PSI - Issue 11

Giorgio Frunzio et al. / Procedia Structural Integrity 11 (2018) 153–160

158

Prof. Ing. Giorgio Frunzio, Ing. Luciana Di Gennaro 00 (2018) 000–000

6

So, the total deflection is given by: = +

(16) The verification of deformations was made up on indications of CNR-DT 206/2007 standards that impose limitations. So in the “short term load” condition the deflection limit is 2 , ≤ 300 ⁄ , in the “long term load” condition the deflection limits are , ≤ 250 ⁄ e 2 , ≤ 200 ⁄ . The architectural project of the Palazzo Ducale di Parete identifies a public function for the monument, with rooms open (Noble Floor) or not open (Attic) to the public. Thus, the verifications are carried out using "crowd loads" for the Noble Floor (4,00 kN/sqm) and ordinary loads for the attic (2,00 kN/sqm). For the realization of the calculation model, the single beam was schematised as a single beam simply supported, without any contribution from the neighboring beams. A grid decking, instead, was modeled where in the original deckings, the presence of transversal thickening elements orthogonal to the main frame was found. To this end, a finite element calculation software was used, allowing the various bending and torsional stiffness components to be considered and making possible to calculate displacements and stresses for the different load conditions required by the standard. The load duration, as well as the class of service, affects the strength properties of the wood. The properties design values of the material starting from the characteristic values, are then assigned with combined reference to the service classes and duration classes. The design value of a property is calculated using the following relationship X d = k mod X k γ M (17) Where X k is the characteristic value of the material property; γ M is the partial safety factor related to the material; k mod is the corrective factor that considers both the duration of the load and the class of service. For the case of study, parameters values are those of table 1 for X k ,1,50 for γ M, and 0,80 for kmod. Moreover, extensive and exhaustive on-site verifications have been performed, and that all the materials test results have corroborated the values considered by the standards, so it's possible to adopt an LC3 Knowledge Level which determines a confidence factor FC equal to 1.00. Therefore the resistance values fm,d and fv,d become: , = , ∙ = 0 , 1 8∙28 , 50∙1 , 00 = 14,93 / 2 ; , = , ∙ = 0 , 1 8∙4 , 50∙1 , 00 = 2,13 / 2 (18, 19) First of all, verifications of double crossed plank, were carried out on the double crossed plank consisting of two orders of solid chestnut boards with a thickness of 30 mm each in placed one orthogonally to the other. A shape equal to the maximum existing wheelbase (1050 mm) and a variable action equal to 0.4 N/sqmm was used in the calculation for the benefit of safety. The verifications were made assuming that the connection of the crossed elements has infinite sitffness. The following is a verifications summary

Table 1. Plank verifications

PLANK VERIFICATIONS Maximum stress value (upper board) , 1 (MPa) Maximum stress value (lower board) , 2 (MPa) Maximum shear stress (MPa) Instant deflection

Limit Value , = 14,93 , = 14,93 , = 2,13 2 , ≤ 300 ⁄ , ≤ 250 ⁄ 2 , ≤ 200 ⁄

Design value

Result

4,379 0,743

verified verified verified verified verified

0,100

L/8882

Long term deflection

L/4303 e L/6001

Calculations were carried out on the existing mandatory standards.