Study of stress distribution and stress concentration factor in notched wood pieces with cohesive surfaces

Abstract

In this study, the stress distribution and stress concentration factor (SCF) of a generic notched wood piece and ASTM D 143:14 notched shear block specimen were analysed. A 2D plane stress finite element model with linear elastic behaviour was assumed for the bulk material and a predefined potential crack path and cohesive behaviour of the crack surfaces were considered. Wood was considered an orthotropic material with transversal isotropy. In the notched wood pieces, the shear stress distribution along the shear plane and the SCF when varying the ratio l/t (length of the heel/depth of the notch) was obtained. The shear stress distribution is not uniform in any situation, approaching a slightly triangular shape. The shear stress concentration increases when l/t is greater and for l/t [ 8 failure occurs due to crack progression. The SCF can be brought fairly close to the natural logarithm of l/t. In the ASTM D 143:14 notched shear block specimen, shear stress distribution only remains a constant value in the central part of the shear plane, while the SCF is greater than 2.

Analysis of the stress state at the double-step joint in heavy timber structures

“…These results confirm the distribution presented in Figure 14, a triangular diagram with a slope increase to the contact face, which represents an SCF greater than two. This distribution is in accordance with other studies (3,5,49,50), a half hammock shape as reported by Verbist et al (11), but even more intense when reaching the corner side in the shear path. These results for the SCF indicates that the theoretical uniform shear stress is around 0.36 (SCF FEM = 2.77 -2.79) and 0.47 (SCF EXP = 2.13) of the highest shear stress reached.…”

Design of three Step Joint typologies: Review of European standardized approaches

“…As illustrated in Figure 8, the design rafter load-bearing capacity, noted , , , must be checked by the equations (1)-(17)-(18)- (19), similar to (9)-(10)-(11) from the SSJ design, in order to prevent the appearance of shear crack in the tie beam for each DSJ heel [6][7][8]25].…”

“…[13,14,15,16]), recent research (e.g. [17,18,19,20,21,22,24,25]) and state-of-the arts (e.g. [6,7,12,23,26]) have focused on determining the mechanical behaviour of the three SJ typologies through analytical, numerical and experimental assessments.…”

“…The reducer coefficients noted , , consider the presence of the non-uniform shear stress distribution at both DSJ heel depths along the grain in the tie beam. The condition , , = 0.8 could then be applied to the design shear strength , ,(19) in the Front and Rear Heels in order to compare the reduced design shear strengths , , , with the design average shear stresses , , uniformly distributed over the related effective shear lengths , , , as illustrated inFigure 8. The recommended values of the crack factor from the SSJ design against the shear crack can also be applied for the Double Step Joint.According to Bocquet[8], a 1-2 mm gap is preconized at the front-notch surface in the Front Heel for the DSJ design against the shear crack.…”

“…Illustration of the non-uniform shear stress distributions , at the Front and Rear Heels depths in the tie beam, in comparison with their uniform average shear stresses , , assumed in(19) [25].…”