Experimental and numerical study on the withdrawal behaviour of lag screws on wood side-grain

. In wood connections using lag screws as mechanical fasteners, the tension force transfer mechanisms occur through the interaction between the screw threads and the wood surface. It is necessary to understand the screw withdrawal behaviour in order to make a simple but representative interaction model instead of modeling the geometry of the screw threads. This study aims to evaluate experimentally and numerically the withdrawal failure modes, stiffnesses, and capacities of lag screws on wood side-grain. The experiment is conducted on the withdrawal of lag screws with different diameters and penetration lengths in Meranti wood cubes. The numerical analysis is carried out using ABAQUS finite element program and compared with the experimental results. Both experimental test and numerical analysis results show that the failure of all specimens occurred in the wood around the hole, not due to the slip between the lag screw and the wood's surface, which validates the proposed interaction model between the screw and the wood ’s surfaces. The wood's effective material stiffness and strength in numerical models are obtained by matching the load-displacement curves with the experiment results. The effective F y value range is between 18.5 MPa - 24 MPa, while the effective E value range is between 115 MPa - 680 MPa.


Introduction
Wood and engineered wood are already known by society as one construction material.In its use as construction tools, using wood and engineered wood in the structural application involves a connector.The connection between a block of wood and other blocks of wood needs to be reviewed and designed as good as possible, it's because, generally, the failure of wood construction happens at the connection.Connectors could be mechanical fasteners such as nails, spikes, screws, bolts, lag screws, drift pins, staples, and metal connectors of various types [1] .In these mechanical connectors, there are two directions of force against the fastener; withdrawal and lateral, and also the combination of those two directions of force.The connector with withdrawal behavior is a connector that is either weighted axially or weighted by a force where the direction is the same as the direction of the fastener.On the other hand, a connector with lateral behavior is a connector that is weighted by a force where the direction is perpendicular to the direction of the fastener.One of the mechanical fasteners that are often used is the lag screw.Using a lag screw, the force transfer mechanism on the connector happens through the geometry of the screw thread and the wood's surface.
The design parameter of a lag screw as a connector on wood material was obtained by experimental and numerical means.The design parameter is represented by withdrawal load and displacement.The maximum direct withdrawal load of lag screws from the side grain of the wood may be computed as [2] *Corresponding author: bryanyehezkiel11@gmail.com where W is the withdrawal load per unit length (N/mm), G is the specific gravity of the wood, D is the shank diameter (mm).The withdrawal load value must be multiplied by the correction factors that affect the connector capacity.Those factors are duration, water density, temperature, and wood end-grain factors.As a result, the maximum direct withdrawal load of lag screws from the side grain of wood after corrected by the correction factors may be computed as [2]  =      2       (2)   where P is maximum withdrawal load (N), W is withdrawal load per unit length (N/mm), CD is duration factor, CM is water density factor, Ct is temperature factor, Ceg is wood end-grain factor, and pt is length (mm) of penetration of threaded part.Numerical modelling on the connector is needed to obtain the design parameter numerically.The geometrical modelling of screw threads is inefficient to be done because it requires a lot of review points on the screw threads.In that case, the interaction modelling between the screw thread and the wood's surface, also known as the interface element, is needed.This research aims to numerically model the withdrawal behavior connector that is representative of actual conditions and evaluate the value of withdrawal load along with the displacement in experiments and numerical models.

Experimental test
The experimental test is done with Universal Testing Machine (UTM).The wood that is used in the experiment is Red Meranti (Shorea spp.).Water content and specific gravity were tested on the timbers, with an average water content of 14.9% and an average specific gravity of 0.707.Timbers are then cut into test specimens with dimensions of 50mm x 50mm x 50mm.The experiment is done with a steel tool that is used to hold the wood specimen to move in the vertical direction and to hold the head of the lag screw so that the lag screw could move according to the speed of the test on the UTM.The experimental test schematic is shown in Fig. 1 with the UTM holding the steel tool on point (1) and (2).The experimental test was carried out with variations in the dimensions of the lag screw and penetration length.Preliminary calculations are carried out according to the equations and formulas in SNI 7973:2013 [2] .The calculation is done by assuming the value of the duration factor,  to be 0.8.The resistance factor, z is taken as 1 for calculation (for design, z = 0.65).Water content factor, CM=1 because the timbers are dry.Temperature factor, Ct assumed to use the lower bound = 0.5.The calculations are done for three variations of diameter, with each diameter having two variations of penetration length.The estimated maximum withdrawal load is shown in Table 1.
Test for determining the bending yield moment of the lag screw was carried out with UTM referring to ASTM F1575-03 [3] .The test is done on three samples of lag screws with a diameter of 9.53 mm (D10).The bending yield moment values of the lag screw were taken from the average of three samples and are shown in Table 2.The bending yield moment of lag screws with a diameter of 7.94 mm (D8) dan 6.35 mm (D6) is assumed to be the same as the 9.53 diameter lag screw (D10).Based on the test, the average bending yield moment of the lag screws used in the calculations and modeling is 899.71MPa.The withdrawal test refers to ASTM D1037-06 [4] .UTM gives a tensile force to the lag screw embedded in the wood specimen.Two LVDT (Linear Variable Differential Transformer) sensors are used to measure displacement.LVDT sensor on channel-1 measures the displacement of the test specimen against UTM, while the LVDT sensor on channel-2 calculates the vertical displacement of the lag screws against the wood surface.The test speed is set at 1.0 mm/min.The test is discontinued when failure on the connection occurs, indicated by a drastic reduction in the load curve.UTM will record the withdrawal load on the connection, while LVDT sensors will record the displacement that occurs during the test.Based on the test data, load-displacement curves are made for the six specimens.The withdrawal test can be seen in Fig. 2.

Numerical modelling and analysis
The finite element method is a numerical analysis for obtaining approximate solutions to a wide variety of engineering problems [5] .Finite elements are small parts of the actual structure.The basic concept of the finite element method is to discretize the elements or state the entire structural system into a series of finite elements.
The modelling of the withdrawal load connection uses two kinds of materials, red Meranti wood, and steel material, on the lag screw.Modeling is done by entering the parameters of wood as an isotropic material.Parameters of wood as an isotropic material use elastic modulus, Poisson ratio, and compressive strength in a tangential direction (perpendicular to the grain) taken from secondary data from previous research [6] .The wood model's parameters are shown in Table 3, and the material stress-strain curve of the wood model is shown in Fig. 3.

Plastic region
Fy Fc┴ (MPa) 7.17 Wood plasticity is defined in ABAQUS by including very small values of stress and strain after defining the tangential compressive strength as Fy.The stress and strain values are defined as very small because the stress on the wood material will drop drastically after the connection fails.Connection behavior in the plastic region will not be reviewed in the modeling.In the connection model, interlocking between the wood and the screw is assumed to be perfect interlocking.In the ABAQUS modeling, the interface between the wood and the screw is defined as a tie constraint, which attaches two separate surfaces so that there is no movement between the attached surfaces.The hole's surface in the wood is selected as the master, and the lag screw's surface is selected as the slave.Fig. 5 shows the parts in the model as master and slave.
The part of the wood retained by the steel tool cannot be deformed so that the part on the surface of the retained wood is given a boundary condition for deformation on the third axis that is equal to zero, or it cannot move in any direction.The withdrawal load on the model is made by giving a boundary condition in the form of a maximum displacement of 2 mm in the direction of the global Z axis on the top surface of the lag screw.The boundary conditions and loading on the model are shown in Fig. 6.The geometry of the model is made according to the conditions in the laboratory, and then the model is meshed.Meshing is the step of dividing a structural system into finite elements.Meshing is done on wood parts and the lag screw.The element shape in Mesh Controls is hex-dominated, where discretization prioritizes hexahedral shape.The mesh size in the wood is 5 mm in the whole wood and 1 mm in the hole.Moreover, the mesh size of the lag screw section is 1 mm along the length of the lag screw.The meshing results on the model are shown in Fig. 7. Thus, the model is run to obtain a load-displacement curve that occurs in the numerical model.

Interface element validation
In the experimental test results, test specimens were cut half.The test specimens after the withdrawal test can be seen in Fig. 8.
It is seen that the wood interacting with the lag screw deforms and the wood grain is lifted.This proves that the failure of all specimens occurred in the wood around the hole, not due to the slip between the lag screw and the wood's surface.Thus, the assumption of perfect interlocking between the wood and the screw in the numerical model is appropriate.

Failure modes
In the experimental test, connection failure occurred in the wood around the hole, not material yielding in steel.In numerical analysis, PEEQ (Equivalent Plastic Strain) contours at maximum withdrawal load can be seen in Fig. 9.
Fig. 9 shows that deformation occurs on the wood at the maximum withdrawal load in all models.Hence, it can be concluded that failure occurs in the wood around the hole, not material yielding in the lag screw.This indicates that the variety of failures in experimental tests and numerical analysis are similar: the failures in wood.

Load-displacement curve evaluation
The load-displacement curve was obtained from data in the UTM and LVDT sensors in the experimental tests.The load-displacement curve obtained from the results of experimental tests and numerical analysis is compared to evaluate a numerical model that is representative of the actual situation.A comparison of the load-displacement curves between the experimental test and numerical modeling was carried out, as well as the connection capacity against the calculation according to SNI 7973:2013 [2] .Fig. 10 shows a comparison of the load-displacement curves of the specimens.
From the load-displacement curve, the peak point on the curve can be taken as the connection capacity.Connection capacity is the maximum load the connection can hold before the connection fails.The connection capacity values for each configuration are shown in Table 4.The results show that the connection capacity in the experimental test is much greater than the connection capacity in the numerical analysis and preliminary calculations based on SNI 7973:2013 [2] .This result represents that the equation from the code is sufficiently conservative.

Effective Fy and effective E
The connection capacity value in all modeling configurations is much smaller than the connection capacity value in the experiment.The wood's effective material stiffness and strength in numerical models are obtained by matching the load-displacement curves with the experiment results.The effective Fy and effective E are values of the wood model parameters in which a connection capacity value is close to the value produced by the experimental test.The effective Fy and E values for each configuration of the numerical model are shown in Table 5.The effective Fy value range is between 18.5 MPa -24 MPa, while the effective E value range is between 115 MPa -680 MPa.

Conclusion
Based on the analysis, it can be concluded that perfect interlocking as an interaction model between screw and wood surfaces can be used, as both numerical and experimental results are in line.From both experimental test and numerical analysis results, the failure of all specimens occurred in the wood around the hole, not due to the slip between the lag screw and the wood's surface.
The withdrawal equation based on the current code is sufficiently conservative as the connection capacity in the experimental test is much greater than that in the numerical analysis and preliminary calculations based on the code, SNI 7973:2013.The wood's effective material stiffness and strength in numerical models are obtained by matching the load-displacement curves with the experiment results.The effective Fy value range is between 18.5 MPa -24 MPa, while the effective E value range is between 115 MPa -680 MPa.
The experimental test facilities and software license are provided by the Department of Civil Engineering, Parahyangan Catholic University (UNPAR).

Fig. 3 .
Fig. 3. Stress-strain curve for Red Meranti wood model.The steel material of the lag screw is defined based on the bending yield moment test that was previously carried out.The modulus of elasticity for steel is 200000 MPa and the Poisson's ratio is 0.3.The lag screw parameters used in the modeling are taken based on the true stress-strain curve in Fig. 4.

Fig. 6 .
Fig. 6.Boundary conditions and loading on the model.
the effective Fy and E values produces a load-displacement curve for each model, as shown in Fig. 11.The load-displacement curves in the elastic region of the numerical models are sufficiently representative of the results of experimental tests.Fig 11.Load-displacement curve with calibrated E and Fy: (a) D6P10; (b) D6P20; (c) D8P15; (d) D8P26; (e) D10P15; (f) D10P28.

Table 1 .
Estimated maximum withdrawal load.

Table 3 .
Wood parameters in modeling.

Table 5 .
Effective Fy and E value.