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The effect of fines on oriented strandboard bending properties Cafferata, Alicia 2003

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The Effect of Fines on Oriented Strandboard Bending Properties By Alicia Cafferata B.Sc. Trent University, 1996 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE in THE F A C U L T Y OF G R A D U A T E STUDIES (Department of Wood Science) We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH C O L U M B I A August 2003 © Alicia Cafferata, 2003 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of The University of British Columbia Vancouver, Canada Date / [ C * f l _ , « g / b 5 DE-6 (2/88) Abstract The presence of fines in oriented strandboard (OSB) can influence the profitability of a mill. Because the disposal of fines can be costly, mill managers may be compelled to incorporate them into the final product. However, the presence of fines in the product diminishes certain technical attributes such as the bending properties. The objective of this study was to assess the effect of the proportion and location of fines on the modulus of elasticity (MOE) and modulus of rupture (MOR) of oriented strandboard. The research program employed a 91 cm by 91 cm (3 ft by 3 ft) electrically heated laboratory press to produce OSB in two phases: alternating layers of strands and fines (a "homogeneous" distribution); and, fines in the core only (sandwich construction with multiple layers of strands adjacent to one another and only one layer of fines). In both cases, the strands were oriented parallel to one another and the parallel orientation was confirmed using an imaging system (SAM-Weyerhaeuser). The homogeneous distribution results showed that for a constant density: • M O E decreased in linear fashion with an increase in fines as confirmed with literature data; • M O R decreased linearly with increased fines; • The mechanical properties are amenable to modeling using the Rule of Mixtures. The sandwich construction results showed that for a constant density: • M O E (in the plank orientation) did not decrease in a linear fashion with an increase in fines; • M O E / M O R (in the joist orientation) decreased linearly with an increase in fines; • The joist properties are amenable to modeling using the Rule of Mixtures; • The plank M O E can be modeled using simple beam bending theory; • The M O R (plank orientation) cannot be modeled using either Rule of Mixtures or simple beam bending theory • Failure mode in the plank orientation can be predicted (for these specific conditions); i.e., boards between 10 to 45% fines typically fail in shear • The end use of the panel (i.e. as a joist or as a plank) affects the degree to which fines affect the bending properties This work suggests that it may be possible to increase the use of fines in sheathing products while maintaining individual mill strength requirements i f the fines are limited to the middle of the panel. The effect of fines on the pressing cycle and the effect of adding fines to the center of the panel on other strength properties such as the nail holding or the shear strength properties are beyond the scope of this work and have yet to be explored. Table of Contents Pa] Abstract Table of Contents List of Tables List of Figures Acknowledgements 1. Introduction . 2. Background 2.1 Particle size effects 2.2 Research on Fines 2.3 Models 3. Experimental Study 3.1 Material 3.2 Blending '. 1 3.3 Mat Formation 3.4 Pressing 3.5 Testing 1 4. Results and Analysis 4.1 Uniform Distribution Results and Analysis 4.1.1 Results-Uniform (homogenous) Fines Distribution... 4.1.2 A N O V A Tables for the Uniform Distribution Bending Data 4.2 Sandwich Distribution Results and Analysis 4.2.1 Results-Sandwich distribution 4.2.2 A N O V A Tables for the Sandwich Distribution Bending Data 5. Physical Models 5.1 Uniform Distribution 5.2 Sandwich Distribution 5.2.1 Predicting mode of failure 6. Discussion 6.1 Density and densification 6.2 Deflection due to shear 6.3 The Rule of Mixtures 6.4 Simple Beam Bending Model (transformation of sections) 6.4.1 Plank-MOE 6.4.2 Plank-MOR 7. Conclusions 8. Future Work •. References Appendix A : Cutting pattern Appendix B- A N O V A Analysis of M O E and M O R values Appendix C- A N O V A Analysis of Panel Density and Maximum Face Density. Appendix D: Statistical Analysis T-tests List of Tables Page Table 3.1 Uruform Distribution of Fines Treatments 9 Table 3.2 Sandwich Distribution of Fines Treatments in the Core 9 Table 3.3 Weight, average length and width of the furnish 10 Table 3.4 Fines Classification using a William's Classifier 11 Table 3.5 The Number of Layers of Strands for Each Mat Formation 13 Table 4.1 Plank (Face) Bending Results-Uniform Fines Distribution 17 Table 4.2 Joist (Edge) Bending Results-Uniform Fines Distribution 17 Table 4.3 A N O V A Table Uniform Fines Distribution MOE-Plank 19 Table 4.4 A N O V A Table Uniform Fines Distribution MOE-Joist 19 Table 4.5 A N O V A Table Uniform Fines Distribution MOR-Plank 19 Table 4.6 Plank (Face) Bending Results-Sandwich distribution 21 Table 4.7 Joist (Edge) Bending Results-Sandwich distribution 22 Table 4.8 A N O V A Table Sandwich Distribution MOE-Plank 23 Table 4.9 A N O V A Table Sandwich Distribution MOE-Joist 23 Table 4.10 A N O V A Table Uniform Distribution MOR-Joist 24 Table 5.1 Predicted Vs Experimental Values for the Uniform Distribution in 25 the Plank Orientation Table 5.2 Predicted Vs Experimental Values for the Uniform distribution in 26 the Joist Orientation Table 5.3 Predicted Vs Experimental Value for Plank and Joist M O E 29 Sandwich Distribution Table 5.4 Predicted Vs Experimental Value for Joist MOR-Sandwich 29 Distribution Table 5.5 Experimental Maximum Loads for Bending and Shear Failures in 32 Sandwich Construction Table 5.6 Maximum Loads as Calculated Using the Estimated Failure 36 Criteria iv List of Figures Page Figure 2.1 Transformed OSB Sandwich Panel (where n = Efl Es) 8 Figure 3.1 Distribution of strand length before and after screening 10 Figure 3.2 33.3% Fines Uniform Distribution prior to pressing 14 Figure 3.4 33.3% Fines Sandwich Distribution prior to pressing 14 Figure 4.1 MOE-Uniform Distribution: Plank vs. Joist 18 Figure 4.2 MOR-Uniform Distribution: Plank vs. Joist 18 Figure 4.3 MOE-Sandwich Distribution: Plank vs. Joist 22 Figure 4.4 MOR-Sandwich Distribution: Plank vs. Joist 23 Figure 5.1 Plank MOE-Experimental vs. Predicted Data by the Rule 26 of Mixtures Figure 5.2 Joists MOE-Experimental vs. Predicted Data by the Rule 27 of Mixtures Figure 5.3 Plank MOR-Experimental Data vs. Predicted Data by the 27 Rule of Mixtures Figure 5.4 Joist MOR-Experimental Data vs. Predicted Data by the 28 Rule of Mixtures Figure 5.5 Planks MOE-Experimental vs. Predicted Data by 30 Transformed Sections Figure 5.6 Joists MOE-Experimental vs. Predicted Data by the Rule 30 of Mixtures Figure 5.7 Joists MOR-Experimental vs. Predicted Data by the Rule 31 of Mixtures Figure 5.8 Shear Failure in the Sandwich Construction (33.3% fines) 31 Figure 5.9 Possible Failure Stresses for the Sandwich Construction 32 Figure 5.10 Failure Prediction for Sandwich Boards Tested in the 36 Plank Orientation v Acknowledgements Completing this thesis was made much easier because of the help and guidance I received from a number of people, most notably Dr. Barret, Dr. Lam and Derek Barnes. The set-up of the test equipment and the testing procedures were simplified thanks to the support of Bob Myronak and Avtar Sidhu. A special thanks to both Ainsworth Lumber Canada, Ltd. and Borden Resins for providing the wood furnish and the necessary resins. vi 1. Introduction Composite wood products were originally developed to fill voids in the market place and to use unwanted wood residues (Maloney, 1993). Up until the later half of the 20 t h century, wood -building materials consisted mainly of solid timber or plywood. By the end of the 20 t h century, the choice of building materials had grown to include particleboard, medium density fibreboard, oriented strandboard, glulam, L V L , parallel strand lumber and finger-jointed lumber to name a few. Each of these products was developed to fill the void in the market place created by a changing resource and a changing market. As the market and the resource base continue to change, wood composites will have to develop to meet the new challenges (Geimer et al, 2000). Presently, oriented strandboard (OSB) is predominantly sold as a commodity product. The largest market for oriented strand board (OSB) is the structural panel market (RISI, 2002). As a commodity-building product, its prices are cyclic with the housing starts and the capacity of the market (RISI, 2002). The large growth rate of OSB has been largely due to its ability to replace plywood in the structural panel market. However, the ability or rate at which it will continue to do this is diminishing (Shell, 2001). Although OSB has just over 50% of the structural panel market (RISI, 2002), it is considered by some to have reached or be nearing the maturity part of the product life cycle (for the structural panel market). In this stage, the supply begins to exceed the demand and the profit margin tends to decrease due to strong competition (Kotler and Turner, 1998). As the level of competition increases, companies strive to improve mill efficiency to lower productions costs and/or create new products with higher profit margins. In order to maintain the growth of the industry, new OSB products are needed in the market in addition to relying on further decreases in plywood capacity. Some of markets available to OSB are the higher strength markets, such as concrete formwork panels, beams, headers and furniture grade panels. Because fines are an inherent part of the process, their impact on both strength and cost properties should be considered when new products are developed. Fines are a byproduct of strand processing and can constitute 20-40% (by weight) of the mills furnish. The definition of fines varies from mill to mill; generally any particle that passes through a 9mm (3/8 inch) opening on a Williams's classifier could be considered a fine. For the purpose of this study, fines are defined as the furnish material which passes through a 14 mm x 14mm (9/16 inch x 9/16 inch) mesh. It is the size of the fine particle that causes problems in the plant. A mill is designed to operate within a given strand geometry range, therefore extremes on either end can pose problems. For example, fines have a higher surface area per weight than strands and tend to attract more resin when blended with strands (Maloney, 1993). This can increase resin costs for a plant. Also, orienter disks or vanes are designed to align the average size strand but they do not orient fines. Loss of alignment has been shown to decrease strength (Candido et al, 1988; Barnes, 2000). This can be significant i f the percentage of fines in the furnish is high. Presently mills employ one or more of the following strategies when dealing with fines: 1 do nothing; screen the fines and then redistribute them to the core of the panel, and/or screen them out and dispose of them by either land filling or burning or both. Wood cost is an important variable to consider when managing fines. Wood cost is the largest component of the final production cost of OSB (RISI, 2002). Depending on fibre availability screening the fines out and/or burning them in a recovery system may not be the economically preferred choice. Increased production capacity of mills, as well as new mills has led to both a shortage of fibre in parts of North America and to an increase in the fibre cost (Geimer et al, 2000). Mills would reduce wood costs i f fines could be used appropriately in panel production. Therefore, understanding the effect of fines on the bending properties would help producers make economically sound decisions related to the use of fines. This study was a first step in assessing the effect of fines on the bending properties of OSB. The material produced did not have a cross-oriented layer common to many of the commercially available OSB and, as such, no industrial comparisons were made. A l l the boards were made at the University of British Columbia using a 91 cm by 91 cm Pathex press. The mats were formed by hand according to a pre-determined plan. In total twenty-seven 63.5 cm x 63.5 cm x 1.9 cm (25 in. x 25 in. by 3A in.) boards were made. The boards were tested for modulus of elasticity (MOE), modulus of rupture (MOR), and internal bond. The bending tests (MOE/MOR) were done on both the face (i.e. plank) and the edge (i.e. joist) orientations of the panels. The results were statistically analyzed and models were developed using the Rule of Mixtures and simple beam bending theory (transformation of sections). 2 2. Background There are six main properties, which can affect the strength of oriented strandboard. These properties are particle geometry (Keiser et al, 1978; Shuler, 1976), density (Maloney, 1993), resin content (Brumbaugh, 1960), moisture content (Kelly, 1977), pressing cycle (Kelly, 1977) and the orientation of the particles (McNatt et al, 1992; Barnes, 1988). Although the properties can act independently of one another, complicated interactions exist between them. Because it is the particle geometry of the fines that mostly affects its strength contribution, only the effect of its particle geometry and the interactions with other key properties are considered in this section. 2.1 Particle size effects The dependence of strength on particle geometry is demonstrated when particleboard is compared to OSB. Particleboard is significantly weaker than OSB (when similar densities are compared). Various research has shown that as the length of the strand increases (with a constant thickness) so do the bending properties of the board (Post, 1958; Turner, 1954; Brumbaugh, 1960; Candido et al., 1988, 1990). Barnes (2001) stated that the increase in strength was due to an increase in the length of the glue line. Longer strands (i.e. longer parallel glue lines) decrease the angle through which stress is transferred from one strand to another; a smaller angle results in a stronger glue line. Conversely, one could predict that fines have shorter and therefore weaker glue lines. Another consideration is that a continuous chain of fiber is stronger than a discontinuous chain linked together through resin bonds. This is demonstrated, for example, when solid wood is compared to composite lumber. Comparing similar densities and species and ignoring the higher variability on solid wood, solid wood is always stronger than composite lumber at the same density level. Blending fines together with strands can lead to a decrease in the final board strength. Increasing the resin content of OSB has been shown to improve the mechanical properties (Avramidis et al, 1989; Barnes, 2000; Lehman, 1974): more resin on the flake is equated with more bonds between the flakes. However, when strands and fines are blended together, the fines tend to have higher resin coverage than strands because of the higher total surface area in the fines (Maloney, 1993; Campbell, 1997). This may decrease the final strength of the board since the main structural components of the board, i.e. the strands, have less resin on them. Including fines may also increase the cost of production by requiring more resin to be added to the mixture. As mentioned earlier, orientation of the particle also affects the strength properties of members. The strength and stiffness of boards can be doubled depending on the degree of orientation of the strands (Candido et al, 1988,1990; Barnes, 2000). When strands are oriented parallel to the main strength axis, the cellulose chains are also aligned and greater strength can be achieved. This is similar to the grain angle effect in solid wood. Hankinson introduced a model that predicts the strength of solid wood as a function of the grain angle based on the parallel and perpendicular to grain strength (Bodig and 3 Jayne, 1993). The equation has been modified to predict the M O E of a specimen (Bodig and Jayne, 1993). F F £ para perp 1 -v Eparasm2e + Eperpcos2d where E para the M O E in the parallel direction Eperp ~ t n e M O E in the perpendicular direction 0 = grain angle E = the predicted M O E of the specimen with a grain angle of 6. From this equation, maximum parallel M O E is achieved when the strands are oriented zero degrees or parallel to the main strength axis. Shaler and Blankenhorn (1990) used this formula to predict the effect of strand orientation on the elastic moduli for flakeboard. Barnes (2000) further modified this equation (see equation 2) and successfully used it to predict the effect of strand orientation on the M O E and M O R of OSB. E = E Q parage E„„rasin" d + Qcos" 6 (2-2) where E para the M O E in the parallel direction Q = (assumed to be) 1 /20 t h of the maximum parallel M O E 6 = strand angle E = the predicted M O E of the composite with a strand angle of 6. n - 3.3 -1.2 db (for M O E calculations) or n = 3.62-16.2 d b (for M O R calculations) where db = in situ strand thickness Again, maximum strength is predicted to occur when the strands are aligned parallel to the main strength axis. Because fines can represent a large portion of the board, their lack of orientation (both in plane and out of plane orientation) may decrease the bending properties of the board (Xu et al, 1998). 2.2 Research on Fines Relatively little research has directly examined the effect of fines on board properties. Keiser and Steck (1978) observed in experiments that smaller particles weakened OSB. When strength properties were compared to the amount of fines in the furnish, a linear 4 decrease in either M O E and/or MOR was observed when the fines were distributed evenly throughout the mat (Mottet, 1967 in Maloney, 1993; Barnes, 2002). A n increase in strength properties (when compared to the even distribution of fines) was observed with the exclusive placement of the fines in the core (Barnes, 2002). Only Barnes (2000, 2002) attempted to model the effect of fines, he used linear and curvalinear equations to describe the observed decrease in strength. The fines model is part of a more complete model that can be used to predict the end strength of OSB. 2.3 Models Another approach to modeling the effect of fines is to consider a mechanistic model. For the purpose of this research, it is assumed that fines are either distributed randomly throughout the board or located mostly in the center of the board. With this in mind, a panel is considered to have alternating layers of strands and fines (homogeneous distribution of fines) or a layered construction of strands-fines-strands (sandwich distribution). This may be further viewed as thin OSB layered with thin particleboard. With this approach, both the Rule of Mixtures and/or simple beam bending theory could be applied to predict the M O E of the composite member provided the MOE's of the strand layer and of the fines layer are known. Both the Rule of Mixtures and the transformation of sections (for beam bending) have been used successfully to calculate the M O E of OSB (Schaler et al, 1990; Filho, 1981; Hoover et al, 1992; Hunt et al, 1985: X u et al, 1998; Lee et al, 1997; Geimer et al, 1975). Shaler (1990) attempted to predict OSB strength using the rule of mixtures with the elastic modulus of the flakes and the elastic modulus of the resin. The values were adjusted for such variables as alignment, density, flake geometry and species. Filho (1981) examined the effect of wood furnish type (strands made from pulp chips vs. strands made from round-wood) on properties of oriented strand board. Using the rule of mixtures he was able to predict the parallel bending properties of the mixed strand boards. Lee (1997) successfully used transformation of sections to estimate the M O E of a bamboo-OSB beam. Hunt (1978, 1983, 1985) had used the transformation of sections extensively in a joint research program between Purdue University and the U.S. Forest Service's Forest Products Laboratory. The objective of the research program was to identify new or improved products manufactured from under-utilized (high density) species. Hunt applied transformation of sections to predict end properties of the boards; the boards that met the specified strength requirements were then made in the laboratory and tested. The M O E values of the furnish of interest were found in the literature (Hunt et al, 1978). Adjustments to literature values were made in order to account for the effect of alignment on M O E (Hunt et al, 1978). For one these investigations, Hunt with Hoover (Hoover et al, 1985) used fine like material as their core material. The core material was comprised of 0.762mm (0.03 inch) thick and 19 mm (3/4 inch) long ring flakes; flakes that passed through a 16-mesh screen were discarded. Hoover and Hunt (1985, 1992) applied the rule of mixtures to mixed species boards. They made experimental panels of single species 5 boards and used those properties to predict the mixed species boards. They then used the mixed board predicted values in the transformation of sections to decide on the final composition of the test panels. The final predicted values matched well with actual test values. Like Hunt and Hoover, Geimer (1975) also used the transformation of sections to predict board properties. Geimer (1975) also used fine-like material in the core of his panels. The core material was 0.51mm (0.020 inch) thick by 19mm (% inch) long strands produced from pulp chips. The face material was 0.51mm (0.020 inch) by 12.7mm (0.5 inch) by 51mm (2 inch) flakes. He produced boards of varying thickness and face to core ratios. For one series of test specimens, he separated the face and core layers and then tested the individual layers for stiffness in tension parallel to the surface. The core was further tested in interlaminer shear. He then used these values to predict the board stiffness and found good agreement between the predicted values and experimental values. He further modified these values to account for a varying density gradient (in the z-plane), which further improved the predictions. The Rule of Mixtures and the transformation of sections as applied to a bending beam are shown below. The above-mentioned papers used either this exact form of the equation or a modified version of these equations. The rule of mixtures is as follows: Ep ~ Vfines E fines ^strands ^strands (2-3) where Ep = the predicted composite M O E value Vfines = t n e t o t a l volume of the fines (expressed as a percentage of the total volume) E fines = m e M O E value of the fines Ktrands ~ m e t o t a l volume of the strands (expressed as a percentage of the total volume) ^strands = m e M O E value of the fines. Transformation of sections applied to a sandwich construction: EPI0 = Estrandsr (2.4) where Ep = the predicted M O E I0 = the second moment of inertia 6 (2.4.1) and b = d •^strands r Or /•=I(/,+M2) where /, = Ai the width of the specimen the depth of the specimen the M O E of the strands the transformed second moment of inertia (2.4.2) the moment of inertia of the i t h simple shape about its own centroidal axis the area of the i t h simple shape distance between the centroidal axis of the i * simple shape and the centroidal axis of the entire section As shown in Figure 2.1, / can be re-written for a sandwich distribution as follows: (2.4.3) / =2 12 V V d / J s / 2 / 2 \2"\ (Ef btl^ Es 12 v * J where Ef Es b d ts tf the M O E of the fines the M O E of the strands the width of the specimen the depth of the specimen the thickness of the strand layer the thickness of the fines layer 7 Strands Fines transformed to an equivalent Strand section Strands Figure 2.1: Transformed OSB Sandwich Panel (where n = E/l Es) Although both the Rule of Mixtures and the transformation of sections have been used effectively to predict flatwise MOE, they have not been used to specifically predict the effect of fines on other OSB properties. Experimental studies conducted by both Filho (1981), Hunt and Hoover (1985), and Geimer (1975) used pulp chips that were close to representing fines but the effect of fines on the edge bending properties of OSB has not been examined. From the previous research, it is known that the flat-wise M O E and M O R properties of OSB are negatively affected by the addition of fines. This research will attempt to build and expand on earlier models based both on the Rule of Mixtures and on transformation of sections. Such models will include M O E and MOR predictions for the different compositions of strands and fines. The panels will also be evaluated on the effect of fines on edge bending properties. 8 3. Experimental Study To evaluate the effect of fines on the bending properties of OSB, 63.5 cm x 63.5 cm x 1.9 cm boards were made in the laboratory. Two types of panels were evaluated: panels with uniformly distributed fines (homogeneous distribution) and panels with a layer of fines in the core (sandwich distribution). The quantity (weight %) of fines was then varied within each part. The experimental design used was a completely random design with three replications and four observations of bending data for each condition. The cells for each group, 12 for the uniform distribution and 15 for the sandwich distribution, were then randomized and the boards were made. The treatments (or fines addition levels) are shown in tables 3.1 and 3.2. Table 3.1:1 Jniform Distribution of Fines Treatments Condition % of Fines % of Strands Replications 1 100 0 3 2 0 100 3 3 33.3 66.6 3 4 66.6 33.3 3 Table 3.2: Sandwich Distribution of Fines Treatments in the Core Condition % of Fines % of Strands Replications 1 10 90 3 2 20 80 3 3 33.3 66.6 3 4 50 50 3 5 66.6 33.3 3 Each panel produced four bending specimens and 10 to 12 internal bond (IB) specimens. In total each condition had 12 bending specimens and 30 to 36 IB specimens. The target density of the lab panels was 641 kg/m 3 (40 lbs/ft3) oven-dry. The target thickness was 19.05 mm (% inch). Because furnish, resin, orientation of the strands, moisture content and pressing cycles affect the end strength of OSB; these factors were controlled and monitored in the laboratory. The following section describes how the panels were made and tested. 3.1 Material A local mill provided the required volume of strands and fines. The furnish was dried and screened at the mill prior to shipment. The entire volume of furnish required for all the proposed panels was shipped at the same time. This was done in an attempt to reduce the potential variation in furnish due to mill processes and seasonal variations. The species mixture was approximately 80% Aspen, and 20% spruce and pine. Before the test panels were made, the strand furnish was analysed to determine the fines content and geometry (length, width and thickness). The geometry measurements were 9 performed using a digital slide caliper on approximately 100 flakes randomly obtained from each of the two boxes of strands. The length of each strand was defined as its longest length and the width at the approximate middle of the strand was taken to be its width. Because the furnish provided by the mill contained a large volume of fines, the strands were re-screened prior to use. Any furnish that passed through a 12.7 mm (Vi inch) opening was discarded. The choice of available screens was limited and this one appeared to screen out the most fines, without a significant loss of other material. The screened strands were again analysed for length and width. The results of the screening are summarized in Figure 3.1 and Table 3.3. 60 i <12.7 12.7-38.1 38.1-63.5 63.5-88.9 88.9- 114.3< 114.3 Length (mm) Figure 3.1: Distribution of strand length before and after screening Table 3.3: Weight, average length and width of the furnish M i l l Screened Laboratory Screened Bin (mm) Weight (g) Average Length (mm) Average Width (mm) Bin (mm) Weight (g) Average Length (mm) Average Width (mm) > 114.3 21.4 119.4 16.5 > 114.3 3.0 116.8 11.7 88.9-114.3 179.7 106.7 15.1 88.9-114.3 28.1 109.2 15.0 63.5-88.9 44.3 76.2 9.8 63.5-88.9 12.1 76.2 11.8 38.1-63.5 49.7 50.8 8.3 38.1-63.5 7.3 50.8 11.2 12.7-38.1 19.1 27.9 6.1 12.7-38.1 2.0 30.5 9.4 <12.7 43.6 10 Furnish less than 12.7 mm (0.5 inch) in length was not measured for dimensions. This was because after screening of the strands in the laboratory the amount of furnish less than 12.7 mm in length was negligible. The average weighted length and width of the strand used was 96mm (3.8 inches) and 14mm (0.6 inch) respectively. The average thickness (as measured on 200 strands with slide calipers) was 0.7 ± 0.2 mm (0.027 ± 0.009 inch). Because both strands and fines dimensions will vary from mill to mill, analysis of the fines material was also completed. The analysis of the as-received fines material (not the material that was discarded) was done using a William's classifier. The percentage of material left on each screen size is listed in Table 3.4. The P stands for pass and R stands for retained. The numbers reference the screen size in imperial units (i.e. R Vi is interpreted as the amount of strands that were retained on a screen with Vi inch openings). The last column (i.e. P 1/8) had the largest amount of material, which means the majority of the fines material consisted of material that would pass through a 3.18 mm (1/8 inch) mesh opening. Table 3.4: Fines Classification using a William's Classifier Screen R3/8 R lA R3/16 R 1/8 Pl/8 Weight (8) 6.1 3 9.7 19.4 126.4 243.4 % 1.5 0.7 2.4 4.8 31.0 59.7 3.2 Blending Prior to blending, both the fines and strands were dried to 1 % moisture. The strands and the fines were placed in an oven set at 105°C for 20 minutes. The furnish was left in a sealed plastic bag for one hour (minimum) to equilibrate prior to blending. The resin used was a liquid phenol formaldehyde resin (Borden GP 45) with 45% solids. It was sprayed onto the furnish at a concentration of 5% (dry-solids-on-dry-weight basis). A n atomizing spray nozzle (1/4 J model number 2850SS from Spraying Systems) was used to apply the resin, but the distribution was not ideal. Ideally, the resin should have been sprayed onto the furnish in a fine mist to improve resin-strand coverage and therefore the number of points that two strands will be bonded together. The atomizer used in the lab produced large droplets of resin. The effects of the non-ideal distribution may have been negated by the large amount of resin added. The normal resin addition rate for commodity product is between 2-3.5%(solids) resin, compared to the addition of 5% (solids) for these experimental panels. The final mat moisture prior to pressing was between 5-8% on an oven-dry basis. Normal industry practice for differentiating core resin and moisture from the face resin and moisture was not followed. The amount of time required to lay-up the panels (about three hours each panel) made it difficult to control the final moisture content of the 11 strands. In addition, the panels did not have a defined and unchanging core section. For example, i f the fines were to be considered the core material, they did not remain constant so there may have been an effect of the changing total moisture content of the board. Different resins were not used for the face and the core because a long cook time was chosen, and therefore curing of the resin would not be an issue. The strands and fines were blended separately. The strands were blended first, removed, the blender was cleaned, and then the fines were blended. Blending the fines first would have contaminated the strands with fines material, or added a large amount of time to cleaning the blender in between the blends. 3.3 Mat Formation Once all the strands and fines were blended the boards were formed. There were two different mat formations used, one was a layered system used to simulate homogenously distributed fines and the sandwich system. The total weight of the board remained constant. The total weight of the strands and fines varied according to the amount of fines being added. In addition for the uniform distribution, because the strands contributed the most to the overall panel strength, the amount of strands (by weight) in each layer was kept (almost) constant and the amount of fines varied (by weight). Each strand layer was approximately 2 strands thick. Strand layers also formed the faces in both distributions. The sandwich distribution was still formed in layers to control the orientation of the strands, but all of the fines were placed in the center of the panel. The number of experimental panels made for the two distributions of fines was different. Because the uniform distribution had already been studied and reported on (Barnes, 2002; Mottet, 1967 in Maloney, 1993), only four different levels (0, 33.3, 66.6 and 100%) of fines content were chosen. This work was done to re-confirm literature data, and to provide the 100% strand and 100% fine boards M O E and M O R values for later calculations. The sandwich distribution repeated the 33.3 and 66.6% fines addition levels, but also included 10, 20, and 50% fines levels. The additional points were added to better define the area of interest for industry (between 0 and 30% fines). The 50% fines level was added to further define the decrease in strength. Table 3.5 shows the different mat formations used for each distribution and the number of strand layers used per panel. 12 Table 3.5: The Number of Layers of Strands for Each Mat Formation Uniform Distribution of Fines Condition % Fines %Strands Layers of Fjnes Layers of Strands 1 100 0 1 0 2 0 100 0 12 3 33.3 66.6 9 10 4 66.6 33.3 4 5 Sandwich Distribution 1 10 90 1 12 2 20 80 1 12 3 33.3 66.6 1 10 4 50 50 1 8 5 66.6 33.3 1 4 The length of time to make each panel (after the completion of the blending) was about three hours. The lay-up of the strands was very time consuming because the average absolute angle of orientation was not to exceed 10 degrees. This was done to remove the variation in strength due to different orientations of the strands. A hand forming technique was used to orient the strands. For each layer of strands laid down, the orientation of the layer was scanned using a commercial scanner device (SAM) provided by Weyerhaeuser (US patent number 5,764,788). S A M outputted the average absolute angle and the standard deviation for that measurement. The layer angles and corresponding standard deviations were then averaged to provide an average absolute angle and average standard deviation for the test specimen. The orientation of the fines was not recorded. S A M did not have the capability to do this. Figures 3.2 and 3.3 show an example of each fines distribution prior to pressing. 13 Figure 3.2: 33.3% Fines Uniform Distribution prior to pressing 3.4 Pressing The panels were pressed using an electrically heated Pathex press. The controls were limited to position, platen pressure and time. The mats were pressed between 6.35 mm (% inch) aluminum caul plates. Because resin cure was important and hot stacking was not an option, a long cook time was used. 14 The press schedule used was a simple two-step program. The press was closed as fast as possible, but was limited to a maximum pressure of 600psi. The press was then held at position for approximately 17 minutes. The opening phase was one minute. The total press time was approximately 18 minutes. The data entered into the press program was as follows: Zone 1 Time: 9999/10 sees (17 minutes) Start pressure: 600 psi (4137 kPa) End pressure: 600 psi (4137 kPa) Position: 98/100 inch* (24.89 mm) * (this produced a % inch thick panel with the two caul plates) Zone 2 Time: 600/10 sees (1 minute) Start pressure: 100 psi (690 kPa) End: 0 psi Position: 98/100 inch (24.89mm) Once the boards were pressed they were left for a day and then cut up for testing (see Appendix A for the cut pattern). 3.5 Testing The internal bond strength (IB) was tested immediately according to A S T M D1037-98 and any board that had an average IB less than 30psi was rejected, and the panel was remade. The bending test pieces were equilibrated in a 65% relative humidity and 20°C room. They were tested according to A S T M D1037-98. The testing machine used was a Sintech 30/D, with Test Works 3 as the computer interface. Because strand composite material is presently used as both a joist product (i.e. Timberstrand) or as a sheathing product (i.e. OSB flooring, roofing, etc.) the two distributions were tested in both face (plank) bending and edge (joist) bending. Once tested the moisture content of the samples was determined and vertical density profile (VDP) test pieces were cut out of the plank bending samples. The moisture content of the samples was 8-9% moisture content for all the samples. In summary each panel was tested for IB, M O E and MOR. However, the IB test was only used as a quality control check. Vertical density profiles were also completed for each bending sample using a QMS density profile system, but this data was not used in the models. Maximum face densities were statistically analysed for differences (Appendix C) because of the effect of density on M O E and MOR. Only the M O E and M O R test data were used for modeling. 15 4. Results and Analysis The results from the experiment included bending values (MOE, MOR, and Maximum Load) for face and edge testing of both panel constructions. The complete results are shown in tabular form, tables 4.1 and 4.2. M O E and MOR are further displayed as graphs. Statistical analysis included analysis of variance (i.e. A N O V A ) and when warranted Scheffe's test was used to determine which differences were statistically significant. For comparing 0% fines results to any of the sandwich distribution results t-tests were used. The majority of the data sets (only the sandwich joist data MOE-MOR were excluded) did not meet the analysis of variance assumption that the variances are equal as determined by Bartlett's test for homogeneity of variances. The data sets were transformed using the natural logarithmic function. Bartlett's test was again completed on the transformed data sets. Two of the data sets after transformation still did not meet the assumption of homogeneous variances between treatments. These were the uniform-distribution-joist M O R and the sandwich-distribution-plank M O R data sets and they were not statistically analysed. 4.1 Uniform Distribution Results and Analysis Summary results of the strength properties of the members with uniform fine distribution are shown in Tables 4.1 and 4.2. Figures 4.1 and 4.2 display the difference in average M O R and M O E values between the plank and joist orientations of the uniform distribution specimens. The plank test specimens failed predominantly in bending (4 of the 48 test pieces failed in shear). The failure mode of the joist test specimens was not easy to determine. The joists either failed in bending or through delamination of the strand layers from the fines layer, but it was not obvious which failure mode occurred first. The A N O V A ' s for the uniform distribution of fines on member strength properties are shown in Tables 4.3 to 4.5. (The complete statistical analysis is in Appendix B). For the uniform distribution of fines, the experimental data shows that there was an effect of fines on both the M O E and M O R properties of the panel in the plank orientation. Further statistical analysis with Scheffe's test indicated that all the treatments in each test group were significantly different from one another. A treatment is defined as 0%, 33.3%,66.6% and/or 100% fines. The A N O V A for the M O E data in the joist orientation showed that there was a difference between experimental panels within each treatment group. Fines were also shown to have affected the joist MOE. Further testing done with Scheffe's test (on the treatments only) concluded that all the differences between treatments were significant. As previously mentioned, the joist-MOR data was not analysed using A N O V A because the variances were not considered homogeneous. One can see (refer to figure 4.2), as the fines were increased the strength decreased in a linearly fashion. 16 The density of the plank bending specimens was also statistically analysed (results are in Appendix C). There was enough variation within the groups that a significant difference was shown for within groups. But there was no significant difference between the groups. The maximum face density (as recorded by the vertical density profilometer) could not be analysed because both the original data set and the transformed data set did not meet the criteria of homogenous variances. 4.1.1 Results-Uniform (homogenous) Fines Distribution Table 4.1: Plank (Face)E tending Results-Uniform "ines Distribution Fines (%) Density (kg/m3) Thick, (mm) M C (% OD) Average Orientation* o IB (kPa) Max. Load (N) M O R (MPa) M O E (MPa) 0 718 (19) 19.7 (0.3) 8.6 (0.2) 8.8 (11.4)** 323 (138) 3222 (307) 66 (7) 11064 (551) 33.3 703 (22) 19.3 (0.2) 8.9 (0.5) 8.6 (10.6) 313 (76) 1856 (222) 39 (4) 8259 (390) 66.6 687 (18) 19.5 (0.3) 8.9 (0.3) 8.7 (10.8) 254 (76) 1362 (178) 29 (4) 5883 (311) 100 687 (16) 19.4 (0.2) 8.9 (0.1) 256 (76) 467 (31) 10.1 (0.7) 1995 (137) * average absolute angle of all the layers ** average standard deviation of the layers () standard deviation Table 4.2: Joist (Edge) Bending Results-Uniform Fines Distribution Fines Density Thick. M C Average IB Max. M O R M O E (%) (kg/m3) (mm) (% OD) Orientation* n (kPa) Load (N) (MPa) (MPa) 0 711 19.3 8.6 8.8 323 645 53 9440 (32) (0.7) (0.2) (11.4)** (138) (129) (8) (786) 33.3 695 19.8 8.9 8.6 313 409 32 6451 (22) (0.7) (0.5) (10.6) (76) (62.3) (4) (492) 66.6 679 19.9 8.9 8.7 254 258 20 3506 (26) (0.5) (0.3) (10.8) (76) (58) (5) (392) 100 681 20.3 8.9 256 93 7.1 1582 (16) (0.4) (0.1) (76) (8.9) (0.7) (110) * average absolute angle of all the layers ** average standard deviation of the layers () standard deviation 17 • Plank-MOE • Joist-MOE Figure 4.1: MOE-Uniform Distribution: Plank vs. Joist 70 n 0 33.3 66.6 100 Fines (%) Figure 4.2: MOR-Uniform Distribution: Plank vs. Joist 18 4.1.2 ANOVA Tables for the Uniform Distribution Bending Data Table 4.3: A N O V A Table Uniform Fines Distribution M O E-Plank Source of Error Degrees of Freedom Sum of Squares MS Fvalue Vl,v2 Fcritical a=0.05 Treatment 3 3.809 1.269 1433 3,8 4.07 Experimental Error 8 0.007 0.001 1.69 8,36 2.2 Sample Error 36 0.019 0.0005 Total 47 3.835 Table 4.4: A N O V A Table Uniform Fines Distribution M O i-Joist Source of Error Degrees of Freedom Sum of Squares MS Fvalue vl ,v2 Fcritical a=0.05 Treatment 3 4.129 1.376 508 3,8 4.07 Experimental Error 8 0.021 0.002 2.4 8,36 2.2 Sample Error 36 0.040 0.001 Total 47 4.192 Table 4.5: A N O V A Table Uniform Fines Distribution MOR-Plank Source of Error Degrees Sum of MS Fvalue vl ,v2 Fcritical of Freedom Squares oc=0.05 Treatment 3 22.51 7.504 688 3,8 4.07 Experimental 8 0.087 0.011 0.960 8,36 2.2 Error Sample Error 36 0.409 0.011 Total 47 23.01 19 4.2 Sandwich Distribution Results and Analysis Summary results of the strength properties of the members with sandwiched fine distribution are shown in Tables 4.6 and 4.7. Figures 4.3 and 4.4 display the difference in average M O R and M O E values between the plank and joist orientations of the test sandwich distribution specimens. In the plank orientation, 39 of the 60 test specimens failed in shear in the core layer. The failure mode of the joist orientation was not determined. As with the uniform distribution, the failure mode of the joists appeared to be either delamination between the fines layer and the strand layer or bending failure, but again it was not obvious which failure mode it was. The results of the statistical analysis of the sandwich distribution of fines on member strength properties are shown in Tables 4.8 to 4.10 (see Appendix B for the complete analysis). Again, not all of the sandwich data sets passed Bartlett's test. The data sets for plank M O R and plank M O E were transformed using the natural logarithmic function and retested. The plank M O R data set still did not pass Bartlett's test and therefore was not statistically analysed. For the bending M O E in the plank orientation there was a difference between the individual observations of each treatment as well as between treatments. For the sandwich distribution, a treatment is 10, 20, 33,3 and/or 66.6% fines. Some of the within treatment variation could be contributed to the variability of formation. There was no significant difference found between the 10, 20 and 33.3% fines addition level and between 33.3 and 50%, but all other differences were significant according to Scheffe's test. Fines affected the joist-MOE value of the sandwich specimens. There was no difference within groups, but there was an effect of treatment. Scheffe's test indicated that there was not a significant difference between the 20% and 33% addition level. A l l other differences were significant. The plank M O R data was not analysed because of the lack of homogeneity of the variances. On visual inspection of the data, there was no obvious trend explaining the effect of fines on the M O R plank strength. For the joist-MOR values there was a difference between treatments, and there was difference within each treatment group. Again variation within treatments was most likely related to local variations of the amount of fines present (i.e. variation in the hand-formed boards) and/or variations in the furnish. Further statistical testing was done to compare the 10% fines sandwich boards with the 0% fines boards for differences in M O E (Appendix D). These comparisons were done using the standard t-test. The only significant difference was found to be between the M O E results of the plank boards. A l l of the sandwich boards (tested in the plank orientation) had significantly lower M O E values than the 0% fines board. The plank M O R 0% and 10% boards were not tested, as there was an obvious difference in the 20 values. Comparing M O E joist values, the 0% and 10% fines boards were not statistically different. Density for only the plank bending data was statistically analysed (see Appendix C). Both the panel density and the maximum face density were compared using A N O V A . The panel density within the groups varied enough that there was a significant difference. There was also a significant difference in panel density between the 10% boards and all the other boards except the 33.3% fines boards. However, the panel density of the 33.3% fines board was significantly different than the density of the 66.7% fines board, as indicated through Scheffe's test. A l l other differences were not significant. The maximum face density analysis showed that there was no differences within the treatments, but between the treatments differences existed. The following pairs had significant differences as tested with Scheffe's test: the 20 and 50% treatments, and the 20 and 66.7% treatments. A l l other differences were not judged significant. Again, t-tests were used to compare the 0% fines board with the sandwich-distributed boards. The panel density of the 0% fines board was significantly higher than the density of all the sandwich boards except for the 10% fines board. When the maximum face densities were compared, the 0% fines board was statistically lower than the sandwich boards except for the 50% and 66.7% fines boards (complete analysis is in Appendix D). 4.2.1 Results-Sandwich distribution Table 4.6: Plank (Face) Bending Results-Sandwich distribution Fines Density Thick. M C Average IB Max. M O R M O E (%) (kg/m3) (mm) (% OD) Orientation* (°) (kPa) Load (N) (MPa) (MPa) 0 718 19.7 8.6 8.8 323 3222 66 11064 (19) (0.3) (0.2) (11.4)** (138) (307) (?) (551) 10 706 19.89 8.9 8 218 1996 39 10552 (11) (0.02) (0.2) (10.3)** (83) (423) (8) (618) 20 676 20.0 8.8 7.2 232 2326 45 10364 (24) (0.3) (0.2) (9.5) (76) (501) (10) (934) 33.3 686 20.3 9.1 8.7 261 2146 43 9775 (14) (0.1) (0.1) (11.6) (48) (225) (4) (497) 50 654 19.9 9.2 7.5 256 2141 40 8527 (11) (0.1) (0.2) (9.7) (48) (183) (4) (343) 66.6 655 20.3 9.1 7.3 248 1787 34 7062 (11) (0.1) (0.2) (9.1) (48) (210) (4) (484) 100 687 19.4 8.9 256 467 10.1 1995 (16) (0.2) (0.1) (76) (3D (0.7) (137) * the average absolute angle of all the layers () standard deviation ()** the average standard deviation of the layers 21 Table 4.7: Joist (Edge) Bending Results-Sandwich distribution Fines (%) Density (kg/m3) Thick, (mm) M C (% OD) Average Orientation* (°) IB (kPa) Max Load (N) M O R (MPa) M O E (MPa) 0 711 (32) 19.3 (0.7) 8.6 (0.2) 8.8 (11.4)** 323 (138) 645 (129) 53 (8) 9440 (786) 10 695 (29) 20.3 (0.3) 9.2 (0.5) 8 (10.3)** 218 (83) 639 (100) 47 (6) 9139 (712) 20 656 (30) 20.6 (0.2) 9.0 (0-9) 7.2 (9.5) 232 (76) 556 (84) 40 (6) 7917 (692) 33.3 684 (22) 20.1 (0.2) 8.8 (0.7) 8.7 (11.6) 261 (48) 494 (59) 37 (4) 7038 (664) 50 642 (8) 20.6 (0.3) 9.2 (0.4) 7.5 (9.7) 256 (48) 382 (61) 27 (4) 5284 (458) 66.6 655 (13) 20.2 (0.4) 8.8 (0.2) 7.3 (9.1) 248 (48) 266 (52) 20 (4) 3825 (711) 100 681 (16) 20.3 (0.4) 8.9 (0.1) 256 (76) 93 (8-9) 7.1 (0.7) 1582 (110) * the average absolute angle of all the layers () standard deviation ()** the average standard deviation of the layers 12000 -i 10 20 33.3 50 66.6 Fines (%) Figure 4.3: MOE-Sandwich Distribution: Plank vs. Joist 22 10 • Plank-MOR • Joist-MOR 20 33.3 Fines (%) 50 66.6 Figure 4.4: MOR-Sandwich Distribution: Plank vs. Joist 4.2.2 ANOVA Tables for the Sandwich Distribution Bending Data Table 4.8: A N O V A Table Sandwich Distribution MOE-Plank Source of Error Degrees of Freedom Sum of Squares MS Fvalue vl ,v2 Fcritical a=0.05 Treatment 4 1.339 0.335 32 4,10 3.48 Experimental Error 10 0.103 0.0103 3.9 10,45 2 Sample Error 45 0.119 0.003 Total 59 1.561 Table 4.9: A N O V A Table Sandwich Distribution N [OE-Joist Source of Error Degrees of Freedom Sum of Squares MS Fvalue V l , v 2 Fcritical oc=0.05 Treatment 4 2.14E+08 53383006 100 4,10 3.48 Experimental Error 10 5326183 532618 1.3 10,45 2 Sample Error 45 18237987 405289 Total 59 2.37E+08 23 Table 4.10: A N O V A Tab! e Uniform Distribution MOR-Joist Source of Degrees Sum of MS Fvalue V l , v 2 Fcritical Error of Freedom Squares a=0.05 Treatment 4 5809.2 1452.3 22.41 4,10 3.48 Experimental 10 647.8 64.8 2.86 10,45 2 Error Sample Error 45 1018.8 22.6 Total 59 7475.9 5. Physical Models From the qualitative inspection of the experimental data, trends were apparent. The joist strength (MOE and MOR) appeared to decrease linearly as the percentage of fines increased, regardless of the distribution. The plank M O E and M O R of the uniformly distributed panels also appeared to decrease in a linear mode when the percentage of fines was increased. The plank M O E of the sandwich panels decreased in a gradual fashion with the increased addition of fines. The plank M O R of the sandwich panels did not appear to be dependent on the amount of fines present. Although it would be possible to model many of these interactions using linear or curvilinear regression, it was decided to develop a model based on the mechanical properties of individual layers. 5.7 Uniform Distribution As previously alluded to, the uniform distribution is merely a homogeneous mixture of strands with a given MOE/MOR and fines with a given MOE/MOR. This type of material lends itself to modeling by the rule of mixtures (i.e. equation 2.1). This equation can also be modified to predict M O R as shown in Equation 5.1. MOR p = Vfmes MOR fines + Vstrands MOR strands (5.1) Again, for both models, the E or M O R values were taken to be the average M O E or M O R value of the 100% strand board and the average M O E or M O R value of the 100% fine board. It was assumed that the volume for each constituent was equal to the percentage of weight (i.e. a board with 33.3% fines by weight would also occupy 33.3% of the volume of the board). The effect of densification on the MOE, M O R and volume was not considered. Tables 5.1 and 5.2 display the predicted M O E and the predicted M O R values for both the plank and joist configurations. Figures 5.1-5.4 illustrate these results. Good agreements can be seen between predicted and test values. Table 5.1: Predicted vs. Experimental Values for the Uniform Distribution in the Plank Orientation Fines (%) Plank M O E (MPa) Plank M O R (MPa) Experimental Predicted % error Experimental Predicted % error 0* 11064 - - 66.2 - -33.3 8259 8044 -2.6% 38.8 47.5 22% 66.6 5883 5014 -15% 28.7 28.8 0.34% 100* 1995 - - 10.1 - -* these were the average M O E and M O R values used in all the equations to predict the other M O E and M O R plank values 25 Table 5.2: Predicted vs. Experimental Values for the Uniform distribution in the Joist Orientation Fines (%) Joist M O E (MPa) Joist M O R (MPa) Experimental Predicted % error Experimental Predicted % error 0* 9439 - 52.7 - -33.3 6451 6823 5.8% 32.2 37.5 16% 66.6 3506 4198 19.7% 20 22.3 12% 100* 1581 - - 7.1 - -* these were the average M O E and M O R values used in all the equations to predict the other M O E and M O R joist values O Experimental O Predicted 100 Fines (%) Figure 5.1: Plank M O E - Experimental vs. Predicted Data by the Rule of Mixtures 26 10000 8000 -6000 -4000 -2000 0 0 25 50 Fines (%) 75 O Experimental O Predicted 100 Figure 5.2: Joist MOE-Experimental vs. Predicted Data by the Rule of Mixtures O Experimental O Predicted 0 25 50 75 100 Fines (%) Figure 5.3: Plank MOR-Experimental Data vs. Predicted Data by the Rule of Mixtures 27 o O Experimental O Predicted 50 Fines (%) —i— 75 100 Figure 5.4: Joist MOR-Experimental Data vs. Predicted Data by the Rule of Mixtures 5.2 Sandwich Distribution Both the Rule of Mixtures and the transformation of sections were used to predict M O E and M O R values for the sandwich distribution. For M O E in the plank orientation simple beam bending theory was used. The fines were transformed into an equivalent strand section (see Figure 2.1). Equations 2.4.1-2.4.3 were used to predict the composite M O E value. The assumptions when using these equations were that there was no densification, plane sections remained plane and that there was no deflection due to shear. Again E s t r a n d s and Efmes were the average M O E values for the 100% strand and fine boards respectively. For the M O E and M O R of the joist orientation, the rule of mixtures was used. This was applicable because in this orientation there was a quasi-homogenous mixture of strands and fines throughout the thickness of the test specimen. Equation 2.1 and 5.1 were again employed with the same restrictions as previously mentioned. Comparisons of the prediction and test results are shown in Tables 5.3 and 5.4. Figures 5.5-5.7 display illustrations of comparisons of these results. Again, very good agreement between model predictions and test results was obtained. 28 Table 5.3: Predicted vs. Experimental Value for Plank and Joist M O E Sandwich Distribution Fines (%) Plank M O E (MPa) Joist M O E (MPa) Experimental Predicted (Transformed Sections) % error Experimental Predicted (Rule of Mixtures) % error 0 11064 - 9440 -10 10570 11054 4.5% 9139 8654 5.3% 20 10364 10991 6.0% 7917 7868 0.61% 33.3 9775 10726 10% 7038 6820 3.1% 50 8526 9930 8.1% 5284 5511 4.3% 66.6 7061 8376 19% 3825 4201 10% 100 1995 - 1582 -Table 5.4: Predicted vs. Experimental Value for Joist MOR-Sandwich Distribution Fines (%) Joist M O R (MPa) Experimental Predicted (Rule of Mixtures) % error 0 52.7 -10 47.4 48.1 1.4% 20 39.7 43.5 9.6% 33.3 37.4 37.5 0.30% 50 26.9 29.9 11% 66.6 19.5 22.3 14% 100 7.1 -CO O O Experimental • Predicted Figure 5.5: Plank MOE-Experimental vs. Predicted Data by Transformed Sections O Experimental • Predicted 0 25 50 75 100 Fines (%) Figure 5.6: Joist MOE-Experimental vs. Predicted Data by the Rule of Mixtures 30 M O R is an estimate of the maximum bending stress of a specimen (Bodig and Jayne, 1993). Because the majority of the sandwich panels in the plank orientation failed in shear (as shown in Figure 5.8), it was not possible to model their MOR. Instead an attempt was made to predict failure mode. Figure 5.8: Shear Failure in the Sandwich Construction (33.3% fines) As shown in Figure 5.9, theoretically a board can fail when the stress experienced exceeds the capacity of any of the following board stresses: 31 Obc (Bending stress-compression) Obfmes (Bending stress-core) < - T (Shear stress) ° b f m e s (Bending stress-core) ^ Gbt (Bending stress-tension) Figure 5.9: Possible Failure Stresses for the Sandwich Construction If the strength (maximum stress) in shear (x) and bending (CTbc, (*bt, <*bfines) * s k 1 1 0 ^ ' m e n the maximum load that the member can carry can be estimated. The samples were regrouped according to the failure modes in order to estimate the failure criteria. To simplify calculations, any board that clearly split in the middle was considered to have failed in shear (x) and all other boards were considered bending-face failures (i.e. tension strand failures or Gbt). It was assumed that no boards failed in bending at the core. As well, any board that failed in shear was considered to have failed at the neutral axis (maximum shear stress region) of the test specimen. As shown in Table 5.5, the average maximum load of the groups was calculated for each failure mode. Table 5.5: Maximum Loads for Bending and Shear Failures in Sandwich Construction Fines (%) Number of Shear Failures (out of 12 samples) Average Maximum load for Shear Failures (N) P T max i Average Maximum load Bending-Face Failures (N) p 6 max/ 10 12 1996(423) -20 8 2074 (318) 2743 (305) 33.3 10 2186 (213) 1946 (304) 50 6 2172 (179) 2109 (198) 66.7 3 1958(185) 1730 (194) () standard deviation The bending loads for each treatment were then used to calculate the bending stress. The average weighted bending stress of the treatments was designated as the strands bending stress capacity. The weighted average was used instead of the bending stress capacity of the 100% strand boards because it was assumed that some of the fines from the core had migrated into the strand layers. The shear stress that was calculated for the 10% fines board was taken as the average shear strength of the fines. Again, densification of the 32 board was not taken into consideration. It was also assumed that the fines layer was discontinuous for boards with less than 10% fines. Therefore the failure mode for boards with less than 10% fines was not predicted. These values are estimates only as the actual failure mode and load capacity of a specimen depends on its ratio of shear and bending strength in relationship to the ratio of applied shear and bending stress. i) Maximum Load as governed by bending stress (cu) The theoretical maximum stress experienced by a beam bending is realized in the outer face fibres of the member. To estimate the maximum bending-face stress for each condition, the following equation was used: 8/* (5.2) where L = test span d = depth of the specimen 1=2 (btl 12 + bt. / 2 / 2 2> (Ef bt)^ E, 12 V ' J (5.2.1) where Ef Es b d ts tf the M O E of the fines the M O E of the strands the width of the specimen the depth of the specimen the thickness of the strand layer the thickness of the fines layer where Pbmai =the measured average maximum load for the bending failure group The maximum bending stress was calculated as follows: it N (5.3) where ni = the number of samples for crn N=2\ 33 ii) Maximum Load as governed by shear Shear stress was calculated using the following equations: where V = (5.4.1) where Pmaxi =the measured average maximum shear load for 10% fines group and Q = b where b d ts tf n Ef . d t t. s- + n s 2 2 8 / (5.4.2) the width of the specimen the depth of the specimen the thickness of the strand layer the thickness of the fines layer EfIEs the M O E of the fines the M O E of the strands Because it is possible that the core failed in bending, maximum loads using that failure criterion were also calculated. The average M O R of the 100% fines board was used as the estimated maximum stress of the core. 5.2.1 Predicting mode of failure The estimated maximum stress of the board was estimated to be 45 MPa for bending-face, 10.1 MPa bending-core and 940 kPa for shear. The maximum loads were re-calculated using both the estimated bending capacity (for both the face and core) and shear capacity values. The predicted (calculated) maximum loads are shown in Table 5.6. Figure 5.10 displays the results (the predicted bending-core failure loads were not graphed due to scale restrictions). P (55 1) 1 max bendingFACE ^ \J.J.l) where L = 40.6cm <Jbt = 45 MPa 34 p _ 8 / abflnes max. bendingCORE LtfTl where <jbflnes = 10.1 MPa n - Efl Es L = 40.6cm P. 2 / T , b max shear , 2 *2 f_ + s 2 2 8 where Tb 940 kPa Table 5.6: Maximum Loads as Calculated Using the Estimated Failure Criteria Fines Predicted Predicted Predicted Predicted Failure Mode (%) Max. Load Max. Load Max Load (shear) (N) (bending-face) (N) (bending-core) (N) 10 1993 2315 28533 Shear 20 2040 2312 14250 Shear 33.3 2057 2194 8123 Shear/Bending-face 50 2245 2133 5258 Shear/Bend ing-f ace 66.6 2350 1791 3315 Bending-Face 36 6. Discussion Two fines distribution schemes were examined: the uniform and the sandwich distribution. These distributions were modeled using the experimentally determined M O E and M O R values of the 100% strand and 100% fine boards. Essentially two theories were employed to model the bending properties: the Rule of Mixtures and simple beam bending theory (transformation of sections). When using these models several assumptions were made. Two of the key assumptions were no densification of the layers and no deflection due to shear. 6.1 Density and densification When comparing the bending properties of OSB it is important to consider both the panel density and the density profile of the boards. Density is one of the key parameters affecting both M O E and M O R (Maloney, 1993). Panel density represents how much material is in the panel and generally the higher the global density the higher the M O E and M O R tend to be (Maloney, 1993). When the density of the individual layers is examined it is generally found that the face layers are denser than the core layers (Kelly, 1977). The density profile can be manipulated by changing pressing strategies. Generally, faster closes enable the face material to heat rapidly and densify, the core takes longer to heat and therefore is not as densified as the face (Kelly, 1977). Stiffer boards tend to have highly densified faces and low-density core, however too low of a core density can also cause poor bending properties. An average board density of 641 kg/m 3 (oven-dry, panel density) may result in a board with 929 kg/m 3 faces and 512 kg/m in the core. The models were designed to predict the M O E and M O R of 641 kg/m 3 (oven-dry, panel density) OSB. The actual densities ranged from 641 to 700 kg/m 3. In the sandwich distribution, the 10% fines board had a higher panel density than the 20%, 50% and 66.7% fines boards. Part of the reason for the lower densities of the higher fines boards was that they spread more during pressing. (The spread was not measured, just observed.) If the panel density of the 100% strand board is compared to the sandwich composite boards, it is higher than all of the combinations except the 10% fines board. The lower densities may explain the apparent over-prediction of the plank-MOE values using the transformation of sections model. When the maximum density of the faces was analysed for the two distributions (Appendix D), there were some differences between the treatments. Interestingly, the composite boards with strands and fines tended to have higher face densities than the 100% strand board. As well, the 100% strand board had the lowest face density, but the highest panel density out of all the combinations. Ideally, the E s t r a n d and Ef i n e s values should have been adjusted according to the densities of the respective layer. However, adjusting the E values may have introduced more error into the models; predicting how boards will densify is not readily or easily done. 37 Not including densification allowed for an easy estimate of the volume and thickness of the strand and fine layers. For example, for the 33.3% fines board it was assumed that the fines occupied 33.3% of the total volume of the board, however on visual inspection it appears that the fines volume should be greater than 33.3% (see figure 5.8). As for the thickness, the fines thickness (i.e. tf) was assumed to be 33.3% of the total thickness of the panel. It was not possible to accurately measure the thickness of the strand or fines layer due to the waviness of the strands/fines boundary. As well, the thickness of the layers varied in both the x-plane and the y-plane. From observation of the test specimens the thickness of the strand layer was overestimated and the thickness of the fines layer underestimated, especially in the sandwich distribution. This over-prediction of the thickness of the strand layer may have helped compensate for the lack of adjustment to the M O E because of higher density faces found in the composite boards. The over-prediction of the thickness of the strand layer is more pronounced in the higher % fines board and may also contribute to the over-prediction of the plank M O E values. 6.2 Deflection due to shear The bending tests were done in accordance with ASTM-D1037 Static bending 1998. The single point loading method was used and the span length was modified from 45.7 cm (24 times the thickness) to 40.6cm (21 times the thickness). The span length requirement was set at 24 times the thickness to reduce the amount of shear present during testing. According to Bodig and Jayne (1993), 21 times the thickness should also have adequately reduced the amount of shear present. Any deflection due to shear would have been incorporated into both models because the M O E values of the 100% strand or fines board were used. These values were obtained by center point loading (as with all the other values) and therefore would also have deflection due to shear incorporated in them. 6.3 The Rule of Mixtures From previously reported results on the uniform distribution of fines (Mottet, 1967 in Maloney, 1993; Barnes, 2000), a decreasing linear trend for M O E and M O R was expected. The Rule of Mixtures was shown to predict the decrease in both the M O E and M O R for the uniform distribution. It also predicted the joist M O E and M O R strength loss for the sandwich distribution. The joists were always lower in stiffness and strength than the plank specimens. The orientation effect was most likely due to the densification of the face layers; the joist orientation does not take advantage of the densified faces and therefore the lower stiffness values. The change in orientation may have also put a weaker region (i.e. the interface between the strands and fines) into a higher stress region, thereby decreasing the ultimate load of the joist. Simple beam bending theory could have been used to predict any of the experimental values mentioned above. However, the goal was to model these properties in the simplest and most effective way. 38 6.4 Simple Beam Bending Model (transformation of sections) 6.4.1 Plank-MOE In the sandwich configuration, the Rule of Mixtures could not be applied to the plank bending results; instead transformation of sections was applied. Simple beam bending theory predicted the gradual decrease in strength shown in the experimental results. The model did over predict the M O E of the higher fines content boards. But as previously mentioned, this may be due (in part) to the lower density of the experimental panels and/or an overestimation of the thickness of the strand section in the model. 6.4.2 Plank-MOR This property was not modeled in the same manner as the other properties and the results were not statistically analysed. There was nd apparent relationship between the amount of fines and the M O R value. When the failure mode of the boards was re-examined it was found that the majority of the panels failed in shear and not bending. Instead of directly effecting ultimate load, fines were affecting how a board failed. According to the developed failure criteria, boards between 10- 45% fines are more likely to fail in shear. This is an important consideration for products where short spans are required such as in concrete formwork. There was no attempt made to predict the failure mode of boards with less than 10% fines or greater than 66.7% fines. Beyond either of these levels continuity of layers may become an issue (i.e. the fines or strands will no longer from a continuous layer). The calculated shear capacity (of the fines) and bending capacity (of the strands) were only rough estimates at best. The experiment was not designed to accurately measure shear. It was assumed that the boards would always fail in bending. The estimated maximum bending-face stress could have been calculated using an estimate of the amount of fines that may have been in the strand layers and the Rule of Mixtures relation. However, the amount of fines that may have migrated into the strands layers would vary depending on the amount of fines in the core. This approach was not used because quantifying the amount of fines was not possible. A shortcoming of both models was that the Estrands and Efines values had to be determined. This could be done through the use of other models, experiments, or possibly from mill data. If the values were determined through experiments or from mill data then the E values would be very specific to those operating conditions. 39 7. Conclusions This work suggests that it is possible to increase the use of fines without adversely affecting the panels bending strength and stiffness properties below accepted values. Previous work (Barnes, 2002; Mottet, 1967 in Maloney, 1993) showed that M O E and M O R decreased in a linear fashion when fines are added uniformly to the panel. This work supports those findings and shows that this decrease is amenable to modeling by the Rule of Mixtures. The Rule of Mixtures was also able to predict the decrease in M O E / M O R of the joists with the fines in the middle (i.e. the sandwich construction). Simple beam bending theory was successfully used to model the decrease in stiffness of the sandwich construction boards. The M O E remained fairly consistent up to the 33.3% fines level, after which the stiffness appears to drop significantly. The joist samples stiffness decreased as soon as fines were added, as mentioned above, it was a linear decrease. The M O R of the sandwich distribution tested as a plank was not modeled. Instead, failure mode was predicted. The predicted failure mode for boards with less than 45% fines is shear. This supports the experimental findings where the majority of panels with less than 50% fines failed in shear. These results pertain only to this study. The end-use of the board influences the effect of fines on the bending properties of OSB. The reduction in stiffness and strength was much more rapid when the boards were tested as a joist. As well, homogeneously distributing the fines was much more detrimental to stiffness and strength than placing the fines in the core. The exception to this finding may be in the case where short spans are required. Generally, shear is the limiting design factor for short spans, so the use of fines in the core is not recommended. 40 8. Future Work This was not a complete study on the effect of fines on the end-properties of OSB. Several tests were left out of this experiment: thickness swells, linear expansion, nail hold ability and shear tests. These properties are equally important to the industry and should be given consideration. Repeating the experiment and concentrating on the 0-33% fines section would be worthwhile. The testing should be done using a five-point-bending test-jig (ASTM D2718 - 00 method b) so that both the bending capacity and shear capacity of the boards could be experimentally determined. Comparing the experimental data and models to commercial boards would also be a worthwhile experiment. 41 References American Society for Testing and Materials. 1998. D 1037-98, Standard methods of evaluating the properties of wood-base fiber and particle panel materials. A S T M , Philadelphia, Pa. i Avramidis, S. and L . A Smith. 1989. The Effect of Resin content and Face-to-core Ratio on Some Properties of Oriented Strand Board. Holzforshung. 43(2) ppl31-133 Barnes, Derek. 1988. Timber-A Material for the Future. In The Marcus Wallenberg Foundation Symposia Proceedings: 4. Sweden. . 2000. An integrated model of the effect of processing parameters on the strength properties of oriented strand wood products. Forest Products Journal 50(11/12) pp. 33-42 . 2001. A model the effect of strand length and strand thickness on the strength properties of oriented wood composites. Forest Products Journal 51(20 pp. 36-46 _ 2002.A model of the effect of fines content on the strength properties of oriented strand wood composites. Forest Products Journal 52(5) pp55-60 and J. Ens. 1998. Strand orientation sensing. USA Patent # 5. 764,788 Bluman, A . G . 2001. Elementary Statistics, A Step by Step Approach 4 t h edition. McGraw-Hill Co., New York. Bodig, J. and B . A Jayne. 1982. Mechanics of Wood and Wood Composites. Van Nostrand Company Inc. New York Brumbaugh, James. 1960. Effect of flake dimensions on properties of particle boards. Forest Products Journal, 10(5) pp. 243-246 Campbell, Craig. 1997. Method and novel composition board products. US Patent # 5,641,819. Canadido, L.S., F. Saito and S. Suzuki. 1988. Effect of particle shape on the orthotropic properties of oriented strand board. Mokuzai Gakkaishi, 34(1) pp.21-27 1990. Influence of strand thickness and board density on the orthotropic properties of oriented strandboard. Mokuzai Gakkaishi, 36(8) pp. 632-636 Filho, M.S. 1981. Influence of wood furnish type on properties of oriented strand panels. Forest Products Journal 31(9) pp 43-52 Geimer et al. 1975. Effects of layer characteristics on the properties of three-layer particleboards. Forest Products Journal 24(3) pp. 19-29 42 Geimer et al. 2000. Flake Furnish Characterization: Modeling Board Properties with Geometric Descriptors, www.fpl.fs.fed.us/documnts/fplrp/fplrp577.pdf Hibbeler, R.C. 1997. Mechanics of Materials 3 r d Edition. Prentice Hall, New Jersey Hoover et al. 1985. Implications of a design approach for mixed hardwood structural flakeboard in Proceedings of the 19 t h International Symposium on Particleboard/Composite Material. Washington State University, Pullman. Hoover et al. 1992. Modeling mechanical properties of single-layer, aligned, mixed-hardwood strand panels. Forest Products Journal, 42(5) pp. 12-18 Hunt, M.O et al. 1978. Red Oak Structural Particleboard for Industrial/commercial roof decking. Purdue University Agricultural Experiment Station RB 954 , W.L. Hoover, and G.B. Harpole. 1983. Hardwood structural flakeboard for industrial/commercial roof decking: success and problems to solve in Proceedings of the 17 t h International Symposium on Particleboard/Composite Material. 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Effect of flake geometry on mechanical properties of eastern spruce flake-type particleboard. Forest Products Journal, 26(6) pp 24-28 Sinchich, Terry. 1994. A Course in Modern Business Statistics, 2 n d Edition. Macmillan College Publishing Company, Inc. New York RISI. 2002. Wood Products Yearbook. Resource Information Systems, Inc, Bedford, M A . Turner, D.H. 1954. Effect of particle size and shape on strength and dimensional stability of resin-bonded wood-particle panels. Forest Products Journal, 4(5) pp.210-223 Xu , W. and O. Suchsland. 1998. Modulus of elasticity of wood composite panels with a uniform vertical density profile: a model. Wood and Fiber Science 30(3) pp 293-300 44 Appendix A : Cutting pattern 1 1 1 2 2 2 3 3 3 4 4 4 5 5 5 6 6 6 7 7 7 8 8 8 9 Plank 1 Plank 2 CN 9 Plank 3 Plank 9 10 Joist Joist 10 Joist Joist 10 Sample sizes: Panel dimensions: IB: Plank bending: Joist bending: 610 mm x 610 mm (24 inch x 24 inch) 50 mm x 50 mm (2 inch x 2 inch) 76 mm x 457 mm (3 inch x 18 inch) 19 mm x 457 mm (3/4 inch x 18 inch) 45 Appendix B- A N O V A Analysis of M O E and M O R values 1. Equations: a. Bartlett's Test for the Homogeneity of Variances: Tj . _ 2 _ 2 _ 2 _ 2 H o G \ =<Ji =o-3.... = o-k Ha: At least two variances differ Test statistic (equal sample sizes): B = _ (n-\)[k\ns2 - £ l n s , 2 ] 1 + -3k(n-l) Where S j 2 = ith variance s = the average variance k= 4 (uniform distribution) k= 5 (sandwich distribution) n=12 Degrees of freedom =(k-l) b. A N O V A H0:^=fi2= = Mk Ha : at least one of the means is different from the others Source of Error Degrees of Freedom Sum of Squares Mean Sum of Squares F value Treatment k-1 SSTR SS T R /(k-l) [SS T R/(k-l)]/ [ SS E E/k(n-l)] Experimental Error k(n-l) SSEE SS E E/k(n-l) [SS E E/k(n-l)]/ [ SS S E/nk(m-l)l Sample Error nk(m-l) SSSE SS S E/nk(m-l) Total nkm-1 SS T 46 Working equations: nkm ^=5>i —tr) nkm ijl SSrR=l(—-I7-) i nm nkm v 1 yl Y.2 » m nkm SS — ss Y SS £g SS where i= the replications n = 3 j= the treatments k = 4 (uniform) or 5 (sandwich) 1= the observations m = 4 c. Scheffe's Test for Significant Differences between Treatments F. = V • J v/n>> Where Fs = test statistic Xj= is the average of the i group Xj = the average of the j group n,=population of the i group nj = population of the j group sw 2= the within group variance (mean sum of squares for the experimental error) F critical = (k-l)(F critical for the Treatment) 47 2. Uniform E listribution: Data Plank MOE Treatments Replications 0 33.3 66.7 100 Sums 1-1 10867 7845 5499 1691 1-2 11403 7779 5918 1974 1-3 11709 9207 6027 2063 1-4 11505 8475 5385 1897 Sum (yij.) 45485 33306 22829 7626 109246 2-1 11106 8234 5739 1958 2-2 10892 8053 5817 1905 2-3 11033 8159 5874 2145 2-4 11749 7856 5785 2186 Sum (yii.) 44779 32302 23214 8195 108490 3-1 9758 8327 5771 1991 3-2 10796 8427 6484 2130 3-3 10599 8206 5929 2078 3-4 11349 8536 6373 1916 Sum (yij.) 42501 33496 24555 8115 108668 Totals (y.j.) 132765 99104 70599 23936 326404 Average 11064 8259 5883 1995 Stdev 551 390 311 137 a. Bartlett's test for Homogeneity of Variances TJ . _ 2 _ _ 2 _ _ 2 _ 2 Ha: At least two variances differ Btest Statistic = 16.9 B critical for 3 degrees of freedom and alpha 0.05 = 7.81 The null hypothesis is rejected; the variances are not equal 3. Transformed data (using the natural logarithmic function) Treatments Replications 0 33.3 66.7 100 Sums 1-1 4.036 3.895 3.740 3.228 1-2 4.057 3.891 3.772 3.295 1-3 4.069 3.964 3.780 3.315 1-4 4.061 3.928 3.731 3.278 Sum (yij.) 16.2 15.7 15.0 13.1 60.0 2-1 4.046 3.916 3.759 3.292 2-2 4.037 3.906 3.765 3.280 2-3 4.043 3.912 3.769 3.332 2-4 4.070 3.895 3.762 3.340 Sum (yij.) 16.2 15.6 15.1 13.2 60.1 3-1 3.989 3.921 3.761 3.299 3-2 4.033 3.926 3.812 3.328 3-3 4.025 3.914 3.773 3.318 3-4 4.055 3.931 3.804 3.282 Sum (yij.) 16.1 15.7 15.2 13.2 60.2 Totals (y.j.) 48.5 47.0 45.2 39.6 180.3 Average 4.0 3.9 3.8 3.3 Stdev 0.022 0.020 0.023 0.031 a. Bartlett's test for Homogeneity of Variances Ha: At least two variances differ B test Statistic = 2.25 B critical for 3 degrees of freedom and alpha 0.05 = 7.81 The null hypothesis is accepted. • b. Analysis of Variance H0-Mx =Mi= = A t Ha : at least one of the means is different from the others A N O V A Table for Uniform Distribution: Plank M O E Source of Error Degrees of Freedom Sum of Squares Mean Sum of Squares F value V i , V 2 F critical (alpha =0.05) Treatment 3 3.809 1.270 1433 3,8 4.07 Experimental Error 8 0.0071 0.000886 1.69 8,36 2.2 Sample Error 36 0.0188 0.000523 Total 47 3.835 At a 95% confidence rate there is not a significant difference within the individual treatments, but there is at least one significant difference between the treatments. c. Scheffe's Test for Significant Differences between Treatments If Fs>F critical the difference is considered significant Differences 0/33.3 0/66.7 0/100 33.3/66.7 33.3/100 66.7/100 Fs 109 510 3754 147 2583 1497 F critical 12.21 12.21 12.21 12.21 12.21 12.21 Significant difference Yes Yes Yes Yes Yes Yes 50 4. Uniform E distribution: Data Joist t M O E Treatments Replications 0 33.3 66.7 100 Sums 1-1 11143 6343 2899 1535 1-2 10729 5907 3449 1608 1-3 9032 7120 3549 1681 1-4 8615 6633 3114 1414 Sum (yij.) 39519 26002 13011 6239 84770 2-1 9952 6168 3611 1650 2-2 9633 5493 4221 1592 2-3 9215 6602 3915 1733 2-4 8972 6197 3889 1407 Sum (yij.) 37772 24461 15636 6382 84250 3-1 9070 6521 3410 1506 3-2 9102 6576 3508 1746 3-3 8940 7327 3562 1557 3-4 8873 6527 2948 1549 Sum (yij.) 35984 26950 13428 6358 82721 Totals (y.j.) 113274 77413 42074 18979 251741 Average 9440 6451 3506 1582 Stdev 786 492 392 110 a. Bartlett's test for Homogeneity of Variances U . ^-2 _ _ 2 _ 2 _ 2 Ha: At least two variances differ B test Statistic = 29 B critical for 3 degrees of freedom and alpha 0.05 = 7.81 The null hypothesis is rejected; the variances are not equal 5. Transformed data (using the natural logarithmic function) Treatments Replications 0 33.3 66.7 100 Sums 1-1 4.047 3.802 3.462 3.186 1-2 4.031 3.771 3.538 3.206 1-3 3.956 3.852 3.550 3.226 1-4 3.935 3.822 3.493 3.150 Sum (yij.) 15.969 15.248 14.043 12.769 58.028 2-1 3.998 3.790 3.558 3.218 2-2 3.984 3.740 3.625 3.202 2-3 3.965 3.820 3.593 3.239 2-4 3.953 3.792 3.590 3.148 Sum (yij.) 15.899 15.142 14.366 12.807 58.213 3-1 3.958 3.814 3.533 3.178 3-2 3.959 3.818 3.545 3.242 3-3 3.951 3.865 3.552 3.192 3-4 3.948 3.815 3.469 3.190 Sum (yij.) 15.816 15.312 14.099 12.802 58.029 Totals (y.j.) 47.684 45.702 42.508 38.377 174.271 Average 3.974 3.808 3.542 3.198 Stdev 0.035 0.033 0.049 0.030 a. Bartlett's test for Homogeneity of Variances r r . _ 2 _ 2 _ 2 ^ . 2 H o °\ =<?2 =0-3.... = (7k Ha: At least two variances differ B test Statistic = 2.98 B critical for 3 degrees of freedom and alpha 0.05 = 7.81 The null hypothesis is accepted. b. Analysis of Variance HQ =fi2 = = Mk Ha : at least one of the means is different from the others A N O V A Table for Uniform Distribution: Joist M O E Source of Error Degrees of Freedom Sum of Squares Mean Sum of Squares F value Vi ,V 2 F critical (alpha =0.05) Treatment 3 4.130 1.377 509 3,8 4.07 Experimental Error 8 0.0217 0.0027 2.4 8,36 2.2 Sample Error 36 0.0405 0.0011 Total 47 4.192 At a 95% confidence rate there is a significant difference within t le individua treatments and there is at least one significant difference between the treatments. c. Scheffe's Test for Significant Differences between Treatments If Fs>F critical the difference is considered significant Differences 0/33.3 0/66.7 0/100 33.3/66.7 33.3/100 66.7/100 Fs 60 412 1333 157 826 263 F critical 12.21 12.21 12.21 12.21 12.21 12.21 Significant difference Yes Yes Yes Yes Yes Yes 53 6. Uniform Distribution: Data Plank MOR Treatments Replications 0 33.3 66.7 100 Sums 1-1 72.4 30.9 27.7 9.2 1-2 72.4 33.5 31.4 11.5 1-3 66.7 44.0 32.0 10.9 1-4 71.5 40.8 21.6 9.7 Sum (yij.) 282.9 149.2 112.6 41.3 586.1 2-1 55.6 34.0 26.9 9.6 2-2 58.8 39.8 30.3 9.6 2-3 68.0 43.0 27.2 10.9 2-4 75.1 40.1 23.8 10.0 Sum (yij.) 257.5 156.9 108.2 40.1 562.7 3-1 54.5 37.2 30.2 10.6 3-2 67.9 40.8 34.0 9.9 3-3 62.0 40.7 30.0 9.8 3-4 69.5 41.1 29.5 9.2 Sum (yjj.) 253.9 159.7 123.7 39.5 576.7 Totals (y.j.) 794.3 465.8 344.5 121.0 1725.6 Average 66.2 38.8 28.7 10.1 Stdev 6.9 4.1 3.5 0.7 a. Bartlett's test for Homogeneity of Variances H0 : o f =CT22 =CT 3 2 . . . . = CT2 Ha: At least two variances differ B test Statistic = 35.1 B critical for 3 degrees of freedom and alpha 0.05 = 7.81 The null hypothesis is rejected; the variances are not equal 7. Transformed data (using the natural logarithmic function) Treatments Replications 0 33.3 66.7 100 Sums 1-1 4.28 3.43 3.32 2.22 1-2 4.28 3.51 3.45 2.44 1-3 4.20 3.79 3.47 2.39 1-4 4.27 3.71 3.07 2.28 Sum (yij.) 17.03 14.44 13.30 9.33 54.10 2-1 4.02 3.52 3.29 2.26 2-2 4.07 3.68 3.41 2.26 2-3 4.22 3.76 3.30 2.39 2-4 4.32 3.69 3.17 2.30 Sum (yjj.) 16.63 14.66 13.18 9.22 53.69 3-1 4.00 3.62 3.41 2.36 3-2 4.22 3.71 3.53 2.29 3-3 4.13 3.71 3.40 2.28 3-4 4.24 3.71 3.38 2.22 Sum (yjj.) 16.58 14.74 13.72 9.15 54.20 Totals (y.j.) 50.25 43.84 40.20 27.70 161.99 Average 4.19 3.65 3.35 2.31 Stdev 0.11 0.11 0.13 0.07 a. Bartlett's test for Homogeneity of Variances H0:a\ =tr22 =cT32.... = cTi2 H&: At least two variances differ B test Statistic = 3.71 B critical for 3 degrees of freedom and alpha 0.05 = 7.81 The null hypothesis is accepted. b. Analysis of Variance HQ =M2 = = / V HA : at least one of the means is different from the others A N O V A Table for Uniform Distribution: Plank MOR Source of Error Degrees of Freedom Sum of Squares Mean Sum of Squares F value Vl,V 2 F critical (alpha =0.05) Treatment 3 22.51 7.504 688 3,8 4.07 Experimental Error 8 0.087 0.011 0.96 8,36 2.2 Sample Error 36 0.409 0.011 Total 47 23.01 At a 95% confidence rate there is not a significant difference within the individual treatments, but there is at least one significant difference between the treatments. c. Scheffe's Test for Significant Differences between Treatments If Fs>F critical the difference is considered significant Differences 0/33.3 0/66.7 0/100 33.3/66.7 33.3/100 66.7/100 Fs 157 386 1943 51 996 597 F critical 12.21 12.21 12.21 12.21 12.21 12.21 Significant difference Yes Yes Yes Yes Yes Yes 8. Uniform I Hstribution: Data Joist M O R Treatments Replications 0 33.3 66.7 100 Sums 1-1 60.9 31.2 13.6 7.5 1-2 62.1 28.1 25.4 7.4 1-3 42.4 36.9 21.2 7.8 1-4 39.1 34.6 17.5 6.0 Sum (y;,.) 204.4 130.7 77.7 28.7 441.6 2-1 50.3 27.1 20.6 7.0 2-2 52.5 30.9 30.8 7.5 2-3 54.7 33.9 26.8 8.1 2-4 46.9 37.3 19.0 7.1 Sum (y i i.) 204.4 129.2 97.1 29.7 460.4 3-1 50.0 31.3 17.4 7.2 3-2 51.9 30.8 18.6 7.2 3-3 58.2 38.3 22.0 6.5 3-4 63.0 26.4 13.5 5.8 Sum (y i i.) 223.1 126.8 71.5 26.6 447.9 Totals (y.j.) 631.9 386.7 246.3 85.0 1349.9 Average 52.7 32.2 20.5 7.1 Stdev 7.6 4.0 5.2 0.7 56 a. Bartlett's test for Homogeneity of Variances /7 a: At least two variances differ B test Statistic = 39 B critical for 3 degrees of freedom and alpha 0.05 = 7.81 The null hypothesis is rejected; the variances are not equal 9. Transformed data (using the natural logarithmic function) Treatments Replications 0 33.3 66.7 100 Sums 1-1 1.785 1.495 1.132 0.875 1-2 1.793 1.448 1.406 0.868 1-3 1.627 1.567 1.327 0.889 1-4 1.592 1.539 1.244 0.781 Sum (y i i.) 6.797 6.048 5.108 3.413 21.366 2-1 1.701 1.433 1.313 0.843 2-2 1.720 1.490 1.488 0.877 2-3 1.738 1.530 1.427 0.907 2-4 1.672 1.572 1.279 0.852 Sum (yij.) 6.831 6.025 5.507 3.479 21.842 3-1 1.699 1.496 1.240 0.856 3-2 1.715 1.488 1.269 0.856 3-3 1.765 1.583 1.342 0.812 3-4 1.800 1.421 1.132 0.763 Sum (yjj.) 6.978 5.988 4.982 3.287 21.236 Totals (y.j.) 20.605 18.062 15.598 10.179 64.444 Average 1.717 1.505 1.300 0.848 Stdev 0.065 0.054 0.109 0.043 a. Bartlett's test for Homogeneity of Variances U . —2 _ _ 2 _ 2 _ 2 HA: At least two variances differ B test Statistic = 10.6 B critical for 3 degrees of freedom and alpha 0.05 = 7.81 The null hypothesis is rejected. 10. Sandwich Distribution: Data Plank MOE Treatments Replications 10 20 33.3 50 66.7 Sums 1-1 10171 9858 9717 8488 6962 1-2 9130 10137 9808 8598 6940 1-3 9911 9513 10035 8867 7065 1-4 10354 8855 9760 8533 7296 Sum (yij.) 39566 38363 39321 34486 28263 179999 2-1 10549 9802 10519 8005 7518 2-2 10874 11483 9969 8886 7209 2-3 10355 9993 9923 8238 7029 2-4 11144 9564 10355 8171 6839 Sum (yij.) 42923 40842 40765 33300 28595 186425 3-1 10710 11737 9832 9164 7147 3-2 11070 10869 9334 9369 7369 3-3 11257 11531 9455 8296 6163 3-4 11100 11032 8595 7705 7207 Sum (y i i.) 44137 45169 37215 34535 27885 188941 Totals (y.j.) 126626 124374 117300 102320 84744 555365 Average 10552 10365 9775 8527 7062 Stdev 618 934 497 484 343 a. Bartlett's test for Homogeneity of Variances Ho : 0 f = C R 2 = C T 3 2 . . . . = CT 2 Ha: At least two variances differ B test Statistic = 12 B critical for 4 degrees of freedom and alpha 0.05 = 9.49 The null hypothesis is rejected; the variances are not equal 11. Transformed data (using the natural logarithmic function) Treatments Replications 10 20 33.3 50 66.7 Sums 1-1 9.227 9.196 9.182 9.046 8.848 1-2 9.119 9.224 9.191 9.059 8.845 1-3 9.201 9.160 9.214 9.090 8.863 1-4 9.245 9.089 9.186 9.052 8.895 Sum (yjj.) 36.793 36.669 36.773 36.247 35.451 181.934 2-1 9.264 9.190 9.261 8.988 8.925 2-2 9.294 9.349 9.207 9.092 8.883 2-3 9.245 9.210 9.203 9.017 8.858 2-4 9.319 9.166 9.245 9.008 8.830 Sum (y i i.) 37.122 36.914 36.916 36.105 35.496 182.553 3-1 9.279 9.371 9.193 9.123 8.874 3-2 9.312 9.294 9.141 9.145 8.905 3-3 9.329 9.353 9.154 9.024 8.726 3-4 9.315 9.309 9.059 8.950 8.883 Sum (yjj.) 37.234 37.326 36.548 36.241 35.389 182.738 Totals (y.j.) 111.149 110.909 110.236 108.594 106.336 547.225 Average 9.262 9.242 9.186 9.049 8.861 Stdev 0.060 0.090 0.052 0.057 0.050 a. Bartlett's test for Homogeneity of Variances H0 :CT,2 =CT 2 2 =CT 2 . . . . = CT2 Ha: At least two variances differ B test Statistic = 5.34 B critical for 4 degrees of freedom and alpha 0.05 = 9.49 The null hypothesis is accepted. b. Analysis of Variance H0:jul=Mi= = Mk Ha : at least one of the means is different from the others A N O V A Table for Sandwich Distribution: Plank M O E Source of Error Degrees -of Freedom Sum of Squares Mean Sum of Squares F value V l , V 2 F critical (alpha =0.05) Treatment 4 1.3387 0.3347 32.4 4,10 3.48 Experimental Error 10 0.1032 0.0103 3.9 10,45 2 Sample Error 45 0.1193 0.0027 Total 59 1.5612 At a 95% confidence rate there is a significant difference within t le individua treatments, and there is at least one significant difference between the treatments, c. Scheffe's Test for Significant Differences between Treatments If Fs>F critical the difference is considered significant Differences 10/20 10/33.3 10/50 10/66.7 20/33.3 20/50 20/66.7 33.3/50 33.3/66.7 50/66.7 Fs 0.2 3 26 94 2 22 84 11 61 21 F critical 13.92 13.92 13.92 13.92 13.92 13.92 13.92 13.92 13.92 13.92 Significant difference No No Yes Yes No Yes Yes No Yes Yes 12. Sandwich Distribution: Data Joist M O E Treatments Replications 10 20 33.3 50 66.7 Sums 1-1 9439 7326 7551 5733 2513 1-2 8429 8677 6932 5046 4428 1-3 8010 8262 6532 5081 3434 1-4 8358 7193 6674 5301 4615 Sum (yij.) 34236 31458 27690 21160 14990 129534 2-1 9968 6456 6107 6112 4658 2-2 9084 8020 7158 5575 4139 2-3 9017 8222 7074 4919 4307 2-4 9074 7318 6790 5639 2660 Sum (yij.) 37144 30016 27128 22245 15764 132298 3-1 10408 8774 8765 5436 4146 3-2 8745 8388 7349 4809 3962 3-3 9209 8151 6688 5333 3467 3-4 9925 8222 6840 4429 3576 Sum (yij.) 38287 33535 29642 20008 15151 136623 Totals (y.j.) 109667 95010 84460 63413 45905 398454 Average 9139 7917 7038 5284 3825 Stdev 712 692 664 458 711 60 a. Bartlett's test for Homogeneity of Variances H o =°~2 = <T3.... = (Tk H: At least two variances differ B test Statistic = 2.54 B critical for 4 degrees of freedom and alpha 0.05 = 9.49 The null hypothesis is accepted. b. Analysis of Variance H0-Mi = M2 = = Mt Ha:at least one of the means is different from the others A N O V A Table for Sandwich Distribution: Joist M O E Source of Error Degrees of Freedom Sum of Squares Mean Sum of Squares F value V i , V 2 F critical (alpha =0.05) Treatment 4 2.14E+08 53383006 100 4,10 3.48 Experimental Error 10 5326183 532618 1.3 10,45 2 Sample Error 45 18237987 405289 Total 59 2.37E+08 At a 95% confidence rate there is not a significant difference within the individual treatments, but there is at least one significant difference between the treatments. c. Scheffe's Test for Significant Differences between treatments If Fs>F critical the difference is considered significant Differences 10/20 10/33.3 10/50 10/66.7 20/33.3 20/50 20/66.7 33.3/50 33.3/66.7 50/66.7 Fs 17 50 167 318 9 78 189 35 116 24 F critical 13.92 13.92 13.92 13.92 13.92 13.92 13.92 13.92 13.92 13.92 Significant difference Yes Yes Yes Yes No Yes Yes Yes Yes Yes 61 13. Sandwich Distribution: Data Plank MOR Treatments Replications 10 20 33.3 50 66.7 Sums 1-1 27.8 42.96 39.78 40.78 33.56 1-2 35.37 39.37 45 42.01 37.44 1-3 34.04 39.09 50.33 45.64 36.77 1-4 34.23 31.34 45.1 42.47 40.27 Sum (yjj.) 131.44 152.76 180.21 170.9 148.04 783.35 2-1 25.93 36.09 42.2 36.89 33.51 2-2 48.19 47.02 43.72 39.52 34.26 2-3 47.16 44.32 43.34 44.08 35.74 2-4 49.4 33.64 40.16 36.85 32.46 Sum (yjj.) 170.68 161.07 169.42 157.34 135.97 794.48 3-1 40.42 61 47.28 37.55 29.39 3-2 32.26 52.44 36.71 46.23 34.88 3-3 42.79 60.66 43.17 39.18 25.21 3-4 47.71 52.19 34.81 35.1 34.07 Sum (yjj.) 163.18 226.29 161.97 158.06 123.55 833.05 Totals (y.j.) 465.3 540.12 511.6 486.3 407.56 2410.88 Average 38.78 45.01 42.63 40.53 33.96 Stdev 8.27 9.90 4.32 3.63 3.86 a. Bartlett's test for Homogeneity of Variances Tr . ^.2 _ 2 _ 2 ^ 2 Ha: At least two variances differ Btest Statistic = 18.5 B critical for 4 degrees of freedom and alpha 0.05 = 9.49 The null hypothesis is rejected; the variances are not equal 14. Transformed data (using the natural logarithmic function) Treatments Replications 10 20 33.3 50 66.7 Sums 1-1 3.325 3.760 3.683 3.708 3.513 1-2 3.566 3.673 3.807 3.738 3.623 1-3 3.528 3.666 3.919 3.821 3.605 1-4 3.533 3.445 3.809 3.749 3.696 Sum (y i i.) 13.952 14.544 15.218 15.016 14.436 73.165 2-1 3.255 3.586 3.742 3.608 3.512 2-2 3.875 3.851 3.778 3.677 3.534 2-3 3.854 3.791 3.769 3.786 3.576 2-4 3.900 3.516 3.693 3.607 3.480 Sum (yij.) 14.884 14.744 14.982 14.678 14.102 73.390 3-1 3.699 4.111 3.856 3.626 3.381 3-2 3.474 3.960 3.603 3.834 3.552 3-3 3.756 4.105 3.765 3.668 3.227 3-4 3.865 3.955 3.550 3.558 3.528 Sum (yij.) 14.795 16.131 14.774 14.686 13.688 74.073 Totals (y.j.) 43.630 45.418 44.974 44.379 42.227 220.628 Average 3.636 3.785 3.748 3.698 3.519 Stdev 0.222 0.219 0.103 0.089 0.121 a. Bartlett's test for Homogeneity of Variances rj . _ 2 _ 2 _ 2 _ 2 Ha: At least two variances differ Btest Statistic = 15 B critical for 4 degrees of freedom and alpha 0.05 = 9.49 The null hypothesis is rejected the variances are not similar. 15. Sandwich Distribution: Data Joist MOR Treatments Replications 10 20 33.3 50 66.7 Sums 1-1 36.45 34.66 35.12 25.61 14.99 1-2 43.71 44.53 41.53 18.89 25.15 1-3 42.22 38.42 38.43 27.95 19.5 1-4 37.94 36.81 38.94 29.59 24.06 Sum to.) 160.32 154.42 154.02 102.04 83.7 654.5 2-1 51.59 29.71 29.42 33.6 24.88 2-2 54.31 40.14 34.67 27.35 15.84 2-3 41.88 51.24 33.12 26.91 22.95 2-4 42.01 35.12 35.15 31.72 17.05 Sum (yii.) 189.79 156.21 132.36 119.58 80.72 678.66 3-1 56.84 42.69 46.83 27.19 16.94 3-2 47.6 34.64 40.42 25.21 20.45 3-3 53.42 43.78 39.31 29.05 13.71 3-4 60.73 44.85 36.27 19.84 18.5 Sum (yij.) 218.59 165.96 162.83 101.29 69.6 718.27 Totals (y.j.) 568.7 476.59 449.21 322.91 234.02 2051.43 Average 47.39 39.72 37.43 26.91 19.50 Stdev 7.85 5.96 4.50 4.26 3.99 a. Bartlett's test for Homogeneity of Variances U . _ 2 7 _ 2 _ 2 Ha: At least two variances differ B test Statistic = 7.29 B critical for 4 degrees of freedom and alpha 0.05 = 9.49 The null hypothesis is accepted. b. Analysis of Variance Ha : at least one of the means is different from the others / A N O V A Table for Sandwich Distribution: Joist M O R Source of Error Degrees of Freedom Sum of Squares Mean Sum of Squares F value V i , V 2 F critical (alpha =0.05) Treatment 4 5809 1452 22.4 4,10 3.48 Experimental Error 10 648 65 2.9 10,45 2 Sample Error 45 1019 23 Total 59 7476 At a 95% confidence rate there is a significant difference within t le individua treatments, and there is at least one significant difference between the treatments. c. Scheffe's Test for Significant Differences between treatments If Fs>F critical the difference is considered significant Differences 10/20 10/33.3 10/50 10/66.7 20/33.3 20/50 20/66.7 33.3/50 33.3/66.7 50/66.7 Fs 5 9 39 72 0.5 15 857 232 30 5 F critical 13.92 13.92 13.92 13.92 13.92 13.92 13.92 13.92 13.92 13.92 Significant difference No No Yes Yes No Yes Yes Yes Yes No 65 Appendix C- A N O V A Analysis of Panel Density and Maximum Face Density 1. Equations: a. Bartlett's Test for the Homogeneity of Variances: rj . _ 2 _ 2 _ 2 _ _ 2 Ha: At least two variances differ Test statistic (equal sample sizes): ( n-l)[tlnJ 2-Xln*,'] 3k(n-l) Where Si 2= ith variance ~s2= the average variance k= 4 (uniform distribution) k= 5 (sandwich distribution) n=12 Degrees of freedom =(k-l) b. A N O V A H0 ://, =fx2 = = /ik Ha : at least one of the means is different from the others A N O V A Table: Summary of Calculations Source of Error Degrees of Freedom Sum of Squares Mean Sum of Squares F value Treatment k-1 SSTR SS T R /(k-l) [SS T R/(k-l)]/ [ SS E E /k(n-l)l Experimental Error k(n-l) SSEE SS E E/k(n-l) [SSE E/k(n-l)]/ [ SS S E/nk(m-l)l Sample Error nk(m-l) SSSE SS S E/nk(m-l) Total nkrn-1 SS T 66 Working equations: nkm y 2 ~ nkm 0 m nkm SS £g — SS j- SS ss TR where i= the replications n = 3 j= the treatments k = 4 (uniform) or 5 (sandwich) 1= the observations m = 4 c. Scheffe's Test for Significant Differences between Treatments AivMv 11A J I A Where Fs = test statistic X,= is the average of the i group Xj = the average of the j group ni=population of the i group n j = population of the j group sw 2= the within group variance (mean sum of squares for the experimental error) F critical = (k-l)(F critical for the Treatment) 67 2. Uniform Distribution: Panel Density Comparison Treatments Replications 0 33.3 66.7 100 Sums 1-1 46.25 42.29 42.50 41.99 1-2 45.61 44.04 43.17 42.80 1-3 46.12 44.42 45.81 44.39 1-4 46.09 43.81 45.06 43.59 Sum (y i i.) 184.06 174.57 176.53 172.76 707.93 2-1 43.71 41.54 42.16 43.42 2-2 43.86 41.32 44.63 44.13 2-3 44.85 43.34 46.15 44.57 2-4 45.23 43.32 44.43 43.15 Sum (yjj.) 177.66 169.52 177.36 175.27 699.82 3-1 42.36 42.61 42.52 41.16 3-2 43.44 42.28 42.59 42.57 3-3 45.04 43.04 43.83 42.47 3-4 44.53 42.39 43.42 41.15 Sum (yij.) 175.37 170.32 172.36 167.35 685.40 Totals (y.j.) 537.1 514.4 526.3 515.4 2093.15 Average 44.8 42.9 43.9 42.9 Stdev 1.217 0.967 1.355 1.149 a. Bartlett's test for Homogeneity of Variances Ho '•<*] =CT 2 2 =CT 3 2 . . . . = CT2 Ha: At least two variances differ B test Statistic = 1.22 B critical for 3 degrees of freedom and alpha 0.05 = 7.81 The null hypothesis is accepted. b. Analysis of Variance H„:/il=fi2 = = Mk Ha : at least one of the means is different from the others A N O V A Table for Uniform Distribution: Panel Density Source of Error Degrees of Freedom Sum of Squares Mean Sum of Squares F value V i , V 2 F critical (alpha =0.05) Treatment 3 28.39 9.464 2.96 3,8 4.07 Experimental Error 8 25.62 3.202 3.23 8,36 2.2 Sample Error 36 35.69 0.991 Total 47 89.70 At a 95% confidence rate there is a significant difference within t le individua treatments but not between treatments. 3. Uniform Distribution: Maximum Face Density Comparison Treatments Replications 0 33.3 66.7 100 Sums 1-1 53.64 54.05 59.28 53.05 1-2 59.68 56.67 57.17 57.37 1-3 54.71 58.68 60.16 59.34 1-4 56.70 55.59 56.05 60.74 Sum (y;j.) 224.72 224.98 232.65 230.49 912.83 2-1 51.71 52.68 49.70 60.23 2-2 48.20 54.08 57.65 62.58 2-3 58.72 55.07 54.43 62.70 2-4 57.20 53.96 61.48 61.89 Sum (yij.) 215.83 215.78 223.25 247.39 902.24 3-1 57.20 56.04 48.79 50.35 3-2 53.45 54.33 58.86 52.45 3-3 55.36 53.85 62.85 57.49 3-4 46.35 54.38 58.48 49.51 Sum (yij.) 212.35 218.58 228.97 209.79 869.68 Totals (y.j.) 652.89 659.34 684.87 687.66 2684.75 Average 54.41 54.94 57.07 57.31 Stdev 4.05 1.60 4.30 4.80 a. Bartlett's test for Homogeneity of Variances Tj . —2 _ 2 _ 2 _ 2 Ha: At least two variances differ Btest Statistic = 11.38 B critical for 3 degrees of freedom and alpha 0.05 = 7.81 The null hypothesis is rejected the variances are not homogenous. 69 4. Transformed Data (using the natural logarithmic function) Treatments Replications 0 33.3 66.7 100 Sums 1-1 3.982 3.990 4.082 3.971 1-2 4.089 4.037 4.046 4.049 1-3 4.002 4.072 4.097 4.083 1-4 4.038 4.018 4.026 4.107 Sum (yij.) 16.111 16.117 16.251 16.210 64.690 2-1 ' 3.946 3.964 3.906 4.098 2-2 3.875 3.990 4.054 4.136 2-3 4.073 4.009 3.997 4.138 2-4 4.046 3.988 4.119 4.125 Sum (yji.) 15.940 15.951 16.076 16.498 64.466 3-1 4.046 4.026 3.887 3.919 3-2 3.979 3.995 4.075 3.960 3-3 4.014 3.986 4.141 4.052 3-4 3.836 3.996 4.069 3.902 Sum (y^.) 15.875 16.003 16.172 15.832 63.882 Totals (y.j.) 47.926 48.071 48.499 48.541 193.038 Average 3.994 4.006 4.042 4.045 Stdev 0.077 0.029 0.078 0.086 a. Bartlett's test for Homogeneity of Variances Ha: At least two variances differ B test Statistic = 11.49 B critical for 3 degrees of freedom and alpha 0.05 = 7.81 The null hypothesis is rejected the variances are not homogenous. 5. Sandwich Distribution: Panel Density Comparison Treatments Replications 10 20 33.3 50 66.7 Sums 1-1 44.02 41.44 41.19 40.28 40.10 1-2 44.59 40.78 42.10 40.45 40.46 1-3 44.26 40.74 43.21 41.07 40.47 1-4 45.01 40.22 42.96 41.18 41.03 Sum (yij.) 177.88 163.17 169.46 162.98 162.05 835.54 2-1 42.89 41.39 43.34 39.96 41.08 2-2 43.72 43.71 43.39 41.66 41.00 2-3 43.87 41.90 41.93 41.38 39.77 2-4 43.51 41.62 43.45 39.89 40.89 Sum (yij.) 173.99 168.62 172.12 162.90 162.74 840.37 3-1 43.44 43.58 44.44 41.52 41.13 3-2 43.64 41.85 42.57 41.63 41.73 3-3 44.23 43.65 42.92 40.09 41.50 3-4 45.63 41.77 42.26 40.42 42.08 Sum (yij.) 176.94 170.85 172.19 163.65 166.44 850.07 Totals (y.j.) 528.81 502.64 513.77 489.53 491.24 2525.98 Average 44.07 41.89 42.81 40.79 40.94 Stdev 0.743 1.174 0.860 0.679 0.664 a. Bartlett' s test for Homogeneity of Variances H0:a2=a22=a2.... = <j2k Ha: At least two variances differ Btest Statistic = 5.17 B critical for 4 degrees of freedom and alpha 0.05 = 9.49 The null hypothesis is accepted. b. Analysis of Variance H0 :MI =M2 = = Mk Ha : at least one of the means is different from the others A N O V A Table for Sandwich Distribution: Panel Density Source of Error Degrees of Freedom Sum of Squares Mean Sum of Squares F value V i , V 2 F critical (alpha =0.05) Treatment 4 89.83 22.46 16.11 4,10 3.48 Experimental Error 10 13.94 1.39 2.47 10,45 2 Sample Error 45 25.37 0.564 Total 59 129.14 At a 95% confidence rate there is a significant difference within the individual treatments, and there is at least one significant difference between the treatments. c. Scheffe's Test for Significant Differences between treatments If Fs>F critical the difference is considered significant Differences 10/20 10/33.3 10/50 10/66.7 20/33.3 20/50 20/66.7 33.3/50 33.3/66.7 50/66.7 Fs 20 7 46 42 4 5 2 10 15 0.1 F critical 13.92 13.92 13.92 13.92 13.92 13.92 13.92 13.92 13.92 13.92 Significant difference Yes No Yes Yes No No No No Yes No 6. Sandwich Distribution: Maximum Face Density Comparison Treatments Replications 10 20 33.3 50 66.7 Sums 1-1 59.10 61.25 59.78 53.74 53.60 1-2 64.06 61.10 63.69 57.58 52.71 1-3 59.38 59.26 58.00 53.36 52.94 1-4 65.13 63.32 61.32 53.03 61.49 Sum (yij.) 247.66 244.92 242.78 217.71 220.72 1173.79 2-1 66.13 54.41 59.37 51.01 54.81 2-2 67.02 64.22 62.16 56.58 57.65 2-3 54.43 66.07 54.22 54.06 48.65 2-4 59.44 62.52 56.92 58.63 56.62 Sum (yij.) 247.01 247.20 232.67 220.27 217.72 1164.87 3-1 56.63 64.18 56.71 59.39 59.00 3-2 64.34 59.77 56.07 60.50 59.26 3-3 70.41 67.92 57.31 61.81 59.50 3-4 68.08 66.89 55.98 58.19 52.27 Sum (yjj.) 259.45 258.76 226.06 239.88 230.03 1214.16 Totals (y.j.) 754.12 750.88 701.51 677.85 668.47 3552.81 Average 62.84 62.57 58.46 56.49 55.71 Stdev 4.94 3.75 2.84 3.39 3.81 72 a. Bartlett's test for Homogeneity of Variances ZJ • _ _ 2 _ _ 2 _ 2 H o - ° \ = C r 2 = ° 3 • - = ° k Ha: At least two variances differ B test Statistic = 3.53 B critical for 4 degrees of freedom and alpha 0.05 = 9.49 The null hypothesis is accepted. b. Analysis of Variance H 0 = M 2 = = Mk Ha : at least one of the means is different from the others A N O V A Table for Sandwich Distribution: Maximum Face Density Source of Error Degrees of Freedom Sum of Squares Mean Sum of Squares F value V i , V 2 F critical (alpha =0.05) Treatment 4 268.60 67.15 7.40 4,10 3.48 Experimental Error 10 90.80 9.08 0.00385 10,45 2 Sample Error 45 106163 2359.19 Total 59 106523 At a 95% confidence rate there is no significant difference within the individual treatments, but there is at least one significant difference between the treatments. c. Scheffe's Test for Significant Differences between treatments If Fs>F critical the difference is considered significant Differences 10/20 10/33.3 10/50 10/66.7 20/33.3 20/50 20/66.7 33.3/50 33.3/66.7 50/66.7 Fs 0.05 12.7 27 34 11 24 31 3 5 0.40 F critical 13.92 13.92 13.92 13.92 13.92 13.92 13.92 13.92 13.92 13.92 Significant difference No No Yes Yes No Yes Yes No No No 73 Appendix D: Statistical Analysis T-tests *NB: all calculations were done using Microsoft Excel 2000 statistical analysis tools 1. F-test and t-test equations used are as follows: a. F- test where s2 = the variance of first sample (the larger of the two) 5 2 = the variance of the second sample b. T-test for unequal variances: _(xi-X2)-(Ml-ju2) where s2 = the variance of first sample (the smaller of the two) s2 = the variance of the second sample Xl = the first sample mean X2 = the second sample mean (//, - ju2) = 0 the expected value « t = the sample size of the first sample n2 = the sample size of the second sample where the degrees of freedom the smaller of ni-1 or n2- l c. T-test for equal variances: t = (x.-X^-^-ju,) where s2 = the variance of first sample (the smaller of the two) s2 = the variance of the second sample Xy = the first sample mean X2 = the second sample mean {jix - ju2) = 0 the expected value n, = the sample size of the first sample n2 = the sample size of the second sample and the degrees of freedom are of n i+ n2-2 2. Summary of the F and t -tests between the 0% fines board and the 10% fines board strength: MOE-plank MOE-joist MOR-joist Fstat 0.795 1.21 0.937 Fcritical 0.355 2.82 0.355 Equal or unequal variances Unequal Equal Unequal Tstat 2.14 0.98 1.67 Tcritical (two tail) 2.07 2.07 2.07 Significant difference Yes No No 3. Panel density of the 0% fine board compared to the panel density of the sandwich boards: 0/10 0/20 0/33.3 0/50 0/66.7 Fstat 2.68 1.07 2.00 3.21 3.36 Fcritical 2.82 2.82 2.82 2.82 2.82 Equal or unequal variances Equal Equal Equal Unequal Unequal Tstat 1.68 5.88 4.52 9.85 9.55 Tcritical (two tail) 2.07 2.07 2.07 2.11 2.11 Significant difference No Yes Yes Yes Yes 4. Maximum face density of the 0% fine board compared to the maximum face density of the sandwich boards: 0/10 0/20 0/33.3 0/50 0/66.7 Fstat 0.671 1.166 2.037 1.424 1.312 Fcritical 0.355 2.818 2.818 2.818 2.818 Equal or unequal variances Unequal Equal Equal Equal Equal Tstat -4.57 -5.12 -2.84 -1.36 -0.809 Tcritical (two tail) 2.07 2.07 2.07 2.07 2.07 Significant difference Yes Yes Yes No No 75 

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