NASTRAN provides coordinates
[ F x F y F z ] 6120 = [ R 6120 ] [ R b o l t T ] [ F x F y F z ] b o l t {\displaystyle \left[{\begin{matrix}F_{x}\\F_{y}\\F_{z}\end{matrix}}\right]_{6120}=\left[{\begin{matrix}&&\\&{\textrm {R}}_{6120}&\\&&\end{matrix}}\right]\left[{\begin{matrix}&&\\&{\textrm {R}}_{bolt}^{T}&\\&&\end{matrix}}\right]\left[{\begin{matrix}F_{x}\\F_{y}\\F_{z}\end{matrix}}\right]_{bolt}}
because [ F x F y F z ] b o l t = [ R b o l t ] [ F x F y F z ] g l o b a l {\displaystyle \left[{\begin{matrix}F_{x}\\F_{y}\\F_{z}\end{matrix}}\right]_{bolt}=\left[{\begin{matrix}&&\\&{\textrm {R}}_{bolt}&\\&&\end{matrix}}\right]\left[{\begin{matrix}F_{x}\\F_{y}\\F_{z}\end{matrix}}\right]_{global}}
[ F x F y F z ] 6120 = [ R 6120 ] [ F x F y F z ] g l o b a l {\displaystyle \left[{\begin{matrix}F_{x}\\F_{y}\\F_{z}\end{matrix}}\right]_{6120}=\left[{\begin{matrix}&&\\&{\textrm {R}}_{6120}&\\&&\end{matrix}}\right]\left[{\begin{matrix}F_{x}\\F_{y}\\F_{z}\end{matrix}}\right]_{global}}
R − 1 = R T {\displaystyle \mathbf {R} ^{-1}=\mathbf {R} ^{T}}
N y i = N y i − 1 + F y 5 D {\displaystyle N_{y_{i}}=N_{y_{i-1}}+{\frac {F_{y}}{5D}}}
N x i = N x i − 1 + F y 5 D {\displaystyle N_{x_{i}}=N_{x_{i-1}}+{\frac {F_{y}}{5D}}}
N x = E ε t {\displaystyle N_{x}=E\varepsilon t}
∴ N x 2 = N x 1 × E 2 E 1 × t 2 t 1 {\displaystyle \therefore N_{x_{2}}=N_{x_{1}}\times {\frac {E_{2}}{E_{1}}}\times {\frac {t_{2}}{t_{1}}}}
K = E π d 2 4 ∑ t = E π d 2 4 ( t s s + t s p a r + t b a c k u p ) {\displaystyle K={\frac {E\pi d^{2}}{4\sum t}}={\frac {E\pi d^{2}}{4(t_{ss}+t_{spar}+t_{backup})}}}
∴ t s s = E π d 2 4 K − t s p a r − t b a c k u p {\displaystyle \therefore t_{ss}={\frac {E\pi d^{2}}{4K}}-t_{spar}-t_{backup}}
K = E π d 2 4 ∑ t = E π d 2 4 ( t s s + t s p a r + t b a c k u p ( n e w ) ) {\displaystyle K={\frac {E\pi d^{2}}{4\sum t}}={\frac {E\pi d^{2}}{4(t_{ss}+t_{spar}+t_{backup(new)})}}}
![{\displaystyle \left[{\begin{matrix}F_{x}\\F_{y}\\F_{z}\end{matrix}}\right]_{6120}=\left[{\begin{matrix}&&\\&{\textrm {R}}_{6120}&\\&&\end{matrix}}\right]\left[{\begin{matrix}&&\\&{\textrm {R}}_{bolt}^{T}&\\&&\end{matrix}}\right]\left[{\begin{matrix}F_{x}\\F_{y}\\F_{z}\end{matrix}}\right]_{bolt}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e8088255b62083d38802a3fa9ac9498feee3b10e)
![{\displaystyle \left[{\begin{matrix}F_{x}\\F_{y}\\F_{z}\end{matrix}}\right]_{bolt}=\left[{\begin{matrix}&&\\&{\textrm {R}}_{bolt}&\\&&\end{matrix}}\right]\left[{\begin{matrix}F_{x}\\F_{y}\\F_{z}\end{matrix}}\right]_{global}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/0d8b69f4f017d991eeab8549a376326b632ffaea)
![{\displaystyle \left[{\begin{matrix}F_{x}\\F_{y}\\F_{z}\end{matrix}}\right]_{6120}=\left[{\begin{matrix}&&\\&{\textrm {R}}_{6120}&\\&&\end{matrix}}\right]\left[{\begin{matrix}F_{x}\\F_{y}\\F_{z}\end{matrix}}\right]_{global}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/7071570e1a162982201d0fde2f74d70ed38ebf86)
