## 4 Application
The LRPD for HEA300 (DP1), Figure 17, and the LRPD for HEA300 (DP2), Figure 18, show substantially the same behavior that has been previously commented upon, with the difference being that the outer portions are less involved in plastic deformation due to the greater length of the inner portion. Figure 16: [PERSON] stress map (MPa) for LRPD IPE400 (DP2) at the ultimate loading condition: (a) perspective view; (b) lateral view. Figure 17: von [PERSON] stress map (MPa) for LRPD HEA300 (DP1) at the ultimate loading condition: (a) perspective view; (b) lateral view. Since the LRPD is thought as a device connecting structural elements subjected to cyclic loadings, such as those arising during earthquakes, it is appropriate to evaluate the cyclic behavior of the designed device in terms of bending moment vs. bending curvature. This evaluation is always performed in the ABAQUS environment, referring to the device designed for the IPE400 profile (design point 1), whose model is sketched in Figure 19a. As it has been performed in the case of the FEM analyses reported above, the model is represented by a cantilever beam with a length of \(3\ell\), plus the thickness of the plate, clamped in section \(A\) and with a pressure loading applied at free section \(D\) whose intensity varies only along the \(y\)-axis. The resultant of the loading is a pure bending moment with the moment axis coincident with the \(x\) geometrical axis. The maximum value of the resultant bending moment lies in the range \((-M_{a}=-215\) kNm, \(M_{a}=215\) kNm), and it constitutes one loading cycle. The reported range is subdivided into 100 steps for the subsequent evaluation of the curvature of the device. This curvature is obtained as the ratio between \(\Delta\varphi_{BC}\) and the length \(\ell\) of the device, where \(\Delta\varphi_{BC}\) is the relative rotation between sections \(B\) and \(C\). In Figure 19b the results in terms of bending moment vs. bending curvature are reported compared with the corresponding one obtained in the case of the IPE400 cantilever beam without the LRPD with the same length and loading. As can be observed, the device, after just one cycle, shows a stationary behaviour (plastic shakedown) and, therefore, no further loading cycles have been performed since the results will be superimposable with those already obtained. In Figure 19b the diagram of the IPE400 cantilever beam shows, as was expected \((M_{a}<M_{pl})\), a linear behaviour due to the linear elastic behaviour of the beam. Further, the analysis of Figure 19b clearly shows that the proposed device perfectly carries out the role of receiver of plastic deformations; it also develops a satisfactory plastic dissipation showing an elastic behaviour coincident with that of the original profile. Analogous analysis has been performed in the case of HEA300 LRPD (design point 1), whose model and results are reported in Figure 20. The examination of these figures leads to analogous remarks, such as those reported above for the IPE400 LRPD and, therefore, for brevity's sake they are not reported. Figure 18: von [PERSON] stress map (MPa) for LRPD HEA300 (DP2) at the ultimate loading condition: (a) perspective view; (b) lateral view. Figure 19: Cyclic analysis for IPE400 LRPD (DP1): (**a**) lateral view of the model; (**b**) bending moment vs. bending curvature curve.