Experimental,analytical,and numerical studies of steel-strengthened glulam wood–PVC composite hollow members under four-point bending

Abstract

This work investigated the flexural performance of glulam wood–polyvinyl chloride composite hollow members (GWPVC), fabricated by assembling individual wood–polyvinyl chloride composite (WPVC) elements with epoxy adhesive and strengthened in singly and doubly reinforced configurations. Shear bonding strength tests were conducted to confirm that the capacity satisfied standard requirements. Several strengthening materials, including carbon fiber-reinforced polymer (CFRP), low-cost glass fiber-reinforced polymer (LC-GFRP), and steel, were evaluated using the VIKOR method within a multi-criteria decision-making (MCDM) framework based on mechanical performance. Steel was identified as the most suitable strengthening material. The study highlights steel strengthening as an approach to improve the flexural performance and serviceability of GWPVC members, with predictions from analytical method with iterative technique (AMIT) that considers shear deformation effects and finite element method (FEM) simulations, validated against experimental results. Four-point bending tests showed that the ultimate load and initial bending stiffness increased by up to 220.63% and 109.22%, respectively, compared with unstrengthened specimens. Parametric results from AMIT demonstrate that flange reinforcement is more effective than web reinforcement, particularly when placed farther from the neutral axis. Strengthening also extended the serviceable span length of GWPVC members from 3.38 m to 5.27 m, confirming feasibility for residential prefabricated floor panel applications.

Keywords

analytical method finite element method glulam WPVC composite strengthening

Introduction

The construction industry is one of the most significant contributors to environmental pollution and natural resource consumption, particularly through the use of timber for beams, columns, and roof frames. With global population growth leading to increased demand for construction materials, sustainability and deforestation have become critical concerns, driving the search for alternative green materials.

One material that is gaining increasing attention is wood–plastic composite (WPC), which is produced by combining wood byproducts such as sawdust with plastics such as high-density polyethylene (HDPE), low-density polyethylene (LDPE), or polyvinyl chloride (PVC).¹ WPC provides good durability, including resistance to weathering, moisture, and termites,^2,3 which are common weaknesses of natural wood, while also allowing flexibility in cross-sectional design for manufacturing. In addition, WPC production uses byproducts from the wood processing industry, adding value to waste materials and reducing their environmental impact. Although WPC has been mainly used in non-structural applications such as decking, railings, and ceiling panels, recent studies have explored its potential in structural applications. For example, composite beams made of WPC and aluminum alloy were strengthened with concrete to enhance flexural performance.^4,5 Similarly, Xu et al.⁶ investigated WPC columns reinforced with GFRP, while Wang et al.⁷ studied the strengthening of WPC panels with GFRP. Beyond beams and panels, other studies have examined the lateral behavior of wall systems composed of wooden frames with WPC veneer panels and the flexural behavior of sheet piles with varying span lengths.^8,9 More recently, Chen et al.¹⁰ explored the strengthening of WPC for broader structural applications. Overall, these studies highlight the growing interest in expanding WPC from decorative purposes to primary structural components.

Among the different WPC types, wood–PVC composites (WPVC) have attracted particular attention for beam applications because of their mechanical properties. Previous studies have examined flexural performance, strengthening with flat bar strips, and long-term behaviors, including creep and cyclic response.^11–16 Although these studies have demonstrated the potential of WPVC for structural applications, previous investigations have focused on small extruded sections (WPVC single elements), which restrict their ability to be primary structural members. To address this limitation, the glued-laminated (glulam) concept provides a practical and effective approach, enabling the assembly of WPVC single elements into larger sections to enhance their structural capacity. Glulam has been adopted to create large sections, either in hybrid form by laminating wood with WPVC or by assembling multiple WPVC elements.^17,18 Previous studies have developed both load-bearing wall panels and glulam WPVC hollow members (GWPVC) using cyanoacrylate adhesive.^13,19–22 However, scaling up this process is challenging in practice, since the rapid setting of the adhesive makes accurate assembly difficult. Furthermore, when these flexural members are applied as floor panels without beams in residential houses, the usable span of GWPVC members is limited to approximately 3 m because of their deflection-governed behavior under service loads. These limitations highlight the need for strengthening to extend their application over longer spans. However, the challenges of adhesive assembly and deflection-governed span capacity have not been fully investigated, showing an important gap that this study aims to address.

Previous studies have explored the use of fiber-reinforced polymer (FRP) and steel in strengthening timber and composite members. Low-cost glass fiber-reinforced polymer (LC-GFRP) improved the ductility of low-strength concrete columns,²³ while its application to glulam beams enhanced flexural performance in both singly and doubly reinforced cases.²⁴ The use of carbon fiber-reinforced polymer (CFRP) plates for glulam strengthening has also been shown to improve structural performance.^25,26 In addition, FRP and steel reinforcements were reported to be effective for timber beams.²⁷ For WPC, the application of FRP sheets increased the stiffness and maximum load capacity of panels.²⁸ Naghipour et al.²⁹ further investigated WPC beams strengthened with GFRP and CFRP, demonstrating improvements in flexural performance while also identifying debonding issues in some specimens. To address this, longitudinal grooves were investigated to improve bond strength.³⁰ For WPVC beams, steel flat bar strips were applied to enhance flexural performance.¹² These studies consistently indicate that strengthening enhances stiffness and load-bearing capacity, although bond performance remains a critical factor.

In this study, CFRP, LC-GFRP, and steel were selected as candidate materials for strengthening GWPVC members. The evaluation criteria were classified into two categories, namely, mechanical properties (strength and modulus of elasticity) and practical considerations (material applicability and installation time). Uniaxial tensile and compressive tests were conducted to determine the mechanical properties, while the practical criteria were integrated into a multi-criteria decision-making (MCDM) framework using the VIKOR method to identify the most suitable material for strengthening.³¹

Bonding quality is critical for the effectiveness of glulam and strengthening systems, as weak shear bonding can cause premature debonding and reduce structural performance. To ensure reliability, the bonding strength was verified through shear bonding tests. Epoxy adhesive (Sikadur-31CF Normal) was used for assembly and steel strengthening,^15,17 while epoxy resin (FOSROC Nitowrap Encapsulation) was applied for FRP strengthening,²⁴ since both exceeded the 5.4 MPa bonding strength specified in JAS 234.³²

Although experimental testing is essential for verifying material performance and bonding reliability, numerical and analytical approaches are effective alternatives for investigating the flexural properties of structural members. The finite element method (FEM) can simulate flexural behavior using only material properties, although model validation is still necessary before practical application.^33–36 Similarly, the analytical method with iterative technique (AMIT) enables prediction of flexural properties through cross-sectional analysis,^5,12,22,29 but in this study, it also included shear deformation for improved accuracy.³⁷ In addition, Castigliano’s theorem is applied to calculate deflection. Once validated, both FEM and AMIT can accurately reproduce flexural behavior using only material properties, thus offering a cost-effective alternative to repeated full-scale flexural tests.

This study focuses on the assembly and strengthening of GWPVC members through a systematic program. First, GWPVC members were assembled and strengthened with the selected materials in both singly and doubly reinforced configurations. Four-point bending tests were then conducted to provide control data for validating both the AMIT and FEM models. After validation, the most appropriate method was employed in a parametric analysis to investigate the influence of strengthening at different locations, identify the most effective positions for enhancing flexural properties, and provide guidance for alternative strengthening configurations. Finally, the span length of GWPVC members with and without strengthening was evaluated to assess their potential application as structural elements, such as prefabricated floor panels without beams.

Materials and methods

Materials

Wood plastic composite

The WPC used in this study consists primarily of PVC and wood sawdust, mixed in a 1:1 weightt ratio. This material is commonly known as WPVC. The manufacturing process begins with mixing pre-dried wood sawdust and PVC using a high-speed mixer, followed by blending through a twin-screw extruder, and finally extrusion through a mold to form the final product. In addition to the plastic and wood components, various additives are used to improve the performance of the WPVC. The WPVC used in this study follows the same production method as reported in previous research,^{13,18–20,22} although some parts of the formulation have been improved and updated from earlier studies.

Strengthening material

In this study, three types of strengthening materials were considered to enhance the flexural performance of GWPVC members: SS400-grade steel, bi-directional LC-GFRP, and unidirectional CFRP. Mechanical properties were the primary basis for selection, while practical aspects such as the complexity of the strengthening process were also considered. Based on these considerations, the most suitable material was selected for strengthening the GWPVC members. Furthermore, the experimental results for the GWPVC members strengthened with the selected material were used to validate the outcomes obtained from the theoretical and numerical simulations.

Adhesive materials

Assembly GWPVC members

Previous research employed cyanoacrylate adhesive to assemble WPVC single elements into a composite flexural member, referred to as a GWPVC member.²² For surface preparation, the contact areas were sanded using #80 grit sandpaper to enhance bonding performance. As a result, the shear bonding strength exceeded 7.93 MPa. However, in practical applications, the rapid setting time of cyanoacrylate made it difficult to align GWPVC members accurately and to assemble longer spans. To address this limitation, Sikadur-31 CF Normal, a two-part epoxy adhesive mixed at a 2:1 weightt ratio (Part A: Part B), was adopted for assembling GWPVC members. Its slower curing rate provided sufficient time for accurate alignment and uniform bonding during lamination, ensuring practical and consistent fabrication for large-scale members.

Strengthening the GWPVC member

LC-GFRP, CFRP, and steel were assessed for their potential as strengthening materials, with the final selection made based on performance and practical applicability. When FRP materials such as low-cost GFRP or CFRP were selected, an epoxy resin (FOSROC Nitowrap Encapsulation) was applied, mixed at a 2:1 weight ratio (Component A: Component B). In contrast, when steel was selected as the strengthening material, the same epoxy adhesive (Sikadur-31 CF Normal) used for assembling the GWPVC members was applied to bond the steel reinforcement to their surfaces.

Bonding characterization tests

Shear bonding specimens and testing

Shear bonding tests were conducted in accordance with the ASTM D905 standard.³⁸ These tests evaluated the maximum shear bonding strength of two types of adhesives: an epoxy adhesive and an epoxy resin. The tests aimed to assess the bonding performance between WPVC and WPVC, as well as between WPVC and strengthening materials, including FRP and steel. All specimens had a bonded area of 38 × 70 mm. The specimen dimensions, adhesive bonding layer configurations (WPVC-WPVC, WPVC-Steel, and WPVC-FRP), and the test setup are shown in Figure 1.

The epoxy adhesive was used to assemble the WPVC single elements, making the evaluation of its bonding performance essential. A curing time study was conducted to determine the appropriate bonding conditions for practical applications. Specimens were tested after curing periods of 1 and 3 days, as recommended by the manufacturer. During the curing process, no external pressure or clamping load was applied to simulate field conditions and assess the adhesive self-bonding capability. Before bonding, the WPVC surfaces were sanded with #80 grit sandpaper and wiped with acetone to remove dust and contaminants. To ensure consistency in adhesive thickness, the epoxy adhesive was subsequently applied using a custom triangular-toothed spreader fabricated with a three-dimensional (3D) printer. The spreader featured teeth 3 mm wide and 1.5 mm high, corresponding to an approximate application rate of 0.15 g/cm². FRP bonding was performed by applying epoxy resin to the fiber surface, removing air bubbles with a roller, and curing for 1 day as recommended by the manufacturer. The estimated adhesive usage was approximately 0.10 g/cm². The overall specimen preparation followed the same procedure as the WPVC-WPVC bonding, with the only difference being the placement of the strengthening material at the middle of the WPVC bonding interface. To bond the steel to WPVC, the steel surfaces were similarly sanded with #80 grit sandpaper and cleaned with acetone to ensure effective adhesion. Steel was bonded using the epoxy adhesive (Sikadur-31 CF), while FRP was bonded using the epoxy resin.

Shear bonding test results

The results of the shear bonding test for the bonding surfaces between WPVC-WPVC (W-W), WPVC-Steel (W-S), and WPVC-FRP (W-F) are shown in Table 1. Epoxy adhesives were used for the W-W and W-S specimens, while epoxy resin was used for the W-F specimens. The results indicate that extending the curing period from 1 to 3 days significantly increased the bonding strength of W-W and W-S. Moreover, the bonding strength of W-W specimens exceeded the minimum requirement of 5.4 MPa specified in JAS234 for structural glued-laminated timber under both curing durations.³² Therefore, a curing time of at least 3 days is recommended when assembling GWPVC members with epoxy adhesive to ensure adequate bonding performance.

Table 1.

Results of shear bonding strength tests.

Specimens	Adhesive	Curing time	Average shear bonding strength	COV
Specimens	Adhesive	Day	MPa	%
W-W-1	Epoxy adhesive (Sikadur-31CF)	1	6.53	7.47
W-W-3	Epoxy adhesive (Sikadur-31CF)	3	8.20	6.99
W-S-1	Epoxy adhesive (Sikadur-31CF)	1	2.87	12.47
W-S-3	Epoxy adhesive (Sikadur-31CF)	3	6.23	8.25
W-F-1	Epoxy resin (Nitowrap Encapsulation resin)	1	8.74	4.20

Note. W-W: WPVC-WPVC bonding; W-S: WPVC-Steel bonding; W-F: WPVC-FRP bonding.

For steel strengthening, the same epoxy adhesive should also be applied with a curing period of at least 3 days. The W-S specimens cured for only 1 day failed to meet the JAS234 requirement, whereas those cured for 3 days successfully exceeded the standard. In the case of FRP strengthening, epoxy resin was sufficient with just 1 day of curing, as the W-F specimens achieved a shear bonding strength of 8.74 MPa, which exceeded the specified minimum. Therefore, both the adhesive type and curing duration have a significant impact on the bonding performance. To ensure sufficient bonding strength, at least 3 days of curing is required for epoxy adhesive, and a minimum of 1 day for epoxy resin.

Mechanical characterization of WPVC and strengthening materials

WPVC tensile and compressive specimens and testing

To evaluate the mechanical properties of the materials used in this study, standard tensile and compressive tests were conducted on WPVC, FRP, and steel specimens. The properties of WPVC were evaluated according to ASTM D638 (tension) and ASTM D6108 (compression).^39,40 Specimens were prepared from WPVC single elements using CNC milling. The tensile specimens had a dumbbell shape with a 50 mm gauge length and a cross-section of 2.5 × 13 mm. The compression specimens were hollow rectangular sections with outer dimensions of 19.6 × 22.6 mm, a wall thickness of 2.8 mm, and a height of 40 mm. Strain gauges were installed at one location on the tensile specimens and at two locations on the compression specimens before testing. Tensile tests were conducted using a universal testing machine (UTM), and compression tests were performed using a triaxial testing machine, as shown in Figure 2(a) and (b), respectively.

FRP and steel tensile specimens and testing

FRP specimens were tested in tension according to ASTM D3039.⁴¹ The preparation process began by placing a PE sheet as a base, applying epoxy resin to unidirectional fibers, removing trapped air using a roller, and allowing the resin to cure for 24 h. After curing, the PE sheet was peeled off, and the laminate was trimmed to the required dimensions using a cutter. Then, end tabs were attached to both ends of the specimen using epoxy resin. Additionally, the surface at the center of each specimen was sanded and fitted with a strain gauge. A total of five specimens were tested for each FRP type. Both types of FRPs were tested in tension using a UTM, as shown in Figure 3(a). SS400-grade steel specimens were prepared in a dumbbell shape using computer numerical control (CNC) milling and tested with a UTM in accordance with ASTM E8,⁴² with a total of three specimens tested,⁴³ as shown in Figure 3(b).

Test results for WPVC and reinforcement materials

The mechanical property tests of WPVC under tensile and compressive loading were conducted to obtain the parameters for predicting the flexural behavior of GWPVC members. Equation (1) represents the stress–strain relationship for both loading types, where a, b, c, and d are constants determined through curve fitting of the experimental data, as shown in Figure 4(a). The abbreviations COM-X and TEN-X denote the uniaxial compression and tension tests for each specimen (X = 1, 2, 3, …), respectively.

σ_{W P V C} (ε) = {\begin{array}{c} \begin{array}{c} a (1 - e^{- b ε}); 0 < ε \leq ε_{u l t, t} (t e n s i l e) \\ 0; ε > ε_{u l t, t} (t e n s i l e) \end{array} \\ \begin{array}{c} - c (1 - e^{d ε}); ε_{u l t, c} < ε < 0 (c o m p r e s s i v e) \\ 0; ε < ε_{u l t, c} (c o m p r e s s i v e) \end{array} \end{array}

(1)

For tensile loading (ε ≥ 0), a and b were 40.569 and 190.624, respectively, with an ultimate tensile strength of 29.82 MPa (COV 8.70%) and ultimate tensile strain of 0.00752 (COV 6.40%). For compressive loading (ε < 0), c and d were 74.125 and 91.222, respectively, with an ultimate compressive strength of 66.12 MPa (COV 1.30%) and ultimate compressive strain of 0.0283 (COV 5.34%). The initial modulus of elasticity (MOE) was approximately 6189.61 MPa in tension and 5317.38 MPa in compression.

The tensile properties of three reinforcing materials (LC-GFRP, CFRP, and steel) were evaluated, and the results are summarized in Figure 4(b). The LC-GFRP used in this study was the same type of material evaluated by Yoddumrong et al.²³ In the present tensile tests, it exhibited an average ultimate tensile stress of 235.44 MPa (COV 7.12%) and an ultimate tensile strain of 0.01908 (COV 6.75%). CFRP showed higher strength with values of 2662.55 MPa (COV 8.94%) and 0.01097 (COV 8.89%), respectively. For steel, the yield stress and yield strain were 340.20 MPa (COV 0.56%) and 0.001693 (COV 1.49%), while the maximum tensile stress reached 412.09 MPa (COV 1.23%). During testing, the strain gauge detached from all specimens before specimen fracture, which resulted in a lower maximum elongation being recorded, as shown in Figure 4(b). Based on the stroke displacement of the UTM, the ultimate tensile strain for steel was calculated as 0.30 (COV 0.18%). The average MOE values for LC-GFRP, CFRP, and steel were 12,332.95 MPa, 238,362.35 MPa, and 214,888.49 MPa, respectively. These results were used as part of the criteria for selecting the most suitable reinforcement material for strengthening WPC beams.

Criteria for selection of strengthening material

In this study, three candidate strengthening materials (LC-GFRP, CFRP, and steel) were considered for application to GWPVC members. As the candidate materials differ not only in mechanical properties but also in practical considerations, the MCDM approach was employed to determine the most suitable option. The VIKOR method was selected because it is designed to obtain compromise solutions when multiple criteria conflict. VIKOR balances overall performance with worst-case scenarios, ensuring that the selected alternative is not only strong in total score but also considers weaknesses in specific criteria.^44,45 Based on this framework, five key criteria were defined for evaluation, as described below.

Modulus of elasticity (E)

WPVC has relatively low stiffness, which results in significant deflection when it is used as a structural member. To address this limitation, materials with higher elastic modulus (E) values are required, since increasing E increases flexural rigidity and reduces deflection.⁷ For reinforced concrete members, reinforcing materials such as steel typically have modulus values approximately 10 times higher than those of the concrete members, and this ratio was defined as the upper reference level for scoring. In contrast, materials only slightly stronger than WPVC (≈1.5 times stronger) were considered unsuitable and rated lowest.

Tensile and compressive strength

The tensile strength of WPVC is about half of its compressive strength, making its tensile capacity its critical weakness. This makes improving tensile resistance the primary focus, with materials showing a significant increase over WPVC receiving the highest scores, while those only slightly stronger were rated lowest. Compressive strengthening was also considered to improve the overall moment capacity after addressing tensile limitations. Both tensile and compressive strengths were evaluated using the same scoring principle: clear improvements above WPVC received higher scores, whereas limited improvements received lower scores.

Material applicability

This criterion was defined based on observations from the bonding test preparation and on practical expectations of strengthening applications. The criterion reflects the complexity of the method required prior to its use, ranging from immediate application without any treatment to additional processes required for surface preparation or modification. A five-level scale was applied, from use without modification (highest score) to materials unsuitable for strengthening GWPVC members (lowest score), ensuring that constructability and feasibility were consistently incorporated into the evaluation.

Installation time

Strengthening downtime is a critical decision factor. This criterion was based on the time observed in bonding test preparation and the relevant literature,⁴⁶ which emphasize the importance of minimizing disruption. In this study, the maximum strengthening period, including adhesive curing, was set at 8 days. Scoring intervals were defined as ≤1 day, 2–3 days, 4–5 days, 6–7 days, and 8 days, with shorter durations assigned higher scores.

The scoring criteria are summarized in Table A1, and the scores of each material under these criteria are illustrated in Figure 5. The VIKOR method was adopted to integrate multi-criteria assessment. The weighting of the criteria was determined based on the structural behavior of GWPVC members. Previous studies and experimental results indicate that GWPVC members used in flexural applications are generally governed by deflection-controlled behavior.²² Therefore, the primary objective of strengthening is to reduce deflection. For this reason, the modulus of elasticity was assigned the highest weight of 0.30, as it directly influences flexural stiffness. Tensile and compressive strengths were considered secondary but still important criteria, as they influence the flexural capacity and failure behavior of reinforced members depending on the strengthening level and configuration. Hence, equal weights of 0.25 were assigned to both criteria, while maintaining a lower priority than stiffness enhancement. Practical considerations, including material applicability and installation time, were assigned equal weights of 0.10 to account for constructability and practical application, while ensuring that structural performance remains the primary consideration. Additionally, v was set to 0.5 to give equal emphasis to group utility (S) and maximum individual regret (R). As a result, steel achieved the best compromise solution, satisfying both the acceptable advantage and stability conditions, while CFRP and LC-GFRP ranked second and third, respectively.

Steel was selected as the strengthening material for the GWPVC members. Equal-angle steel (1 × 1 in, 3 mm thick) was positioned at the flange–web junction to maintain the original appearance while enhancing flexural capacity. Reinforcing only the inner flange at the joint level would be ineffective if failure occurs in that flange, as no anchorage would remain to hold it in place. In contrast, placing the reinforcement at the joint ensures that the steel remains anchored to the web, allowing it to continue carrying load even after flange failure. Two reinforcement configurations were considered: singly and doubly reinforced. In the singly reinforced configuration, steel was first applied to the tension side to compensate for the relatively low tensile capacity of WPVC, which is approximately half of its compressive capacity. In the doubly reinforced configuration, steel was applied to both the tension and compression sides to assess the improvement in flexural capacity compared with singly reinforced members. In addition, both reinforcement types were used to validate the prediction model and simulation.

Specimen preparation and test setup for flexural tests

Fabrication of GWPVC members

The GWPVC cross-section was designed using commercially available WPVC profiles. Instead of producing a single large WPVC section that would require a new mold and higher manufacturing cost, smaller WPVC elements were assembled using a glulam concept to form a structural-scale member. This approach enables the use of WPVC for structural applications while maintaining cost efficiency. The cross-sectional dimensions were designed to be compatible with typical residential timber floor systems used in Thailand, where the member is used directly as a floor element, similar to a precast concrete slab supported by beams. The initial load-carrying capacity was estimated based on Thai residential building standards. A double I-shaped section was selected to enhance flexural capacity while also providing wide bearing flanges. The additional web elements improve load transfer and stiffness, allowing the flanges to carry floor loads more effectively than a single I-shaped section. This cross-section serves as a prototype for investigating the feasibility of using WPVC in structural applications and can be adapted to other configurations using the same assembly process.

The assembling of GWPVC members began with surface preparation of the WPVC single elements at the bonding areas. These surfaces were sanded and then cleaned with acetone to remove dust and contaminants. To ensure a uniform adhesive thickness, epoxy adhesive was applied to the bonding areas and distributed using a custom triangular-toothed spreader. Another WPVC single element was then assembled with the prepared elements to form the composite cross-section, carefully aligned and clamped to prevent joint movement during curing. This assembling process followed the same procedure used for preparing WPVC-WPVC specimens in the shear bonding strength tests. The cross-sectional configuration of the GWPVC member prior to strengthening is shown in Figure 6.

Strengthening procedure with steel plates

As Figure 7 shows, the GWPVC member was strengthened by bonding equal-angle steel using the same method as in the shear bonding tests to maintain consistency between the test specimens and the strengthened members. The procedure began with surface preparation of both the GWPVC members at the strengthening location and the steel, followed by cleaning. Next, epoxy adhesive was applied to the prepared area, and a spreader was used to achieve a uniform and consistent layer. The steel was placed in position, and clamps were applied to ensure full contact between the steel and the adhesive, compensating for any deviation in the straightness of the steel. The clamps were kept in place for 1 day before removal. The assembly was left for more than 3 days to allow the epoxy adhesive to fully cure, in accordance with the results of the shear bonding test.

Setup test for four-point bending

The four-point bending tests to evaluate the flexural capacity of the GWPVC members, both with and without strengthening, were conducted in accordance with ASTM D198, as shown in Figure 8.⁴⁷ Five specimens were tested for each condition (unstrengthened and strengthened). A span length of 2130 mm (L/d ≈ 15) was used to ensure that failure was primarily caused by bending and to reduce the influence of shear effects.^11,22 The loads were applied at the L/3 and 2 L/3 locations, with a displacement rate of 10 mm/min as specified in ASTM D198. Two displacement transducers (DTs) were placed at midspan to measure deflection.

Theoretical and numerical modeling

Theoretical method (MATLAB)

The flexural capacity of the GWPVC members was predicted from cross-sectional force equilibrium, assuming Euler–Bernoulli kinematics (plane sections remain plane), perfect bonding, and no buckling. Material properties obtained from uniaxial tension and compression tests were used in the analysis.²⁹ Deflection at midspan was computed using the unit-load form of Castigliano’s theorem: a dummy unit vertical force was applied at the midspan to generate the influence functions for bending moment and shear. The overall process is summarized in Figure 9.

The analysis began by assuming that the GWPVC member was bent, producing tensile or compressive strains at the top surface. A linear strain distribution across the cross-section was applied with material properties obtained from fitted curves, as given in equation (1) for WPVC and equation (2) for the steel reinforcement. The steel properties were represented by a bilinear model, where E, $σ_{y i e l d}$ and $ε_{y i e l d}$ represent the MOE, yield stress, and yield strain, respectively.

σ_{s t e e l} (ε) = {\begin{cases} E ε; | ε | \leq ε_{y i e l d} \\ sgn (ε) σ_{y i e l d}; | ε | > ε_{y i e l d} \end{cases}

(2)

F = \int σ (ε_{y}) d A; ε_{y} = \frac{ε_{t o p}}{h} \cdot y

(3)

The internal force can be calculated using equation (3), where h, $ε_{y}$ , and $ε_{t o p}$ denote the distance from the top surface of the GWPVC member to the neutral axis (N.A.), the strain at any point located a distance y from the N.A, and the strain at the top surface of the GWPVC member, respectively, as shown in Figure 10(a). The N.A. is defined as the zero-strain location.

{[\int_{- h}^{t_{f f, T} - h} (σ (y) \cdot b_{f f, T}) d y - 10 \cdot \int_{t_{f 1, T} - h}^{t_{f 1, T} + t_{f h, T} - h} (σ (y) \cdot b_{f h, T}) d y + 2 \cdot \int_{t_{f f, T} - h}^{t_{f f, T} + t_{w f} - h} (σ (y) \cdot b_{w f}) d y - 2 \cdot \int_{t_{f f, T} + t_{w 1} - h}^{t_{f f, T} + t_{w 1} + t_{w h 1} - h} (σ (y) \cdot b_{w h 1}) d y - 2 \cdot \int_{t_{f f, T} + t_{w 1} + t_{w h 1} + t_{w 2} - h}^{t_{f f, T} + t_{w 1} + t_{w h 1} + t_{w 2} + t_{w h 2} - h} (σ (y) \cdot b_{w h 2}) d y - 2 \cdot \int_{t_{f f, T} + t_{w 1} + t_{w h 1} + t_{w 2} + t_{w h 2} + t_{w 3} - h}^{t_{f f, T} + t_{w 1} + t_{w h 1} + t_{w 2} + t_{w h 2} + t_{w 3} + t_{w h 3} - h} (σ (y) \cdot b_{w h 3}) d y + \int_{t_{f f, T} + t_{w f} - h}^{t_{f f, T} + t_{w f} + t_{f f, B} - h} (σ (y) \cdot b_{f f, B}) d y - 10 \cdot \int_{t_{f f, T} + t_{w f} + t_{f 2, B} - h}^{t_{f f, T} + t_{w f} + t_{f 2, B} + t_{f h, B} - h} (σ (y) \cdot b_{f h, B}) d y]}_{W P V C} + 2 \cdot {[\int_{t_{f f, T} - h}^{t_{f f, T} + t_{r t, 2} - h} (σ (y) \cdot b_{r t, 2}) d y + \int_{t_{f f, T} + t_{r t, 2} - h}^{t_{f f, T} + t_{r t, 2} + t_{r t, 1} - h} (σ (y) \cdot b_{r t, 1}) d y + \int_{t_{f f, T} + t_{w f} - t_{r b, 2} - h}^{t_{f f, T} + t_{w f} - h} (σ (y) \cdot b_{r b, 2}) d y + \int_{t_{f f, T} + t_{w f} - t_{r b, 2} - t_{r b, 1} - h}^{t_{f f, T} + t_{w f} - t_{r b, 2} - h} (σ (y) \cdot b_{r b, 1}) d y]}_{s t e e l} = 0

(4)

The equilibrium of forces in the cross-section, shown in Figure 10(b), is then used to determine the N.A. location (h) according to equation (4). This equation is then solved to obtain h, where the symbols represent the dimensions of the GWPVC member, as shown in Figure 10(c).

κ = \frac{ε_{t o p}}{h}

(5)

Once h is determined for each $ε_{t o p}$ , the corresponding curvature ( $κ$ ) and moment capacity ( $M_{c}$ ) are evaluated using equations (5) and (6), respectively. For the case of four-point bending, the maximum moment ( $M_{\max}$ ) is given by equation (7). Therefore, the maximum load ( $P_{\max}$ ), which represents the beam capacity in four-point bending, can be calculated using equation (8).

{M_{c} = [\int_{- h}^{t_{f f, T} - h} (σ (y) \cdot b_{f f, T} \cdot y) d y - 10 \cdot \int_{t_{f 1, T} - h}^{t_{f 1, T} + t_{f h, T} - h} (σ (y) \cdot b_{f h, T} \cdot y) d y + 2 \cdot \int_{t_{f f, T} - h}^{t_{f f, T} + t_{w f} - h} (σ (y) \cdot b_{w f} \cdot y) d y - 2 \cdot \int_{t_{f f, T} + t_{w 1} - h}^{t_{f f, T} + t_{w 1} + t_{w h 1} - h} (σ (y) \cdot b_{w h 1} \cdot y) d y - 2 \cdot \int_{t_{f f, T} + t_{w 1} + t_{w h 1} + t_{w 2} - h}^{t_{f f, T} + t_{w 1} + t_{w h 1} + t_{w 2} + t_{w h 2} - h} (σ (y) \cdot b_{w h 2} \cdot y) d y - 2 \cdot \int_{t_{f f, T} + t_{w 1} + t_{w h 1} + t_{w 2} + t_{w h 2} + t_{w 3} - h}^{t_{f f, T} + t_{w 1} + t_{w h 1} + t_{w 2} + t_{w h 2} + t_{w 3} + t_{w h 3} - h} (σ (y) \cdot b_{w h 3} \cdot y) d y + \int_{t_{f f, T} + t_{w f} - h}^{t_{f f, T} + t_{w f} + t_{f f, B} - h} (σ (y) \cdot b_{f f, B} \cdot y) d y - 10 \cdot \int_{t_{f f, T} + t_{w f} + t_{f 2, B} - h}^{t_{f f, T} + t_{w f} + t_{f 2, B} + t_{f h, B} - h} (σ (y) \cdot b_{f h, B} \cdot y) d y]}_{W P V C} + 2 \cdot {[\int_{t_{f f, T} - h}^{t_{f f, T} + t_{r t, 2} - h} (σ (y) \cdot b_{r t, 2} \cdot y) d y + \int_{t_{f f, T} + t_{r t, 2} - h}^{t_{f f, T} + t_{r t, 2} + t_{r t, 1} - h} (σ (y) \cdot b_{r t, 1} \cdot y) d y + \int_{t_{f f, T} + t_{w f} - t_{r b, 2} - h}^{t_{f f, T} + t_{w f} - h} (σ (y) \cdot b_{r b, 2} \cdot y) d y + \int_{t_{f f, T} + t_{w f} - t_{r b, 2} - t_{r b, 1} - h}^{t_{f f, T} + t_{w f} - t_{r b, 2} - h} (σ (y) \cdot b_{r b, 1} \cdot y) d y]}_{s t e e l}

(6)

M_{\max} = P \cdot a

(7)

P_{\max} = \frac{M_{c}}{a}

(8)

Additionally, a shape-preserving interpolation technique based on the Piecewise Cubic Hermite Interpolating Polynomial (PCHIP) is applied to construct a continuous $κ (M)$ from discrete $κ - M$ data, ensuring monotonicity and avoiding overshoot for the subsequent calculation of bending strain energy. The deflection due to pure bending ( $Δ_{M}$ ) was evaluated with Castigliano’s theorem using equation (9), where $M_{i} (x)$ , $m (x)$ , $κ (M_{i} (x))$ , and $Q$ represent the actual bending moment, the dummy bending moment, the curvature at the actual moment, and the dummy load at midspan, respectively. Since the bending stiffness (EI) of the GWPVC member varies with each bending state, it was normalized using $κ (M)$ derived from the actual capacity. A key advantage of this approach is its ability to capture stiffness degradation under large deformations, as the analysis employs the $κ (M_{i} (x))$ relationship derived from the actual section capacity.

Δ_{M, i} = \int_{0}^{L} \frac{M_{i} (x)}{E I} \cdot \frac{\partial m (x)}{\partial Q} d x = \int_{0}^{L} κ (M_{i} (x)) \cdot \frac{\partial m (x)}{\partial Q} d x

(9)

For deflection due to shear, this study assumes a perfect bond between the WPVC and the reinforcement material, resulting in equal shear strain at corresponding levels of the section. Since the materials in the section do not resist shear equally, the effective shear stiffness is calculated using equation (10). For sections with multiple materials, the shear stiffness can be calculated using a method similar to that for parallel springs, consistent with Niederwestberg et al.,⁴⁸ where k, G_i, and A_i denote the shear correction factor, the shear modulus, and the area of each material in the section, respectively. Moreover, for isotropic materials, the flexural member has a constant N.A. location. In contrast, a GWPVC member is anisotropic, which causes changes in the N.A. location and results in varying shear correction factors in each bending state ( $k_{i}$ ), evaluated using equation (11). For a single, isotropic material, the factor reduces to the standard form for a rectangular cross-section, consistent with Madabhusi-Raman et al.⁴⁹ The shear flow ( $q_{i} (y)$ ) is defined in equation (12) using the E-weighted first moment of area from equation (13) and the E-weighted second moment of area from equation (14), where $V_{i} (x)$ is the shear force at the location under consideration along the member, $\bar{y}$ is measured from N.A., and A(y) denotes the area above level y referenced to the N.A.. The local shear stiffness per unit length ( $S_{i} (y)$ ) is given in equation (15), where $b_{i} (y)$ is the effective width of the section at level y.

{(G A)}_{e f f} = k {(G A)}_{r e f} = k \sum_{i = 1}^{n} (G_{i} A_{i})

(10)

k_{i} = \frac{{(\int q_{i} (y) d y)}^{2}}{(\int \frac{{(q_{i} (y))}^{2}}{S_{i} (y)} d y) \cdot {(G A)}_{r e f}}

(11)

q_{i} (y) = \frac{V_{i} (x) Q_{E, i} (y)}{I_{E, i}}

(12)

Q_{E, i} (y) = \int_{A (y)} (E (\bar{y}) \cdot \bar{y}) d A

(13)

I_{E, i} = \int_{A} (E (\bar{y}) \cdot {\bar{y}}^{2}) d A

(14)

S_{i} (y) = \sum_{i = 1}^{n} (G_{i} (y) \cdot b_{i} (y))

(15)

After determining $k_{i}$ , compute ${(G A)}_{e f f}$ = $k {(G A)}_{r e f}$ to evaluate the shear-related deflection. Using the shear force defined in equation (16), obtain the shear deflection component. Then, combine the bending deflection ( $Δ_{M, i}$ ) and the shear deflection ( $Δ_{S, i}$ ) to obtain the midspan total deflection ( $Δ_{t o t a l, i}$ ) as given in equation (17).

Δ_{S, i} = \int_{0}^{L} \frac{V_{i} (x)}{k_{i} {(G A)}_{r e f}} \cdot \frac{\partial v (x)}{\partial Q} d x = \int_{0}^{L} \frac{V_{i} (x)}{{(G A)}_{e f f, i}} \cdot \frac{\partial v (x)}{\partial Q} d x

(16)

Δ_{t o t a l, i} = Δ_{M, i} + Δ_{S, i}

(17)

Following the above procedure, the process is repeated with $ε_{t o p}$ incremented by $ε_{i n c}$ in each loop, and it stops when the force decreases.

Numerical method (ABAQUS)

ABAQUS was used for the finite element simulation of the flexural behavior of GWPVC members with and without strengthening. Models of the WPVC single elements, PL-08A and DE-04, were created. These single elements were then assembled to form the GWPVC member. All parts were connected using tie constraints,²⁰ which simulate a perfect bond and assume no premature delamination at the adhesive interfaces. For strengthened specimens, the same procedure was applied. The steel was modeled with the actual dimensions used for strengthening and attached to the GWPVC member with tie constraints. In ABAQUS, the WPVC was defined using the low-density foam model, which allows direct input of the uniaxial tensile and compressive test data to capture its nonlinear and anisotropic behavior. For the steel, an isotropic material property was assumed, and a bilinear model was adopted. The model included an elastic behavior for the initial stage and a plastic behavior for the post-yield response to represent its stress–strain relationship realistically. The material parameters for WPVC were defined using nonlinear stress–strain coordinate data obtained by separately averaging the uniaxial tensile and compressive test results, as shown in Figure 4. For the steel material, an elastic–plastic bilinear constitutive model was adopted to represent the stress–strain relationship of steel, which is commonly used in structural analyses.^12,20 The model was defined using an elastic modulus of 214,888.49 MPa and a yield stress of 340.20 MPa, obtained from the experimental results. After yielding, the stress was assumed to remain constant up to an ultimate strain of 0.3. A Poisson’s ratio of 0.3 was adopted for the steel material based on values reported in previous studies.²⁰

In selecting the element type for the analysis, it was noted that some parts of both the strengthening material and the GWPVC member are thin. Using shell or plate elements to focus only on bending effects could have reduced the calculation time. However, in this study, the C3D20R element (20-node quadratic brick, reduced integration) was selected to enable direct modeling using the actual member dimensions. This approach also avoids the complexity of shell modeling, including defining mid-surfaces for each part and specifying thickness by offset, which are often sources of modeling error. C3D20R can report more cover stress components compared to shell elements. The use of reduced integration helps to reduce shear locking and reduce the calculation time. C3D20R is a quadratic element that has built-in hourglass control, which helps prevent such modes when a proper mesh and aspect ratio are used. This ensures the analysis achieves both high accuracy and computational efficiency. To accurately represent the loading and support conditions in the simulation, the supports and loading heads were modeled as rigid bodies, with contact surfaces defined using four-node, 3D discrete rigid surface elements (R3D4) that remain undeformed during the simulation. Each rigid surface was tied to a reference point (RP). The RP of the supports was constrained to prevent movement, while the RP of the loading head was subjected to displacement-controlled loading. Based on previous four-point bending studies,⁵⁰ only half of the full-span length (2130 mm) was modeled because of the symmetric bending behavior of the specimen, which significantly reduced computation time.²² The loading head was positioned at L/3 from the support. Additionally, boundary conditions were applied at the midspan cross-section to restrict all rotations and longitudinal translation, while allowing vertical and lateral translations to represent the full-span test behavior. The mesh size in this study was in the range of 5–7.5 mm.

A maximum stress failure criterion was adopted for WPVC. Failure was assumed to occur when the tensile or compressive stress at any location exceeded the ultimate strength of the material. This criterion appropriately represents the brittle failure behavior of WPVC observed in the experiments. Furthermore, if the maximum tensile or compressive stress in the steel exceeded its ultimate tensile strength, the simulation was also terminated.

Results and discussion

Flexural performance

Load–deflection response and initial stiffness

Four-point bending tests were conducted to evaluate the flexural behavior of unstrengthened (control), singly reinforced, and doubly reinforced GWPVC members. The results are presented in Figure 11. In the legend, EXP, C, S, and D denote an experimental specimen, the control (unstrengthened) group, the singly reinforced group, and the doubly reinforced group, respectively. The number X represents the specimen index (e.g., EXP-C1 … EXP-C5). This behavior was primarily governed by the properties of the WPVC.

From the four-point bending tests on GWPVC members, the control specimens exhibited nonlinear behavior, as shown in Figure 11. The singly reinforced specimens showed a slightly combined nonlinear–bilinear response, while the doubly reinforced specimens exhibited a more pronounced nonlinear–bilinear response. This difference in behavior between the unreinforced and reinforced specimens is attributable to the presence of steel, as the significantly higher stiffness and strength of steel compared to those of WPVC result in a steel-dominated flexural response. The effect was more evident in the doubly reinforced specimens because of the greater amount of steel reinforcement. The initial EI of the control specimens averaged 172.92 kN·m². When strengthened with angle steel in singly and doubly reinforced configurations, the average initial EI increased by 45.76% and 220.63%, respectively. All specimens exhibited low coefficients of variation (COV) in the initial EI (Table 2), lower than the conservative 22% specified for MOE of clear wood in ASTM D2555,⁵¹ indicating high quality control and confirming the uniformity of both unstrengthened and strengthened members. Previous studies also reported low COV values despite different adhesives, supporting the reliable use of WPVC in composite cross-sections.²² The consistency of these results provides strong evidence that the strengthening technique employed in this study is both reliable and practically applicable.

Table 2.

Comparison of flexural behavior of GWPVC members without and with strengthening.

Specimens	Condition	Ultimate deflection (mm)			Ultimate load (kN)			Initial bending stiffness (kN·m²)
		Test result	AVG	Increase ref. Control (%)	Test result	AVG	Increase ref. Control (%)	Test result	AVG	Increase ref. Control (%)
		Test result	(COV)	Increase ref. Control (%)	Test result	(COV)	Increase ref. Control (%)	Test result	(COV)	Increase ref. Control (%)
GWPVC-C1	Unstrengthening (control)	52.39	51.79 (3.89%)	-	21.93	21.79 (3.31%)	-	172.46	172.92 (0.64%)	-
GWPVC-C2		53.62			22.83			174.09
GWPVC-C3		52.94			21.83			171.56
GWPVC-C4		48.45			20.83			174.04
GWPVC-C5		51.56			21.55			172.44
GWPVC-st-s1	Singly	64.30	63.30 (4.53%)	22.22	35.87	36.04 (1.14%)	65.41	255.25	252.04 (1.19%)	45.76
GWPVC-st-s2		61.26			35.73			251.34
GWPVC-st-s3		67.81			35.84			251.56
GWPVC-st-s4		62.44			36.75			247.62
GWPVC-st-s5		60.71			36.03			254.43
GWPVC-st-d1	Doubly	44.45	40.64 (7.11%)	−21.53	44.32	45.59 (2.54%)	109.22	556.50	554.43 (1.38%)	220.63
GWPVC-st-d2		41.08			46.69			550.25
GWPVC-st-d3		36.84			45.07			562.50
GWPVC-st-d4		41.86			46.94			559.52
GWPVC-st-d5		38.97			44.93			543.36

Ultimate load and failure mode

The average ultimate load of the control specimen was 21.79 kN. The singly reinforced specimens showed an average increase of 65.41%, while the doubly reinforced specimens increased by 109.22%. These findings are consistent with previous research that showed that strengthening WPVC single elements using steel strips bonded with Sikadur-31CF adhesive significantly improved their flexural capacity.¹⁵ In the singly reinforced case, failure still occurred on the tension side as in the control specimen, despite the additional reinforcement, because the amount of steel provided was insufficient. Therefore, the failure mode remained tension-controlled, governed by the fracture of the WPVC on the tension flange. In the doubly reinforced case, the addition of steel on the compression side strengthened the top zone, enabling the bottom reinforcement to support higher tensile forces and use more of its capacity before failure. As a result, the flexural strength of the specimens increased, although the failure mechanism was still governed by tension.

All specimens failed suddenly within the maximum bending region (L/3–2L/3), with most failures initiating near the loading points. The control specimens shown in Figure 12(a) failed suddenly and without warning on the tension side because the WPVC exhibited brittle behavior, and its ultimate tensile strain was reached before its ultimate compressive strain. The singly reinforced specimens shown in Figure 12(b) failed on the tension side. Bottom reinforcement provided partial restraint and delayed separation. Slight sound indications were observed before failure. The doubly reinforced specimens shown in Figure 12(c) failed suddenly, fracturing more violently, because of their higher load capacity, and slight sound indications of impending failure were noted. Overall damage was reduced because reinforcement on both sides held the fractured parts together, although the residual capacity remained very small. Similarly, in both the singly and doubly reinforced cases, failure occurred in the same mode as in the control specimens, as shown in Figure 12(b) and (c). This resulted from the combined capacity of WPVC and steel in tension remaining lower than the compressive capacity of WPVC (or WPVC with steel), indicating that the amount of tensile reinforcement was insufficient to change the failure mode.

Debonding behavior and interface response

In the singly reinforced specimens, debonding occurred only within the pure-bending zone (L/3–2L/3), where the shear force is zero. No debonding was observed in the shear spans outside L/3–2L/3. A weak epoxy adhesive bond would have produced debonding in those higher-shear spans. However, no debonding was detected in those spans. Therefore, debonding on the tension side resulted from stress concentrations generated by cracking of the WPVC at the steel–WPVC interface. The doubly reinforced specimens showed the same behavior. Debonding appeared only within the pure-bending zone on the tension side. These observations confirm that the interface-shear demand did not exceed the bonding capacity of the epoxy adhesive.

An additional mechanism related to tensile cracking was observed in both reinforcement cases. Prior to cracking, the tensile force at the bottom section was shared between the WPVC and the steel reinforcement, with the epoxy adhesive ensuring effective composite action. Once the WPVC cracked and the crack propagated to the reinforcement level, the tension flange fractured across the section. Afterward, the load decreased, and the steel carried almost all of the tensile force. At this stage, the load-carrying capacity of the steel depended solely on the bond with the remaining uncracked portion of the WPVC. Stress concentrations at the cracked region generated higher interface-shear stresses than in other regions, exceeding the available bond strength and resulting in the debonding of the bottom reinforcement, as shown in Figure 12(b) and 12(c).

Observed debonding and failure mechanism

Observations showed that the reinforcing steel in the strengthened WPVC specimens yielded, as evidenced by the permanent deformation of the reinforcement after failure without recovery to its original shape. This confirms that the steel contributed to load sharing with the WPVC beyond the yield point, which is typically adopted as the reference for structural design. As shown in Figure 11, the singly and doubly reinforced cases exhibited two slopes, with a flatter slope after yielding, whereas the control specimen showed a single slope. Clearer bilinear behavior was observed in the doubly reinforced case than in the singly reinforced case because the addition of steel on both flanges increased the overall bending stiffness, resulting in a steel-dominated flexural response. Once the steel yielded, it governed the stiffness transition, producing a more pronounced post-yield response.

When comparing the deflection at the average maximum load of the unstrengthened specimens (21.79 kN), as shown in Figure 11, the deflection decreased from 51.79 mm to 31.44 mm (39.30%) for the singly reinforced case and to 12.94 mm (75.01%) for the doubly reinforced case. Additionally, when considering the ultimate deflection, the control specimen showed an average of 51.79 mm. In the singly reinforced case, the deflection increased by 22.22% because the added tension steel-strengthened tensile zone, which changed the strain distribution. The compression zone was then forced to carry higher stresses and larger strains to balance the internal forces, leading to greater ultimate deflection. In the doubly reinforced case, the addition of steel on both the top and bottom provided almost equal capacity, resulting in a flexural response similar to that of the control specimen in terms of the overall mechanism of failure, although the member exhibited higher initial stiffness and ultimate load capacity. However, because the reinforcement increased the EI of the section, the ultimate deflection was smaller even though the load capacity was higher.

Summary and practical considerations

The test results confirmed that steel reinforcement significantly enhanced the flexural strength of GWPVC members, particularly in the doubly reinforced case, which provided the highest stiffness and load capacity of the studied configurations. These results are presented primarily to validate the AMIT and FEM simulations discussed in the following sections, not to propose the most practical strengthening method. Therefore, although the doubly reinforced configuration performed best within the scope of this study, it may not be the most effective in structural applications. For practical applications, strengthening should be designed more carefully. The location, amount, and type of reinforcement should be adjusted to suit actual structural requirements.

Validation of AMIT

Computational approach of AMIT

The analysis was performed using MATLAB coding. In the previously used method,^12,22 each possible N.A. location was coded as a separate case, significantly increasing coding time. Moreover, any major change in the cross-sectional geometry required reclassification and re-coding for each case. This approach simplified the calculations, making them easier to understand and reducing confusion, as all integrations were computed with positive values. In contrast, the present method applies the sign convention, eliminating the necessity for case-by-case classification. Positive and negative signs represent downward and upward directions, respectively, with compressive stresses and strains assigned negative values and tensile stresses and strains assigned positive values.

Prediction of flexural response and ultimate load

AMIT predictions of flexural response for GWPVC members without and with strengthening are shown in Figure 11. The AMIT predictions are labeled as AMIT-X:B (pure bending) and AMIT-X:B + S (pure bending + shear effect), where $X \in {C, S, D}$ denote the control, singly reinforced, and doubly reinforced groups, respectively. The predicted ultimate loads for the control, singly reinforced, and doubly reinforced cases were 20.79, 37.55, and 44.41 kN, differing from the experimental results by 4.61%, 4.17%, and 2.59%, respectively.

Effect of shear deformation on deflection prediction

For ultimate deflection, analyses that considered only bending deformation and neglected shear produced accurate predictions with small differences from the test results for all cases. To represent actual behavior, shear deformation was then included. After including shear deformation, differences in ultimate deflection remained small across all cases. The largest difference was 5.70% for the doubly reinforced case, while the control and singly reinforced cases remained below 5% compared with the experiments.

For the initial EI, the pure-bending analysis (equation (9)) yielded 180.63 kN·m² for the control specimen, overestimating the experimental average by 10.36%. The singly and doubly reinforced specimens had bending stiffnesses of 261.94 and 647.88 MPa, overestimating the experimentally measured values by 3.93% and 16.86%, respectively. These results are consistent with those of Pulngern et al.¹² and Mrówczyński et al.,³⁷ whose pure-bending analyses of strengthened WPVC single elements also overestimated initial EI in some cases. When shear deformation was considered equation (16), the differences decreased to 1.33%, 0.62%, and 8.03% for the control, singly, and doubly reinforced cases. These results show that consideration of the effect of shear deformation yields predicted values closer to the experimentally measured values and that the influence of shear deformation increases with load, becoming more pronounced at higher strengthening levels.

Neutral axis location and strain distribution

The N.A. location varies with the strengthening configuration and the load level because WPVC exhibits nonlinear behavior. In Figure 13, the x-axis limits are the ultimate tensile and compressive strains of WPVC, and the y-axis denotes depth measured from the top surface of the GWPVC section. In the unstrengthened case, as shown in Figure 13(a), the N.A. is located slightly above mid-depth because WPVC is stronger in compression than in tension. In the singly reinforced case, as shown in Figure 13(b), the N.A. shifts downward because the tensile reinforcement is stiffer and stronger than WPVC, so a larger WPVC compression zone is required to balance the tensile force carried by the steel and WPVC. In the doubly reinforced case, as shown in Figure 13(c), the N.A. returns close to mid-depth because of symmetric reinforcement and the similar responses of steel in tension and compression, so WPVC continues to govern the N.A. location as in the unstrengthened case. For all configurations, the maximum tensile strain in WPVC reached the ultimate tensile strain, confirming a tension-controlled failure mode consistent with the experiments. Therefore, AMIT provides accurate predictions of the flexural response of GWPVC members with and without strengthening.

Validation of ABAQUS

Overview of finite element modeling and simulation setup

Finite element analysis using ABAQUS was employed to simulate the flexural response of GWPVC members with and without strengthening. Material properties were obtained from uniaxial tests. A half-span model with a midspan symmetry configuration was created, and boundary conditions were applied on the midspan plane to reflect the actual behavior, which significantly reduced the computational time compared with the full-span simulation.²² The model was subjected to displacement-controlled loading applied through the loading head. The simulation was terminated once the maximum stress failure criterion was met for either the WPVC or the steel. The WPVC-steel interface was modeled with a tie constraint to represent perfect bonding, since no interfacial debonding was observed prior to failure in the experiments. Furthermore, since the specimens exhibited brittle fracture without a clear post-peak stage, as shown in Figure 11, the simulation focused on the behavior up to cracking, which was sufficient to capture the peak load.

Simulation of flexural response and experimental comparison

The simulated responses are shown in Figure 11, where FEM-X denotes the finite element model results for the control (C), singly reinforced (S), and doubly reinforced (D) cases. For the initial EI, the model yielded 184.48, 268.09, and 590.55 kN·m² for the control, singly reinforced, and doubly reinforced cases, differing from the experiments by 6.69%, 6.37%, and 6.51%, respectively. For ultimate load, the simulated values were 21.09, 36.97, and 45.59 kN, with deviations of 3.23%, 2.58%, and 0.64%, respectively. For maximum midspan deflection, the predicted values were 47.72, 64.19, and 41.94 mm, differing from the tests by 7.85%, 1.41%, and 3.20%, respectively. These results demonstrate that FEM accurately simulates the flexural behavior of both unstrengthened and strengthened members, confirming that the modeling assumptions were appropriate for this study.

Failure criterion and stress-based failure assessment

Failure in the FE simulations was assessed using a stress-based criterion, where failure was declared when the computed stress in any region exceeded the ultimate tensile or compressive stress obtained from the material testing. This approach mirrors the sudden experimental failure, as WPVC exhibits brittle behavior. Regions exceeding the ultimate stress are shaded in gray, as shown in Figure 14 for both unstrengthened and strengthened members. In every case, the overstressed zone appeared in the tensile WPVC region, consistent with the experimental observations. Consistency with the experimental results validates this stress-exceedance criterion as a practical failure indicator for GWPVC under flexural behavior, both with and without strengthening.

Applicability and comparison with AMIT

Based on experimental validation, this method can be extended to other GWPVC cross-sections and strengthening configurations without additional full-scale tests, provided that the material properties of each component have been determined. A comparison between AMIT and FEM shows that the FEM provides slightly higher accuracy and can identify potential failure regions, whereas the AMIT requires less computational time while maintaining close agreement with the experimental results. Additionally, the slight differences between the AMIT and FEM results and the experimental responses indicate that failure was governed by WPVC material failure prior to any interfacial debonding. Due to the brittle behavior of WPVC, failure occurs suddenly without a clear post-peak stage and may appear similar to interfacial debonding in the experiments. Therefore, the failure mechanism was identified based on the overall structural response and analytical interpretation rather than visual observation alone.

Parametric studies

Parametric study framework and setup

The results obtained from AMIT and FEM showed good agreement with the experimental test results and with each other, with only minor differences observed. After validation with the experimental results, the AMIT model was selected for the parametric studies because of its combination of computational efficiency and predictive reliability. In addition to efficiency, AMIT offers greater flexibility in systematically varying parameters such as material properties and geometric dimensions and automating multiple cases through coding. This approach ensures that the parametric investigation can be carried out efficiently and comprehensively while maintaining consistency with the experimental and FEM results. The parametric study focuses on the geometry of the steel angle (L-section) used for strengthening, which consists of two legs at the web–flange junctions. Both singly and doubly reinforced configurations were analyzed. Consistent with the experimental observations where no bond failure occurred, a perfect bond between the steel and WPVC was assumed.

Effect of reinforcement geometry in singly reinforced members

In the singly reinforced configuration, the study varied the size of the steel angle by changing one parameter at a time, either the thickness or the length of the flange leg and the web leg. The load–deflection responses obtained from the analyses are presented in Figure 15. In the notation, X denotes the dimension in millimeters. The parametric cases are denoted as LF-TX and LW-TX for thickness variations of the legs adjacent to the flange and the web, respectively, and as LF-LX and LW-LX for length variations of the flange and web legs, respectively. Figure 15(a) shows that reducing the thickness of the web leg caused a smaller decrease in ultimate load and initial EI compared with reducing the thickness of the flange leg, indicating that reinforcement at the flange has a more pronounced effect on flexural capacity. This is because the flange lies farther from the N.A., contributing more to the moment of inertia and overall flexural rigidity of the section. Figure 15(b) illustrates the influence of leg length, where the changes in ultimate load, ultimate deflection, and initial EI were more pronounced when modifying the flange leg length, while variations in the web leg length had almost no effect. Overall, the singly reinforced results confirm that reducing the amount of reinforcement, whether by decreasing thickness or shortening leg length, resulted in reductions in initial EI, ultimate load, and ultimate deflection.

Effect of reinforcement geometry in doubly reinforced members

In the doubly reinforced configuration, the study followed the same procedure as in the singly reinforced case but fixed the amount of reinforcement at the bottom while varying the thickness and length of the top reinforcement. The prediction results are presented in Figure 15(c) and (d). Figure 15(c) shows that reducing the thickness of the web leg, which is closer to the N.A., led to decreases in initial EI and ultimate load, but increased ultimate deflection. These changes were smaller compared with reducing the thickness of the flange leg, which is located farther from N.A. Figure 15(d) illustrates the effect of varying leg length. Increasing the web leg length slightly reduced ultimate load and deflection, whereas increasing the flange leg length enhanced both initial stiffness and ultimate load while reducing ultimate deflection.

Influence of reinforcement position on bending stiffness and deflection

The prediction results presented above are consistent with the theoretical principle that increasing or decreasing the reinforcement area farther from the N.A. has a greater effect on the moment of inertia, which directly influences the initial EI. Therefore, any increase in reinforcement raises the initial EI, while a reduction decreases it. The magnitude of this change depends on the reinforcement position, with the effect becoming more significant as the distance from the N.A. increases. However, the primary purpose of strengthening GWPVC members remains the reduction of ultimate deflection, since this material is generally governed by deflection control when used as a flexural structural component. For this reason, strengthening should primarily aim to improve the initial EI, which directly reduces deflection under loading and enhances the serviceability limit governed by deflection control.

Span length capacity and serviceability evaluation

In addition, span lengths applicable for GWPVC members as small-scale structural components were investigated for both unstrengthened and strengthened cases. The strengthened specimens used the same reinforcement configuration as the experimental specimens and were considered prefabricated floor panels. Factored load calculations were performed in accordance with Thai residential design standards, adopting a live load of 150 kg/m² and considering the actual self-weight of the specimens as the dead load. According to the deflection criterion, the ultimate deflection under the design load must not exceed L/240. Based on this requirement, the relationship between span length and load capacity was investigated, and the flexural behavior of GWPVC members at different spans is presented in Figure 16. Figure 16(a) shows the load capacities of unstrengthened members with spans ranging from 1 to 6 m at 0.25 m intervals, Figure 16(b) shows the results for singly reinforced members, and Figure 16(c) shows those for doubly reinforced members. For each case, the equations to calculate the ultimate load at different span lengths are provided within the figure.

Span length evaluation based on deflection limit

Considering the design standard requirements, both unstrengthened and strengthened GWPVC members can sustain loads up to a span length of 6 m. The safety factor (SF), defined as the ratio of maximum load capacity to the required load for spans from 1 to 6 m, was satisfied for all cases. The lowest safety factors were 1.74 for unstrengthened members, 3.29 for singly reinforced members, and 3.32 for doubly reinforced members at a span of 6 m, all exceeding the required limit. However, when the allowable deflection limit of L/240 was applied, the load capacities corresponding to this deflection limit for each case were plotted against the span length, as illustrated in Figure 17. The intersection between these capacity curves and the line representing the minimum design load for prefabricated floor panels at each span denotes the maximum usable span that satisfies both load-bearing capacity and deflection criteria. In the figure, the region above the red zone indicates spans that meet both the load-bearing and deflection requirements. The analysis showed that strengthening significantly increased the maximum usable span governed by the L/240 deflection limit. Compared to the 3.38 m span of the unstrengthened member, the singly reinforced member achieved 3.86 m, while the doubly reinforced member reached 5.27 m. According to Aunyingcharoen et al.,²² unstrengthened GWPVC members bonded with cyanoacrylate adhesive had a maximum span capacity of approximately 3 m under similar conditions, which is consistent with the unstrengthened members in this study. The results indicate that strengthening can extend the practical span from 3.38 m to 5.27 m, representing an increase of 55.75%. Notably, a 3 m span is rarely used in typical residential applications, whereas spans of 4–5 m are common in residential buildings.

Conclusions

This work demonstrated the potential of assembling WPVC single elements into GWPVC members using Sikadur-31CF Normal as an effective bonding adhesive. The flexural behavior of GWPVC members with and without strengthening was investigated. The choice of strengthening material was guided by material property tests and multi-criteria decision analysis through the VIKOR method. The main findings can be summarized as follows.

1. The assembly of GWPVC members with Sikadur-31CF Normal exhibited an average bond strength exceeding 8.20 MPa. Failure occurred within the WPVC rather than at the adhesive interface, confirming the effectiveness of the adhesive.

2. VIKOR-based MCDM identified steel as a more suitable strengthening material than CFRP or LC-GFRP. The bonding shear strength of Sikadur-31CF Normal used for strengthening GWPVC members exceeded 6.23 MPa, which is higher than the minimum requirement specified in JAS234.

3. The experimental results showed that singly reinforced members increased the initial bending stiffness and ultimate load by 45.76% and 65.41%, respectively, while doubly reinforced members exhibited increases of 220.63% and 109.22%. The ultimate deflection was 22.22% higher for singly reinforced members but 21.53% lower for doubly reinforced members.

4. Predictions from the AMIT (including shear effects) and FEM simulations demonstrated excellent agreement with the experimental results, with differences in ultimate load, initial stiffness, and ultimate deflection all within 10%.

5. Flange strengthening, especially when placed farther from the N.A., was more effective than web strengthening. Appropriate strengthening extends the deflection-limited span of GWPVC members from 3.38 m to 5.27 m, enabling their use as prefabricated floor panels.

However, given the use of GWPVC members in structural applications, future research should focus on their long-term performance, including creep behavior, fatigue resistance, and durability of the adhesive bond under environmental exposure such as temperature variation and moisture. Fire resistance of GWPVC members may also be investigated to evaluate fire resistance capacity under strengthened and unstrengthened conditions.

Footnotes

Acknowledgments

The authors gratefully acknowledge the support of V.P. Wood Co., Ltd. for providing WPVC composite material for this research.

ORCID iDs

Tawich Pulngern

Narongrit Sombatsompop

Author contributions

Phatthana Aunyingcharoen: Data curation, Formal analysis, Investigation, Methodology, Software, Writing – original draft. Tawich Pulngern: Conceptualization, Funding acquisition, Project administration, Visualization, Supervision, Validation, Writing – review & editing. Kasan Chanto: Formal analysis, Software, Validation, Writing – review & editing. Vichai Rosarpitak: Resources. Narongrit Sombatsompop: Conceptualization, Project administration, Visualization, Supervision, Validation, Writing – review & editing.

Funding

The authors disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: The authors gratefully acknowledge the financial support from the Petchra Pra Jom Klao PhD Research Scholarship from King Mongkut’s University of Technology Thonburi (Grant No. 18/2563). Additional support was provided by King Mongkut’s University of Technology Thonburi (KMUTT), Thailand Science Research and Innovation (TSRI) through the Basic Research Fund, Fiscal Year 2026, for the project “Numerical Modeling and Structural Analysis of Composite Sections Built-up from Local Timber in Thailand.”

Declaration of conflicting interests

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Data Availability Statement

The data that support the findings of this study are available from the corresponding author upon reasonable request.*

Appendix

Table A1.

Scoring criteria and justification for strengthening material selection.

Criterion	Weight	Score
Criterion	Weight	5	4	3	2	1
1. Modulus of elasticity ( $r = \frac{E_{m a t e r i a l}}{E_{W P V C}}$ )	0.30	r ≥ 10	6 ≤ r < 10	3 ≤ r < 6	1.5 ≤ r < 3	r < 1.5
2. Tensile strength (relative to WPVC, %)	0.25	≥100%	80–99%	50–79%	20–49%	<20%
3. Compressive strength (relative to WPVC, %)	0.25	≥100%	80–99%	50–79%	20–49%	<20%
4. Material applicability	0.10	Directly applicable (no modification)	Minor preparation (e.g., surface roughening, cleaning)	Moderate modification (e.g., resizing)	Major modification or processing	Not suitable for strengthening of GWPVC members
5. Installation time*	0.10	≤1 day, minimal disruption	2–3 days, short disruption	4–5 days, manageable downtime	6–7 days, significant disruption	≥8 days, major downtime

Installation time includes surface preparation and adhesive curing and is measured until the member can be safely returned to service.

References

Ramesh

Rajeshkumar

Sasikala

, et al. A critical review on wood-based polymer composites: processing, properties, and prospects. Polymers 2022; 14: 589. https://doi.org/10.3390/polym14030589

Chetanachan

Sookkho

Sutthitavil

, et al. PVC wood: a new look in construction. J Vinyl Addit Technol 2001; 7: 134–137. https://doi.org/10.1002/vnl.10280

Jile

Huo

Liu

, et al. Mechanical properties of PVC-based wood–plastic composites effected by temperature. Front Mater 2022; 9: 1018902. https://doi.org/10.3389/fmats.2022.1018902

Zhao

Doctor

. Flexural performance of reinforced aluminum–wood–plastic composite beam: An experimental and numerical investigation. Thin-Walled Struct 2022; 180: 109910. https://doi.org/10.1016/j.tws.2022.109910

Zhao

Wei

, et al. Flexural properties on aluminum alloy - wood plastic composite beam strengthened by concrete. Constr Build Mater 2025; 460: 139792. https://doi.org/10.1016/j.conbuildmat.2024.139792

Wang

Huo

, et al. Axial compressive properties of GFRP-reinforced PVC-based glued wood-plastic composites column. J Reinf Plast Compos. 2024; 07316844241302884. https://doi.org/10.1177/07316844241302884

Wang

Huo

, et al. Flexural reinforcement of wood plastic composite panels by bonding glass fiber reinforced polymer sheets and embedding bars. Polym Compos 2024; 45: 14595–14607. https://doi.org/10.1002/pc.28784

Fang

Zhang

, et al. Lateral behavior of wood frame shear wall using PVC wood-plastic composite (WPC) veneer panels. J Build Eng 2024; 89: 109367. https://doi.org/10.1016/j.jobe.2024.109367

Alvarez-Valencia

Dagher

Davids

, et al. Structural performance of wood plastic composite sheet piling. J Mater Civ Eng 2010; 22: 1235–1243. https://doi.org/10.1061/(ASCE)MT.1943-5533.0000132

10.

Chen

Gao

Liu

, et al. Enhancing wood-plastic composites for high-performance structural applications. Compos Part B Eng 2025; 299: 112410. https://doi.org/10.1016/j.compositesb.2025.112410

11.

Pulngern

Chucheepsakul

Padyenchean

, et al. Effects of cross-section design and loading direction on the creep and fatigue properties of wood/PVC composite beams. J Vinyl Addit Technol 2010; 16: 42–49. https://doi.org/10.1002/vnl.20227

12.

Pulngern

Chimkhlai

Rosarpitak

, et al. Analytical, numerical and experimental investigations on flexural strengthening for wood/PVC composite members using flat bar strips. Constr Build Mater 2013; 41: 545–556. https://doi.org/10.1016/j.conbuildmat.2012.12.017

13.

Pulngern

Eakintumas

Rosarpitak

, et al. Compressive load, thermal and acoustic properties of wood/polyvinyl chloride composite log-wall panels. J Reinf Plast Compos 2017; 36: 1183–1193. https://doi.org/10.1177/0731684417699712

14.

Pulngern

Kaewkalya

Rosarpitak

, et al. Experimental and computational investigations of creep responses of wood/PVC composite members. Int Polym Process 2014; 29: 307–316. https://doi.org/10.3139/217.2927

15.

Pulngern

Padyenchean

Rosarpitak

, et al. Flexural and creep strengthening for wood/PVC composite members using flat bar strips. Mater Des 2011; 32: 3431–3439. https://doi.org/10.1016/j.matdes.2011.02.005

16.

Sombatsompop

Prapruit

Chaochanchaikul

, et al. Effects of cross-section design and testing conditions on the flexural properties of wood/PVC composite beams. J Vinyl Addit Technol 2010; 16: 33–41. https://doi.org/10.1002/vnl.20202

17.

Udtaranakron

Pulngern

Rosarpitak

, et al. Structural performance of full-scale hybrid hollow core wall with WPVC composite materials under axial compression load via experimental investigation. Constr Build Mater 2025; 470: 140656. https://doi.org/10.1016/j.conbuildmat.2025.140656

18.

Udtaranakron

Pulngern

Sombatsompop

. Analytical and experimental investigation of the flexural and bond adhesive properties of thermally modified rubberwood and hybrid glulam beams with WPVC composites. Structures 2023; 58: 105498. https://doi.org/10.1016/j.istruc.2023.105498

19.

Eakintumas

Pulngern

Rosarpitak

, et al. Experimental investigation of lateral resisting elements for the wood polyvinyl chloride composite log-house under in-plane lateral loads. J Vinyl Addit Technol 2022; 28: 153–171. https://doi.org/10.1002/vnl.21877

20.

Eakintumas

Pulngern

Rosarpitak

, et al. Load-bearing capacity of wood polyvinyl chloride composite log-walls with openings strengthened with steel flat bars via experimental and numerical studies. Structures 2022; 37: 242–254. https://doi.org/10.1016/j.istruc.2022.01.003

21.

Eakintumas

Pulngern

Rosarpitak

, et al. Finite element modeling and experimental investigation for wood/PVC composites log-walls under in-plane lateral load. Polymers 2022; 14: 4673. https://doi.org/10.3390/polym14214673

22.

Aunyingcharoen

Pulngern

Rosarpitak

, et al. Analytical method with iteration technique (AMIT) and finite element method (FEM) for predicting the flexural performance of glulam wood/PVC composite hollow member. BioResources 2024; 19(3): 5197–5226. https://doi.org/10.15376/biores.19.3.5197-5226

23.

Yoddumrong

Rodsin

Katawaethwarag

. Seismic strengthening of low-strength RC concrete columns using low-cost glass fiber reinforced polymers (GFRPs). Case Stud Constr Mater 2020; 13: e00383. https://doi.org/10.1016/j.cscm.2020.e00383

24.

Udtaranakron

Pulngern

Mahasuwanchai

, et al. Flexural strengthening of thermally modified rubberwood glulam beams with FRP under static and cyclic loads. Wood Res 2024; 69: 469–484.

25.

İşleyen

Ghoroubi

Mercimek

, et al. Behavior of glulam timber beam strengthened with carbon fiber reinforced polymer strip for flexural loading. J Reinf Plast Compos 2021; 40: 665–685. https://doi.org/10.1177/0731684421997924

26.

Glišović

Stevanovic

Todorovic

, et al. Glulam beams externally reinforced with CFRP plates. Wood Res 2016; 61: 141–154.

27.

Wdowiak-Postulak

Wieruszewski

Bahleda

, et al. Fibre-reinforced polymers and steel for the reinforcement of wooden elements—experimental and numerical analysis. Polymers 2023; 15: 2062. https://doi.org/10.3390/polym15092062

28.

Tamrakar

Shaler

Lopez-Anido

, et al. Mechanical property characterization of fiber-reinforced polymer wood-polypropylene composite panels manufactured using a double belt pressing technology. J Mater Civ Eng 2012; 24: 1193–1200. https://doi.org/10.1061/(ASCE)MT.1943-5533.0000489

29.

Naghipour

Nematzadeh

Yahyazadeh

. Analytical and experimental study on flexural performance of WPC–FRP beams. Constr Build Mater 2011; 25: 829–837. https://doi.org/10.1016/j.conbuildmat.2010.06.104

30.

Naghipour

Arefi

Nematzadeh

. Performance of longitudinal grooves to prevent debonding of GFRP sheets used for the reinforcement of WPC beams. Eur J Environ Civ Eng 2013; 17: 761–776. https://doi.org/10.1080/19648189.2013.815136

31.

Chakraborty

Chatterjee

. Selection of materials using multi-criteria decision-making methods with minimum data. Decis Sci Lett 2013; 2: 135–148. https://doi.org/10.5267/j.dsl.2013.03.005

32.

Nadir

Nagarajan

Ameen

, et al. Flexural stiffness and strength enhancement of horizontally glued laminated wood beams with GFRP and CFRP composite sheets. Constr Build Mater 2016; 112: 547–555. https://doi.org/10.1016/j.conbuildmat.2016.02.133

33.

Wang

, et al. An experimental and analytical study on the bending performance of CFRP-reinforced glulam beams. Front Mater 2022; 8: 2021.

34.

Abdelshahid

Nassar

Youssef

, et al. Evolutionary algorithm-based design and performance evaluation of wood–plastic composite roof panels for low-cost housing. Polymers 2025; 17: 795. https://doi.org/10.3390/polym17060795

35.

Fajdiga

Šubic

Kovačič

. Bending stiffness of hybrid wood-metal composite beams: an experimentally validated numerical model. Forests 2021; 12(7): 918. https://doi.org/10.3390/f12070918

36.

Glišović

Pavlović

Stevanovic

, et al. Numerical analysis of glulam beams reinforced with CFRP plates. J Civ Eng Manag 2017; 23: 868–879. https://doi.org/10.3846/13923730.2017.1341953

37.

Mrówczyński

Gajewski

Garbowski

. Application of the generalized nonlinear constitutive law in 2D shear flexible beam structures. Arch Civ Eng 2021; 67: 157–176. https://doi.org/10.24425/ace.2021.138049

38.

ASTM D905 . Standard test method for strength properties of adhesive bonds in shear by compression loading.

39.

ASTM D638 . Standard test method for tensile properties of plastics.

40.

ASTM D6108 . Standard test method for compressive properties of plastic lumber and shapes.

41.

ASTM D3039 . Standard test method for tensile properties of polymer matrix composite materials.

42.

ASTM E8 . Standard test methods for tension testing of metallic materials.

43.

Ogbonna

Akinlabi

Madushele

, et al. Grey-based taguchi method for multi-weld quality optimization of gas metal arc dissimilar joining of mild steel and 316 stainless steel. Results Eng 2023; 17: 100963. https://doi.org/10.1016/j.rineng.2023.100963

44.

Jing

Niu

Chang

P-C

. The application of VIKOR for the tool selection in lean management. J Intell Manuf 2019; 30: 2901–2912. https://doi.org/10.1007/s10845-015-1152-3

45.

Kiani

Liang

Gross

. Material selection for repair of structural concrete using VIKOR method. Case Stud Constr Mater 2018; 8: 489–497. https://doi.org/10.1016/j.cscm.2018.03.008

46.

Gentile

Galasso

. Simplified seismic loss assessment for optimal structural retrofit of RC buildings. Earthq Spectra 2020; 37: 346–365. https://doi.org/10.1177/8755293020952441

47.

ASTM D198 . Standard test methods of static tests of lumber in structural sizes.

48.

Niederwestberg

Zhou

Chui

Y-H

. Comparison of theoretical and laboratory out-of-plane shear stiffness values of cross laminated timber panels. Buildings 2018; 8: 146. https://doi.org/10.3390/buildings8100146

49.

Madabhusi-Raman

Davalos

. Static shear correction factor for laminated rectangular beams. Compos Part B Eng 1996; 27: 285–293. https://doi.org/10.1016/1359-8368(95)00014-3

50.

Garcia

Lotz

Martinez

, et al. Fatigue crack growth in residual stress fields. Int J Fatigue 2016; 87: 326–338. https://doi.org/10.1016/j.ijfatigue.2016.02.020

51.

ASTM D2555 . Standard practice for establishing clear wood strength values original title.