\end{array}\right]$

iii$),{}_1=7\mathrm{.}203{10}^{-4}$rads$={}_B$;${}_2=14\mathrm{.}8134{10}^{-4}$rads$={}_C$;

iv$)M_{CB}=37\mathrm{.}89kNm$;$M_{BC}=-7\mathrm{.}19kNm$;$M_{CD}=-52\mathrm{.}69kNm$

Q$.1$ The frame structure ABCDE shown in Figure Q$.1$ represents an idealised crane geometry and is fully fixed at A and E and has a pin joint support at D$.$ Member CD carries a uniformly distributed load of $15k\frac{N}{m}$ and a discrete force of $30kN$ is applied to $BC$ at the position shown. The members each have their relative flexural rigidities as indicated, where $EI$ is $10MN{m}^2.$ Determine:

i$)$ The stiffness matrix $[$K$]$ for the structure using the Displacement $($Stiffness$)$ method of matrix analysis and considering flexural deformation only;

$[6]$

ii$)$ The load vector $P$ for the applied loading;

$[4]$

ii$)$ The displacements at $B$ and $C$;

$[5]$

iv$)$ The bending moments $M_{BC}{M}_{CB}$ and $M_{CD}$ and the vertical reaction at $C.$

$[10]$

Note: Use may be made of DATASHEET Q$.1$

Figure Q$.1$