Problem $5$

A plane frame of $3$ beams has fixed supports in A and $D.$

Figure $5$: Frame with fixed supports in A and D

Neglect axial deformations in the beam elements. Assume a model with three beam finite

elements.

a$)$ Define the active degrees of freedom of the frame. Establish the $($non$-$singular$)$ system matrix

that operates on the active dof you defined above.

The frame is loaded in $B$ with moment $M_{zB}=100Nm$ and a horizontal force $F_B=1kN.$

Properties of the frame: $a=5m,b=4m,$ elastic modulus $E=2*{10}^{11}Pa$ and $Iz=6\mathrm{.}667*{10}^{-6}{m}^4.$

b$)$ Determine the unknown displacements and the support reactions in A and D$.$