User:Eml4500.f08.gravy.sms/HW3

Element 1:



Element 2:



Solving for AC and AB:

Since $$ d = \frac{f}{k} $$,

$$\ AC= \frac{|P_{2}^{(1)}|}{k^{(1)}} = \frac{5.1243}{3/4} = 6.8324 \,$$

$$\ AC= \frac{|P_{1}^{(2)}|}{k^{(2)}} = \frac{5.1243}{5} = 1.0249 \,$$

Filling in K matrix for 3-bar truss:

$$ \begin{bmatrix} k^{(1)}_{11} & k^{(1)}_{12} & k^{(1)}_{13} & k^{(1)}_{14} & 0 & 0 & 0 & 0\\ k^{(1)}_{21} & k^{(1)}_{22} & k^{(1)}_{23} & k^{(1)}_{24} & 0 & 0 & 0 & 0\\ k^{(1)}_{31} & k^{(1)}_{32} & k^{(1)}_{33}+k^{(2)}_{11}+k^{(3)}_{11} & k^{(1)}_{34}+k^{(2)}_{12}+k^{(3)}_{12} & k^{(2)}_{13} & k^{(2)}_{14} & k^{(3)}_{13} & k^{(3)}_{14}\\ k^{(1)}_{41} & k^{(1)}_{42} & k^{(1)}_{43}+k^{(2)}_{21}+k^{(3)}_{21} & k^{(1)}_{44}+k^{(2)}_{22}+k^{(3)}_{22} & k^{(2)}_{23} & k^{(2)}_{24} & k^{(3)}_{23} & k^{(3)}_{24}\\ 0 & 0 & k^{(2)}_{31} & k^{(2)}_{32} & k^{(2)}_{33} & k^{(2)}_{34} & 0 & 0\\ 0 & 0 & k^{(2)}_{41} & k^{(2)}_{42} & k^{(2)}_{43} & k^{(2)}_{44} & 0 & 0\\ 0 & 0 & k^{(3)}_{31} & k^{(3)}_{32} & 0 & 0 & k^{(3)}_{33} & k^{(3)}_{34}\\ 0 & 0 & k^{(3)}_{41} & k^{(3)}_{42} & 0 & 0 & k^{(3)}_{43} & k^{(3)}_{44} \end{bmatrix} $$