User:Eml4500.f08.wiki1.ambrosio/hw7

Correction to HW 6
After HW6 was submitted, an important error was discovered in the pylon code. The -1000 lb force was intended to be applied at node 33 in the y direction. This was mistakenly entered into the R matrix as row 33. The problem is that row 33 is DOF 33, not node 33. As a result, the code has been changed so the 1000 lbs is in row 66, which is the vertical DOF on node 33.

With these new results, it is determined that the highest compressive stress is -8.6957e+006 Pa, which is located in element 55. The highest tensile stress is 9.0511e+006 Pa in element 81.



HW 7 Code
The highest bending moment is 6.287 N-m which is located on element 81. The highest shear stress is -5.48269 Pa, which is also located on element 81.



Notes 12/5 Meeting 40
At this point, a dimensional analysis of Eqn. (2) from page 39-2 is done.

$$ \begin{Bmatrix} u(\tilde{x})\\ v(\tilde{x}) \end{Bmatrix} = \begin{bmatrix} N_1&0 &0 &N_4 &0&0\\ 0& N_2 & N_3&0&N_5&N_6 \end{bmatrix} \begin{Bmatrix} \tilde{d}_1^{(e)}\\ \tilde{d}_2^{(e)}\\ \tilde{d}_3^{(e)}\\ \tilde{d}_4^{(e)}\\ \tilde{d}_5^{(e)}\\ \tilde{d}_6^{(e)} \end{Bmatrix} $$

The dimensional values of N1, N2, N4, and N5 are known to be 1, and the dimensional value of N3 and N6 are known to be L. $$\begin{bmatrix} \tilde{d}_1 \end{bmatrix}$$, $$\begin{bmatrix} \tilde{d}_2 \end{bmatrix}$$ , $$\begin{bmatrix} \tilde{d}_4 \end{bmatrix}$$ , and $$\begin{bmatrix} \tilde{d}_5 \end{bmatrix}$$ are deformations in the $$\tilde{x}$$ and $$\tilde{y}$$ axis, so their dimensional values are L. $$\begin{bmatrix} \tilde{d}_3 \end{bmatrix}$$ and $$\begin{bmatrix} \tilde{d}_6 \end{bmatrix}$$ are roational DOF's, so their deimensional values are 1.

When expanded, the the result is

$$ \begin{bmatrix} N_1 \end{bmatrix} \begin{bmatrix} \tilde{d}_1 \end{bmatrix} = L $$

$$ \begin{bmatrix} N_4 \end{bmatrix} \begin{bmatrix} \tilde{d}_4 \end{bmatrix} = L $$

$$ \begin{bmatrix} N_2 \end{bmatrix} \begin{bmatrix} \tilde{d}_2 \end{bmatrix} = L $$

$$ \begin{bmatrix} N_3 \end{bmatrix} \begin{bmatrix} \tilde{d}_3 \end{bmatrix} = L $$

$$ \begin{bmatrix} N_5 \end{bmatrix} \begin{bmatrix} \tilde{d}_5 \end{bmatrix} = L $$

$$ \begin{bmatrix} N_6 \end{bmatrix} \begin{bmatrix} \tilde{d}_6 \end{bmatrix} = L $$