2. Benchmark solution#
2.1. Calculation method used for the reference solution#
Travel:
Points \(B\) and \(E\)
\(f=\frac{{\mathrm{Pl}}^{3}}{96{\mathrm{EI}}_{1}}+\frac{{\mathrm{Pl}}^{3}}{96{\mathrm{EI}}_{2}}\) with \({I}_{i}=\frac{b\times {e}_{i}^{3}}{12}\)
Points \(G\) and \(H\)
\(f=-\frac{{\mathrm{Pl}}^{3}}{192{\mathrm{EI}}_{1}}(\frac{{I}_{1}}{{I}_{2}}+\frac{7}{2})\)
Bending moment:
\(M(x)=\frac{\mathrm{P.x}}{2}\)
2.2. Reference quantity#
\(\mathrm{DZ}\) move from \(z\) to points \(B\) and \(G\).
\(\mathrm{MXX}\) soft moment for \(x=\frac{L}{2}\) and \(x=\frac{L}{4}\)
2.3. Reference quantity and result#
Point |
Component |
Reference |
\(B\) |
\(\mathrm{DZ}\) |
\(0.3515625m\) |
\(\mathrm{DRZ}\) |
\(0.\) |
|
\(\mathrm{MXX}\) |
\(-50\times {10}^{4}\mathrm{m.N}\) |
|
\(G\) |
\(\mathrm{DZ}\) |
\(-0.2629743m\) |
\(\mathrm{DRZ}\) |
\(0.\) |
|
\(\mathrm{MXX}\) |
\(-25.\times {10}^{4}\mathrm{m.N}\) |