Q$2.$ The horizontal bracket a shown in the figure is fixed at support a and free at end $d.$ It has a circularcross section with flexural rigidity $EI$ and torsional rigidity $GJ.$ Let $l_1$ denote the lengths of members $ab$ and $cd,$ and let $l_2$ denote the length of member $bc.$ Ignore deformations due to shear and use the unit load method to determine the vertical deflection and the angle of twist $($rotation in its plane$)$ of the cross$-$section at $d.$ Note that torsion may not be ignored. Take $P=1kN,l_1=1\mathrm{.}5m,l_2=1\mathrm{.}2m,I=3\mathrm{.}0{10}^{6}m{m}^4,E=70$GPa,$G=26$ GPa $($ans: $76\mathrm{.}8mm,0\mathrm{.}0150$rad $).$