Laminated Veneer Lumber (LVL) panels made from poplar (Populus ussuriensis Kom.) and birch (Betula platyphylla Suk.) veneers were tested for mechanical properties. The effects of the on the (MOE) and modulus of rupture () of the LVL with vertical load testing were investigated. Three analytical methods were used: composite material mechanics, computer simulation, and static testing. The reliability of the different LVL assembly patterns was assessed using the method of Monte-Carlo. The results showed that the theoretical and ANSYS analysis results of the LVL MOE and MOR were very close to those of the static test results, and the largest proportional error was not greater than 5%. The veneer amount was the same, but the strength and reliability of the LVL made of birch veneers on the top and bottom was much more than the LVL made of poplar veneers. Good assembly patterns can improve the utility value of wood.
Mechanical properties analysis and reliability assessment of laminated veneer lumber (LVL) having different patterns of assembly
Bing Xue,a,b and Yingcheng Hu a,*
Laminated Veneer Lumber (LVL) panels made from poplar (Populus ussuriensis Kom.) and birch (Betula platyphylla Suk.) veneers were tested for mechanical properties. The effects of the assembly pattern on the modulus of elasticity (MOE) and modulus of rupture (MOR) of the LVL with vertical load testing were investigated. Three analytical methods were used: composite material mechanics, computer simulation, and static testing. The reliability of the different LVL assembly patterns was assessed using the method of Monte-Carlo. The results showed that the theoretical and ANSYS analysis results of the LVL MOE and MOR were very close to those of the static test results, and the largest proportional error was not greater than 5%. The veneer amount was the same, but the strength and reliability of the LVL made of birch veneers on the top and bottom was much more than the LVL made of poplar veneers. Good assembly patterns can improve the utility value of wood.
Keywords: Laminated veneer lumber (LVL); Mechanical properties; Assembly pattern; Reliability; Poplar; Birch
Contact information: a: Key Laboratory of Bio-based Material Science and Technology of Ministry of Education of China, College of Material Science and Engineering, Northeast Forestry University, Harbin, 150040, China; b: Heilongjiang Institute of Science and Technology, Harbin, 150027, China;
* Corresponding author: email@example.com
Wood is a hard fibrous tissue found in many plants. It has many favorable properties such as its processing ability, physical and mechanical properties, and aesthetics, as well as being environmentally and health friendly. People have used wood in many ways for thousands of years, primarily as either a fuel or a construction material for making houses, tools, weapons, furniture, packages, artworks, and paper (Bodig and Jayne 1982; Liu 2004). In many countries wood is widely used as the main source of building material.
Laminated Veneer Lumber (LVL) is defined as “a general description for an assembly of veneers laminated with an adhesive in which the grain direction of the outer veneers and most other veneers are in the longitudinal direction” (ISO 18776:2008). An increasing demand for environmentally friendly materials has resulted in an increased interest in laminated veneer lumber, as it can be manufactured from sustainable wood resources. Because of the low energy requirement and the ability for high production, LVL has become more and more popular, deemed as a highly reliable engineered wood product (Hata et al. 2001). LVL proved its usefulness and efficiency in construction framing materials such as girders, beams, joists (either in association with OSB for I-beams, or alone to produce long structural beams), headers, lintels, and columns, as well as scaffold planks and panels. LVL can also be manufactured in different sizes to suit architectural and structural aims if necessary. The LVL manufacturing process is reported to generate products of several dimensions. LVL has advantages over solid wood in strength, predictability of performance, available sizes, dimensional consistency, dimensional stability, and treatability, along with a higher wood utilization rate (13% more than that of sawn wood) (Pirvu et al. 2000; Deam et al. 2008; Hayashi et al. 2005; Kurt 2010).
There are many factors that affect the mechanical properties of LVL, such as compression ratio, size, wood species, binding agent, veneer defects, growth ring characteristics, and density of LVL. Compression control has significant effects on the modulus of elasticity, modulus of rupture, specific gravity, and thickness swelling of poplar LVL (Zhang et al. 1994). The influence of the partial moments of inertia and binding agents (mixture of epoxy or phenol-formaldehyde resins with sawdust) on bending properties of the primary perforated spruce and lime elements have been investigated (Reinprecht and Joščăk 1994). The effect of size on bending strength has been experimentally determined for laminated veneer lumber. Size was found to have no effect on the modulus of elasticity or modulus of rigidity (Fonselius 1997). The compression strength and the static bending strength of both beech and spruce LVL panels were higher than those of the respective solid wood groups obtained from the same logs. The impact strength of LVL panels, unlike the static bending strength and compression strength, was lower than those of the solid samples, which were not steamed and aged (Semra et al. 2007). The effects of assembly pattern and loading direction on the bending strength and modulus of elasticity in laminated wood materials produced from 3 mm thick veneers of beech (Fagus orientalis L.) and lombardy poplar (Populus nigra L.) placed one on top of the other in various arrangements were examined. The bending strength and modulus of elasticity of the solid woods (measured both perpendicular and parallel to the glue line) were observed to be smaller than those of laminated woods made of the same species of wood (Erol et al. 2007). Veneer defect and growth ring pattern measurements, obtained via optical scanning, were hypothesized to improve LVL static tensile strength property predictions. Improved LVL static tensile strength predictions could be achieved by integrating ultrasonic and optical systems (DeVallance et al. 2011).
Reliability analysis and design traditionally consider an ultimate limit state (ULS) to define a failure event. For an ULS, the resistance or capability is represented by some measure of structural strength, representing a maximum value of the structural resistance. Failure is said to occur when the predicted load or demand exceeds the predicted strength. The dominant strength failure modes are usually some form of collapse or ductile overload. Proper inclusion of a strength prediction in a structural reliability context requires the characterisation and consideration of all possible strength uncertainties (Chen 2003).
In the present study, the structure reliability of LVL was investigated. Particular attention was paid to the effects of the assembly pattern on the mechanical properties of the LVL. Three analytical methods were used to analyze the LVL mechanical properties: composite material mechanics, finite element analysis software, and static testing.
The rotary-cut veneers were made from panels composed of poplar (Populus ussuriensis Kom.) and birch (Betula platyphylla Suk.). The poplar and birch trees were harvested from Inner Mongolia. Round logs obtained from the trees were cut into stocks in rough sizes by taking into consideration final layer dimensions of 600 mm × 500 mm × 3.0 mm (length×width×thickness). A special emphasis was put on the selection of the wood material. Accordingly, non-deficient, proper, knotless, and normally grown (without zone line, reaction wood, decay, insect and fungal damages) wood materials were selected, making sure that the growth rings were perpendicular to the surface. The stocks were dried in a drying kiln until a moisture content of 7±1% was reached and were then stored in a natural environment. These stocks were later used to make 25 mm-thick ten-ply LVL in the laboratory.
The LVL panels were bonded with a commercial phenol-formaldehyde (PF) resin. The glue was spread at a rate of 150 g/m2 onto a single surface of each layer. Glue was spread uniformly on the veneers by manually hand brushing. The glued layers were brought together immediately, one on the top of the other, and were kept this way for 30 min before being hot-pressed in a pressing machine for a duration of 40 min under a pressing temperature of 160 ºC and pressure of 1.5 MPa. The target thickness of LVL panels was 25 mm.
There were ten-ply samples in nine different assembly patterns with 3.0 mm thickness veneers: (AAAAAAAAAA), (BBBBBBBBBB), (ABBBBBBBA), (AABBBBBBAA), (AAABBBBAAA), (AAAABBAAAA), (ABABAABABA), (BBAAAAAABB), and (BBBBAABBBB), with (A) representing birch wood and (B) representing poplar wood (Fig. 1).
Fig. 1. Assembly patterns of the samples: (A) birch, (B) poplar
Preparation of Test Samples
Test samples with dimensions of 575×90×25 mm were obtained from the LVL panels and used for vertical load testing (Fig. 2). Ten specimens were produced for each assembly pattern. All test samples were placed in a climatization chamber (temperature of 20±2 ºC and relative humidity of 65±5%) until the weights of the samples remained constant, for the purpose of homogenization of moisture by volume before the experiments.
Experiment and Analysis
Theoretical analysis, computer simulation, and experimental research were conducted on the mechanical properties of the LVL.
Mechanical property analysis included stiffness and strength testing. For the stiffness evaluation, the analysis was divided into three main groups: micro-mechanics, macro-mechanics, and structural mechanics. For the application of composite materials, the macro-mechanics were analysed to grasp the actual performance of the composite structure.
The computer simulation used in this experiment is widely applied in all kinds of fields due to its ability to carry out large calculations. First, the mechanical properties of the LVL were simulated using the computer program to determine the feasibility of this method for the LVL, and reusing the reliability analysis function for the reliability assessment of the LVL.
The static bending tests were conducted on the specimens in accordance with the Japanese Agricultural Standard (JAS) of Structural Laminated Veneer Lumber.
Fig. 2. Vertical load static test
The modulus of rupture is given by the equation:
where MOR is the modulus of rupture (MPa), F is the maximum load (N), l is the span in bending between the testing machine grips (mm), b is the cross sectional width in the bending test (mm), and h is the cross sectional thickness in the bending test (mm).
The modulus of elasticity is given by the equation:
where MOE is the modulus of elasticity in bending perpendicular to the grain (GPa), ΔF is the increment of load on the regression line with a correlation coefficient of 0,99 or better (N), Δy is the increment of deformation corresponding to F2 – F1 (mm), and l, b, and, h are the same as in Equation (1).
Composite Material Mechanics Analysis
In the theory of laminated beams in pure flexure, Young’s modulus, or the extensional modulus, can be estimated using the rule of mixtures (Gibson 2011; Bodig and Jayne 1982)
where Ex is Young’s modulus, or extensional modulus, of the laminated beam, E1 is Young’s modulus, or extensional modulus, of the first ply, E2 is Young’s modulus, or extensional modulus, of the second ply, V1 is the volume fraction of the first ply, and V2 is the volume fraction of the second ply.
The set of LVL panels was as a whole analyzed for mechanical properties. The thickness of the glue-lines was very thin, so the following presuppositions were enumerated for simplified analysis.
(1) The MOE of each veneer of a given wood species in the LVL panel was the same value;
(2) The adhesive spread in each glue-line was identical, and the glue was spread uniformity.
The deformation and breach of cell wall tissue texture was the provenance of the breach and deformation of the pure wood, as the cell wall is made of wood cellulose, lignin, and hemicellulose. The elasticity and strength of the panels were from the wood cellulose content. The cleavage strength of wood was attributed to hemicellulose. The elasticity and strength of wood was attributed to lignin (Liu 2004). The resistance to outside force was not changed after hot pressing because the amount of wood cellulose content in the LVL did not change. So the following expressions were found by introducing the theoretics of elasticity mechanics according as presuppositions,
where EL is the longitudinal MOE of LVL after hot pressing, VL is the volume of the LVL after hot pressing, EC is the longitudinal MOE of clear wood before hot pressing, and VC is the volume of clear wood before hot pressing.
In Eq. 5, Eb is the longitudinal MOE of birch clear wood, Vb is volume fraction of birch veneers, Ep is the longitudinal MOE of poplar clear wood, and Vp is volume fraction of poplar veneers.
The theoretical MOE of the LVL panels can be obtained from Eqs. (4) and (5), and Eb and Ep can be obtained from the static bending tests.
Macromechanical failure theories in composite materials include the maximum stress theory, maximum strain theory, Tsai-Hill theory (deviatoric strain energy theory), and Tsai-Wu theory (interactive tensor polynomial theory).
The maximum stress criterion states that failure occurs when at least one stress component along the principal material axes exceeds the corresponding strength in that direction. It can be expressed as,
Tensile stresses: (Fiber break) or (Matrix crack), (6)
Compressive stresses: (Fiber crushing) or (Matrix yielding), (7)
where 1 and 2 are the longitudinal and transverse principal stresses, and F1 and F2 are the longitudinal and transverse allowable tensile (t) or compressive (c) stresses.
The maximum strain criterion states that failure occurs when at least one of the strain components along the principal material axes exceeds the ultimate strain in that direction. It can be expressed as,
Tensile stresses: (Fiber break) or (Matrix crack), (8)
Compressive stresses: (Fiber crushing) or (Matrix yielding), (9)
where and are the longitudinal and transverse principal strains and and are the longitudinal and transverse allowable tensile (t) or compressive (c) strains.
The Tsai-Hill theory originated from an extension of the Von Mises criterion for ductile anisotropic materials. Azzi-Tsai extended this equation to include anisotropic fiber reinforced composites. The Tsai-Wu theory is a simplification of the Gol’denblat and the Kapnov generalized failure theories for anisotropic materials (Gibson 2011). Both apply to material strength analysis in a complex stress state. Maximum stress or strain criterion can satisfy the requirements of strength analysis in this study.
ANSYS offers a comprehensive range of engineering simulation solution sets, providing access to any virtual field of engineering simulation that a design process requires. This finite element analysis program was applied to simulate the mechanical properties of the LVL in this study. Structural mechanical solutions from ANSYS provide the ability to simulate every structural aspect of a product. In order to examine the distribution of internal stress of each ply of the LVL, simulating by the PLANE82 element, the simulation analysis was executed using the same acting point of force as a static experiment.
As a generalization in structural design, the variables representing the load effects the resistance properties of the structure and cannot be known completely; therefore, they must be described as random variables, which have a mean and an assumed underlying probability distribution. A given design situation can be described mathematically by a function of the basic random variables in the form,
where X = (X1, X2,…Xn) is the vector of these basic random variables. By convention, the limit state function g(X) is formulated such that g(X)<0 when the structure does not perform as intended (known as “failure”).
In this study, the generalized reliability level was assessed by the first order second moment method, the second order second moment method, and the stochastic finite element method, etc. (Gong and Wei 2007).
The Monte-Carlo method is a stochastic finite element method. Monte-Carlo simulations have the major advantage of producing accurate solutions, which can be obtained for any problem whose deterministic solution is known, since it statistically converges to the correct solution provided that a large number of simulations are employed. The basic principles of direct Monte-Carlo simulations are used to generate a sampling of the input parameters in accordance with their probability distributions and correlations. For each input sample, a deterministic finite element analysis is carried out, giving an output sample. Finally, a response sampling is obtained, from which the mean and the standard deviation of the response can be derived.
The estimator of the response is defined by
where n is the number of samples and y(i) is the response corresponding to the ith input sample (Schenk and Schuëller 2005). The estimator is a random variable whose mean and variance are given by
where and denote the unknown mean and variance of the response, respectively. Tchebychev’s inequality provides a basis for error assessment, i.e.,
where ε denotes a tolerance. A confidence level 1–δ can be defined where . According to the central limit theorem, the distribution of is normal and the confidence interval corresponding to the confidence level 1-δ is,
where Φ is the normal cumulative distribution function.
Derivation of serviceability limit state function
A serviceability limit state for LVL systems can be defined in terms of a limiting maximum mid-span deflection, typically expressed as a fraction of the span. The span cannot be arbitrarily chosen, since the design of the LVL system must be in accordance with existing code provisions. The mid-span deflection calculation of flexural members is not more than,
where Zn is the allowable deflection and l is the span length.
where Zu is the deflection due to the factored nominal loads and is a serviceability resistance factor.
The deflection Zu in this study’s static bending tests should be expressed as,
where F is the test load, En is the nominal elastic modulus, b is the cross sectional width in a bending test specimen, and h is the cross sectional thickness in a bending test specimen.
To ensure conservative results in the reliability analyses, the upper limit of the span length was used. After establishing the relationship between the span and the size, the serviceability limit state function is written as,
where is the maximum deflection occurring during the reference period due to the characteristic of the random variable.
Derivation of Strength Limit State Function
A strength checking equation for a LVL system may be written in a form that includes a system factor,
where Zn is the nominal strength (i.e. the flexural moment capacity), Zu is the required strength (i.e. the moment created by the factored loads), λ is a factor that accounts for duration of-load effects, and γ is a strength resistance factor. The Zn can be regarded as the theoretical and experimental MOR of the LVL in this study.
Individual members in the system were deemed to have failed the strength limit state when either the flexural stresses exceeded the MOR or the accumulated damage reached the limit state defined by,
where αi is the damage increments produced by each of the random variable pulses.
RESULTS AND DISCUSSION
The MOR ( ) and MOE (EC) of poplar and birch clear wood before hot pressing were obtained by a bending statics test. Ten specimens were produced for each wood, and the average values are provided in Table 1, along with the standard deviations (STD) of each wood test. The theoretical MOR and MOE of each LVL assembly pattern after hot pressing could be determined by substituting into Eqs. (6) and (7) or by substituting EC into Eqs. (4) and (5). All the theoretical MOR and MOE of each assembly pattern after hot pressing are provided in Tables 3 and 4 in order to facilitate the comparison of all analysis results.
Table 1. The MOR and MOE of Clear Wood
The mechanical properties of different LVL assembly patterns were simulated using the finite element analysis program ANSYS to examine the practicability of finite element analysis on LVL. With a vertical loading of 1 N, the stress distributions on the vertical longitudinal section of the LVL test specimens for assembly patterns (I), (II), and (III) are provided in Fig. 3. The changes in stress distribution gradient were a pretty clear distinction among those various LVL assembly patterns; these results were consistent with the composite material mechanical analysis results and therefore the maximum plus-minus stress on each assembly pattern were different.
In order to show a clearer stress distribution of each LVL specimen, assembly patterns (I) and (VII) were chosen, and the stress distribution along the thickness direction of the mid-span section for the two assembly patterns are shown in Figs. 4 and 5, and the maximum stress for each assembly pattern are shown in Table 2.
The analysis results of MOR and MOE were obtained by ANSYS, and are provided in Tables 3 and 4 in order to facilitate the comparison of all analysis results.
Table 2. The Maximum Stress in Each Assembly Pattern
Fig. 3. The stress distribution on vertical longitudinal section of assembly patterns (I), (II), and (III)
Fig. 4. The stress distribution along the thickness direction of the mid-span section of assembly pattern (I)
Fig. 5. The stress distribution along the thickness direction of the mid-span section of assembly pattern (VII)
As shown in Figs. 4 and 5, the ply direction path mid-span stress distribution curves of assembly patterns (I) and (II) were straight lines, while those of other patterns not provided and assembly pattern (VII) were curves. Obviously, the different wood species of each layer caused the change in stress distribution: the form of the stress distribution had become more complicated, the slope had an obvious change in the place of the two different wood species junction, and the curve line slope of assembly pattern (VII) had the greatest change (so it was chosen to show stress change). The main reason for the change is that birch (A) and poplar (B) have different MOE. LVL assembly patterns (I) and (II) were nearly uniform in rigidity, because of the effective bonding between (A) and (B), which affected deformation coordination, so other assembly patterns were not. Nevertheless, assembly pattern (VII) was assembled with an alternative distribution of (A) and (B) and its MOE varied for each ply.
As shown in Table 2, the maximum stress was associated with assembly pattern (III), and the minimum with assembly pattern (VIII). The main reason of the aforementioned results was that the MOE of birch (A) is greater than that of poplar (B), meaning a greater resistance to deformation for (A), so the existence of deformation coordination made the birch veneers a major contributor; the margin plate was (A) in LVL assembly pattern (III) and the margin plate was (B) in LVL assembly pattern (VIII).
The result of ANSYS analysis was consistent with the composite material mechanics analysis, so the ANSYS software can be applied to LVL mechanical analysis.
The MOE and MOR of each LVL assembly pattern were obtained by a bending statics test, and the average values are provided in Tables 3 and 4. The failure mode of each LVL specimen was veneer breakdown during the flexural testing, the phenomemon of adhesive debonding did not occur, all test results were available.
Table 3. The Three Results of MOE of Each Assembly Pattern (GPa)
As shown in Table 3, MOE1 or MOE2 of each assembly pattern was very close to the MOE results, with each proportional error absolute value not greater than 2.43% or 4.19% with the confidence coefficient being greater than the general confidence limit of 95%. So Eqs. 3 to 5 and ANSYS simulation analysis were appropriate for the rigidity solution of LVL mechanical properties, which can be applied to the reliability analysis of LVL in serviceability limit states.
Table 4. The Three MOR Results of Each Assembly Pattern (MPa)
As shown in Table 4, MOR1 or MOR2 of each assembly pattern was very close to the test results MOR, with each proportional error absolute value not greater than 3.98% or 4.90%, with a confidence coefficient greater than 95%. So obviously, Eqs. 6 and 9 and ANSYS simulation analysis were appropriate for the strength solution of LVL mechan-ical properties, and they can be applied to the reliability analysis of LVL in strength limit states.
There was the same amount of poplar and birch veneers in assembly patterns (III) and (IX). Pattern (V) had the same amount as (VII) and (VIII), but their MOR were much different; the MOR of assembly pattern (III) was more than that of assembly pattern (IX), and the MOR of assembly pattern (V) was close to that of (VII) and more than that of (VIII). The main reason is as follows: although the veneer dosages were the same, the internal stress was a symmetric triangular distribution along the vertical cross section, the stress was zero on the plane of symmetry, lower elastic layers receiving less stress (Serrano et al. 1996), so the strength of the LVL with high strength birch veneers on the top and bottom was much more than the strength of the LVL with low strength poplar veneers on the top and bottom. So a good assembly pattern can improve the utility value of wood and get a better ratio of strength to price.
The reliability analysis of LVL was divided into two parts. The first was serviceability limit state and the second was strength limit state. The random variables included the MOR and MOE of poplar and birch clear wood, the width and thickness of LVL specimens, and the different load conditions. The existing random variables from the test are provided in Table 5. The load conditions referenced the related standard, as the applications that confine the two kinds limit states are different. Two load conditions were chosen; the first condition was used for the reliability analysis of the serviceability limit state, and the other was used to for the reliability analysis of the strength limit state.
The relevant data was input to the ANSYS, using the reliability analysis function. The reliability of each LVL was obtained and provided in Table 6, with Pr representing the reliability by the serviceability limit state and Pr’ representing the reliability by the strength limit state.
Table 5. The Random Variables of Test Data
Table 6. The Reliability of Different Assembly Patterns LVL
As shown in Table 6, the maximum reliability achieved was with assembly patterns (I) and (III) in the serviceability limit state and (I) in the strength limit state. The minimum reliability was with assembly pattern (II) in the serviceability limit state, and the strength limit state was the same for all patterns. As described above, there were equal amounts of poplar and birch veneers in assembly patterns (III) and (IX); (V) was the same as (VII) and (VIII), but their mechanical properties were much different. The reliability was also different under the same load conditions; the reliability of assembly pattern (III) was more than that of assembly pattern (IX), and the reliability of assembly pattern (V) was close to that of (VII) and (VIII) in the serviceability limit state, but the reliability of assembly patterns (V) and (VII) were more than that of (VIII) in the strength limit state. The main reason for this is as follows: the same veneer dosage of LVL had similar MOE and different MOR, the central interlayer had less of an effect on the strength and strength reliability of LVL.
- The MOE results of theoretical analysis of each LVL assembly pattern were very close to the test results. The confidence coefficients were above the general confi-dence limit at 95%. Thus, Eqs. 4 and 5 can be considered as appropriate for the rigidity solution of LVL mechanical properties.
- The MOR results of the theoretical analysis of each LVL assembly pattern were very close to the test results. The maximum stress and maximum strain criterion were found to be appropriate for the strength solution of LVL mechanical properties.
- Similarly, the ANSYS simulation analyses were appropriate for the LVL mechanical property analysis.
- Although the veneer dosages were the same, the strength of LVL with birch veneers on the top and bottom were much greater than the strengths of LVL with poplar veneers on the top and bottom. A good assembly pattern can improve the utility value of wood and provide a better strength-to-price ratio.
- When the veneer dosages were the same, the MOE of each LVL assembly pattern was very close, and the serviceability limit state reliabilities were close as well. The strength limit state reliability was different, however, with the reliability of LVL with birch veneers on the outer surface being greater.
- These results pertain to LVL that is defect-free and may not hold true if defects and varied grain deviations are present in the veneer that makes up typical LVL.
This project was supported by the National Natural Science Foundation of China (31170516), the Program for A Foundation for the Author of National Excellent Doctoral Dissertation (200764), the Fundamental Research Funds for the Central Universities (DL09DB02), and the Scientific Research Fund of Heilongjiang Provincial Education Department (NO: 12511488).
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Article submitted: December 1, 2011; Peer review completed: January 15, 2012; Revised version received and accepted: February 11, 2012; Published: February 14, 2012.