## 4 Application
The adopted mechanical behavior for the material is an elastic-perfectly plastic one with Young's modulus equal to 210 GPa, yield stress equal to 235 MPa, ultimate strain equal to 25% and adopted mesh is 5 mm with hexahedral standard 3D stress elements. The loading plate is constituted by linear elastic material with a stiffness that is much greater than the \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{2}{c}{**IPE400**} & \multicolumn{2}{c}{**HEA300**} \\ \cline{2-5}  & **DP1** & **DP2** & **DP1** & **DP2** \\ \hline \(b_{i}\) & 130.280 & 165.175 & 233.957 & 219.196 \\ \(t_{f,i}\) & 13.500 & 7.743 & 14.000 & 10.761 \\ \(\ell_{i}\) & 200.000 & 200.000 & 290.000 & 290.000 \\ \(h^{*}\) & 368.835 & 368.524 & 262.128 & 261.655 \\ \(t_{f,\rho}\) & 31.165 & 31.476 & 27.872 & 28.345 \\ \(\ell_{o}\) & 120.043 & 208.876 & 179.900 & 362.786 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Optimal designs (all dimensions are in mm). \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{2}{c}{**IPE400**} & \multicolumn{2}{c}{**HEA300**} \\ \cline{2-5}  & **DP1** & **DP2** & **DP1** & **DP2** \\ \hline \(b_{p}\) & 180.0 & 180.0 & 300.0 & 300.0 \\ \(h_{p}\) & 400.0 & 400.0 & 290.0 & 290.0 \\ \(t_{w,p}\) & 8.6 & 8.6 & 8.5 & 8.5 \\ \(t_{f,p}\) & 13.5 & 13.5 & 14.0 & 14.0 \\ \(l_{p}\) & 231,300,000 & 231,300,000 & 182,600,000 & 182,600 one of the adopted steel (210 TPa), so that any influence of the pressure distribution is avoided. Two different pressure loads (pink arrows in Figure 14) have been applied to the plate: the first one is uniform and its resultant represents the axial force acting on the device; the second one is a linearly varying one (along \(y\)-axis) with zero value at barycentric \(x\)-axis of the plate and its resultant is equal to the bending moment acting on the device. The intensity of each load ranges between zero and the maximum value (corresponding to the design load of LRPD) and this interval has been divided in 100 steps. The evaluation of the mechanical behavior of the proposed LRPD has been performed by evaluating the yielding level of the inner part when the loads reach their assigned maximum values. To do this in Figures 15-18, the von Mises' stress maps obtained by FEM analysis are reported, for each profile and for each design point. An examination of these figures immediately reveals that in all the examined cases the inner part of the LRPD is fully plasticized confirming the validity and the effectiveness of the proposed optimal design. Figure 12: Dimensionless domains: IPE400 elastic (red line); IPE400 yield (black line); \(LRPD\) elastic (green line); \(LRPD\) yield (blue line). (**a**) design point 1; (**b**) design point 2. Figure 13: Dimensionless domains: HEA300 elastic (red line); HEA300 yield (black line); \(LRPD\) elastic (green line); \(LRPD\) yield (blue line). (**a**) design point 1; (**b**) design point 2. In particular, the LRPD for IPE400 (DP1), Figure 15, shows a perfect plastic behavior strictly concentrated just in correspondence of the inner portion while the close outer portions behave in a substantially elastic way. This very good behavior is related to the special load condition characterized by a high bending moment and small axial force. Figure 14: ABAQUS model adopted for the numerical simulation of the device related to the IPE 400 profile. Figure 15: von [PERSON] stress map (MPa) for LRPD IPE400 (DP1) at the ultimate loading condition: (**a**) perspective view; (**b**) lateral view. Even the LRPD for IPE400 (DP2), Figure 16, shows the full plastic behavior of the inner portion but the close outer portions are strongly interested by the spread of the plastic deformations. However, it is worth noting that the flanges remain in elastic regime so that the elastic response to the acting moment is ensured. This particular behavior is related to the special load condition characterized by a high axial force and small bending moment.