Analyzing the Variability of the Flexural Rigidity in Pre-stressed Laminated Wood Plates

Abstract

Although geometrical data describing structures are generally represented by their nominal values, practice has revealed that this is not the more appropriate for prestressed laminated wood plates, once the lamellae present significant size variability. The importance of this variability increases when it affects the height of plate cross sections, they also affect their moments of inertia which depends on the value of the height raised to the third power. Preliminary studies showed standard deviations of almost 10%. As far as stress-laminated plates are regarded, the variability of dimensions along the length of the length of the pieces introduces a new source of variability for the cross section moment of inertia. The obtained surfaces aren’t completely flat, presenting variability due the size variability along the length of the pieces. Consequently, the moment of inertia of the cross section of a stress-laminated plate is not obtained by summing up the individual moment of inertia of each piece. On the other hand, modulus of elasticity also presents a strong variability not only among the height of pieces, but also along their length. Preliminary experiments reveal a standard deviation of 23% for plates from <i>Pinus</i> <i>taeda</i>. The variability of moment of inertia of pieces and of the plate itself was determined, as well as the variability of the modulus of elasticity. The results show that rigidity just can be estimated probabilistically; that softwoods are suited for system of high redundancy; that the calculation of deformations and stress distribution along the structures are dependent on this variability and thus the referred calculations are nothing more than estimations with a certain level of confidence to be established according to the control procedures adopted; and finally that further research must be developed on probabilistic numerical factors to be incorporated to the calculation expressions of rigidity of the cross section of stress-laminated plates.