Finite Element Model for Axial Stiffness of Metal-Plate-Connected Tension Splice Wood Truss Joint

Jose M. Cabrero

Assistant Professor University of Navarra, Department of Structural Analysis and Design, School of Architecture

Navarra, Spain Kifle G. Gebremedhin

Professor Department of Biological and Environmental Engineering, Cornell University

Ithaca, NY, 14853, U.S.A.

Abstract

A finite element model that predicts stiffness for metal-plate-connected (MPC) tension splice joint of wood trusses is developed. The commercial software ABAQUS was used in developing the model. The model is two-dimensional, and the properties of the wood and metal plate are assumed to be linearly isotropic. Contacts between wood and teeth of the metal plate are modeled with finite sliding formulation. The contact elements model the slip behavior that occurs at the wood-tooth interface. The tangential contact properties are set to a specified coefficient of friction while the normal contact properties are set to a “hard” contact formulation, allowing for a possible separation of the nodes after contact is achieved. Contact elements represent the stiffness of the interface, and stiffness is lost once the contact elements are disengaged due to tooth withdrawal. Model predictions are validated against experimentally measured stiffness values obtained in the literature. The data covers two wood species and three levels of modulus of elasticity (MOE). The model predicts within 5 percent of the experimentally measured stiffness values.

1. Introduction

Conventional methods of design of metal-plate connected (MPC) wood truss joints assume that connections between the metal-plate connector and wood are either pinned or rigid. In reality, these joints exhibit a semi- rigid behavior, i.e., not purely pinned or rigid but somewhere in-between [1,2,3]. Therefore, the challenge is to determine the stiffness of these joints so that their semi rigidity could be accounted for in design of MPC wood trusses. Modeling the behaviour of the connector in the truss member is complicated by the composite nature of the metal and wood and the configuration of the system (a row of teeth embedded in wood and a gap existing between the wood elements). The metal plate connection is the lease understood in truss design.

The simplified approach of truss design is to assume truss joints to be pin connected, which means no moment is transferred between adjacent members. This assumption violates the continuity of chord members at the joints. To account for the indeterminacy of a truss when analyzed as pin-joined approximations, the Truss Plate Institute (TPI) has provided empirically-based Q-factors to modify the bending moment or the buckling length of truss members [4]. The Q-factors were developed based upon many years of experience of design and extensive simulated investigation of wood trusses of standard configurations using the Purdue Plane Structures Analyzer (PPSA) [5]. The PPSA is a matrix method of structural analysis that determines the axial forces and bending moments of truss-frame models. The

tabulated Q-factors provided by TPI do not cover all ranges and combinations of loading conditions, spans, and geometry. Therefore, theoretical models that provide realistic treatment of joints are needed so that forces and moments can be predicted with greater accuracy. Because of the wide application of MPC wood trusses in commercial, industrial, residential and agricultural buildings, even a reasonably small improvement in characterization of truss joints may result in significant cost savings.

The main focus of this research is to develop a finite element model for the wood-tooth interface of MPC tension-splice joint based on fundamental principles of contact mechanics that, apart from basic material properties, does not require empirical corrections. Linear elastic finite elements represent the metal plate, teeth, and wood; and contact elements are virtual (imaginary) spring elements that transfer compressive and frictional forces between the wood and the teeth of the metal plate as the joint is externally loaded. The commercial software package ABQUS is used to develop the contact elements. Modeling the interface using contact elements can have wide engineering applications such as in modeling the bondage between steel and concrete in reinforced concrete structures, the transfer of frictional forces between piles and soil in pile foundations, and modeling rotational stiffness of MPC wood joints.

1.1 Objectives

The specific objectives of this study were:

1. To develop a finite element model for the wood-tooth interface of metal-plate connected tension-splice joint of wood trusses using linear contact elements.

2. To predict the stiffness of a tension-splice joint.

3. To validate the predicted stiffness against measured values.

2. Literature Review

A thorough literature review of experimental and theoretical studies conducted on MPC wood-truss joints are reported in Amanuel et al. [1]. The reader is referred to that study for extensive literatura review.

3. Model Formulation

A bi-dimensional finite element (FE) model that predicts stiffness of MPC tension-splice joints is developed using the ABAQUS software.

3.1 Assumptions

1. Since the main deformation arises from the axial force in the x-direction, the deformation along the z-direction (perpendicular to the direction of the axial force) is assumed to be zero. Because of this assumption, the model is reduced to a plane strain model.

2. The behavior of the joint is governed by teeth-wood contacts and the resulting deformation of the teeth.

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3.6 Contact

Load transfer between teeth and wood occurs at the contact interfaces. Contact interface is defined by two surfaces, one for the wood and the other for the metal plate. The required contact elements are internally defined by the software.

ABAQUS requires that one of the surfaces to be defined as “master” and the other surface as “slave”. The specification of the surfaces is critical because of the way the surface interactions are discretized. For each node on the slave surface, ABAQUS attempts to find the closest point on the master surface of the contact pair where the normal of the master surface passes through the node on the slave surface. The interaction is then discretized between the point on the master surface and the slave node. In the model, the surface corresponding to the metal plate is defined as master, and the wood is defined as the slave (see Figure 3 for definition of contact surfaces).

Figure 3. Definition for contact surfaces.

A “hard” contact formulation is employed for the properties of the contact elements. This relationship minimizes the penetration of slave nodes into the master surface and does not allow transfer of tensile stress across the interface. The classical Lagrange multiplier method was applied to enforce no penetration between the surfaces. When the surfaces are in contact, any contact pressure can be transmitted between them. When the contact pressure reduces to zero, the surfaces separate. Once contact is achieved, the related nodes are allowed to separate again.

In addition to pressing on the wood, the teeth may also slip and transmit tangential forces. A basic isotropic Coulomb friction model with a coefficient of friction equal to 0.5 was used. In this model, for the sake of simplicity, the same static and kinetic friction coefficients were assumed. No shear limit is indicated, therefore, any tangential force could be transferred.

A finite sliding model formulation is applied. This formulation allows the defined contact surfaces to separate and slide with finite amplitude and arbitrary rotation.

As mentioned previously, the hole in the wood is made a little bit smaller (by 0.01 mm) than the thickness of the idealized tooth. This assures an initial contact between wood and tooth. The initial contact is adjusted automatically by the finite element program by “moving” the over passing nodes to the exact contact position. This technique assures the necessary initial contact.

4. Results and Discussion

The predicted results were compared against test results of Riley and Gebremedhin [6]. The test results were based on two wood species (Southern Yellow Pine and Spruce Pine Fir). Riley and Gebremedhin [6] experimentally obtained the modulus of elasticity of these species

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es

of E,

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