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An application of the Tsaï criterion as a plastic flow law for timber bolted joint modelling

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Summary

This paper describes a modelling approach to predict the behaviour of an elementary thin timber bolted joint. The application concerns principally joints with steel side members; bolts have a constant 12 mm diameter with two ratios of end distance to bolt diameter and two bolt clearances. The behaviour of the bolted joints is characterized by a double non linearity; the first one is due to the contact area evolution between the bolt and the hole of the jointed elements. The second one is owing to the evolution of plasticity on the wood. A spring element compatible with isoparametric plane finite elements represents the contact evolution. The elastic-plastic wood is provided with a plastic flow rule according to the Tsaï criterion. This study allows an investigation on the parameters characterizing the Tsaï criterion, particularly F12 which represents the interaction between the principal axis of orthotropy. A two-dimensional model is used. It permits the assessment of the clearance bolt, joint dimensions, wood plasticity and wood grain angle effect on the joint behaviour. The wood grain angle has a non negligible effect on the plastic strains distribution and it can create a parasite loading because the joint tends to rotate even for an axial loading. The results showed a good agreement between experimental values given by some authors and numerically-predicted stresses on the joint. So, the applications concern a two-dimensional joint with anisotropic plastic material. The generalization in the three-dimensional modelling is desirable to take into account the interaction between the wood and a metallic fastener in thick joints with different geometric characteristics.

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Abbreviations

d:

bolt diameter

φ, phi:

hole diameter

Ex :

elastic modulus — longitudinal direction (grain direction)

Ey :

elastic modulus — transversal direction (radial or tangential)

G(XY) :

stiffness shear modulus —XY plane

V(XY) :

Poisson's ratio — XY plane, loading on X-direction

σx, σy :

wood tensile strengths, in the longitudinal and transversal directions

σ′X, σ′Y :

wood compressive strengths, in the longitudinal and transversal directions

τxy :

wood shear strength on the XY plane

θ:

wood grain angle

dσ:

effective stress increment in the general set of axis

dσe :

increment of stress assumed to be elastic

[D]:

matrix of elastic constants

Y:

Tsaï equivalent stress (=1 without strain hardening)

dλ:

plastic multiplier

F(σ):

Tsaï as a flow plastic criterion

dS:

effective stress increment in the matrix [W] eigenvectors set of axis

dSe :

Increment of stress assumed to be elastic according to the eigenvectors of [W]

Xi :

eigenvalues of the matrix: [W] = [D] [M]

[Φ]:

matrix of eigenvectors of [W]

[I]:

unit matrix

k:

strain hardening parameter

a:

end distance of the joint

b:

half-width of the joint

CASTEM:

finite element program for structural analysis (CISI-CEA)

INCA:

program of CASTEM for two-dimensional mechanical and thermal problems

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Authors and Affiliations

  1. Civil Engineering Laboratory, Blaise Pascal University, Clermont-Ferrand, B.P. 206, 63174, Aubière-Cedex, France

    A. Bouchair & A. Vergne

Authors
  1. A. Bouchair
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  2. A. Vergne
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Bouchair, A., Vergne, A. An application of the Tsaï criterion as a plastic flow law for timber bolted joint modelling. Wood Sci.Technol. 30, 3–19 (1995). https://doi.org/10.1007/BF00195264

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