PSI - Issue 44

Maria Maglio et al. / Procedia Structural Integrity 44 (2023) 550–557 M. Maglio, R. Montuori, E. Nastri, V. Piluso / Structural Integrity Procedia 00 (2022) 000–000

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3.2. Lateral displacements limitation For the SD Limit state, the inter-storey drift should be limited at any storey of the building by complying with the condition given by Formula 6.5 of the prEN1998-1-2 (2021): , ≤ ℎ (10) where , is the design inter-storey drift as defined above, is a coefficient accounting for the sensitivity of ancillary elements to the interstorey drift, in general = 0.02 for moment frames; ℎ is the interstorey height. Displacement is obtained considering the analysis developed applying the SD reduced design spectrum without the lower bound. Drift limitation at SD applies to all ductility classes and all design approach. 3.3. Soft-storey mitigation rule In DC2 class brittle failure or the premature formation of unstable mechanisms shall be avoided (prEN1998-1-1, 2021) and in multi-storey buildings the formation of a soft-storey plastic mechanism should be prevented. For Moment Resisting Frames, in case a force-based approach, this condition is considered satisfied if the following inequality, formulated by Plumier (2022) and inserted in the prEN1998-1-2 (2021), is verified at all the storeys: ( − ) , ≤ 2 � . . ( ) =1 (11) where = 1.50 and = 1.30 for MRFs and DC2 ductility class; is the total storey shear in the seismic design situation; i is the index of a column in the storey; n is the number of columns in the storey; . is the displacement calculated under the reduced spectrum associated to the design seismic action at the level of the roof top under the design seismic action; . . ( ) is the moment of resistance of column section i where plastic hinge can occur, at the storey under consideration, taking into account the influence of the axial force in that same section under the gravity load due to masses considered in the seismic analysis of the structure; is the minimum value of the plastic part of the ultimate chord rotation among all the column sections i where a plastic hinge can occur at a given level, as reported in prEN1998-1-1 (2021). The plastic rotation for the interior columns of I-shaped and H-shaped steel columns may be calculated using the following formula: θ upl = 7,37 � � −0 , 95 � � −0 , 5 (1 − ) 2 , 4 ≤ 0,15 (12) where / is the web slenderness ratio of the cross-section, is the unbraced length of the steel column, is the radius of gyration of a steel cross-section with respect to its weak axis and = . / . where . is the axial load in the gravity load part of the seismic load combination and . = γ . In this case γ = 1 should be used. The plastic rotation of I- or H- shaped steel columns with > 0.60 or with ⁄ > 43 and ⁄ > 120 should be taken equal to zero. Instead, for the exterior columns experiencing variations in axial load demands due to dynamic overturning effects, the rotation may be evaluated using Eq. (12) by considering only . This statement is not currently clear as it cannot be understood how only should be used in the formula. 3.4. Genesis of the soft storey mitigation criteria (Plumier, 2022): critical analysis The criterion to assess the risk of a soft-storey failure is based on the comparison between the work of external force applied by an earthquake and the internal work in plastic hinges of the soft-storey in a deformed shape of the structure in which the whole of the top displacement in the post elastic range is allocated to the potential soft-storey. This criterion is combined with the limitations of second order effect and drift of prEN1998-1-2 (2021). In particular this criterion starts assuming that “ if a displacement δ is imposed in a kinematically acceptable yield mechanism, stability is realized if the virtual work of external forces V is smaller than or equal to the virtual work developed by internal forces” (in MRFs the internal work is represented by the bending moment of resistance, . ). The fundamental statement of DC2, i.e. the criterion that must be satisfied at each storey is: