This question is from a module called aircraft structures, on the shearing of thinned$-$walled beam structures. Show me the steps to solve CA$22024-25$ Sem $1$

A thin$-$walled open cell section supports an unknown shear force $S_y$ as shown in Figure $1.$

The section has wall thicknesses as shown in the figure with the lengths $AD=BC=500mm$

and $AB=CD=1000mm.$ Given $E=70$GPa,$G=28$GPa,$v=0\mathrm{.}3,$ allowable shear stress of $50$

MPa and allowable rate of twist of $0\mathrm{.}10$ degree$/$millimetre$.$

$($a$)$ Assume that the gap at C is negligibly small. Determine:

$($i$)$ the position of the shear centre $e_x$ from wall AB and $e_y$ from wall AD $,$

$(50$ marks$)$

$($ii$)$ the allowable shear force $S_y,$

$(30$ marks$)$

$($b$)$ The gap at C is now welded and the section can be considered a closed section. Compare

and comment on the torsional stiffness of this closed section with that of the original

open section.

$(10$ marks$)$

$($c$)$ Discuss the importance of knowing the location of the shear centre.

$(10$ marks$)$