User:Eml4500.f08.bottle.barnes/HW6

=Tapered Bar with Constant Modulus of Elasticity=

Let $$\displaystyle E_1 = E_2 = E = 70 GPa $$ and let $$\displaystyle A( \tilde{x}) $$ be linear. Also let $$\displaystyle A_1 = 2400 mm^2 $$, $$\displaystyle A_2 = 600 mm^2 $$ and $$\displaystyle L = 300 mm $$.

Given the following equation

$$\displaystyle {E \over L^{(i)}} {(A_1 + A_2) \over 2} \begin{bmatrix} 1 & -1 \\ -1 & 1  \end{bmatrix} = \textbf{k}^{(i)} $$

$$\displaystyle {(70 GPa) \over (300mm)} {(2400mm^2 + 600 mm^2) \over 2} \begin{bmatrix} 1 & -1 \\ -1 & 1  \end{bmatrix} = \textbf{k}^{(i)} $$

$$\displaystyle \textbf{k}^{(i)} = \begin{bmatrix} 714 & -714 \\ -714 & 714  \end{bmatrix} $$