## 5 Strategies for Tackling Excessive Inter-Story Drifts and Stability Phenomena in Diagrids
[11] propose the adoption of a secondary bracing system (SBS), realized with limited modifications of the simple frames of the interior service core. Either rigid connections at beam-column joints or triangulation of the structural framework are proposed, thus obtaining a moment resisting frame (MRF) or concentric braced frame (CBF), respectively. The design of the SBS is carried out to address the lack of stability of the interior columns, the excessive inter-story drift, or both. Under the authors' assumptions, the first issue gives rise to a force in the bracing system \(F_{br}\) equal to 0.004 \(P_{cr,col,NS}\), \(P_{cr,col,NS}\) being the buckling load of the fully braced column. This force can be directly employed to design the members of the SBS, e.g., the diagonals of the CBF, for the stabilization of the internal gravity columns. Similarly, the second local issue is tackled with the design of an SBS able to provide a required lateral stiffness \(\beta_{req,d}\) equal to \(250\alpha(\Sigma F_{i})/(500h\)-\(\alpha h)\)[11]. In the paper, the authors analyze a 90-story tall diagrid building, with diagonal angles equal to \(60^{\circ},70^{\circ}\) and \(80^{\circ}\), to test the efficacy of the proposed formulation for the SBS. Application of Equation (20) shows that almost all the diagonal members of \(70^{\circ}\) and \(80^{\circ}\) buildings have inertia less than the minimum required for the stability of internal columns, whereas in the \(60^{\circ}\), case only the upper diagrid modules are able to provide enough resistance against the multi-sway mode. This is mainly due to the lower number of intra-module floors in the \(60^{\circ}\) solution. Thus, a SBS is found to be necessary to stabilize interior columns. Similarly, the application of Equation (21) reveals that, in all cases, SBSs are needed to limit the excessive inter-story drift at the upper modules. For this reason, SBSs are designed consisting of four CBFs, to both stabilize interior columns and comply with the imposed drift limitation (\(\alpha=300\)). In Figure 14, the results are shown for the three building solutions, in terms of lateral deflections (Figure 14a,c,e) and inter-story drift ratios (Figure 14b,d,f) under wind forces. Resulting in a 3% total increase of the total structural weight due to the insertion of the SBS, the additional structural system is proven effective in limiting the inter-story drift. As can be seen in Figure 14b,d,f, the inter-story drift ratios before the insertion of the SBS are much greater than the maximum allowable value, especially at the upper modules, and they increase as the diagonal angle increases, due to the greater number of intra-module floors. From Figure 14a,c,e, it is also evident that the insertion of the SBS does not affect the global stiffness of the building, since the top lateral deflection remains the same. Figure 14: Efficacy of secondary bracing system (SBS) in limiting inter-story drifts: (**a**,**b**) \(60^{\circ}\); (**c**,**d**) \(70^{\circ}\); (**e**,**f**) \(80^{\circ}\) diagonal pattern. (**a**,**c**,**e**) lateral deflections; (**b**,**d**,**f**) inter-story drift ratios. Used with permission from [PERSON] et al. [11]. The efficacy of the SBSs has also been assessed in the investigation of real diagrid buildings, i.e., the Hearst Tower (New York) and The Bow (Calgary) [14]. Since the majority of diagrids are not stand-alone systems but present central cores that provide local floor-to-floor restraints to the diagonal members, avoiding their flexural engagement, the adoption of SBS-like structures can preserve the axial-dominated behavior in the diagrid structure, thus better exploiting the extraordinary efficiency of the external tube mechanism [14]. The stability requirements for diagrid tubes are also investigated by [PERSON] in [37]. SBSs are introduced in this paper, with suggestions regarding their design for column lateral bracing, similarly to the considerations of [PERSON] et al. [11].