User:Eml4500.f08.delta 6.castrillon/P & K Values Problem

=Problem: Get the p and k values for the stretching of each truss element=

Determining p values
We know that $$p^{(e)}$$ = $$T^{(e)}$$ $$f^{(e)}$$, where


 * $$T^{(e)}$$ = $$\begin{bmatrix}

l^{(e)} & m^{(e)} & 0 & 0\\ 0 & 0 & l^{(e)} & m^{(e)}\\ \end{bmatrix}$$

and, from past exercises,


 * $$f^{(e)}$$ = $$\begin{bmatrix}

-4.4378\\ -2.5622\\ 4.4378\\ 2.5622\end{bmatrix}$$

Therefore, we can say that the p values become:


 * $$p^{(1)}_{2}$$ = |-4.4378cos(30°) + (-2.5622)sin(30°)|= 5.1243
 * $$p^{(2)}_{1}$$ = |4.4378cos(30°) + 2.5622sin(30°)|= 5.1243

Determining k values
From past exercises it is known that the axial stiffness for both bar elements are as follow:


 * $$k^{(e)}$$ = $$\frac{E^{e}A^{e}}{L^{e}}$$

Therefore,


 * $$k^{(1)}$$ = $$\frac{(3)(1)}{4}$$ = 0.75


 * $$k^{(2)}$$ = $$\frac{(5)(2)}{2}$$ = 5

Determining the displacements
Following the same idea of $$d = \frac{f}{k}$$, we have


 * AC = $$\frac{p^{(1)}_{2}}{k^{(1)}}$$ = $$\frac{5.1243}{0.75}$$ = 6.8324


 * AB = $$\frac{p^{(2)}_{1}}{k^{(2)}}$$ = $$\frac{5.1243}{5}$$ = 1.0249