Benchmark solution ===================== Calculation method used for the reference solution -------------------------------------------------------- The problem is solved analytically. The result of the efforts (equal to the total weight) is equal to: * concrete weight: :math:`\mathrm{Pb}=V{\rho }_{b}g` * cable weight: :math:`\mathrm{Pc}=AL{\rho }_{c}g` in the direction in which gravity is applied. The structure is isostatic. Prestressing forces are self-balanced. Let :math:`{S}_{b}` be the area of the concrete in a plane perpendicular to the cable :math:`{S}_{b}=(2\times \mathrm{0,6}){m}^{2}`, :math:`{E}_{a}` and :math:`{E}_{b}` the modules of steel and concrete, :math:`{N}_{a}` the tension in the cable and :math:`{\sigma }_{b}` and the stress in the concrete after tension. The balance of the concrete and cable assembly is written: :math:`{N}_{a}+{\sigma }_{b}{S}_{b}\mathrm{=}0` therefore :math:`{\sigma }_{b}\mathrm{=}\mathrm{-}\frac{{N}_{a}}{{S}_{b}}` Since the macro command CALC_PRECONT is used, and since there is no friction or losses in the cable, the tension in the cable is equal to the initial tension, unlike the case where RELA_CINE_BP is used, which suffers prestress losses due to the shortening of the concrete (see test SSNP108, [:external:ref:`V6.03.108 `]) The deformation of concrete is: :math:`{\varepsilon }_{b}=\frac{{\sigma }_{b}}{{E}_{b}}` Benchmark results ---------------------- * Result of efforts: :math:`R=132N` * Stress in concrete: :math:`{\sigma }_{b}\mathrm{=}\mathrm{-}\mathrm{1,66666667}{10}^{5}\mathit{Pa}` * Normal force in steel: :math:`{N}_{a}\mathrm{=}2{10}^{5}\mathit{Pa}` * Deformation in concrete: :math:`{\varepsilon }_{b}=-\mathrm{5,555555555}{10}^{\text{-}6}` Uncertainty about the solution --------------------------- It is an analytical solution. The solution gives the average stress in concrete. When there are several elements (models :math:`B` and :math:`C`) it is necessary to average the values of the cells.