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Quasi-brittle fracture and size effect of glued laminated timber beams

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Abstract

The load bearing capacity of glued laminated timber beams is size dependent. A material based size effect occurs due to the natural variability of the timber properties and can be explained with the Weibull weakest link theory. The Weibull type size effect has received much attention in the timber research community in the past as it is the dominating size effect regarding the load bearing capacity of timber beams. In this paper, it is shown that a further deterministic size effect, which originates from the timber fracture behavior, influences the load bearing capacity of glued laminated timber beams. It is the size effect associated with quasi-brittle behavior. The paper covers a short theoretical review on fracture related size effects and a study comparing experimentally tested beams of several sizes with detailed numerical simulations considering the natural growth characteristics of timber. Further, an analytical model illustrating the features of the fracture related size effect on the load bearing capacity of glued laminated timber beams is presented. It is demonstrated that the simulated load bearing capacity of the tested glued laminated timber beams distinctively improves if the quasi-brittleness is taken into account by using a softening constitutive law.

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Abbreviations

a :

Depth of failure region

\(a_0\) :

Depth of initial crack

b :

Width of the specimen

d :

Size, any dimension

\(d_0\) :

Size (length) of the fracture process zone

f :

Load bearing capacity (bending strength)

\(f_{\rm pl}\) :

Plastic limit state load bearing capacity

\(f_{\rm t}\) :

Tensile strength; fracture initiation stress

h :

Height of the specimen

k :

Slope of the failure region

l :

Length of the specimen

m :

Slope ratio of the softening branch

r :

Distance from the crack-tip

t :

Timber board thickness; time

E :

Modulus of elasticity

F :

Limit state function

\(G_{\rm f}\) :

Fracture energy

K :

Stress intensity factor

\(K_{\rm c}\) :

Fracture toughness

\(L_{\rm f}\) :

Length of failure region

\(L_{\rm cr}\) :

Hillerborg’s critical length

M :

Bending moment

\(M_{\rm el}\) :

Elastic bending resistance

\(\delta\) :

Separation or virtual crack width

\(\delta _{\rm r}\) :

Crack width at complete separation

\(\kappa\) :

Attained maximum level of strain

\(\sigma\) :

Stress

\(\varepsilon\) :

Strain

\(\varepsilon _{\rm u}\) :

Strain at failure

\(\tilde{\varepsilon }\) :

Smeared strain

\(\tilde{\varepsilon }_{\rm r}\) :

Smeared strain at complete separation

\(\omega\) :

Damage variable

\(\chi\) :

Curvature

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Acknowledgements

The authors thank Claude Leyder for her most valuable contributions during the preparation of this paper.

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Authors and Affiliations

  1. Institute of Structural Engineering, ETH Zurich, Stefano-Franscini-Platz 5, 8093, Zurich, Switzerland

    Lukas Blank, Robert Jockwer & Andrea Frangi

  2. Department of Civil Engineering, Aalto University, Rakentajanaukio 4A, 02150, Espoo, Finland

    Gerhard Fink

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  1. Lukas Blank
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Correspondence to Lukas Blank.

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Blank, L., Fink, G., Jockwer, R. et al. Quasi-brittle fracture and size effect of glued laminated timber beams. Eur. J. Wood Prod. 75, 667–681 (2017). https://doi.org/10.1007/s00107-017-1156-0

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