Benchmark solution
=====================


Calculation method
-----------------

The moment reduction coefficients resulting from linear elastic analyses are determined according to chapters RB 3651.1132 and RB 3651.1142 of RCC - MRx (Roche post- method).

spectral).

the determination of the equivalent stress, taking into account the moments knocked down and

moments not recorded, corresponding to all the loads in question.


Reference quantities and results
-----------------------------------

The following quantities are tested at each node of the structure:


1. reference constraint :math:`S`, calculated from the moments dependent on the movements,


2. reference constraint :math:`S2`, calculated from the moments dependent on the forces,


3. local reversibility :math:`t`, calculated from :math:`S`,


4. local reversibility :math:`{t}_{s}`, calculated from :math:`S2`,


5. total reversibility :math:`T`, calculated from :math:`S` and :math:`t`,


6. total reversibility :math:`{T}_{s}`, calculated from :math:`S2` and :math:`{t}_{s}`,


7. spring effect factor :math:`{r}_{M}`, calculated from :math:`t` and :math:`T`,


8. spring effect factor :math:`{r}_{S}`, calculated from :math:`{t}_{s}` and :math:`{T}_{s}`,


9. maximum spring effect factor :math:`{r}_{\mathit{MMax}}`,


10. maximum spring effect factor :math:`{{r}_{S}}_{\mathit{Max}}`,


11. reduction coefficient :math:`g`, calculated from :math:`{r}_{M}` and material parameters,


12. reduction coefficient :math:`{g}_{s}`, calculated from :math:`{r}_{S}` and material parameters,


13. optimized reduction coefficient :math:`{g}_{\mathit{opt}}`, calculated from :math:`{r}_{M}` and material laws,


14. optimized reduction coefficient :math:`{{g}_{s}}_{\mathit{opt}}`, calculated from :math:`{{r}_{S}}_{\mathit{Max}}` and material laws,


15. equivalent stress :math:`{\sigma }_{\mathit{eq}}`, obtained by combining the moments of the various analyses and the coefficients :math:`g` and :math:`{g}_{s}`,


16. optimized equivalent stress :math:`{{\sigma }_{\mathit{eq}}}_{\mathit{opt}}`, obtained by combining the moments of the various analyses and the coefficients :math:`{g}_{\mathit{opt}}` and :math:`{{g}_{s}}_{\mathit{opt}}`,


17. indicator :math:`{\sigma }_{V}<P`,


18. indicator :math:`{\sigma }_{\mathit{Vs}}<{\sigma }_{P}`,


19. indicator :math:`{{\sigma }_{V}}_{\mathit{opt}}<{\sigma }_{P}`,


20. indicator :math:`{{\sigma }_{\mathit{Vs}}}_{\mathit{opt}}<{\sigma }_{P}`.