$(20)$ i$)$ the global unconstrained stiffiness matrix; Assemble

$(20)$ i$)$ the global unconstrained stiffness matrix;

$(5)$ ii$)$ the global load vector.

Elements c$,$ d and e are truss elements with two dofs per node $($horizontal and vertical

displacements $u_x$ and $u_y).$

Element $b$ is a membrane with two dofs per node $($horizontal and vertical displacements $u_x$ and

uy$).$

Element a is a frame element with three dofs per node $($horizontal and vertical displacements

and $u_y$ and in$-$plane rotation ${}_z).$

The list of nodes of each element $($aka connectivities$)$ is also given for each element. Node $1$ is on a

vertical frictionless roller which allows vertical displacement and rotation of the node while node $2$ is

pinned to the wall. Fill the global matrix with entries $a_{ij},b_{ij},c_{ij},d_{ij}$ and $e_{ij}$ from the element stiffness matrices given below. Use a global displacement vector with the dofs arranged as: $u=\{[u_{x1},u_{y1},{}_{z1},u_{x2},u_{y2},u_{x3},u_{y3},u_{x4},u_{y4},{}_{z4},u_{x5},u_{ys}]{\}}^T$

Ka=[a11a12a13a14a15a16a22a23a24a25a26a32a33a34a35a36a41a42a43a44a45a46a51a52a53a54a55a56

a61a62a63a64a65a66]

$a_{61}$

$a_{51}$

$a_{41}$

$a_{31}$

$a_{61}$

$a_{51}$

$a_{41}$

$a_{31}$

$a_{21}{K}_b=\left[\begin{array}{ccccccccccccccccccccccccccccccc}{b}_{11}& b_{12}& b_{13}& b_{14}& b_{15}& b_{16}& b_{22}& b_{23}& b_{24}& b_{25}& b_{26}& b_{32}& b_{33}& b_{34}& b_{35}& b_{36}& b_{42}& b_{43}& b_{44}& b_{45}& b_{46}& b_{52}& b_{53}& b_{54}& b_{55}& b_{56}& b_{62}& b_{63}& b_{64}& b_{65}& b_{66}\end{array}\right]$

$b_{61}$

$b_{51}$

$b_{41}$

$b_{31}$

$b_{21}$

$K_c=\left[\begin{array}{ccccccccccccc}{c}_{11}& c_{12}& c_{13}& c_{14}& c_{22}& c_{23}& c_{24}& c_{32}& c_{33}& c_{34}& c_{42}& c_{43}& c_{44}\end{array}\right]$

$c_{41}$

$c_{31}$

$c_{21}{K}_d=\left[\begin{array}{ccccccccccccc}{d}_{11}& d_{12}& d_{13}& d_{14}& d_{22}& d_{23}& d_{24}& d_{32}& d_{33}& d_{34}& d_{42}& d_{43}& d_{44}\end{array}\right]$

$d_{41}$

$d_{31}$

$d_{21}{K}_e=\left[\begin{array}{ccccccccccccc}{e}_{11}& e_{12}& e_{13}& e_{14}& e_{22}& e_{23}& e_{24}& e_{32}& e_{33}& e_{34}& e_{42}& e_{43}& e_{44}\end{array}\right]$

$e_{41}$

$e_{31}$

$e_{21}$

Hints: Assembly of global load vector finvolves no calculations. You are not being asked to compute the global solution $u.$

$(5)$ ii$)$ the global load vector.

Elements c$,$ d and e are truss elements with two dofs per node $($horizontal and vertical

displacements tex and $dzy).$

Element b is a membrane with two dofs per node $($horizontal and vertical displacements it and

thy$).$

Element a is a frame element with three dofs per node $($horizontal and vertical displacements $ux$

and try and in$-$plane rotation ${}_2).$

The list of nodes of each element $($aka connectivities$)$ is also given for each element. Node I is on a

vertical frictionless roller which allows vertical displacement and rotation of the node while node $2$ is

pinned to the wall.

Fill the global matrix with entries $a_{ij},b_{yj},c_{ij},d_{ij}$ and $c_y$ from the element stiffess matrices given below.

Use a global displacement vector with the dofs arranged as:

Fill the global matrix with entries $a_{ij},b_{ij},c_{ij},d_{ly}$ and $e_y$ from the element stiffiness matrices given below.

Use a global displacement vector with the dofs arranged as:

$\{\begin{array}{ccc}\text{:}u=\{[u_{21},& u_{y1},{}_{21},u_{n2},u_{y2},u_{23},u_{y3},u_{24},u_{y4},{}_{24},u_{n5},& u_{y5}]{\}}^T\end{array}$

Hints: Assembly of global load vector finvolves no calculations. You are not being

asked to compute the global solution $u.$