# Mechanical Characterization of Timber-to-Timber Composite (TTC) Joints with Self-Tapping Screws in a Standard Push-Out Setup

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## Abstract

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## 1. Introduction

## 2. Background

#### 2.1. Reference Experimental Approach

#### 2.2. Selected Push-Out Specimens and Configurations

- S#1 = is a 2 + 2 screwed joint (−45° ≤ α ≤ 45°)
- S#2 = represents a 4 + 4 screwed joint (−45° ≤ α ≤ 45°), with a
_{1}= 70 mm ≈ 8d and d = D_{3} - S#3 = is a 4 + 4 screwed joint like S#3 (−45° ≤ α ≤ 45°), but a
_{1}= 160 mm ≈ 18d - S#4 = denotes a 2 + 2, X-shaped screwed joint (0° ≤ α ≤ 45°)

## 3. Reference Numerical Modelling Approach

#### 3.1. Solving Strategy and Model Assembly

_{2}= 6.3 mm from Figure 3d) and total length L.

_{1}= 8.1 mm from Figure 3d).

#### 3.2. Material Properties

_{y}= f

_{u}= 940.3 MPa. An ultimate strain δ

_{u}= 0.5% is considered. At the same time, an orthotropic constitutive law is used for spruce [21]. To ensure more realistic behaviours for the timber members, this constitutive law is integrated with a Hill plastic criterion and a brittle failure parameter. The Hill criterion allows to account for different resistance values in the principal directions of timber, and thus for different potential critical mechanisms for the examined PO setup. The additional brittle failure law, moreover, is used to include possible crushing phenomena in the timber close to the fasteners. Once attained the ultimate resistance f

_{c,90}, a linear propagation of compressive damage is taken into account for timber. Due to lack of more detailed experimental feedback, this material degradation is set to maximize at a failure deformation of δ

_{u}= 4mm. This value is adapted from [20], where C24 timber members have been investigated, based on the similarity in the resistance parameters for GL24h spruce. The final input parameters for timber are listed in Table 1, based on the nominal mechanical properties for GL24h strength class [24,25].

#### 3.3. Mechanical Interactions and CZM Properties

_{timber}= 0.5 [28] the static friction coefficient). A second surface-to-surface contact interaction, see Figure 6b, is introduced between the bottom face of timber (lateral member) and the base steel support (μ

_{base}= 0.2 [28]). Finally, see Figure 6c,d, a double restraint is used in the region of the steel fasteners. Each screw is first rigidly connected with the surrounding soft layer via a distributed “tie” constraint, so that relative rotations and displacements among the interested surfaces could be avoided. The external surface of the soft layer and the timber elements are then interconnected by a surface-based CZM behaviour, that is conventionally defined in its basic features (linear elastic traction-separation model (Figure 6e), damage initiation criterion, damage evolution law). In this study, the “default contact enforcement method” of ABAQUS library is used for the definition of the interface stiffness parameters prior to damage onset. The “Damage initiation”, in this regard, is set to coincide with timber failure, based on Table 1 and Table 2. This limit condition is implemented in the form of a maximum nominal stress (MAXS) criterion:

_{u}= 4 mm (Table 2).

#### 3.4. Analysis of Force Contributions

## 4. Discussion of FE Results

#### 4.1. Force-Slip Curves

_{max}can be conventionally detected as the first condition between the attainment of the (a) actual maximum force or (b) a total force corresponding to a joint slip s = 15 mm (if any). The corresponding serviceability stiffness K

_{ser}is then given by [22,23]:

_{04}and s

_{01}the measured sliding amplitudes at the 40% and 10% part of the maximum resistance F

_{max}.

#### 4.2. Damage Mechanism

- crushing phenomena in timber (in the region of screws);
- progressive yielding of screws and
- damage of the CZM contact (screw-to-timber interface).

## 5. Mechanical Characterization of TTC Joints

#### 5.1. Experimental Assessment of Maximum Force Predictions (F_{max})

_{max}values with. Despite such a stable numerical dependency of F

_{max}estimations on α, however, in some cases the scatter between numerical and past experimental predictions was found to be in the order of ±30%. The numerical results were in fact found to either underestimate or overestimate the corresponding experiments, depending on the number and inclination of STSs. For the majority of the examined TTC joints, the FE results proved to be non-conservative especially for the specimens under shear-tensile loads (0 < α ≤ 45°).

_{max}. In the figure, the scatter F

_{max}is calculated as:

_{FE}denotes the numerical force peak for each FE analysis and x the corresponding experimental average value (for each test series), as derived from [6].

_{max}is mostly regular, for all the examined series of TTC specimens. This can be also perceived by the linear fitting curve that is proposed in Figure 11, as a function of the screw inclination α.

#### 5.2. Analytical Assessment of Maximum Force Predictions (F_{max})

#### 5.3. Experimental and Analytical Assessment of Serviceability Stiffness Predictions (K_{ser})

_{ser}is then estimated for the examined TTC joints, based on Equation (3) and the collected numerical force-slip curves. In Figure 14, the FE stiffness values are reported for the S#1-to-S#3 type (average) or S#4 type of specimens, as a function of α. Comparisons are proposed towards the past experimental data from [6], as well as the enhanced analytical formulation proposed in [6].

## 6. Parametric FE Investigation

#### 6.1. Mechanical Interactions and CZM Damage Parameters

_{u}= 4 mm, Table 2). Among these two conditions, further FE analyses are carried out with the CZM input parameters of Section 3 (Table 2), but progressively increasing the reference failure displacement δ

_{u}in the range from 4mm to a maximum of 10 × 4 = 40 mm. From a practical point of view, such a variation in δ

_{u}represents a residual capacity of the soft-layer to provide a certain mechanical interaction between each STS and the surrounding timber. Such an input value was in fact magnified so as to reproduce an ideal bonding condition with a weak mechanical degradation for the soft-layer interface, even under large slip amplitudes (Figure 6e). Selected numerical results are proposed in Figure 16 for two different screw arrangements (S#1 joints), in terms of measured vertical (F) and horizontal (H) base reaction forces as a function of the measured slip s.

_{ser}and ultimate resistance F

_{max}. Such a combination of phenomena, finally, was also found associated to a remarkable modification of the measured reaction forces (see for example Figure 16b–d).

_{u}was commonly associated to a rather constant elastic response for the examined TTC joints, but to a marked decrease of residual resistance and stiffness for most of the tested configurations. Such an effect can be notice in Figure 16. As far as the critical displacement δ

_{u}for the CZM interaction increases, a reduced slope can be observed for the descending arm of the collected force-slip curves. Compared to the available experimental data from [6], a reliable fitting of degreasing arms for the comparative force-slip curves was observed in the range of δ

_{u}= 6–7mm. This fitting value δ

_{u}, however, results from a numerical calibration in which the nominal mechanical properties of timber are taken into account (Table 1 and Table 2). Accordingly, further refined, multi-objective and multi-parameter calculations should be carried out in this direction. Moreover, given that the CZM failure data were found to do not affect the initial stage of the collected force-slip curves (and thus the calculated serviceability stiffness and ultimate resistance for the examined joints), the reference value δ

_{u}= 4mm could be taken into account for preliminary conservative calculations on timber members with similar mechanical properties/class.

#### 6.2. Base Restraints

- BC#2: a distributed, rigid restraint at the base of the lateral timber members (Figure 17b); and
- BC#3: a mixed restraint, as obtained with a surface contact interaction between the timber member and the rigid base (to avoid possible compenetration) and an additional linear simply support (external edge of the timber member, see Figure 17c).

#### 6.3. Friction Coefficient

_{timber}is progressively modified in the range from 0 and 0.8.

_{timber}for TTC joints with an imposed shear-compression stress regime (α < 0) were found to have negligible effects on the collected force-slip contributions, given that:

_{timber}. Regarding the force contribution F

_{timber}sustained by the timber members, see Figure 19b, this is estimated as a limited part of the total F, thus agreeing with Equations (6) and (7).

_{timber}= 0) was extended to several TTC joints under shar-compressive stresses. In Figure 20, comparative numerical results are proposed for the S#1 specimens as a function of μ

_{timber}. The parametric numerical results were post-processed from the collected force-slip curves according to Figure 8. As far as the relevant mechanical parameters are taken into account for them, their trend with μ

_{timber}can be investigated.

- ultimate total force F
_{max}for a TTC given joint, as a function of μ_{timber}; - shear force contribution F
_{screw}taken up by the STSs only, as a function of μ_{timber}. - and serviceability stiffness K
_{ser}(calculated in accordance with Equation (4)), as a function of μ_{timber}.

_{timber}= 0 are set as a reference condition for Δ calculations.

_{max}of S#1 joints in Figure 20a) for example, it is possible to see that F

_{max}progressively increases as far as μ

_{timber}increases, for a given α. A relatively regular trend can be observed for the collected FE dots, as also suggested by the linear fitting curves. At the same time, however, it is possible to see that the increase of is indirectly proportional to α, thus maximum benefits deriving from additional frictional phenomena can be expected for STSs with limited inclination α only (α = 15°, in this study).

_{timber}≈ 0.25–0.5), moreover, it is interesting to notice that the predicted F

_{max}values show a mean + 20–30% variation for STSs joints under shear-compression loads. This result from Figure 20a is thus a further confirmation of the relatively high sensitivity of ultimate resistance predictions for the examined TTC joints, under a standard PO setup.

_{screw}= 100% coincides with F

_{max}for the whole TTC specimen when μ

_{timber}= 0. Otherwise, the progressive increase of frictional effects with μ

_{timber}lead to a mostly linear increase of the total resistance F

_{max}in Figure 20a. As a result of such a kind of phenomenon, the load-bearing contribution of the STSs (in percentage terms) progressively decreases with μ

_{timber}, with variations that can be expected up to −20% compared to frictionless TTC joints (Figure 20b).

_{ser}is taken into account in Figure 20c, an opposite trend can be noticed for the collected FE results, as a function of and μ

_{timber}. This is in line with the general expectations and past literature efforts on the topic, where the serviceability stiffness of a given TTC joint reasonably increases when increasing the inclination α of the STSs. As a further remark for the FE results in Figure 20c, it can be noticed a relatively scattered variation of K

_{ser}estimates with μ

_{timber}, as far as α increases (i.e., Figure 14).

## 7. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 1.**Available tools for the mechanical characterization and analysis of design parameters of timber-to-timber composite joints.

**Figure 2.**Conventional experimental procedure for the mechanical characterization of TTC joints with inclined STSs.

**Figure 3.**TTC joints with inclined STSs under a standard PO setup. (

**a**)–(

**c**): selected configurations and (

**d**) nominal dimensions (in mm).

**Figure 4.**Reference FE numerical model for TTC joints with inclined STSs under a standard PO setup (S#1, α = −15°).

**Figure 5.**Example of (

**a**) typical FE assembly (1/4th the S#1 geometry, with = −15°) and (

**b**) detail of the STS region (ABAQUS/Explicit, hidden mesh pattern). Reproduced from [21] with permission from Elsevier

^{®}, Copyright license number 4895820420991, August 2020.

**Figure 6.**FE modelling TTC joints with inclined STSs under a standard PO setup. In evidence, the mechanical contact interactions for: (

**a**) timber-to-timber, (

**b**) base support and (

**c**,

**d**) STS details (hidden mesh pattern), with (

**e**) traction-separation law.

**Figure 7.**Monitored force contributions for the mechanical analysis and characterization of TTC joints with inclined STSs under a standard PO setup.

**Figure 8.**Force-slip curves of selected TTC joints with inclined STSs under a standard PO setup (ABAQUS/Explicit, S#1, α = var) and corresponding experimental results (data from [6]).

**Figure 9.**Typical damage propagation in the selected TTC joints with inclined STSs, under a standard PO setup (ABAQUS/Explicit). Example for the S#1 specimen with α = −15°, with evidence of: (

**a**) local damage of timber (stress values in Pa), (

**b**) yielding of screws (stress values in Pa) and (

**c**) CZM damage parameter. Reproduced from [21] with permission from Elsevier

^{®}, Copyright license number 4895820420991, August 2020.

**Figure 10.**Comparison of numerical (ABAQUS/Explicit) and experimental [6] maximum force estimates for TTC joints with inclined STSs: (

**a**) S#1, (

**b**) S#2, (

**c**) S#3 and (

**d**) S#4 joints.

**Figure 11.**Percentage scatter of maximum force values for TTC joints with inclined STSs (Equation (5)), as obtained from the FE numerical analyses (ABAQUS/Explicit) and by the experiments in [6].

**Figure 14.**Comparison of numerical (ABAQUS/Explicit) and analytical [6] serviceability stiffness estimates for TTC joints with inclined STSs: (

**a**) S#1-to-S#3 (average) or (

**b**) S#4 joints.

**Figure 15.**Percentage scatter of stiffness values for TTC joints with inclined STSs (Equation (5)), as obtained from the FE numerical analyses (ABAQUS/Explicit) and by literature [6]: (

**a**) experimental data, (

**b**) single stiffness analytical model, (

**c**) double stiffness analytical model.

**Figure 16.**Analysis of mechanical interaction and CZM effects on the PO numerical response of TTC joints with inclined STSs (S#1). Vertical (F) and horizontal (H) reaction forces as a function of slip, for (

**a**,

**b**) α= −15° and (

**c**,

**d**) α= 45° (ABAQUS/Explicit).

**Figure 18.**Analysis of boundary effects on the PO numerical response of TTC joints with inclined STSs. In evidence, the (

**a**) vertical and (

**b**) horizontal base reaction force, as a function of the measured slip for a selected TTC joint (ABAQUS/Explicit).

**Figure 19.**Analysis of static friction effects on the PO numerical response of TTC joints with inclined STSs. In evidence, the (

**a**) vertical and (

**b**) horizontal base reaction force, as a function of the measured slip (ABAQUS/Explicit).

**Figure 20.**Percentage variation (Equation (4)) of performance indicators for TTC joints with inclined STSs, as a function of the timber-to-timber friction coefficient (S#1 joints under shear-compression): (

**a**) maximum force; (

**b**) load-bearing contribution of the STSs and (

**c**) serviceability stiffness (ABAQUS/Explicit).

Elastic Moduli(Mean Values, in MPa) | Parallel to the grain E_{┴} | 11600 |

Perpendicular to the grain E_{║} | 390 | |

Radial E | 390 | |

Longitudinal shear modulus G | 690 | |

Resistance(Mean Values, in MPa) | Compression parallel to the grain f_{c,0} | 37.5 |

Compression perpendicular to the grain f_{c,90} | 3.57 | |

Shear f_{v} | 3.85 | |

Failure(Mean Values) | Maximum stress f_{c,90} (MPa) | 5 |

Damage evolution | Linear | |

Failure displacement δ_{u} (mm) | 4 |

**Table 2.**Input mechanical properties for the soft layer and for the CZM contact interaction (ABAQUS/Explicit).

Soft Layer | Elastic moduli (mean values) | Longitudinal (screw axis) | MPa | 370 |

Tangential | MPa | 370 | ||

Shear | MPa | 720 | ||

Radial | MPa | 50 | ||

Failure | Maximum shear (MPa) | MPa | 5 | |

Damage evolution | - | Linear | ||

Failure displacement δ_{u} (mm) | Mm | 4 | ||

CZM Contact Interaction | Resistance (mean values) | Longitudinal | MPa | 37.55 |

Transverse | MPa | 3.85 | ||

Shear | MPa | 3.85 | ||

Rolling shear | MPa | 3.5 |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

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**MDPI and ACS Style**

Bedon, C.; Sciomenta, M.; Fragiacomo, M. Mechanical Characterization of Timber-to-Timber Composite (TTC) Joints with Self-Tapping Screws in a Standard Push-Out Setup. *Appl. Sci.* **2020**, *10*, 6534.
https://doi.org/10.3390/app10186534

**AMA Style**

Bedon C, Sciomenta M, Fragiacomo M. Mechanical Characterization of Timber-to-Timber Composite (TTC) Joints with Self-Tapping Screws in a Standard Push-Out Setup. *Applied Sciences*. 2020; 10(18):6534.
https://doi.org/10.3390/app10186534

**Chicago/Turabian Style**

Bedon, Chiara, Martina Sciomenta, and Massimo Fragiacomo. 2020. "Mechanical Characterization of Timber-to-Timber Composite (TTC) Joints with Self-Tapping Screws in a Standard Push-Out Setup" *Applied Sciences* 10, no. 18: 6534.
https://doi.org/10.3390/app10186534