PSI - Issue 78

Elisabetta Bonaguro et al. / Procedia Structural Integrity 78 (2026) 1016–1023

1019

=

·

(1)

The unreinforced condition is a timber floor with single sheathing, modeled as an orthotropic surface with the mechanical properties reported in Tab. 2. Its shear modulus G xy =7.5 MPa is determined according to Eq. (1), assuming an equivalent stiffness K d of 250 kN/m, average between thevalues specified bythe draft of the European (Comitato Europeo di Normazione (CEN), 2023) and American regulations (Federal Emergency Management Agency (FEMA), 2000),for singlestraightsheathing.ThesamevalueofG xy is presented in the studies byValluzzi (2015) and Brignola (2009) for unreinforced timber floors. For dry strengthening techniques, the equivalent shear modulus is obtained through (1): while for OSB panels (G = 27MPa) and additional diagonal sheathing (G = 45 MPa) it is determined using the stiffness values defined in CEN (2023), for diagonal steel strips (G = 128 MPa) it is derived from the stiffness value defined in Baldessari (2010). Other parameters are derived from Valluzzi (2015). The elasticity modulus E x accounts for the orientation of the beam layout along the X direction, thereby maximizing the stiffness contribution, and is assumed as 1.1·10 7 MPa, while bothE y andE z are smaller - 3.7·10 5 MPa. Since the actual beam layout is variable and considering that its influence is more significant on the out-of-planerather than its in-plane behavior, an equivalent thickness accounting for it isnot considered. Instead, a uniform thickness of 4 cm - slightly thicker than the standard 2.5 cm typically assumed for a single sheathing - is adopted. The wood material constituting the floorboard is assigned a specific weight of 455 kg/m³. The hollow clay block concrete slab is modeled as an isotropic surface with an equivalent thickness of 15 cm, derived from theequivalenceofmomentsofinertiabetween afictitiousslabandthecompositesectionmadeofthereinforced concrete slab and joists. As this thickness would result in an unrealistically high self-weight, an equivalent mass density of 1500 kg/m³ is assumed, by equating the areas of the actual and the modeled slab. The implemented value of the longitudinal elastic modulus E is 2·10 10 Pa, accounting for a reduction of the mechanical properties of concrete, which is necessary when dealing with the presence of hollow clay blocks; the implemented Poisson modulus has a 0.3 value. The corresponding value of G, obtained from the constitutive law for isotropic materials, is equal to 7700 MPa. A sensitivityanalysis to the shearmodulusisconducted onmodels ofa single SU(Fig. 1-d), throughmodal analysis, toobtainthethreemainmodesofvibration.TheGvaluesimplementedarederivedfromexperimentaltests andstudies on floors (Baldessari, 2010; CEN, 2023) retrofitted with dry strengthening techniques (i.e.: additional sheathing of both OSBpanelsanddiagonalplanks,steel strips) and from Young’s modulus (E xy ) values representativeofisotropic slabs (i.e.: concrete and ribbed concrete). The results (Fig. 2) show that by progressively stiffening the floors and roof, mass participation associated with the thirdmodeof vibration (always a torsional one) reduces to zero, statingthat increasing the floor stiffness significantly affects the overall dynamic response of the model and that bending effects in this mode are progressively avoided.

Fig. 2. Progressive reduction of mass involved along the three axes in the third mode while increasing the diaphragms stiffness.