User:Eml4500.f08.jamama.jan/Meeting35

Mtg. 5 $$ \Rightarrow $$ 2-bar truss
 * $$ \downarrow $$

Element 1: $$ E_1^{(1)} = 2;\ A_1^{(1)} = 0.5 $$
 * $$ E_2^{(1)} = 4;\ A_2^{(1)} = 1.5 $$

Element 2: $$ E_1^{(2)} = 3;\ A_1^{(2)} = 1 $$
 * $$ E_2^{(2)} = 7;\ A_2^{(2)} = 3 $$

HOMEWORK

Frame elem = truss(bar) elem + beam elem
 * $$ \uparrow \qquad \qquad \qquad \nwarrow $$
 * $$  {\color{Blue} \begin{matrix}

axial\ deformation & & transverse\ deformation \end{matrix}}$$

Model frame problem with 2 elements:



FBDs



In general $$,\ \underbrace{\mathbf{d_i^{(e)}}}\qquad \Rightarrow \qquad \underbrace{\mathbf{f_i^{(e)}}}$$
 * $$ {\color{blue} \begin{matrix}

generalized & & generalized \\ displacement & & force \end{matrix}}$$

e = 1,2

i = 1,...,6

$$ \begin{matrix}

d_3^{(e)}\\ d_6^{(e)} \end{matrix} \}\ contains\ dofs \Rightarrow \begin{matrix} f_3^{(e)}\\ f_6^{(e)} \end{matrix} \}\ bending\ forces $$

2-D Frame Global dofs



2 element stiffness matrix >> $$ \mathbf{k_{6 \times 6}^{(e)}}$$, e = 1,2

Global stiffness matrix >> $$ \mathbf{k_{9 \times 9}} = \mathbf{\underset{e=1}\overset{e=2}Ak_{6 \times 6}}$$