## 7 Non-Linear Analyses and Seismic Performance of Diagrid Structures
A crucial aspect in conducting such tests relies on the correct definition of the geometrical, inertia, stiffness and damping parameters of the prototype, which should reflect the real parameters of the tall building based on similarity laws. This procedure can also be a rational way to validate FE models [45]. The seismic assessment of diagrid towers has been further investigated in more recent papers [46; 47; 48; 49; 50; 51]. In [46], [PERSON] and [PERSON] quantify the seismic performance factors (SPFs) of steel diagrid buildings, i.e., the response modification coefficient (\(R\)-factor), the overstrength factor (\(\Omega_{0}\)) and the displacement modification factor (\(C_{d}\)), based on FEMA P695 methodology [52]. FE push-over analyses and incremental dynamic analyses (IDAs) are carried out. It is found that diagrids exhibit a rather brittle behavior, as observed from the push-over curves, and the ductility increases as the diagonal angle increases. \(R\)-factors also depend on the diagonal inclination, varying between 1.5 and 3, for diagonal angles ranging from 45\({}^{\circ}\) to 71.5\({}^{\circ}\). The restraining end-conditions of the diagonals (pinor rigid) do not have a significant influence on the stiffness of the structure; however, the pin-ended solutions better tolerate larger displacements, improving the building's ultimate seismic performance. In a series of following studies, [PERSON] et al. [47; 48; 49] perform a comprehensive investigation of the non-linear performance of low- to mid-rise steel diagrid structures, using static, time-history dynamic, and incremental dynamic analyses. Special attention is paid to corner columns, due to the shear-lag effect, as well as to the diagonal inclination, in the evaluation of the seismic assessment and loss estimation of very short (4- and 8-story tall) diagrid buildings [47]. Mid-rise buildings, in the 8- to 30-story range, are also investigated, and their non-linear behavior is analyzed and compared to traditional solutions, such as moment resisting frames and concentrically braced frames, in terms of weight, story drift, lateral stiffness, fundamental period and evolution of plastic hinge formation [48]. A set of 4- to 30-story tall diagrid buildings is further investigated for the evaluation of the SPFs, and the authors recommend specific values for the SPFs of diagrid frames lying in different story ranges [49]. Very recently, [PERSON] et al. [50] investigated the influence of the interior cores on the seismic performance of diagrid tubes. By the application of push-over analysis, it is found that the interior tube can indeed help as a backup load-resisting system after the yielding of the perimeter diagrid structure, procrastinating the insurgence of damage and providing an enhanced safety margin. Non-linear time-history analyses also reveal that most of the buildings perform well under severe earthquakes, dissipating large amounts of the input energy and leading to fairly uniform plastic hinge distribution [50]. The seismic reliability of diagrids was also recently investigated by [PERSON] et al. [51], who developed an efficient performance-based design strategy, based on a new multi-level response modification factor. All these studies show that the non-linear and dynamic behavior of diagrids should be carefully taken into account right after the preliminary design stage, since satisfying the static requirements often strongly depends on the diagrid features (diagonal angle, building height, etc. ), as shown in Section 4. As briefly remarked in the papers cited above, the analyses of the seismic assessment of structural systems can be very diverse. Various types of analyses can be carried out, such as linear modal analysis, non-linear static analysis (i.e., push-over analysis), time-history analysis, etc.