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$\left(\begin{array}{cccccccc}\frac{2A^{2}E\eta }{3{\ell }_0}& 0& -\left(\frac{2A^{2}E\eta }{{\ell }_0^2}\right)& 0& \frac{A^{2}E\eta }{3{\ell }_0}& 0& 0& 0\\ 0& \frac{2A^{2}E\eta }{3{\ell }_0}& -\left(\frac{A^{2}E\eta }{4{\ell }_0^2}\right)& -\left(\frac{\sqrt{3}{A}^{2}E\eta }{4{\ell }_0^2}\right)& \frac{A^{2}E\eta }{6{\ell }_0}& -\left(\frac{A^{2}E\eta }{2{\ell }_0^2}\right)& 0& \frac{A^{2}E\eta }{6{\ell }_0}\\ -\left(\frac{2A^{2}E\eta }{{\ell }_0^2}\right)& -\left(\frac{A^{2}E\eta }{4{\ell }_0^2}\right)& \frac{A^{2}E\eta +3{\ell }_0^{2}AE}{2{\ell }_0^3}+\frac{8A^{2}E\eta }{{\ell }_0^3}& 0& -\left(\frac{2A^{2}E\eta }{{\ell }_0^2}\right)& -\left(\frac{A^{2}E\eta +3{\ell }_0^{2}AE}{4{\ell }_0^3}\right)& \frac{\sqrt{3}{A}^{2}E\eta -\sqrt{3}{\ell }_0^{2}AE}{4{\ell }_0^3}& \frac{A^{2}E\eta }{4{\ell }_0^2}\\ 0& -\left(\frac{\sqrt{3}{A}^{2}E\eta }{4{\ell }_0^2}\right)& 0& \frac{3A^{2}E\eta +{\ell }_0^{2}AE}{2{\ell }_0^3}+\frac{2AE}{{\ell }_0}& -\left(\frac{\sqrt{3}{A}^{2}E\eta }{2{\ell }_0^2}\right)& \frac{\sqrt{3}{A}^{2}E\eta -\sqrt{3}{\ell }_0^{2}AE}{4{\ell }_0^3}& -\left(\frac{3A^{2}E\eta +{\ell }_0^{2}AE}{4{\ell }_0^3}\right)& -\left(\frac{\sqrt{3}{A}^{2}E\eta }{4{\ell }_0^2}\right)\\ \frac{A^{2}E\eta }{3{\ell }_0}& \frac{A^{2}E\eta }{6{\ell }_0}& -\left(\frac{2A^{2}E\eta }{{\ell }_0^2}\right)& -\left(\frac{\sqrt{3}{A}^{2}E\eta }{2{\ell }_0^2}\right)& \frac{4A^{2}E\eta }{3{\ell }_0}& -\left(\frac{A^{2}E\eta }{4{\ell }_0^2}\right)& \frac{\sqrt{3}{A}^{2}E\eta }{4{\ell }_0^2}& \frac{A^{2}E\eta }{6{\ell }_0}\\ 0& -\left(\frac{A^{2}E\eta }{2{\ell }_0^2}\right)& -\left(\frac{A^{2}E\eta +3{\ell }_0^{2}AE}{4{\ell }_0^3}\right)& \frac{\sqrt{3}{A}^{2}E\eta -\sqrt{3}{\ell }_0^{2}AE}{4{\ell }_0^3}& -\left(\frac{A^{2}E\eta }{4{\ell }_0^2}\right)& \frac{A^{2}E\eta +3{\ell }_0^{2}AE}{4{\ell }_0^3}+\frac{A^{2}E\eta }{{\ell }_0^3}& -\left(\frac{\sqrt{3}{A}^{2}E\eta -\sqrt{3}{\ell }_0^{2}AE}{4{\ell }_0^3}\right)& -\left(\frac{3A^{2}E\eta }{4{\ell }_0^2}\right)\\ 0& 0& \frac{\sqrt{3}{A}^{2}E\eta -\sqrt{3}{\ell }_0^{2}AE}{4{\ell }_0^3}& -\left(\frac{3A^{2}E\eta +{\ell }_0^{2}AE}{4{\ell }_0^3}\right)& \frac{\sqrt{3}{A}^{2}E\eta }{4{\ell }_0^2}& -\left(\frac{\sqrt{3}{A}^{2}E\eta -\sqrt{3}{\ell }_0^{2}AE}{4{\ell }_0^3}\right)& \frac{3A^{2}E\eta +{\ell }_0^{2}AE}{4{\ell }_0^3}+\frac{AE}{{\ell }_0}& \frac{\sqrt{3}{A}^{2}E\eta }{4{\ell }_0^2}\\ 0& \frac{A^{2}E\eta }{6{\ell }_0}& \frac{A^{2}E\eta }{4{\ell }_0^2}& -\left(\frac{\sqrt{3}{A}^{2}E\eta }{4{\ell }_0^2}\right)& \frac{A^{2}E\eta }{6{\ell }_0}& -\left(\frac{3A^{2}E\eta }{4{\ell }_0^2}\right)& \frac{\sqrt{3}{A}^{2}E\eta }{4{\ell }_0^2}& \frac{2A^{2}E\eta }{3{\ell }_0}\end{array}\right)\cdot \left(\begin{array}{c}{W}_{1,0}\\ U_{1,0}\\ {\mathrm{\Phi }}_{1,0}\\ W_{2,0}\\ U_{2,0}\\ {\mathrm{\Phi }}_{2,0}\\ W_{3,0}\\ U_{3,0}\\ {\mathrm{\Phi }}_{3,0}\\ W_{4,0}\\ U_{4,0}\\ {\mathrm{\Phi }}_{4,0}\end{array}\right)=\left(\begin{array}{c}0\\ 0\\ 0\\ 0\\ 0\\ F\\ 0\\ 0\end{array}\right)$

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Element-Steigigkeitsmatrizen mit globalen Koordinaten
Element #1
$k_1=\left(\begin{array}{cccccc}\frac{8A^{2}E\eta }{{\ell }_0^3}& 0& \frac{2A^{2}E\eta }{{\ell }_0^2}& -\left(\frac{8A^{2}E\eta }{{\ell }_0^3}\right)& 0& \frac{2A^{2}E\eta }{{\ell }_0^2}\\ 0& \frac{2AE}{{\ell }_0}& 0& 0& -\left(\frac{2AE}{{\ell }_0}\right)& 0\\ \frac{2A^{2}E\eta }{{\ell }_0^2}& 0& \frac{2A^{2}E\eta }{3{\ell }_0}& -\left(\frac{2A^{2}E\eta }{{\ell }_0^2}\right)& 0& \frac{A^{2}E\eta }{3{\ell }_0}\\ -\left(\frac{8A^{2}E\eta }{{\ell }_0^3}\right)& 0& -\left(\frac{2A^{2}E\eta }{{\ell }_0^2}\right)& \frac{8A^{2}E\eta }{{\ell }_0^3}& 0& -\left(\frac{2A^{2}E\eta }{{\ell }_0^2}\right)\\ 0& -\left(\frac{2AE}{{\ell }_0}\right)& 0& 0& \frac{2AE}{{\ell }_0}& 0\\ \frac{2A^{2}E\eta }{{\ell }_0^2}& 0& \frac{A^{2}E\eta }{3{\ell }_0}& -\left(\frac{2A^{2}E\eta }{{\ell }_0^2}\right)& 0& \frac{2A^{2}E\eta }{3{\ell }_0}\end{array}\right)$
Element #2
$k_2=\left(\begin{array}{cccccc}\frac{A^{2}E\eta +3{\ell }_0^{2}AE}{4{\ell }_0^3}& \frac{\sqrt{3}{A}^{2}E\eta -\sqrt{3}{\ell }_0^{2}AE}{4{\ell }_0^3}& \frac{A^{2}E\eta }{4{\ell }_0^2}& -\left(\frac{A^{2}E\eta +3{\ell }_0^{2}AE}{4{\ell }_0^3}\right)& -\left(\frac{\sqrt{3}{A}^{2}E\eta -\sqrt{3}{\ell }_0^{2}AE}{4{\ell }_0^3}\right)& \frac{A^{2}E\eta }{4{\ell }_0^2}\\ \frac{\sqrt{3}{A}^{2}E\eta -\sqrt{3}{\ell }_0^{2}AE}{4{\ell }_0^3}& \frac{3A^{2}E\eta +{\ell }_0^{2}AE}{4{\ell }_0^3}& \frac{\sqrt{3}{A}^{2}E\eta }{4{\ell }_0^2}& -\left(\frac{\sqrt{3}{A}^{2}E\eta -\sqrt{3}{\ell }_0^{2}AE}{4{\ell }_0^3}\right)& -\left(\frac{3A^{2}E\eta +{\ell }_0^{2}AE}{4{\ell }_0^3}\right)& \frac{\sqrt{3}{A}^{2}E\eta }{4{\ell }_0^2}\\ \frac{A^{2}E\eta }{4{\ell }_0^2}& \frac{\sqrt{3}{A}^{2}E\eta }{4{\ell }_0^2}& \frac{A^{2}E\eta }{3{\ell }_0}& -\left(\frac{A^{2}E\eta }{4{\ell }_0^2}\right)& -\left(\frac{\sqrt{3}{A}^{2}E\eta }{4{\ell }_0^2}\right)& \frac{A^{2}E\eta }{6{\ell }_0}\\ -\left(\frac{A^{2}E\eta +3{\ell }_0^{2}AE}{4{\ell }_0^3}\right)& -\left(\frac{\sqrt{3}{A}^{2}E\eta -\sqrt{3}{\ell }_0^{2}AE}{4{\ell }_0^3}\right)& -\left(\frac{A^{2}E\eta }{4{\ell }_0^2}\right)& \frac{A^{2}E\eta +3{\ell }_0^{2}AE}{4{\ell }_0^3}& \frac{\sqrt{3}{A}^{2}E\eta -\sqrt{3}{\ell }_0^{2}AE}{4{\ell }_0^3}& -\left(\frac{A^{2}E\eta }{4{\ell }_0^2}\right)\\ -\left(\frac{\sqrt{3}{A}^{2}E\eta -\sqrt{3}{\ell }_0^{2}AE}{4{\ell }_0^3}\right)& -\left(\frac{3A^{2}E\eta +{\ell }_0^{2}AE}{4{\ell }_0^3}\right)& -\left(\frac{\sqrt{3}{A}^{2}E\eta }{4{\ell }_0^2}\right)& \frac{\sqrt{3}{A}^{2}E\eta -\sqrt{3}{\ell }_0^{2}AE}{4{\ell }_0^3}& \frac{3A^{2}E\eta +{\ell }_0^{2}AE}{4{\ell }_0^3}& -\left(\frac{\sqrt{3}{A}^{2}E\eta }{4{\ell }_0^2}\right)\\ \frac{A^{2}E\eta }{4{\ell }_0^2}& \frac{\sqrt{3}{A}^{2}E\eta }{4{\ell }_0^2}& \frac{A^{2}E\eta }{6{\ell }_0}& -\left(\frac{A^{2}E\eta }{4{\ell }_0^2}\right)& -\left(\frac{\sqrt{3}{A}^{2}E\eta }{4{\ell }_0^2}\right)& \frac{A^{2}E\eta }{3{\ell }_0}\end{array}\right)$
Element #3
$k_3=\left(\begin{array}{cccccc}\frac{A^{2}E\eta +3{\ell }_0^{2}AE}{4{\ell }_0^3}& -\left(\frac{\sqrt{3}{A}^{2}E\eta -\sqrt{3}{\ell }_0^{2}AE}{4{\ell }_0^3}\right)& \frac{A^{2}E\eta }{4{\ell }_0^2}& -\left(\frac{A^{2}E\eta +3{\ell }_0^{2}AE}{4{\ell }_0^3}\right)& \frac{\sqrt{3}{A}^{2}E\eta -\sqrt{3}{\ell }_0^{2}AE}{4{\ell }_0^3}& \frac{A^{2}E\eta }{4{\ell }_0^2}\\ -\left(\frac{\sqrt{3}{A}^{2}E\eta -\sqrt{3}{\ell }_0^{2}AE}{4{\ell }_0^3}\right)& \frac{3A^{2}E\eta +{\ell }_0^{2}AE}{4{\ell }_0^3}& -\left(\frac{\sqrt{3}{A}^{2}E\eta }{4{\ell }_0^2}\right)& \frac{\sqrt{3}{A}^{2}E\eta -\sqrt{3}{\ell }_0^{2}AE}{4{\ell }_0^3}& -\left(\frac{3A^{2}E\eta +{\ell }_0^{2}AE}{4{\ell }_0^3}\right)& -\left(\frac{\sqrt{3}{A}^{2}E\eta }{4{\ell }_0^2}\right)\\ \frac{A^{2}E\eta }{4{\ell }_0^2}& -\left(\frac{\sqrt{3}{A}^{2}E\eta }{4{\ell }_0^2}\right)& \frac{A^{2}E\eta }{3{\ell }_0}& -\left(\frac{A^{2}E\eta }{4{\ell }_0^2}\right)& \frac{\sqrt{3}{A}^{2}E\eta }{4{\ell }_0^2}& \frac{A^{2}E\eta }{6{\ell }_0}\\ -\left(\frac{A^{2}E\eta +3{\ell }_0^{2}AE}{4{\ell }_0^3}\right)& \frac{\sqrt{3}{A}^{2}E\eta -\sqrt{3}{\ell }_0^{2}AE}{4{\ell }_0^3}& -\left(\frac{A^{2}E\eta }{4{\ell }_0^2}\right)& \frac{A^{2}E\eta +3{\ell }_0^{2}AE}{4{\ell }_0^3}& -\left(\frac{\sqrt{3}{A}^{2}E\eta -\sqrt{3}{\ell }_0^{2}AE}{4{\ell }_0^3}\right)& -\left(\frac{A^{2}E\eta }{4{\ell }_0^2}\right)\\ \frac{\sqrt{3}{A}^{2}E\eta -\sqrt{3}{\ell }_0^{2}AE}{4{\ell }_0^3}& -\left(\frac{3A^{2}E\eta +{\ell }_0^{2}AE}{4{\ell }_0^3}\right)& \frac{\sqrt{3}{A}^{2}E\eta }{4{\ell }_0^2}& -\left(\frac{\sqrt{3}{A}^{2}E\eta -\sqrt{3}{\ell }_0^{2}AE}{4{\ell }_0^3}\right)& \frac{3A^{2}E\eta +{\ell }_0^{2}AE}{4{\ell }_0^3}& \frac{\sqrt{3}{A}^{2}E\eta }{4{\ell }_0^2}\\ \frac{A^{2}E\eta }{4{\ell }_0^2}& -\left(\frac{\sqrt{3}{A}^{2}E\eta }{4{\ell }_0^2}\right)& \frac{A^{2}E\eta }{6{\ell }_0}& -\left(\frac{A^{2}E\eta }{4{\ell }_0^2}\right)& \frac{\sqrt{3}{A}^{2}E\eta }{4{\ell }_0^2}& \frac{A^{2}E\eta }{3{\ell }_0}\end{array}\right)$
Element #4
{k_4} = \begin{pmatrix}\frac{{{A}^{2}} E \eta }{{\ell_{0}^{3}}} & 0 & \frac{{{A}^{2}} E \eta }{2 {\ell_{0}^{2}}} & -\left( \frac{{{A}^{2}} E \eta }{{\ell_{0}^{3}}}\right) & 0 & \frac{{{A}^{2}} E \eta }{2 {\ell_{0}^{2}}}\\ 0 & \frac{A E}Vorlage:\ell 0 & 0 & 0 & -\left( \frac{A E}Vorlage:\ell 0\right) & 0\\ \frac{{{A}^{2}} E \eta }{2 {\ell_{0}^{2}}} & 0 & \frac{{{A}^{2}} E \eta }{3 {\ell_0}} & -\left( \frac{{{A}^{2}} E \eta }{2 {\ell_{0}^{2}}}\right) & 0 & \frac{{{A}^{2}} E \eta }{6 {\ell_0}}\\ -\left( \frac{{{A}^{2}} E \eta }{{\ell_{0}^{3}}}\right) & 0 & -\left( \frac{{{A}^{2}} E \eta }{2 {\ell_{0}^{2}}}\right) & \frac{{{A}^{2}} E \eta }{{\ell_{0}^{3}}} & 0 & -\left( \frac{{{A}^{2}} E \eta }{2 {\ell_{0}^{2}}}\right) \\ 0 & -\left( \frac{A E}Vorlage:\ell 0\right) & 0 & 0 & \frac{A E}Vorlage:\ell 0 & 0\\ \frac{{{A}^{2}} E \eta }{2 {\ell_{0}^{2}}} & 0 & \frac{{{A}^{2}} E \eta }{6 {\ell_0}} & -\left( \frac{{{A}^{2}} E \eta }{2 {\ell_{0}^{2}}}\right) & 0 & \frac{{{A}^{2}} E \eta }{3 {\ell_0}}\end{pmatrix}

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