PSI - Issue 11

Giorgio Frunzio et al. / Procedia Structural Integrity 11 (2018) 153–160 Prof. Ing. Giorgio Frunzio, Ing. Luciana Di Gennaro 00 (2018) 000–000

157

5

=

ℎ 1 2 + ℎ 2 2 + ; (5, 6, 7)

1 = − 2 ; 2 = 1 ∙ 1 1 ∙ 1 ∙ 1 1 + 2 2

K is the sliding module given by the following equations: = for SLE (Operating Limit State); = = 2 3 for SLU (Ultimate Limit state) The realization of an union, whatever the chosen typology is, entails a structural discontinuity. The Eurocode n° 5 proposes different values of K ser according to the type of union, in the topic case (connections with pins) the value of K ser is given from the following equation: = 1 , 5 ∙ 2 3 (10) Where is the density (kg/m 3 ) and d is the pin diameter (mm). Having determined the Effective Stiffness EJ ef , the Möhler theory allows to calculate the stress state at the edges of the inflected section. The normal and bending stresses, N d and M d , on the i th element are given by the following equations: , = ∙ ∙ ( ) ∙ ; , = ( ) ( ) ∙ (11, 12) As a consequence, the stress state of bending at the edges of the section is given by: ± , = , ± , ∙ ℎ 2 = � ∙ ∙ ( ) ± 0 , 5∙ℎ ∙ ( ) � ∙ (13) Where σ i = barycentric stress on the i th element; σ m,i = bending stress component to be added or subtracted from the barycentric stress to obtain the stresses at the edges of the constituent elements. The maximum shear stress acting on the beam is: 2 , = 0 , 5∙ 2 ∙ℎ 2 ( ) ∙ (14) Where V = shear stress value acting on section; ℎ = = ℎ 2 2 + 2 = distance of centre of gravity from inferior edge of the composed section Therefore, the verification of the strengths consists in the comparison of the stress values, described above, and the material design strengths. The wooden structure deformations are due to several causes as: the conditions of coaction, the variations of humidity and the sliding between elements in the connections. The deformation values must have acceptable limits, in relation both to the damages that can be induced to the coating materials, to the floors, partitions, finishes etc., and to the aesthetic requirements and to the functionality of the work. Considering the rheological behaviour of wood and wood-derived materials, both instantaneous deformations and long-term deformations were evaluated. For bending deformations on beams, the total deflection is composed of the contributions of several types of loads u 0 = possible camber, u 1 = deflection due to permanent loads (G k ) and u 2 = deflection due to variable loads (Q k ) Net deflection is: , = 1 + 2 − 0 (15) Furthermore, in relation to the duration of the load is possible to define u ist as instant deflection or initial deflection due to short term loads, and u dif as deferred deflection due to long term loads (8, 9)