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Under varying humidity and temperature conditions, with the constraint of metal fasteners to wood shrinkage, cracks along the bolt lines are generally observed in bolted glulam joints. A three-dimensional (3D) numerical model was established in software package ANSYS to investigate the cyclic behavior of bolted glulam joints with local cracks. A reversed cyclic loading was applied in the parallel-to-grain direction. The accuracy of numerical simulation was proved by comparison with full-scale experimental results. Typical failure modes were reproduced in the numerical analysis with the application of wood foundation zone material model and cohesive zone material model. The effect of crack number and length on the hysteretic behavior of bolted glulam joints was quantified by a parametric study. It was found that initial cracks impair the peak capacity and elastic stiffness of bolted glulam joints significantly. More decrease in capacity was observed in joints with more cracks, and longer cracks affect elastic stiffness more dramatically. Moreover, with the existence of initial cracks, the energy dissipated and equivalent viscous damping ratio of bolted joints are reduced by 24% and 13.3%, respectively.

Connections are always recognized as the weakest part of timber structures. It was reported that nearly 80% of structural collapses arise from connections [

In terms of modeling the mechanical behavior of bolted glulam joints, several methods have been proposed by previous researchers. An analytical method named Beam-on-Foundation model was first applied [

Extensive researches have been conducted on mechanical behavior and strength enhancement of bolted glulam joints as above. However, little attention was paid to the mechanical behavior of bolted glulam joints with local cracks. Shrinkage cracks are generally observed in bolted glulam joints due to their sensitivity to varying relative humidity of the environment. Shrinkage and swelling strains of wood are restrained with the existence of steel fasteners in the joint area, and cracking of wood is easily caused by perpendicular-to-grain restrained stress [

To reveal the influence law of cracks on the cyclic behavior of bolted glulam joints intuitively, a 3D numerical model was established in this paper. Hill yield criterion and wood foundation model were applied to simulate the behavior of wood in compression and wood around fasteners, respectively. Brittle failure of wood and propagation of initial cracks were modeled with the application of cohesive zone material model. Several contact pairs were defined to model the interaction between different parts in the joint, and reversed cyclic loading was applied in the parallel-to-grain direction. The experimentally observed failure modes and hysteretic curves were used to verify the numerical results, and the influence of different crack patterns was explored by a parametric study.

To model the mechanical behavior of wood in compression, the transversely isotropic plastic material model was defined with the application of the Hill yield criterion, which had been incorporated in business software ANSYS. To take into account the embedment behavior of wood underneath bolts, a foundation zone was set around bolts with a radius of 1.8-time bolt diameter. The generalized Hill plasticity model with anisotropic hardening rule was applied to represent the mechanical behavior of wood foundation. 1% of initial modulus was taken as tangent modulus of hardening segment. With embedment tests loaded in perpendicular- and parallel-to-grain directions, a bilinear relationship between load per unit length and deformation was obtained, as shown in Figure

Load-embedment curves obtained from embedment tests and corresponding bilinear relationships. (a) Parallel to grain. (b) Perpendicular to grain.

where

where

Bilinear stress-strain relationship for steel material.

To simulate the propagation of initial cracks and brittle failure (i.e., splitting and row shear) of wood in bolted glulam joints, surface-to-surface contact pairs with elements CONTA174 and TARGE170 were defined on the predicted cracking path. To characterize the constitutive relationship of the interface, the cohesive zone material model with damage initiation and growth criteria was implemented in the numerical model. As shown in Figure

Cohesive zone material behavior. (a) Fracture mode I. (b) Fracture mode II.

where

A 3D finite-element model of bolted glulam joints was established in FE-software ANSYS. Eight-node solid element SOLID185 was applied to embody the joints. To model the interaction between bolts and steel plate, timber and bolts, timber and steel plate, and timber and steel gasket, surface-to-surface contact pairs were defined with CONTA174 and TARGE170 elements. For bolt-to-steel plate and wood-to-steel contacts, coefficients of friction were taken as 0.001 and 0.3, respectively [

An example of the distribution zones of different material models. (a) Front view. (b) Side view.

Fictitious fracture layers set in joints with four bolts. (a) Without initial cracks. (b) With initial cracks.

Material constants applied in this model.

Component | Bolt | Steel plate | Wood | Wood foundation |
---|---|---|---|---|

Modulus of elasticity (N/mm^{2}) | ||||

Modulus of rigidity (N/mm^{2}) | — | — | ||

Poisson ratio | ||||

Yield stress (N/mm^{2}) | ||||

Strengths (N/mm^{2}) | — | — | ||

Fracture energies (N/mm) | — | — | ||

To study the cyclic behavior of bolted glulam joints, a gap of 30 mm was set between the top surface of steel plates and the slot, as presented in the side view of Figure

Loading protocol recommended in EN 12512 (2001).

To validate the feasibility of the numerical model, a bolted glulam joint with five replicates was manufactured and tested. The configuration of tested joints is presented in Figure

Detailed configurations of test bolted joint.

Failure modes of bolted glulam joint obtained from numerical analysis and experiment.

The numerical model of the tested joint was established and the results obtained from numerical analysis were compared to experimental findings for verification purposes. The failure modes of bolted joints predicted by numerical analysis are shown in Figure

Comparison between experimentally obtained and numerical predicted hysteretic curves.

Mechanical parameters obtained from experimental and numerical results.

Elastic stiffness (kN/mm) | Peak load (kN) | Accumulated energy dissipation (J) | |
---|---|---|---|

Test result | 38.0 | 52.9 | 1650.8 |

Numerical result | 49.5 | 50.7 | 1766.4 |

To investigate the effects of crack patterns on the cyclic behavior of bolted glulam joints, a parametric study was conducted with the consideration of different bolt configurations. A single-bolt line with two bolts was included in Joint 1, as shown in Figure

Two bolted glulam joints considered in the parametric study. (a) Joint 1. (b) Joint 2.

Different crack patterns considered in Joint 1 and Joint 2. (a) Joint 1-SB. (b) Joint 1-DB. (c) Joint 1-ST. (d) Joint 1-DT. (e) Joint 2-LS. (f) Joint 2-LD. (g) Joint 2-RLS. (h) Joint 2-RLD.

For initially perfect Joint 1, splitting failure of wood is observed under positive loading (i.e., tension load), as shown in Figure

Failure mode of initially perfect Joint 1: (a) splitting failure of wooden parts; (b) von Mises stress distribution of bolts.

Hysteretic curves of Joint 1: (a) initially perfect Joint 1; (b) comparison between initially perfect Joint 1 and Joint 1-DT; (c) comparison between Joint 1-SB and Joint 1-DB; (d) comparison between Joint 1-DB and Joint 1-DT.

To investigate the effect of different numbers of cracks on the hysteretic behavior of bolted glulam joints, a comparison is conducted between Joint 1 with crack patterns SB and DB as presented in Figure

The main failure modes of initially perfect Joint 2 include the embedment failure of wooden parts around bolt holes and brittle failure of wood in the joint area, as shown in Figure

Failure mode of initially perfect Joint 2: (a) embedment deformation of wood; (b) splitting failure in the joint area; (c) von Mises stress distribution of bolts.

Compared to Joint 1, a more significant pinch phenomenon is observed in the hysteretic curve of Joint 2, as shown in Figure

Hysteretic curves of Joint 2: (a) comparison between initially perfect Joint 2 and Joint 2-RDT; (b) comparison between Joint 2-LD and Joint 2-RLD.

The skeleton curves of Joint 1 are presented in Figure

Comparisons of skeleton curves for Joint 1.

Mechanical parameters of Joint 1 under positive and negative loading were calculated and listed in Table

Summary of the mechanical parameters of Joint 1.

Joint 1-NO | Joint 1-SB | Joint 1-DB | Joint 1-ST | Joint 1-DT | |
---|---|---|---|---|---|

Elastic stiffness (kN/mm) | 32.7/33.6 | 28.9/33.5 | 24.5/33.6 | 24.6/33.5 | 17.2/33.0 |

Yield force (kN) | 35.8/−36.0 | 30.5/−35.8 | 22.4/−35.7 | 30.3/−35.9 | 24.1/−35.6 |

Yield displacement (mm) | 1.7/−1.68 | 1.65/−1.62 | 1.52/−1.64 | 1.85/−1.63 | 1.87/−1.68 |

Peak load (kN) | 37.6/−38.8 | 31.4/−37.7 | 29.4/−37.3 | 31.6/−37.7 | 29.4/−37.3 |

Ultimate displacement (mm) | 2.55/−3.97 | 3.27/−3.82 | 4.33/−3.80 | 3.02/−3.82 | 4.33/−3.80 |

Ductility ratio | 1.50/2.36 | 1.98/2.36 | 2.85/2.32 | 1.63/2.34 | 2.32/2.26 |

The method of 5% diameter used to determine the yield point.

As can be seen from Figure

Different crack lengths are considered in Joint 1-DB and Joint 1-DT. As can be seen from Table

The skeleton curves and mechanical parameters of Joint 2 are presented in Figure

Comparisons of skeleton curves for Joint 2.

Summary of the mechanical parameters of Joint 2.

Joint 2-NO | Joint 2-LS | Joint 2-LD | Joint 2-LRS | Joint 2-LRD | |
---|---|---|---|---|---|

Elastic stiffness ( | 49.6/52.2 | 46.2/52.2 | 42.9/52.2 | 44.8/50.7 | 40.2/52.1 |

Yield force ( | 61.7/−63.3 | 60.3/−63.2 | 57.6/−62.6 | 59.6/−60.9 | 56.0/−63.0 |

Yield displacement ( | 1.85/−1.79 | 1.92/−1.79 | 1.96/−1.81 | 1.92/−1.79 | 2.0/−1.82 |

Peak load ( | 71.4/−78.6 | 68.4/−75.8 | 64.8/−75.5 | 65.3/−75.1 | 60.1/−71.8 |

Ultimate displacement ( | 5.91/−5.21 | 5.90/−5.28 | 5.91/−5.27 | 5.91/−5.27 | 5.94/−5.17 |

Ductility ratio | 3.19/2.91 | 3.08/2.95 | 3.02/2.91 | 3.08/2.94 | 2.94/2.84 |

Under reversed cyclic loading, the stiffness of bolted glulam joints declined gradually with increased loading amplitudes with wood crushing or bolting yielding. The secant stiffness of primary loading cycles was calculated as follows:

where

Stiffness degradation observed in bolted glulam joints: (a) Joint 1; (b) Joint 2.

At the early loading stage, the gradual growth of secant stiffness is observed with full contact interaction. For initially perfect Joint 1, the largest secant stiffness of 36.5 kN/mm is obtained at the displacement of 0.5 mm, as shown in Figure

Similar to Joint 1, a first growing tendency of secant stiffness is observed in Joint 2, as shown in Figure

To estimate the accumulative energy dissipation of the joint under reversed cyclic loading, the enclosed area of the hysteretic loop was calculated for each loading cycle based on numerical integration, and the accumulative energy dissipation was presented in Figure

Comparisons of energy dissipation curves: (a) Joint 1; (b) Joint 2.

For initially perfect Joint 2, a similar increasing tendency is observed and the total energy dissipated is 932 J. As can be found from Figure

Equivalent viscous damping ratios have been calculated at different amplitude levels as follows:

Determination of energy dissipation.

Relationships between equivalent viscous damping ratio and displacement: (a) Joint 1; (b) Joint 2.

It can be seen from Figure

As can be seen from Figure

In the paper, a 3D numerical model was developed to investigate the influence of initial cracks on the cyclic behavior of bolted glulam joints under parallel-to-grain loading. Cohesive zone material law was applied to simulate the propagation of initial cracks and brittle failure of wood. With the application of the Hill yield criterion and wood foundation zone model, the local crushing behavior of wood was reproduced by numerical results. The feasibility of the numerical model was verified by comparison with full-scale experimental results, and different crack patterns and bolt configurations were further considered in a parametric study.

It was found that peak capacity and elastic stiffness of bolted glulam joints were reduced with the existence of initial cracks. More decrease in capacity was observed in joints with more cracks, and longer cracks affect elastic stiffness more dramatically. For Joint 1 with splitting failure occurring under positive loading, the decreasing ratios can be up to 21.8% and 47.4%, respectively. The ductility behavior of Joint 2 with controlled failure mode of wood embedment is impaired by initial cracks. Moreover, under reversed cyclic loading, less energy dissipated is observed in bolted glulam joints with initial cracks, which is only 76% of energy dissipated in the initially perfect joint. Further, the equivalent viscous damping ratio of bolted glulam joint is reduced by 13.3% with the existence of initial cracks.

The data used to support the findings of this study are included within the article and available from the corresponding author upon request.

The authors declare that they have no conflicts of interest.

The authors gratefully acknowledge the National Natural Science Foundation of China (Grant no. 51908147) for supporting this research.