Home Work $5($for Chapter $6)$

Figure $1$ shows a beam of $2$ m length that is supported by a truss member at the middle point A and clamped on the rigid walls at the two ends. It carries a uniformly distributed vertical load over the left span. The truss and beam are all of uniform cross$-$section and made of the same material with the Young's modulus $\backslash ($ E$=200\mathrm{.}0\backslash$mathrm$\{$GPa$\}\backslash ).$ The cross section of the beam is circular, and the area of the cross$-$section is $\backslash (0\mathrm{.}01\backslash$mathrm$\{$~m$\}^\{2\}\backslash ).$ The area of the crosssection of the truss member is $\backslash (0\mathrm{.}0002\backslash$mathrm$\{$~m$\}^\{2\}\backslash ).$ Using the finite element method with two elements for the entire beam, using an efficient approach to

$($a$)$ calculate the nodal displacement at the middle pint A $,$

$($b$)$ calculate the reaction forces at the supports for the beam and truss members,

$($c$)$ calculate the internal forces in the truss member.

$(100$ marks$)$