**Analytical method with iteration technique (AMIT) and finite element method (FEM) for predicting the flexural performance of glulam wood/PVC composite hollow member**,”

*BioResources*19(3), 5197-5226.

#### Abstract

The flexural performance of a glulam wood/PVC composite (GWPVC) hollow member, which was assembled from four elements with WPVC composite hollow sections to create a double I-section, was studied using two methods: the analytical method with iteration technique (AMIT) and the finite element method (FEM). Experiments verified the predictions from AMIT and simulations from FEM to determine the most suitable method for the parametric studies. This investigation explored the variations in slenderness ratio and the flange and web thickness to enhance and study their impact on flexural performance. In parametric studies, equal cross-sectional areas were used to facilitate comparisons and maintain production costs. The importance of bond strength at the contact surfaces in assembling a GWPVC hollow member led to bonding tests and confirmed sufficient strength at contact surfaces. In four-point bending tests, the GWPVC hollow member exhibited a brittle mode with flexural tensile failure without delamination. The initial MOE, MOR, and maximum deflection values were 5,140 MPa, 29.8 MPa, and 47.8 mm, respectively. The parametric study employs AMIT to investigate flexural performance and reveals that varying the slenderness ratio affected the initial stiffness, maximum deflection, and ultimate load. Flexural performance can be improved by making minor adjustments.

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#### Full Article

**Analytical Method with Iteration Technique (AMIT) and Finite Element Method (FEM) for Predicting the Flexural Performance of Glulam Wood/PVC Composite Hollow Member**

Phatthana Aunyingcharoen,^{a} Tawich Pulngern,^{b,}* Vichai Rosarpitak,^{c} and

Narongrit Sombatsompop ^{d}

The flexural performance of a glulam wood/PVC composite (GWPVC) hollow member, which was assembled from four elements with WPVC composite hollow sections to create a double I-section, was studied using two methods: the analytical method with iteration technique (AMIT) and the finite element method (FEM). Experiments verified the predictions from AMIT and simulations from FEM to determine the most suitable method for the parametric studies. This investigation explored the variations in slenderness ratio and the flange and web thickness to enhance and study their impact on flexural performance. In parametric studies, equal cross-sectional areas were used to facilitate comparisons and maintain production costs. The importance of bond strength at the contact surfaces in assembling a GWPVC hollow member led to bonding tests and confirmed sufficient strength at contact surfaces. In four-point bending tests, the GWPVC hollow member exhibited a brittle mode with flexural tensile failure without delamination. The initial MOE, MOR, and maximum deflection values were 5,140 MPa, 29.8 MPa, and 47.8 mm, respectively. The parametric study employs AMIT to investigate flexural performance and reveals that varying the slenderness ratio affected the initial stiffness, maximum deflection, and ultimate load. Flexural performance can be improved by making minor adjustments.

*DOI: 10.15376/biores.19.3.5197-5226*

*Keywords: Analytical method; Ethyl cyanoacrylate; Finite element method; Glulam WPVC composite; Iteration technique; WPVC composite*

*Contact information: a: Ph.D. candidate, Department of Civil Engineering, Faculty of Engineering,
King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit, Bangmod, Thungkru, Bangkok, 10140, Thailand; b: Associate Professor, Department of Civil Engineering, Faculty of Engineering, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit, Bangmod, Thungkru, Bangkok, 10140, Thailand; c: V.P. Wood Co., Ltd., 72/1 Moo. 4, Suksawat 41, Banphueng, Phra Pradaeng, Samut Prakan, 10130, Thailand; d: Polymer PROcessing and Flow (P-PROF) Research Group, Materials Technology Programme, School of Energy, Environment and Materials, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit, Bangmod, Thungkru, Bangkok, 10140, Thailand;*

**Corresponding author: Tawich.pul@kmutt.ac.th*

**GRAPHICAL ABSTRACT**

INTRODUCTION

Timber is a natural material that is widely used due to its aesthetic appeal and impressive strength. It is used in various applications, including buildings, decorations, and furniture. Different processing techniques, such as cutting, sanding, chemical treatment, or thermal modification (Pulngern *et al.* 2020), are employed to enhance its usability.

In Thailand, the growing demand for timber in structural and decorative applications has resulted in rising prices, a shortage of trees, and a continual reduction in their numbers. Therefore, conserving the remaining trees is necessary. One alternative to timber is a wood-plastic composite (WPC). Such composites offer advantages, such as a wood-like appearance, lightweight nature, resistance to swelling, non-flammability, low maintenance requirements, and protection against moisture and termite damage (Chetanachan *et al.* 2001). WPC primarily consists of plastic and wood sawdust; thus, producing WPC increases the value of wood sawdust by recycling it as a raw material instead of incinerating it. Furthermore, several types of plastic can be used in WPC production (Jian *et al.* 2022). Recycled plastics have been investigated for their potential as WPC matrix materials (Bhaskar* et al.* 2012; Luo and Cheng 2021). Therefore, the use of WPC may increase due to the current growing trend of environmental conservation.

Typically, WPC is produced using polyethylene (PE) or polypropylene (PP); both are polyolefins. While polyolefins remain widely used as matrix materials, the superior mechanical properties of polyvinyl chloride (PVC) make it an outstanding option for the matrix of WPC. The confirmation of these mechanical properties is supported by previous research on WPC made from PVC (WPVC composite). This research has revealed higher tensile, compressive, and flexural strength in WPVC composites compared to WPC produced from PE and PP (Tunsakul 2006). However, another study has found that differences in the type or quantity of wood sawdust and additives may influence outcomes (Ratanawilai and Taneerat 2018). Therefore, using PVC as the matrix material offers improved durability and enhanced strength, making it a popular choice for producing WPC in Thailand. Moreover, WPVC composites are commonly used in applications such as Anderson windows. As a result, WPVC composite has become a material of interest.

PVC is a plastic that is different from other types of plastic due to its polar nature, which, in principle, makes it compatible with the surface of wood. Because hydrogen bonds are formed between the polar nature of PVC and the hydroxyl groups of wood, this enhances the adhesion between PVC and wood particles. However, these hydrogen bonds can be broken if they contain moisture. The formation of new hydrogen bonds with water results in reduced adhesion between the wood and the PVC, causing a reduction in mechanical properties (Sombatsompop and Chaochanchaikul 2004). Additionally, the wood particles are treated with a coupling agent (aminosilane) before producing the WPVC composite to increase the adhesion between wood fiber and PVC, resulting in higher mechanical properties (Sombatsompop *et al.* 2003). The adhesion increases because the coupling agent changes the surface of the wood fiber from hydrophilic to hydrophobic, causing the surface tension of the wood to decrease, which improves wetting, diffusion of the polymer into the surface of wood fibers, and mechanical interlocking. This results in increased adhesion (Shah *et al.* 2005; Prachayawarakorn *et al.* 2008).

The properties of WPVC composite are heterogeneous; they are likely anisotropic (Sombatsompop* et al.* 2010). The composite has demonstrated lower mechanical properties than timber (Chetanachan *et al.* 2001; Pulngern* et al.* 2011). Several studies have aimed to enhance its mechanical properties by adjusting the composition, for example, increasing the amount of untreated sawdust in a WPVC composite mixture. However, when its quantity in the mixture reached a certain point, the mechanical properties decreased at a slower rate (Sombatsompop* et al.* 2003). In contrast, using chemically surface-treated wood sawdust in an appropriate quantity has been shown to improve mechanical properties (Jeamtrakull* et al.* 2012). Additionally, recent research has found that using a higher proportion of rubberwood sawdust compared to teak sawdust in the WPVC composite mixture resulted in better mechanical properties (Kanking* et al.* 2023). Furthermore, incorporating compatibilizers improved the compatibility between the wood sawdust and the plastic, enhancing tensile properties (Sombatsompop and Chaochanchaikul 2005). Moreover, integrating various types of fibers into the mixture of WPVC composites has been shown to enhance their mechanical properties (Chen* et al.* 2017).

For the production process of WPVC composite, the production temperature is between 140 and 170 °C (Kanking *et al.* 2021), which is considered a high temperature. Therefore, the risk of wood particles scorching should be considered. Due to the decomposition temperature (*T*_{d}) of the WPVC composite being approximately 235 °C (Sombatsompop *et al.* 2008) and the glass transition temperature (*T*_{g}) of the PVC being in the range of 80 to 100 °C (Prachayawarakorn *et al.* 2005), the temperature used in the production process was higher than *T*_{g} but lower than *T*_{d}. This results in the PVC being molten without decomposing and encapsulating the wood particles, which prevents the wood particles from being directly exposed to excessively high temperature used in production, resulting in no scorching. In addition, additives such as PVC emulsion, thermal stabilizer, and lubricants (Kanking *et al.* 2021) are used to prevent PVC from decomposing and ensure smooth flow during the production process.

External factors significantly influence the properties of WPVC composites in practical applications. For instance, the WPVC composite has better flexural and tensile properties in the direction of extrusion than in the direction perpendicular to the extrusion (Roman* et al.* 2018). Moisture levels vary inversely with their mechanical properties (Sombatsompop* et al.* 2004). Exposure to UV weathering affects the thermal degradation of PVC and the color fading of the wood in WPVC composites. However, incorporating Tinuvin P, a UV stabilizer, improved the color stability of WPVC composites under

UV weathering conditions (Chaochanchaikul* et al.* 2013). Furthermore, several research studies have attempted to enhance the resistance of WPVC composites to degradation using approaches such as coating them with CeO_{2}-based acrylic, a UV absorber, as a surface layer. This process enhanced UV resistance while maintaining hydrophilicity levels and mechanical properties under UV weathering conditions (Pattamasattayasonthi* et al.* 2011). Additionally, incorporating 3-iodopropinyl-N-butylcarbamate (IPBC), a fungicide, into the WPVC composite composition significantly retarded deterioration from fungal attack (Kositchaiyong* et al.* 2014). These methods effectively maintained the mechanical properties and aesthetics of WPVC composites in practical applications.

Due to the limited size and shape of the WPVC composite hollow element cross-sections currently available in Thailand and their material properties, which are lower than timber, they are primarily used for decorative or non-structural purposes, such as ceilings and facades. Despite attempts to strengthen WPVC composite hollow elements with flat bar strips, their modulus of rupture (MOR) remained moderate. However, it was higher than that of the unstrengthened WPVC composite hollow element (Pulngern* et al.* 2011, 2013). Additionally, research has attempted to enhance the flexural performance of WPC composite beams with an I-section, a cross-section rarely used for this material in Thailand, by using a grooving technique and reinforcing with glass fiber–reinforced polymer (GFRP), resulting in improved flexural performance without delamination (Naghipour* et al.* 2013). Furthermore, increasing the depth of the section is an alternative option to enhance the flexural performance of the member without reinforcement. This approach can enhance flexural performance and reduce the additional processes required for reinforcing the member with other materials. Therefore, expanding the cross-section becomes

an interesting choice to enhance flexural performance, which may be improved until it is sufficient for structural purposes, similar to glulam timber, where this technique has been successfully applied.

The glulam method, which is commonly used to expand the cross-section of timber material, has been extensively studied. In this method, small pieces of wood are typically used, and finger joints are employed to extend the length of the laminated lumber. Subsequently, these laminate lumber pieces are bonded to form glulam timber, resulting in a laminating effect value calculated from the ratio of the flexural strength to the tensile strength within a range between 0.95 and 2.51 (Falk and Colling 1995). This finding aligns with another study, which suggested that the glulam technique can enhance cross-sectional dimensions by bonding small timbers with adhesive while maintaining material properties comparable to an equivalently sized timber (Udtaranakron* et al.* 2023). Furthermore, the glulam process offers unlimited flexibility in shaping and improves overall performance by reducing or eliminating the negative aspects of wood (Mohamad* et al.* 2011; Nadir and Nagarajan 2014; Maricar* et al.* 2022). In addition to using the glulam method for expanding cross-sectional dimensions, previous research using the glulam method has focused on strengthening glulam timber to reduce the amount of top-grade timber on the extreme tension face (Issa and Kmeid 2005) or enhancing flexural performance through strengthening techniques, such as incorporating carbon fiber–reinforced polymer (CFRP), glass fiber–reinforced polymer (GFRP), and steel in various forms (Glišović* et al.* 2016; Nadir* et al.* 2016; İşleyen* et al.* 2021; Yang and Zhang 2021; Peixoto* et al.* 2022; Zamli* et al.* 2022; Ulaşan* et al.* 2023). However, the glulam method of timber preparation may necessitate finger joints, which have been identified as the weak points in glulam timber (Hamid* et al.* 2015). Thus, there have been efforts to strengthen the glulam timber at the finger joints to improve flexural performance (Khelifa* et al.* 2016). Adapting the glulam method to WPVC composite hollow elements may offer many advantages, such as enhanced cross-sectional and improved flexural performance. Furthermore, WPVC composite hollow elements can be manufactured with long spans, eliminating the finger joints that are the weak points in glulam timber.

Prior research has expanded WPVC composite hollow elements using the glulam method, employing adhesive bonding to create a log wall. The present study investigated compressive load, as well as thermal and acoustic properties. Increased web thickness and reduced flange spacing in WPVC log wall cross-sections enhanced ultimate compressive load and reduced noise (Pulngern* et al.* 2017). Similarly, the glulam method has been used to enhance lateral load resistance in large-scale structures of WPVC log walls, and the behavior of first log-foundation connections under in-plane lateral loads, both monotonic and cyclic, has been investigated. The findings revealed differences in the load-resisting behavior of connections despite equal load-bearing areas (Eakintumas* et al.* 2022a). Furthermore, the load-bearing capacity of a WPVC log wall with openings has been investigated using FEM and validating the accuracy of the model by comparing the results with other research that studied timber log walls (Bedon and Fragiacomo 2015). The results revealed that a WPVC log wall with two openings met the ACI318 requirements for a load-bearing wall in a single-story house with a roof span of up to 4 meters (Eakintumas* et al.* 2022b). Moreover, comparing the temperature profiles and energy consumption of WPVC and fiber cement houses under solar exposure revealed that WPVC composite is a better housing insulator than fiber cement board, commonly used for walls (Kanking* et al.* 2021).

WPVC composites have limitations in applications due to moderate mechanical properties and the dimensional constraints of commercially available WPVC composite hollow elements in Thailand. Although recent research has used the glulam method with WPVC composite hollow elements to overcome dimensional constraints for creating load-bearing walls (Pulngern* et al.* 2017; Eakintumas* et al.* 2022a, 2022b), the application of this method for creating flexural members remains unexplored. This research uses the glulam method to enhance the cross-sectional dimensions of WPVC composite hollow elements to extend their usage as flexural members in building structures, such as floors or beams. The assembly of glulam WPVC composite (GWPVC) hollow members use commercially available WPVC composite hollow elements. The cross-section of the GWPVC hollow member is assembled with adhesive to form a double I-beam section, which has lightweight characteristics and contains channels for sanitary or electrical systems. In this study, the finite element method (FEM) was employed for simulating flexural performance. Furthermore, the analytical method was also used to predict flexural performance and broaden the investigation options for GWPVC hollow members. This method is based on previous research that calculates the position of the neutral axis from the equilibrium of forces in the cross-section and then calculates the curvature to evaluate deflection of the beam (Naghipour *et al.* 2011). However, the analytical method is similar to the generalized nonlinear constitutive law (GNCL), which is used to analyze the bending of beams and plates. The next step was to employ the Finite Element Method to determine deflections and rotations, ultimately leading to the calculation of curvature (Mrówczyński *et al*. 2021a,b; Staszak *et al.* 2021, 2022). Therefore, this research explored flexural performance through four-point bending tests and used both methods, FEM simulations (ABAQUS software) and AMIT predictions (MATLAB), to assess flexural performance.

After assembling a GWPVC hollow member, one of several convenient methods for enhancing flexural performance is adjusting the thickness of the various sections within the cross-section. Molds can be adjusted in several ways. In cases where the molds have not yet been created, 3D printing can create a small-scale model that can be easily fine-tuned to find the appropriate cross-section before creating the mold at full scale. However, existing molds can be slightly adjusted to change the thickness of various sections within a cross-section, which is more cost-effective than creating an entirely new mold. Typical extrusion molds for producing WPVC composites consist of a large outer mold, which controls the overall size of the WPVC hollow element, and small inner molds that block the material to create hollow sections during the extrusion process. Additionally, the inner molds have slightly larger holes than the size of the bolts, which are used to lock their position. The larger holes than the bolts allow for slight repositioning. The slight repositioning of inner molds can be made by loosening the bolts and adjusting the position of the inner mold slightly up, down, left, or right to achieve the preferred thickness. However, if the inner mold cannot be repositioned, new inner molds can be designed and created to replace the old one to increase or decrease the thickness in various parts without creating an entirely new mold. Before adjusting the thickness of each section, it is necessary to specify which parts should be adjusted to enhance flexural performance. Therefore, this research also aims to identify appropriate cross-section adjustments.

To identify the appropriate cross-section adjustments, parametric studies focus on the impact of variations in thickness on flexural performance. This can be achieved by adjusting the thickness within the WPVC composite hollow element while maintaining the same cross-sectional area and overall dimensions. This approach maintains production costs and facilitates the comparison of its effects on flexural performance. This research provides a prototype or guidance for glulam assembly with various cross-sectional shapes of WPVC composite, reducing the number of repetitive four-point bending tests needed to assess flexural performance.

EXPERIMENTAL

In the glulam method, GWPVC hollow members were assembled by bonding WPVC composite hollow elements with adhesive. The properties of the WPVC composite under tensile and compressive forces were tested to determine the stress–strain curve. Subsequently, these results were used to predict and simulate flexural performance under

four-point bending conditions using AMIT and FEM, respectively. AMIT used MATLAB code based on Euler’s beam theory, while FEM employed ABAQUS for modeling and simulation. The results obtained from AMIT and FEM were validated by experimental results to determine the most suitable method for use in the parametric study.

Materials for GWPVC Hollow Member

The GWPVC hollow member was assembled using WPVC composite hollow elements. The WPVC composite material consisted of 1:1 wood sawdust to PVC (by weight) and additives. Thermal stabilizers are used in PVC compounds such as Pb–Ba-based organic polyfluorene and polyfluorene. External and internal lubricants, such as a high molecular weight complex compatible lubricant and calcium stearate, are included. Additionally, emulsion PVC and processing aids are added to achieve the appropriate flow in the production process. The production process, as used previously (Pulngern* et al.* 2011, 2013, 2014; Eakintumas* et al.* 2022b), begins by drying wood particles at 80 °C for 24 h, blending them with PVC using a high-speed mixer, melting and blending them in a twin-screw extruder at 180 °C, and finally extruding them through a mold and solidifying using a cooling system. Two cross-sectional shapes are bonded with cyanoacrylate adhesive YOKOMO 505 from Taiwan during the assembly of the GWPVC hollow member.

**Material Properties of WPVC Composite**

The WPVC composite was tested under tensile and compressive forces following ASTM D638 (2014) and ASTM D6108 (2019), respectively. Specimens for tensile testing had dimensions of 19 mm × 165 mm × 2.8 mm, with a central width of 13 mm, as shown in Fig. 1(a), and the hollow specimens for compressive testing had dimensions of

19.6 mm × 22.63 mm × 39.2 mm, as shown in Fig. 1(b).

**Fig. 1.** Specimens for material properties testing in mm (a) Tensile test and (b) Compressive test

Strain gauges, 1 and 2 per specimen for tensile and compressive tests, respectively, were installed. Each test was performed on five specimens, and the results fit a curve. The constants *a* and *b* obtained from fitting the curve to the material properties under tensile or compressive force are determined for the Boxlucas1 function, as shown in Eq. 1,

(1)

where σ and ɛ represent stress and strain, respectively.

**Bonding Test**

The shear strength of the adhesive for bonding WPVC composite hollow elements to assemble the GWPVC hollow member was tested following ASTM D905 (2021). Specimens, sized 50.8 × 44.4 mm, were sanded with #120 or #80 grit sandpapers. After sanding, the prepared surfaces were cleaned with acetone. A cyanoacrylate adhesive was applied, and another WPVC composite piece was attached immediately without pressure. The adhesive was left to dry for a day at room temperature. Five specimens were prepared for each coarseness of sandpaper.

Preparing Specimens and Setting up the Test for Four-Point Bending

The GWPVC hollow member was assembled from WPVC composite hollow elements (PL-08A and DE-04) using the glulam method to create a double I-shape, as shown in Fig. 2(a). This assembly method followed the same preparation process as the bonding test specimens. Three specimens were prepared with a 2,130-mm span length (*L*) and a slenderness ratio of 15 (Sombatsompop* et al.* 2010). External loads were applied at *L*/3 and 2*L*/3 with a 10 mm/min loading rate following ASTM D198 (2022), and the deflection at mid-span was measured using two displacement transducers (DT), as shown in Fig. 2(b).

**Fig. 2.** The glulam WPVC composite hollow member specimen and testing setup (a) Cross-section of glulam WPVC composite hollow member (all values are given in mm) and (b) Flexural testing setup for glulam WPVC composite hollow member with a span length of 2,130 mm

**Flexural Performance Prediction with AMIT**

The AMIT predictions integrate a theoretical analysis of the GWPVC hollow member based on Euler’s beam theory (Naghipour* et al.* 2011) with calculations using the iterative technique. The objective is to predict the flexural performance under four-point bending testing, assuming that it includes no delamination, small deflections, minimal shear deformation, and excludes buckling effects. The analysis assumes that the GWPVC hollow member is bent, resulting in a non-zero strain at the top. The equilibrium of the forces on the cross-section is employed to locate the neutral axis (NA) corresponding to that strain. Finally, Euler’s beam theory is used to calculate the deflection and applied loads.

The AMIT process is divided into two parts: locating the NA and determining GWPVC hollow member load–deflection curve**, **as shown in Fig. 3.

**Fig. 3.** Flowchart of the analytical method with iteration technique (AMIT) process for calculating load and deflection of glulam WPVC composite hollow member

*Locating the neutral axis*

It is assumed that the GWPVC hollow member is bent with a non-zero strain at the top and a linear strain distribution in the cross-section. The strain at each level can be expressed in terms of the strain at the top surface, as defined in Eq. 2

(2)

where *ε _{top}*,

*h*,

_{n}*y*, and

*ε*represent the strain at the top surface, the distance from the top surface to the NA, the distance from the NA to the strain location, and the strain at any level from the NA, respectively. The force (

_{y}*F*) within the considered area is determined by substituting Eq. 2 into Eq. 3.

(3)

Subsequently, the location of the NA (*h _{n}*) is determined by solving the equilibrium of forces on the cross-section and substituting the non-zero strain value (the balancing method). Additionally, the strain values at the top and bottom surfaces of the GWPVC hollow member are calculated to monitor potential failure. These processes are repeated until the top or bottom strain exceeds the maximum strain obtained from material properties testing. The iterative process is facilitated using MATLAB software, and the details of each step are as follows:

**1. **The initial strain is defined at the top surface (*ε _{top,i}*), assuming the GWPVC hollow member is bent, as shown in Fig. 4(a).

**2. **The location of the NA (*h _{n,i}*) is calculated for each

*ε*using the equilibrium equations when the NA is aligned with the central web area, as shown in Fig. 4(b), expressed as Eq. 4.

_{top,i}3. Substituting Eq. 2 and Eq. 3 into Eq. 4 yields Eq. 5. Subsequently, Eq. 5 is solved using the Newton–Raphson method and the function to solve symbolic equations numerically (vpasolve) in MATLAB. Both methods are applied within a limited range for the location of the NA to determine the value of *h _{n,i}*. The results from both methods are cross-checked to ensure accuracy.

**Fig. 4.** GWPVC hollow member overview (a) strain distribution (b) force diagram and (c) cross-section

(4)

In Eq. 2, terms are as follows:

*C _{ff}* : Compressive force on the upper flange, excluding the cavities.

*C _{fh}* : Compressive force resulting from the cross-sectional area of the cavities in the

upper flange.

*C _{wf }*: Compressive force on the web above the NA location, excluding the cavities.

*C _{wh1}*: Compressive force resulting from the area of the first cavities in the web above the NA location.

*C _{wh2}*: Compressive force resulting from the area of the second cavities in the web above the NA location.

*T _{ff }*: Tensile force on the lower flange, excluding the cavities.

*T _{fh }*: Tensile force resulting from the area of the cavities in the lower flange.

*T _{wf }*: Tensile force on the web below the NA location, excluding the cavities.

*T _{wh1 }*: Tensile force resulting from the area of the first cavities in the web below the NA

location.

*T _{wh2 }*: Tensile force resulting from the area of the second cavities in the web below the NA

location.

where *a* and *b* represent the constants obtained from the curves fit to the material properties under tensile force, while *c* and *d* represent the constants obtained from the curves fit to the material properties under compressive force.

**4.** The maximum strain at the bottom surface (*ε _{bot,i}*) is calculated in each iteration using the triangle proportionality theorem, as shown in Fig. 4(a).

5**.** The *ε _{top,i}*,

*ε*, and

_{bot,i}*h*are recorded. The conditions are checked to determine whether to stop or proceed to the next iteration. The NA location calculation stops if

_{n,i}*ε*or

_{top,i}*ε*exceeds the maximum strain from tensile or compressive testing. Otherwise,

_{bot,i}*ε*is increased for the next iteration. Additionally, the number of iterations (

_{top,i}*N*) for calculating the NA location is recorded for use as the iteration limit of the load and deflection calculations.

*Determining GWPVC hollow member load–deflection curve*

The load determination begins with calculating the moment capacity of the cross-section, which is obtained by summing the moments generated by all forces acting on the cross-section around the NA. Subsequently, the moment capacity is substituted into the bending moment equation for four-point bending to calculate the load. Calculating the deflection starts by determining the curvature using Eq. 6. The curvature is calculated based on the strain at the top surface and the NA location is referenced from the top surface. Furthermore, the analysis assumes a small deflection and employs a differential equation derived from Euler’s beam theory, which approximates the curvature based on a ratio of the moment at its location and bending stiffness, as shown in Eq. 7.

(6)

(7)

where *ϕ*, *M*(*x*), and *EI* represent the curvature, the moment at the location of *x* on the GWPVC hollow member, and the bending stiffness of the GWPVC hollow member, respectively.

The deflection (Δ) is determined from the curvature approximation in Eq. 7 by substituting the curvature into the four-point bending deflection equation, as presented in Eq. 8. The load and deflection calculations are facilitated using MATLAB for the iterative process. The details of each step are as follows:

(8)

where *L* and *a *represent the span length and the loading span, respectively.

*Load determination*

The moment capacity (*M _{i}*) is calculated using Eq. 9 by substituting

*ε*,

_{top,i}*h*, and the dimensions of the cross-section, as illustrated in Fig. 4(c). Eq. 9 is specifically used to determine the moment capacity for

_{n,i}*h*aligned with the central cavity of DE-04.

_{n,i}where,

The load is calculated by substituting *M _{i}* and

*a*into the bending moment equation for four-point bending (

*M*=

_{i}*P*×

_{i }*a*). The moment of inertia (

*I*) is determined for each iteration. The maximum stress of the GWPVC hollow member is calculated for each iteration. The number of loops for the calculated load is checked. If it is not equal

_{i}*N*,

the calculation proceeds to the next step. Otherwise, the calculation is stopped.

*Determining mid-span deflection*

The curvature (*ϕ _{i}*) for each iteration was calculated using Eq. 6 by substituting

*ε*and

_{top,i}*h*. The deflection (Δ

_{n,i}_{i}(

*x*)) is calculated by substituting

*ϕ*into Eq. 8. The calculation of

_{i}*ϕ*and Δ

_{i}_{i}(

*x*) is repeated

*N*times.

After obtaining the load–deflection curve, the result is validated by comparing it with the experimental data. Furthermore, the AMIT result is compared with the FEM result to select the most suitable method for use in parametric studies.

**Flexural Performance Simulated with FEM**

The flexural performance of the GWPVC hollow member was simulated using FEM in ABAQUS. The model uses two cross-sections of WPVC composite hollow elements to form a double I-shape, which is connected with tie constraints to simulate adhesive bonding without slippage or separation (Eakintumas* et al.* 2022b). A simply supported configuration with a span length of 2,130 mm is used for four-point bending conditions. The material properties of the WPVC composite are assumed to be isotropic (Eakintumas *et al.* 2022b) to reduce complexity and make modeling more accessible. A hyper-elastic material, specifically the Marlow model, is chosen to simplify the material properties and represent isotropic properties with nonlinear characteristics (Pulngern *et al.* 2013). When selecting material properties, the tensile strength is approximately 1.5 times lower than the compressive strength (Pulngern* et al.* 2013). Therefore, the tensile property is chosen as the material model because its lower value will control the failure and provide a safety margin for application in other cross-sectional simulations.

Before using the material properties, the uniaxial tensile test results on five specimens are averaged by fitting the curve to the Boxlucas1 function in OriginLab.

The outcome is used to evaluate the Marlow strain energy function, providing material properties for simulating the GWPVC hollow member. Additionally, a Poisson’s ratio of 0.4 is applied (Eakintumas* et al.* 2022b). The element type of twenty-node quadratic brick elements with reduced integration (C3D20R) is employed, resulting in excellent performance under bending conditions and minimizing hourglassing despite the reduced number of integration points (Boumezbeur* et al.* 2023). The surfaces between the specimen and supports are modeled with normal behavior and hard contacts. The specimen surfaces are assigned as the slave surface, while the support surfaces are considered the master surface. This configuration prevents the specimen from penetrating the supports (Dassault Systèmes 2014). The tangential behavior is assumed to be frictionless, allowing the specimen to slide freely on the support after loads are applied at *L*/3 and 2*L*/3 (710 and 1,420 mm). The simulation terminates if the maximum stress reaches the tensile strength or the maximum strain reaches the limit from tensile testing. After the simulation, the FEM result is validated with experimental data and compared to the AMIT results to determine which method is suitable for parametric studies.

**Parametric Studies**

After validating the AMIT and FEM results with experimental data, the most suitable method is chosen to investigate the impact of variations in the slenderness ratio and cross-section on the flexural performance of the GWPVC hollow member.

The investigation begins with variations in span lengths, leading to changes in the slenderness ratio. Subsequently, variations in the flange and web thicknesses of DE-04 and PL-08A are considered while the overall size and total cross-sectional area are maintained.

RESULTS AND DISCUSSION

**Material Properties for Tensile and Compressive Testing**

The tensile and compressive properties of the WPVC composite were determined following ASTM D638 (2014) and D6108 (2019), respectively. Figure 5 shows the results for the tensile and compressive behavior of the WPVC composite.

**Fig. 5.** Material properties testing and curves fit to the Boxlucus1 equation (CX denotes the behavior under compressive testing of WPVC composite specimen X, and TY represents the behavior of WPVC composite specimen Y under tensile testing)

**Table 1. **Material Model Constants for WPVC Composite and the Ultimate Stress and Strain under Tensile and Compressive Loading

Curve-fitting was applied to average the results from tensile and compressive testing and determine the constants of the Boxlucas1 equation. The R-squared values for tensile and compressive testing were 0.99414 and 0.99178, respectively. The ultimate stress, ultimate strain, and constants of tensile and compressive testing for Eq. 1 are shown in Table 1.

**Bonding Test Results**

The bonding tests were conducted according to ASTM D905 (2021); the results are presented in Table 2. The control specimens exhibited a bonding strength of 7.93 MPa, with delamination observed at the bonded area, as shown in Fig. 6(a). Although the bonding strength of specimens sanded with #80 and #120 grit sandpapers could not be precisely calculated, it was estimated to exceed 7.93 MPa. This estimation was supported by the failures observed within the WPVC composite material (Figs. 6(b) and 6(c)), where all specimens failed due to the insufficient shear strength of the WPVC composite, and no debonding or slipping occurred in the bonded area. The bonding method with surface preparation using #80 and #120 grit sandpaper demonstrated perfect bonding and could withstand shear stress more effectively than the control specimens. These bonding strengths exceeded the requirements of the JAS234 (2003), which specifies a bond strength of 5.4 MPa for structural glued laminated timber (Nadir* et al.* 2016). A comparison between the control and prepared surfaces suggested that a rougher surface achieved better bonding. Thus, #80 and #120 grit sandpapers were chosen for surface preparation. Although #80 and #120 grit sandpaper are the same price, the #80 grit sandpaper takes less time to prepare the surface than the #120 grit. Thus, #80 grit sandpaper was selected to prepare the surfaces of WPVC composite hollow elements for assembling the GWPVC hollow member. Furthermore, bonding failure is assumed to occur at a strength limit of 7.93 MPa.

**Table 2. **Results of Testing the Bonding Strength Capability of Adhesives with Varying Surface Roughness Preparations in the Bonding Area

Note: C-SX refers to specimens assembled using cyanoacrylate adhesive and prepared surface with #X grit sandpapers.

**Fig. 6.** Failure of specimens for bonding test (a) Specimen without sanding (b) Specimen with sanding #120 grit sandpapers and (c) Specimen with sanding #80 grit sandpapers

**Four-Point Bending Experiment**

The four-point bending tests of GWPVC hollow members were conducted according to ASTM D198 (2022), and the results are shown in Fig. 7. The initial modulus of elasticity (MOE) was 5,140 MPa, and the MOR was 29.8 MPa for the NA locations assumed to align with the middle of the cross-section (the approximate method). The MOR was compared with previous research on WPVC composite hollow elements using the same mixture and production process and showed a 6.55% higher value for the flatwise loading direction and a 3.16% lower value for the edgewise loading direction

(Pulngern* et al.* 2011). Additionally, compared with another study testing the four-point bending of WPVC composite hollow elements under similar conditions, the MOR was 19.3% lower for the flatwise loading direction and 1.55% higher for the edgewise loading direction (Pulngern* et al.* 2013). The differences in MOR may be attributed to variations in cross-sectional shape, area, and testing conditions that affect stress distribution within the specimens. For the maximum load and deflection of the GWPVC hollow member, the average values were 17.39 kN (CV 0.23%) and 47.76 mm (CV 0.51%), respectively.

**Fig. 7. **Flexural testing of WPVC composite with four-point bending test (SP-X indicates the test results for specimen X in the laboratory)

All of the GWPVC hollow members exhibited flexural tensile failure in a brittle mode due to the lower tensile strength of the WPVC composite compared to its compressive strength. Furthermore, the failures occurred within the 710 to 1,420 mm range, as shown in Fig. 8, where these locations experienced the maximum bending moment while the shear force equals zero. Thus, the failure patterns were consistent with the locations of failures. When the bonded areas were examined, the specimens showed no delamination or separation, confirming the effectiveness of the bonding method for assembling GWPVC hollow members. The experimental results demonstrated similar load–deflection curves with minor differences, as shown in Fig. 7, showing that the glulam method can be applied to WPVC composite hollow elements, effectively controlling quality with very low variation in flexural behavior compared to glulam timber beams.