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Parallel strand lumber (PSL) is an attractive structural wood composite which may have prospective use in building constructions. Conducting nonlinear analysis for the bending of PSL beams is a critical step in the determination of ultimate strength and deflection of them, which is an essential requirement of the building design philosophy based on probability of ultimate state. For the purposes of this article, an inelastic theoretical model regarding the load-carrying capacity of the PSL bending component has been developed. Based on the uniaxial loading tests, the stress-strain behaviors of PSL composite in the grain direction were measured. 4-point bending experiments were also performed in this study to investigate the failure mechanism of the PSL components. The results show that the tensile stress-strain relationship of PSL materials in the grain direction remains linear until breaking, while the compressive stress-strain relationship exhibits nonlinear characteristics once the compressive stress exceeds the proportional limit, which can be expressed by a quadratic polynomial. The failure mode of the PSL beam can be summarized that the fibres in the top of the broken section were buckling and those in the bottom of the section were broken when failure occurred. Significant nonlinear behavior was exhibited based on the load-deflection curves of the PSL beams. To predict the nonlinear bending performance of the PSL beams, a theoretical model that could consider the nonlinear stress-strain relations of PSL and predict the damage modes of the PSL beams was developed. Well agreements can be observed between the results of calculations and experiments.

PSL is a wood-based composite material with outstanding mechanical properties for construction. It is fabricated by gluing raw wood strands together along the grain direction under high pressure and microwave heat, which are often a by-product during the plywood manufacturing process [

It is a vital work for safeguard design to precisely evaluate the strength and deflection of the structural members in the condition of strength limit state. However, the structure and mechanical properties of PSL have a strong orientation. As a matter of fact, PSL is a natural oriented fiber-reinforced composite. The approach of strength theory and mechanical model proposed by classical theories to analyze the behaviors of the component made of homogeneous or isotropic materials cannot be suitable to conduct the inelastic analysis for PSL structural members. Additionally, linear principles are currently employed in design code for wood buildings to predict the load-carrying capacity and deflection in the strength limit state as the nonlinear behaviors of wood or wood composites have not been well modelled [

Some analytical or numerical models have been proposed to evaluate the nonlinear performances of wood or wood composite structure members. Naghipour et al. [

In this paper, considering nonlinear behaviors of material, a theoretical model to predict the bending bearing capacity of PSL beams was developed and the ultimate deformation of the beam in midspan was also given by assuming a fictitious plastic hinge at the critical cross section. Firstly, mathematical formulas for describing the stress-strain relationships of PSL composite along the grain were proposed based on tests. Secondly, to investigate the failure mode and the failure mechanism of PSL beams, four-point bending tests were performed. A novel model, which takes the nonlinear stress-strain relationship of PSL composite into account, to predict the responses during all service periods from loading to failure for PSL bending members was developed at last. Well agreements can be observed between the results of calculations and experiments.

The stress-strain curve was obtained by experiments. Test materials were offered by FPInnovations, Vancouver, Canada. Tests were carried out in the laboratory of FPInnovations, Vancouver, Canada. Compressive test along the grain direction was referred to ASTM D143-09 [

Dimension of tensile specimens (unit: mm).

The curve of uniaxial stress-strain relationships of PSL composites along the grain can be divided into three stages, i.e., first, the linear elasticity in tension, the linear elasticity in compression, and the nonlinear in compression, as shown in Figure

Uniaxial stress-strain relationships.

Considering the continuum and compatible conditions of the stress-strain curves, the coefficients can be expressed as follows:

According to equations (

Figure

Mechanical parameters of the PSL specimen.

Parameters | Proportional limit | Ultimate limit | Modulus (MPa) | ||
---|---|---|---|---|---|

Strain ( | Stress (MPa) | Strain ( | Stress (MPa) | ||

Tension | — | — | 1200 | 80.0 | 1650 |

Compression | 2800 | 55.0 | 5700 | 62.5 |

The methodology for analyzing the nonlinear bending of the PSL beam in this research is based on Euler’s beam theory and Huang’s method [

Diagrams of the stress and strain over the moment section. (a) stress diagram and (b) strain diagram.

Therefore, to exactly calculate the actual nonlinear stress distribution by using equation (

Therefore, the stress distribution with respect to the coordinate

Also, taking the geometric relations of the zones over the section into account and referring to Figure

The moment at the section can be calculated by

According to the plane assumption over the bending section cut, the strain at any point with respect to the coordinate,

Finally, the function of the moment yielded by compressive force in the plastic zone can be expressed as

In the case of critical condition, on which the stress on the top surface of the beam is just reached the proportional limit,

Deriving

Let

Let the plastic moment be zero, and substituting for

Referring to Figure

Deflection analysis model.

The boundary and continuum conditions can be expressed as

From equations (

Replacing _{m} in equation (

According to Huang’s method [

In order to validate the analytical model developed above, load-carrying capacities and deformations of three PSL beams were analyzed by the model above and by experiments. 4-point bending test was adopted to investigate the bending performances of the PSL beam. Test method was referred to ASTM D198-09 [

4-point bending test.

Damage mode of the PSL beam.

Comparison of the load-deflection curves of PSL beams obtained by test and analysis.

Based on the theories of mechanics of composite, PSL was treated as a transversely isotropic composite, and this paper aimed at studying the stress-strain relationships, the failure mechanism, and the nonlinear flexural of PSL beams through the experiments and theoretical analysis. The main contents and results can be concluded as follows:

The uniaxial tensile and compressive properties in parallel to grain direction were studied by experiments. Failure mechanisms and the stress-strain relationship of each stress state were investigated. It was found that the tensile failure of PSL in parallel to grain direction presents the progressive process and higher strength, and the tensile stress-strain relationship exhibits linear behavior. The compressive strength of the material shows lower strength and brittle behavior, and then the compressive stress-strain relationship exhibits nonlinear characteristics.

4-point bending tests for PSL beams were carried out to investigate the flexural behaviors and the damage mechanism of them. 3 stages of bending failure of PSL beams under pure bending loading can be observed. The first is the perfect elastic bending stage, and the beams were in the elastic state when the loading is less than the proportional limit. The second is the nonlinear hardening stage, i.e., when the loading exceeded the proportional limit, part of fibres in the compressive zone in the critical section came into a nonlinear state, the inelastic compressive zone was gradually expanding towards the neutral axis, and the stiffness of PSL beams was continuously degraded with the augment of loading. The last one is the failure stage, i.e., when the depth of the inelastic compressive zone reached the ultimate value, the fibres in the outer surface of the compressive zone were bulking and those in the outer surface of the tensile zone were broken. Hence, the PSL beam was failed.

A theoretical model to evaluate the loading capacity and the deflection of PSL beams was proposed based on experimental studies and theoretical analysis. Well agreements were achieved between the results obtained by using the proposed model and those obtained by experiments.

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

The authors declare that there are no conflicts of interest regarding the publication of this paper.

The research was supported by the National Science Fund of China (no. 51978338), the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD), and the Doctorate Fellowship Foundation of Nanjing Forestry University.