The length effect on Norway spruce boards: An investigation on indicating properties based on axial dynamic and edgewise bending MOEs

Master's Thesis in Structural Engineering

The length effect on Norway spruce boards

An investigation on indicating properties based on axial dynamic and edgewise bending MOEs

Authors: Anders Engström, Toma Sumbasacu

Supervisor LNU: Anders Olsson, Jan Oscarsson

Abstract

When using timber for construction purposes it is important to know its strength. One way to do this is by sorting the boards into strength classes that are defined by European standards. A commonly used method for strength grading is based on dynamic excitation in the longitudinal direction of the board to obtain an average dynamic longitudinal modulus of elasticity (MOE). This in turn correlates with the bending strength of the board in such a way that it can be used as an indicating property (IP) to bending strength. The use of MOE as an IP has proven to give the highest coefficient of determination (R

²

) to both bending and tensile strength in boards. Through the research described in this thesis, one might find that both reducing the length of a board to half its initial length and by removing the part containing the lowest local MOE in edgewise bending provided similar results, the axial dynamic MOE remaining within a 1% tolerance whereas the lowest IP based on local MOE in edgewise bending increased by 6–7%.

Key words: length effect, dynamic modulus of elasticity, edgewise bending,

indicating property, Norway spruce.

Acknowledgement

This thesis is the culmination of the one year master program within structural engineering at Linnaeus University, 2014–2015. However the concept for this thesis is not something we can take credit for as it was formulated by professor Anders Olsson and lecturer Jan Oscarsson. We owe them many thanks for their support and guidance, as our supervisors they have helped us clear up many problems that arose during the research and their careful examination of the content of this thesis has been a tremendous help for us. We must also extend our gratitude to Bertil Enquist and Andreas Briggert for their help with the laboratory equipment and the input they have had on this research.

Toma Sumbasacu and Anders Engström

Växjö 10

^th

of december 2015

Table of contents

1. INTRODUCTION... 1

1.1 B

ACKGROUND

... 2

1.2 A

IM AND

P

URPOSE

... 2

1.3 H

YPOTHESIS AND

L

IMITATIONS

... 3

2. THEORY ... 4

2.1 S

TRENGTH GRADING

... 4

2.1.1 Indicating Property ... 6

2.1.2 Fast Fourier Transform ... 8

2.2 T

HE LENGTH EFFECT

... 9

3. METHOD ... 10

3.1 L

ABORATORY WORK

... 11

3.1.1 Group 1 – End sections gradually removed... 14

3.1.2 Group 2 – Largest defect removed... 15

3.2 M

ATLAB

... 17

4. RESULTS ... 20

4.1 G

ROUP

1 – E

ND SECTIONS GRADUALLY REMOVED

... 20

4.2 G

ROUP

2 – L

ARGEST DEFECT REMOVED

... 23

5. ANALYSIS ... 26

5.1 G

ROUP

1 – E

ND SECTIONS GRADUALLY REMOVED

... 26

5.2 G

ROUP

2 – L

ARGEST DEFECT REMOVED

... 26

6. DISCUSSION ... 28

7. CONCLUSION ... 29

REFERENCES ... 30

APPENDIX ... 32

1. Introduction

Wood is a living material, available in most parts of the world and it requires little processing to become a material suitable for construction purposes.

However, in contrast to i.e. concrete and steel that are produced by man and can have their mechanical properties altered to the users benefit and better suit their intended applications, wood is produced by nature itself. The mechanical properties of timber are dependent on the genetic heritage and local growth conditions and therefore the ability to alter these properties is very limited [1]. The local conditions can vary for every tree which makes each one unique and therefore it is important to identify the mechanical properties of each timber board used as a structural material with the purpose of ensuring a safe construction.

An option to classify timber by its properties is to grade the individual timber considering their strength. In Europe such grading is based on a number of standards that apply to both softwood and hardwood. According to the European standard EN 338 [2] timber is labelled between C14 – C50 for softwood and D18 – D70 for hardwood, the classification depending on the bending strength of the board. This property can be predicted in several ways; one way is by using axial dynamic excitation. In this process the modulus of elasticity (MOE) is determined with the use of density, dimension and resonance frequency. The MOE obtained from this method can be correlated to the actual strength of the timber, but this method yields rather poor results with a coefficient of determination as low as 0.5 [3]. The method of axial dynamic excitation does not provide information regarding knots or other defects which is of high interest to take into account when determining the MOE, since a knot can result in a considerable reduction of the local MOE of the timber [1]. The impact the knots and the deviation of the surrounding fibre actually have on the strength and the stiffness of the board is best illustrated by the fact that in fracture testing of 1000 timber boards, 90% of the failures were directly related with the knots in the boards [4].

The occurrence of knots is of course a limitation when using timber in

construction. However, such products have several other advantages; timber

has a very high strength-to-weight ratio which will reduce the costs

associated with manufacturing and transporting [5]. Furthermore, the

greatest advantage timber possesses over other construction materials is that

it is natural and comes from a renewable source, the forest. When compared

to materials as steel and concrete which generate greenhouse gases in their

manufacturing processes, a forest will absorb carbon dioxide during its

growth through the process of photosynthesis. The amount of carbon dioxide

(CO

2

) absorbed is so large that when comparing concrete buildings with

wood framed houses, the latter will actually have a negative carbon footprint

meaning that the absorption of CO from the growth period of the tree will

sustainable construction material which is of great importance in the modern society.

1.1 Background

A commonly used method for strength grading of timber is to use a dynamic excitation in the longitudinal direction of the board. Vibrations induced by means of a hammer blow in one end are measured using an accelerometer, a microphone or a laser vibrometer [1] and the frequency content of the vibrations are calculated. Having determined the board’s natural frequencies, mass and dimensions it is easy to calculate an average dynamic longitudinal modulus of elasticity (MOE). This in turn correlates with the bending strength of the board in such a way that it can be used as an indicating property (IP) [4] to bending strength. This means that the determined dynamic MOE of a board decides to which strength class the board is assigned.

Timber is not homogeneous since it contains knots and other defects that may cause considerable reduction in local stiffness and strength [4]. It is more likely that a long board, rather than a short one, contains a section with large knots that reduces local MOE and bending strength substantially and of course the weakest section along a board should be the one that decides to which strength class the board should be assigned. Reduced local MOE also affects the average dynamic longitudinal MOE but to what extent is not very well investigated. When considering a batch of long boards and a batch of short boards, respectively, it is not certain that the dynamic MOEs of long boards have the same relationship to bending strength as the dynamic MOEs of short boards have. It should be investigated to what extent the relationship between dynamic MOE and bending strength depend on the length of the boards. It should also be investigated how the length of the board will affect a local IP based on edgewise bending MOE that is determined through results obtained from laser scanning with the optical WoodEye scanning machine and processed with Matlab. If these effects are substantial, it should be considered when a setting value, i.e. a minimum IP value required for assignment of a board to a certain strength class, is determined.

1.2 Aim and Purpose

The aim of this thesis is to examine and describe the length effect on timber

boards from the species Norway spruce, i.e. how the indicating properties

determined by the average dynamic MOE change as a function of the length

of the board and, furthermore, how the length affects the indicating

properties based on edgewise bending MOE.

1.3 Hypothesis and Limitations

All tests have been performed on timber from Norway spruce (Picea abies) where the initial modulus of elasticity is determined by the board’s mass, dimensions and resonance frequency that is generated by axial dynamic excitation. Throughout the current thesis work a batch of 57 boards was used. The boards were provided by Södra in Torsås, Kalmar County.

Considering the data sampling procedure, as well as the described method used for the laboratory work, which are a product of literature review and discussions between the supervisors and authors of this thesis, a minor limitation apart from the size of the batch has been introduced. It concerns disregarding pieces of boards smaller than one meter from the analysis due to a limitation of the range at which the instruments measuring axial resonance frequency would deliver reliable data.

At the basis of the provided research there is an assumption that, when

systematically reducing the length of a board to half of the initial one, by

alternatively removing parts from root and top end, there might be changes

within the two investigated IPs. This hypothesis is also studied on a second

group of boards, for which the worst defects (sections containing the lowest

local edgewise bending MOEs) are removed.

2. Theory

2.1 Strength grading

Using timber as a construction material has several advantages such as high strength-to-weight ratio and many environmental advantages when compared to materials such as steel and concrete. However, there are some challenges associated with the use of wood arising from the natural variation of the wood properties. Timber is recovered from trees which are living things and can undergo several changes in their growing conditions throughout their life; the spacing of trees in the forest, wind loads acting on the trees and changes in the soil are all things that can affect the material properties. These variations can cause trees from the same population and species to differ from each other but the properties can also vary significantly within the same tree [5]. Therefore there is a need to classify these properties in the production of timber products before they can be utilized for construction purposes. This is where strength grading comes into use.

By definition, strength grading refers to various wood properties that can be measured in order to predict the mechanical properties (strength) of a timber board or related products. Most of the background of this thesis has its roots within the field of strength grading; therefore, strength grading is a key theory topic. There are various methods of sorting the timber into their appropriate strength class; however, the only way to precisely determine the strength of a timber board is through destructive testing. This means subjecting the board to bending until failure, measure the load and calculate the strength. However this destroys the board and therefore other methods of strength grading must be used. These other methods rely on indicating properties (IP) to determine the strength class and the most important of these strength grading methods will be described in this chapter.

It is probable that ever since humans started to use timber for construction

purposes there has been knowledge of the properties of different wood

species through experience. This was the basis of timber sorting until the

second half of the 19

^th

century [1]. The first actual rules for sorting timber

which came at this time was appearance grading. This method of sorting

timber was used when the visual appearance of the timber was important and

this method is still used on the market today. In Europe it is regulated by the

European standard EN 1611-1 [20]. In the early 20

^th

century the first rules

concerning visual strength grading where implemented, the principles for

this grading were published in 1927 [6]. This method of strength grading is

functional but it only regards the visual defects such as knots, cross-grained

wood and compression wood that can be observed while the intrinsic

properties of the timber are disregarded.

Another method of strength grading that is more accurate than visual grading is machine strength grading. In general the principle for machine strength grading is to establish a relationship between measured IP’s and the strength of the board in question. The IP can be a mean or a local MOE of the board, knot size and position, annual ring width and so on. From Table 1 it is clear that the indicating properties that involve the MOE have the highest coefficient of determination; therefore, according to the authors they are the most important IPs.

The use of MOE as an IP has proven to give the most accurate correlation to the bending strength of timber with a coefficient of determination of more than 0.7, as can be seen in Table 1. In the 20

^th

century research into the relationship of MOE and bending strength for use in strength grading was in progress. The MOE was determined by three-point bending in the flatwise direction and between the 1960’s and 1970’s machine strength grading with MOE as an IP was approved in the UK and Sweden [1]. Although the machines utilized for this purpose are big and cumbersome and, therefore, not ideal for industrial purposes, these machines have dominated the market for almost half a century and are still in use all over the world today. They result in R

²

values of about 0.5.

Another method of determining IPs for strength grading is the use of axial dynamic excitation. This method involves the dimension, density and resonance frequency of a board and through equation 1 an IP that represents the mean MOE of the board is determined. The dimension and density can easily be measured with a simple scale and a measuring tape but the resonance frequency also has to be obtained. One way of determining this is by inducing a longitudinal vibration in the board with the use of e.g. a metallic hammer and then measure the sound wave in the board with a microphone or measure the axial oscillation with either a laser vibrometer or an accelerometer. These measurements can then with the help of Fast Fourier transform (FFT) be converted into resonance frequencies corresponding to the different axial modes. This resonance frequency in combination with length and density of the board is used to calculate a mean MOE for the board which can be used as an indicating property to the actual bending strength [1] [3].

The method of axial dynamic excitation in combination with just length to

determine a MOE has proven to yield an R

²

value of around 0.5 for Norway

spruce (Picea abies). When the density is also regarded the accuracy of the

grading increases [3]. The MOE determined by this method is only the mean

MOE of the board but the accuracy of this method for determining strength

is often as good as machine strength grading where the boards are subject to

flatwise bending. The advantage of using axial dynamic excitation is that the

machines used are relatively small and easy to handle. There are even hand

held, wireless devices approved for strength grading of structural timber

the industry since the axial dynamic excitation can be carried out at saw mill production speed where the length is measured by laser and the average density of the timber species is utilized [1].

Another way of estimating the strength of timber is through scanning, in combination with dynamic excitation. A machine which can be utilized for this purpose is the WoodEye. This scanner is equipped with four sets of multi sensor cameras and dot lasers which allow it to scan the fibre direction and knot distribution with a high resolution. Boards are fed through the scanner with a conveyor belt in the longitudinal direction. The WoodEye makes use of the tracheid effect. This is where the dot projected by the laser is distorted into an ellipse due to the fact that the distribution of concentrated light on a board surface is larger in the fibre direction than in directions perpendicular to the fibres. The principal direction of the ellipse indicates the fibre direction, see Figure 2. By means of the described technique, R

²

values of about 0.7 can be achieved [4].

Other scanning machines make use of X-ray technologies to determine the density of the timber, which can be correlated for determining the knot size and distribution since there is a clear difference in density between knots and clear wood [1]. The X-ray scanning results give information about density and knots but, as one can see in Table 1, the accuracy for these IPs is rather poor. However, when the IPs are combined with the average MOE obtained through axial dynamic excitation, the accuracy increases. Both these techniques are suitable for the industry since they can function at the production speed of sawmills, and, as a consequence, it is possible to achieve a higher yield.

Table 1. Statistical relationships, in terms of coefficient of determination (R²), between strength of Norway spruce timber and various non-destructively measured wood properties (Hoffmeyer 1995) [7].

The investigations referred to are 1. Johansson et al. (1992) [8], 2. Hoffmeyer (1984) [9], 3. Hoffmeyer (1990) [10], 4. Lackner and Foslie (1988) [11], 5. Glos and Heimeshoff (1982) [12], and 6. Johansson (1976) [13].

Non-destructively measured wood properties

Coefficient of determination (R²) Bending strength Tensile strength Source: 8 9 10 11 8 12 13

Knots 0.27 0.20 0.16 0.25 0.36 0.42 0.30

Annual ring width 0.21 0.27 0.20 0.44 0.36 0.33 0.28

Density 0.16 0.30 0.16 0.40 0.38 0.29 0.38

MOE, bending or tension 0.72 0.53 0.55 0.56 0.70 0.69 0.58 MOE, flatwise bending, short span 0.52 0.65 0.74 Knots + annual ring width 0.37 0.42 0.39 0.49 0.48

Knots + density 0.38 0.38 0.55 0.61 0.64

Knots + MOE 0.73 0.58 0.64 0.70 0.76 0.78

2.1.1 Indicating Property

One of the most important tasks in classifying timber products on the basis

of their strength is finding a relevant criterion that, with as little statistical

analysis processing as possible, would be able to predict the mechanical

behaviour of the products. As described above, this variable is referred to as an Indicating Property or IP. Usually, the IP can be described as an MOE value. These MOEs can be determined by means of several different measurement techniques such as bending tests in the edgewise or flatwise direction, respectively, axial dynamic excitation, or a combination between such excitation and laser scanning.

Figure 1: Relationship between IP and bending strength [4].

The relationship between an IP and bending strength can be shown by means of so called scatter plots, see Figure 1. In the figure, R describes information concerning linearity between IP and strength, and its value is within the interval [-1,1]. Regarding the coefficient of determination, R

²

, it is interpreted as the proportion of strength variation that is explained by the linearity between strength and IP.

2.1.1.1Axial dynamic MOE as IP

The use of MOE as an IP has proven to be the most accurate indicator to both bending and tensile strength in boards when applied as a single IP, that is without any other IP being used, see Table 1. More accuracy can be achieved when combining different IPs. One way of determining the MOE of a board is by axial dynamical excitation, basically this is where the board is excited by, for example a hammer and the resonance frequency of the board is determined. The MOE can then be calculated if the density and the length of the board are known. The equation for this method of determining MOE is

𝐸

_𝑎,𝑛

= 4𝜌 (

^{𝑓𝑎,𝑛}_𝑛^{∗𝐿𝑡𝑜𝑡}

)

²

(1)

were f

_a,n

is the axial resonance frequency, L

_tot

is the length of the board and n refers to the n

^th

axial mode of vibration. In this case n was equal to one since the first resonance frequency had been chosen for this study.

2.1.1.2 Edgewise bending MOE based on fibre angles as an IP.

Considering one of the peculiarities of wood, the fact that it is an orthotropic material having a very high strength and stiffness on the fibre direction and rather weak strength and stiffness in the other directions [4] [5], one of the modern grading techniques makes a connection between the defects such as knots of a board and its strength capacity. This is due to the fact that the fibre direction can deviate strongly from the longitudinal direction around knots [4]. Therefore, the more defects a board has, the weaker it is. When an optical scanner, in this case the WoodEye 5, is used for edgewise dot laser scanning, high-resolution information about the fibre angle on the surface of the board can be found. Adding all the response data together, a map regarding the fibre orientation can be made, see Figure 2. An area with a higher amount of defects would have a lower local MOE. The IP for the scanned board is defined as the lowest edgewise bending MOE [14].

Therefore, depending on the resolution of the scanning process, this approach would be highly relevant.

Figure 2: A piece of timber including a knot (left), a picture showing how the light spreads from a dot laser scanner on the timber surface (middle) and the fibre orientation on the wood surface (right) (Pictures from [19]).

2.1.2 Fast Fourier Transform

The Fast Fourier Transform (FFT) is an efficient numerical algorithm used for determining the results of the Discrete Fourier transform (DFT) which is used to convert time or space into frequencies and wavelengths. The FFT as a mean to calculate DFT was introduced in 1965 by Cooley and Tukey [15]

and the introduction of the FFT has led to a revolution within many fields of

science [16]. The results of the FFT are the same as those that are obtained

from the DFT only the calculation time is reduced drastically. The DFT

method of determining the natural response of e.g. a board was described to

be too slow to be practical, whereas the FFT can significantly reduce the

calculation time.

2.2 The length effect

As stated in previous chapters, timber is not a homogenous material but contains defects such as knots and compression wood. These properties of timber are a result of millions of years of evolution for trees which has optimized the timber properties to suit the natural state of trees. However, these defects even though they are excellent for trees, can have a negative effect on the load carrying capacity of timber that is to be used for structural purposes since the strength of timber strongly depends on the occurrence of knots. This can be explained by the so called weakest link theory which states “When subjected to tension, a chain is only as strong as its weakest link” [17]. When applying this weak link theory on structural timber one can say that the timber will only be as strong as its largest defect. This is how the length effect of timber can be described.

The length effect is a term for how strength in bending or tension for a material can vary depending on the length of the material in question.

Timber contains a lot of natural defects such as knots, which in soft wood

occur in a more or less regular interval along the stem. This reduces the

strength of the timber since a knot will make the grain angle deviate around

it and therefore produce tension perpendicular to the grain, which is the

weakest direction for timber [17]. A shorter board is less likely to contain

these natural defects than a longer board, so, when regarding the weakest

link theory and the fact that a short board is less likely to contain a weak

link, shorter boards should be stronger than longer boards. This is the basis

of the length effect. In short words, the length effect can be described as the

variation of the strength depending on the length of the boards. This means

that in order to evaluate this effect one must look into how strength grading

is carried out, what factors are involved and to what extent the difference

between a longer board and a shorter one is of significance.

3. Method

Due to the fact that timber is a non-homogeneous material, the mechanical behaviour under certain circumstances may not be fully predicted by qualitative means. Therefore, a quantitative approach is used in this investigation. Data is collected from a sample of sawn timber. The results of the investigation, when analysed and interpreted, will result in a description of the length effect that will have statistical significance for the species.

The gathering of data was done by testing a sample consisting of 57 boards from the species Norway spruce (Picea abies) with the dimensions 45×145×4800 mm. These tests were carried out in the laboratory located at Linnaeus University. In order to examine how the mechanical properties relate to the length of the board, the boards have been divided into two groups, the first group consisting of 30 boards whilst the second group the remaining 27. These two groups were then tested using two different methods so, when comparing the results, a clear picture of the length effect could be observed.

For Group 1, it was investigated how the dynamic MOE and the edgewise bending MOE changes when originally long boards are shortened, i.e. when the length is reduced a bit at a time, see Figure 3. The question that should be answered is if the mean value and standard deviation of the dynamic MOE and the edgewise bending MOE, respectively, of short boards is significantly different from the corresponding values of the long boards and, if so, what is the relationship between length and the two MOEs?

Figure 3: Illustration of shortening boards in Group 1.

For Group 2, the experiments regard how the removal of the worst defect,

defined as the part containing the lowest local MOE, in a board affects the

dynamic MOE of the remaining parts compared to the dynamic MOE of the

original full length board, see Figure 4. The change in dynamic MOE when

removing a weak section should be compared with the change in another

indicating property, namely one that reflects the lowest local bending MOE

along the board.

Figure 4: Illustration of removing the worst defect for Group 2.

3.1 Laboratory work

For the experiments the boards were first numbered, 1 through 57, so that each board could be identified throughout the experiment. In order to keep the results of the experiment unbiased the numbering of the boards was done randomly. When the boards had been numbered they were measured and weighed. The boards received from Södra should have had the specified dimensions stated previously in this chapter but millimetre precision from sawmill production is not likely to occur. Therefore more precise measurements were taken in order to get a more accurate result.

For the thickness of the boards, measurements were taken on three places (both edges and in the middle of the flat surfaces) at both ends, and on two places (both edges) in the middle of the board length. This gave an average thickness of the entire board that was used for the calculations. The height was similarly taken at both ends and in the middle of the board length to yield an average height. All cross-sectional dimensions were measured using a sliding calliper ruler and each measure was rounded off to one decimal.

The length of the board was measured using a measuring tape, rounding off to whole millimetres. The measurements that were taken were written down for each board and the results are presented in Table I and Table II in the appendix.

Simultaneously, as the dimensions were measured, the moisture content of

the boards was taken. The moisture content was taken with a moisture

content meter, where two probes are inserted parallel to the grain, in the

middle of the board, see Figure 5. The value of the moisture content was

written down for each board in the same document as the dimension

measurements. The applied moisture content meter was of resistance meter

type which measures the conductance of an electric current between the two

probes that are hammered into the wood [18].

Figure 5: Moisture content meter.

This method of determining moisture content relies on the linear relationship that exists between the logarithm of conductance and the logarithm of moisture content. This relationship varies depending on wood species and therefore the machine will have to be set to the specific species that is to be tested. However, the relationship is only linear below the saturation point of the wood, which is around 27% moisture content, and the machine is not being able to measure values lower than approximately 7%. This means the method only has a working range between 7 and 27% moisture content [18].

However, this was not a problem for this study since the boards had been stored for several months in a climate room where the temperature was set to 20˚C and a relative humidity of 65%. This allowed the boards to dry out and stabilize their moisture content to around 12% and, since the machine only measures the conductance between the two probes, it is not certain that the given moisture content is representative for the entire board. Nevertheless, the upside to using this moisture content meter over other methods is the speed of the measurement [18].

When the dimensions and moisture content for a board had been decided, the board was placed on a scale and the weight was noted. With the dimension and weight the board’s density was then calculated using Equation 2.

𝜌 =

_{𝑉𝑜𝑙𝑢𝑚𝑒}^{𝑀𝑎𝑠𝑠}

(2)

In order to determine the axial dynamic MOE, using Equation 1, the axial

resonance frequency of the board had to be determined. This was done by

the use of a hammer and a microphone, see Figure 6. Using the hammer the

board is excited in one end and the microphone registers the soundwave

within the board and with use of the Fast Fourier Transform, or FFT for

short, the result is displayed as a graph of the resonance frequency. When the density, the length and the axial resonance frequency were known, the average axial dynamic MOE was calculated. This average axial dynamic MOE is an indicating property (IP) to the actual bending strength of the board.

Figure 6: Axial excitation of a board using hammer and microphone.

When the initial measurements were completed, the boards were scanned with

the WoodEye 5 to make a map of the fibre orientation, knots and defects. For the

scanning the boards were run through the machine from root end to top end with

the pith of the tree facing upwards, see Figure 7. The resolution of the dot laser

scanning in the longitudinal board direction is dependent on the belt speed at

which the boards pass through the machine. For this investigation, the belt speed

was set to a rate of 200 meters per minute. This resulted in a longitudinal

resolution of 2 mm. In the lateral board direction the resolution is determined by

a grid that is installed on the laser source. In this case, the applied grid resulted in

a lateral resolution of 4 mm. The information obtained from the WoodEye was

thereafter processed in Matlab in order to obtain the maps of defects and fibre

orientation. This process also yielded a map of the variation of longitudinal MOE

on the surface of the boards. The Matlab code was provided by professor Anders

Olsson at Linnaeus University, and revised by the authors.

Figure 7: WoodEye 5 scanning at Linnaeus University.

After the measurements and scanning, the boards were divided into two groups. As stated previously the first 30 boards were assigned to Group 1 and the remaining 27 boards to the second group. The processes for how the length effect was observed in these groups are described in the associated chapters.

3.1.1 Group 1 – End sections gradually removed

The first group of boards had their length systematically reduced as indicated by Figure 3, by 300 mm so that the total length of the board was reduced from 4800 mm to around 2500 mm after eight cuts were made. A total of 8 cuts were made at alternating ends of the board, see Figure 8. The reduction length of 300 mm was chosen since it would coincide with the standard lengths available from sawmills.

Figure 8: Details for length reduction in Group 1.

After each reduction, the boards went through the initial process of

measurements, aside from the fact that the moisture content was only taken

after the last cut to observe how the moisture content varied during the

experiment and that the scanning was not performed again since a map of

the entire board already existed. The measured heights and widths that were taken as an average when the boards were at full length were considered to be constant.

After each cut, new measurements of length, weight and resonance frequency were used to determine a new axial dynamic MOE for the shorter length. A new local edgewise bending MOE was also determined after every cut on the basis of fibre angle obtained from scanning and processed in the Matlab software. These MOEs was then compared with corresponding MOEs achieved for the other lengths. This process was repeated for all 30 boards in Group 1.

3.1.2 Group 2 – Largest defect removed

For the second group of boards the worst defect was identified from the results obtained from the scanning process after the results had been analyzed in Matlab. The identified section with the lowest local MOE was then removed; see principle according to Figure 4. The results that were obtained from Matlab were presented as graphs with the length on the X- axis and the MOE on the Y-axis, see Figure 9. Several graphs of this sort were obtained, representing a moving average MOE and a high resolution MOE graph for edgewise bending, flatwise bending, position of neutral axis and longitudinal stiffness. For this study the graph of interest was the moving average MOE of edgewise bending. This moving average was a representation of integration over 9 cm.

From the moving average MOE graph of edgewise bending the section

containing the worst defect was identified by Matlab algorithms and

confirmed by visual inspection of both board and graph. After the section of

the board that had the weakest moving average MOE was identified, the

length of the section of the board that was to be removed was calculated

through Matlab. The section´s position and length was calculated on the

basis of the point of the lowest local MOE. The positions of the saw cuts on

the left and on the right side of this point were determined as the position

where the average moving MOE was equal to the average MOE of the entire

board, see Figure 15. This section was then removed and the remaining two

parts of the board were considered to be two new boards on which

measurements of moisture content, length, weight and resonance frequency

were carried out. The results from these “new” boards were then put in

relation to the original measurements of the un-cut boards.

Figure 9: Moving average MOE in edgewise bending from scanning of a board in Group 2.

The “new” boards that were tested had to be disregarded if their length was less than 1000 mm. This was due to the limitations of the equipment and procedure used for measuring the dynamic excitation in boards shorter than 1000 mm.

The boards were then divided into three sub groups, A, B and C, depending on the position of the lowest local edgewise bending MOE i.e. where the section of the board was removed. This grouping was established for obtaining results that had higher relevance for this thesis and any upcoming research on the topic.

 Group A contained boards that had a part with a length of less than 1 meter; this part was then disregarded due to limitations of the equipment, therefore a complete investigation on this section of the board was impossible to achieve. Ten boards were assigned to this group.

Figure 10: Illustration of Group A.

 Group B contained the boards that had the lowest MOE in one end of the board. This resulted in a reduction of the length from either top or root end of the board. Five boards were assigned to this group.

Figure 11: Illustration of Group B.

 Group C contained the boards that had the lowest MOE towards a centred position along the length, i.e. the removed part was in the interval of 1 – 3.8 meters. Due to the fact that there were two parts available for measurements, a weighted average dynamic MOE was obtained. This meant that each of the two dynamic MOEs contributed to the final value depending on the length of each part with respect to the total length. Eleven boards were assigned to this group.

Figure 12: Illustration of Group C.

3.2 Matlab

Apart from the dynamic excitation, from which the axial dynamic modulus of elasticity was found, the boards were subjected to scanning through the WoodEye machine. Raw data concerning the fibre orientation was collected and processed in Matlab software.

Most of the code needed was provided by professor Anders Olsson. The first

task regarding the post-processing was to configure the code such that it

would output valid data. In order to achieve that, input regarding the

samples’ dimensions, weight and axial resonance frequency was

display it through plots regarding the fibre direction, see Figure 13, MOE in board’s direction, high resolution MOEs in edgewise bending as well as flatwise bending and longitudinal stiffness.

Figure 13: Fiber direction of a board.

The following phase implied that agreements were reached with the supervisors upon some choices that had to be transposed to the code. Even though the pace at which the scanning of the boards was conducted provided 2 mm fidelity for the high resolution MOEs, that is not likely to represent the material’s mechanical behaviour as timber would distribute the stresses over an area or along a length. Therefore, an average of the high resolution MOEs over a board length of 9 cm was preferred, see Figure 15. As one can see, it provides a smoother curve and small differences compared to the high resolution plot, see Figure 14. Nevertheless, both the authors and their supervisors consider it better reflects reality.

Figure 14: High resolution MOE in edgewise bending.

Figure 15: Moving average MOE in edgewise bending.

Even though Matlab processing was used for both of the Groups 1 and 2 regarding the timber boards, there were different aspects that were of interest in each group.

Considering the first group, for which the length was systematically reduced at the ends, there was an initial run through the algorithm of the scanning data achieved from scanning the boards at full length. After each cut, input data corresponding with the remaining board length was again run through the algorithm and output data was added to another file in which results were summed up. This was later used for post-processing and obtaining boxplots.

Group 2 was the one in which the worst part was removed from the initial

timber plank, see Figure 15 where the red markings denote the section

containing the worst defect and the brown line represents the average MOE

of the board. Input data was only provided once and, in addition to the

lowest local MOE that revealed the section that was removed, there was a

search for the second lowest MOEs as well. It was of interest to reveal if the

weakest section of the remaining part or parts, after the removal, got stiffer,

and how much did it improve.

4. Results

The results from the laboratory work that was processed in Matlab are presented here as boxplots, graphs and tables with relevant information and some short remarks. A boxplot represents statistical data regarding a set of values. The top and bottom ends of the rectangle represent the 75

^th

and 25

^th

percentile of the distribution whereas the ends of the whiskers denote the lowest and highest value within the set. As for the red line, it represents the median value of the group.

4.1 Group 1 – End sections gradually removed

Due to the relatively small sample size, both axial dynamic MOEs and local lowest edgewise bending MOEs experienced rather odd values for 4.5 meters, as in Figures 16 and 17. This phenomenon happened as a result of the first cut removing sections containing large defects, followed by the removal of sections having little to no defects. For a larger sample group, the regression line for the median value would have a clearer trend.

Figure 16: Box plots of the IP determined as the average axial dynamic MOE for the 30 boards in Group 1.

Figure 17: Box plots of the IP determined as the lowest local edgewise bending MOE for the 30 boards in Group 1.

On a broader scale, the median value of each box plot of the MOEs would

converge to the mean values. However, as a consequence of the small

sample size, it is not that obvious. Therefore, it was more relevant to make a

trend line representing the mean values of the MOEs as seen in Figure 18

and 19.

Figure 18: A scatter plot of the mean average axial dynamic MOE for the 30 boards in Group 1, the regression line showing the tendency of the mean average dynamic MOE when a board’s length is systematically reduced.

Figure 19: A scatter plot of the mean lowest local edgewise bending MOE’s used as IP’s for the boards in group 1 with a regression line showing the tendency of the mean of the lowest IPs when a board’s length is systematically reduced.

4.2 Group 2 – Largest defect removed

The boards in Group 2 where divided into three subgroups, A, B and C. A comparison between the average axial dynamic full length MOE and the corresponding reduced length MOE for all the boards in Group 2 are shown in Figure 20. Table 2 shows the statistical information with respect to the data plotted in Figure 20 as well as the variation from full to reduced length.

This shows that the mean of the average dynamic MOE change was rather small.

Figure 20: The variation of the average axial dynamic MOE of each board prior and after the removal of the worst defect for Group A, B and C.

Table 2: Variation of the average axial dynamic MOE in sub Groups A, B and C within Group 2 with the full length MOE of appropriate boards for comparison.

Group

Measured properties 2 A B C Unit

No. of samples 26 10 5 11

Mean value of full length MOE 13766 14858 13241 13011 [MPa]

Mean value of reduced length MOE 13900 14999 13280 13183 [MPa]

StDev of full length MOE 2728 3131 2118 2455 [MPa]

StDev of reduced length MOE 2710 3113 2253 2375 [MPa]

Variation of the MOE 0.97% 0.95% 0.30% 1.32%

Variation of the StDev -0,67% -0.58% 6.37% -3.28%

In Group A the change of the mean average MOE was an increase of 0.95%

when the section containing the lowest local MOE was removed, compared to the full length MOE. Similarly, for Group B and C, there was an increase of 0.3% and 1.3% respectively, as can be seen in Table 2.

In Figure 21 a comparison of the lowest and the second lowest edgewise bending MOE for all the boards in Group 2 is shown. This is complimented with more information in Table 3.

Figure 21: Comparison of the lowest and second lowest edgewise bending MOE for the boards in Group 2.

Table 3: Mean values and standard deviation for Figure 21.

Measured properties Group 2 Unit

No. of samples 26

Mean value of lowest MOE 10342 [MPa]

Mean value of second lowest MOE 11090 [MPa]

StDev of lowest MOE 3023 [MPa]

StDev of second lowest MOE 3050 [MPa]

Variation of the MOE 7.23%

Variation of the StDev -0.89%

From Table 3, it is apparent that after the worst defect is removed, the

edgewise bending MOE will increase by approximately 7%, since this is the

average difference between the lowest and second lowest edgewise bending

MOE.

5. Analysis

5.1 Group 1 – End sections gradually removed

When reviewing the boxplots in Figure 16 and 17, the most obvious fact that stands out is the low variation in the median value of the axial dynamic MOE across the length reduction. Other information that can be distinguished is the fact that the distribution of the values within a length group remained close to the values for the initial length.

Comparing the data of Figure 16 with the scatter plot in Figure 18, due to the fact that the medians are close to the mean values, the batch size is considered sufficient. The mean axial dynamic MOE for the initial length was approximate 13 GPa and the change was about 1.3 % from initial to final length, with small changes in all intermediate reductions. Moreover, the regression line with the R

²

value of 0.5 proves there is a small trend.

Moving on to the second boxplot, Figure 17, which represents the lowest local IPs based on the edgewise bending MOE obtained from the scanning and processed in Matlab, one can observe that between the 25

^th

and the 50

^th

percentile of the distribution the values are noticeably more condensed than between the 50

^th

and the 75

^th

percentile. This is shown by the median line in relation with the bottom and top ends of the rectangle.

From the scatter plot in Figure 19 a clear trend for the mean of the lowest IPs emerge. This is shown by the regression line and the R

²

value, close to 0.94. The change of the edgewise bending MOE from initial to final cut was around 6.5 %.

5.2 Group 2 – Largest defect removed

In order to analyse the results for Group 2, the first thing that should be observed is the content of Figure 20. In this graph the average axial dynamic MOEs for all subgroups (A, B and C) are plotted with the full length MOEs for comparison.

Considering subgroup A, where the weighted average axial dynamic MOE

could not be determined due to equipment limitations, the dynamic MOE of

the measurable part was used for comparison with the full length dynamic

MOE. By analysing both Figure 20 and Table 2 one can see that there is a

very small difference before and after the removal of the worst defect. The

mean of the full length dynamic MOEs was fairly high, around 15 GPa and

it increased by 0.94% after the reduction. The standard deviation changed

with 0.58%, though, it is of greater importance to recognize that its value is

close to one fifth of the mean average dynamic MOE.

Concerning subgroup B, less data is available due to only 5 samples being in this group. The dynamic MOE was in this group given by a new measurement on the board since the worst defect was located at the end of the board. Therefore, no part has been disregarded which means information on this subgroup is more precise. The mean of the full length dynamic MOE was close to 13.3 GPa and it increased by 0.3% after the reduction. The standard deviation changed with approximately 6%, its value being close to one sixth of the mean average dynamic MOE.

Subgroup C, the one in which a proper weighted average dynamic MOE was possible to compute, due to a central position of the lowest local MOE, displayed the most obvious improvement when compared to the full length average dynamic MOE. The mean of the values for the full length was around 13 GPa and it increased by 1.3% after the reduction. The standard deviation changed with approximately 3%, its value also being close to one sixth of the mean average dynamic MOE.

Regarding the lowest local edgewise bending MOE, obtained from the

scanning of the boards’ profiles aided by Matlab software, there is a clear

increase when the section containing the lowest value for a board is

removed. This is illustrated in Figure 21. This is even more obvious when

comparing the mean values before and after the removal of the section

containing the worst defect, as shown in Table 3, where the improvement is

around 7%.

6. Discussion

The aim of this thesis was to examine and describe the length effect on timber boards from the species Norway spruce. When analyzing the results it is clear that there is an increase in both the axial dynamic MOE and the edgewise bending MOE when the length is reduced and, similarly, when the worst defect is removed. However, regarding the axial dynamic MOE, the change is quite small; around a 1% increase could be observed for both groups. So one can conclude that this indicating property, the axial dynamic MOE, do vary as a function of the length, although this has small significance on a broader scale.

The change was more obvious when observing the edgewise bending MOE, for both Group 1 and 2 this indicating property increasing with between 6 and 7%. This result can be useful in e.g. finger jointing of boards. When removing the sections containing the lowest local MOE and finger jointing the remaining parts, a board with a higher MOE than the original board can be created. The length can then be chosen to fit the intended use by adding more sections. Even though the improvement is more evident when observing the edgewise bending MOE, further research linking it with economical and resource liability is needed to confirm the benefits of removing parts of the board.

There is, most likely, more knowledge provided by these experiments, phenomena that might have not been that clear for the authors, or were not noticed due to being less in connection with the aim of this dissertation.

These may be discernible for some readers, therefore self-thinking is encouraged.

The sample used for the experiment consisted of 57 boards where one board,

board 56, had to be disregarded due to problems with the scanning of this

board. Some root or top end parts smaller than one meter within boards from

Group 2 also had to be disregarded due to limitations with the method and

equipment used for determining the axial dynamic MOE as mentioned in the

Method chapter, this being the criterion used in subgroup 2A. For a better

statistical significance, the sample group should have been larger; however

there is no reason to doubt that the results obtained from these experiments

are of great interest. Nevertheless, with a larger sample group, some results

may have been more exact.

7. Conclusion

For the species Norway spruce, (Picea abies), removing the section of a board that contains the lowest local edgewise bending MOE will result in the remaining timber increasing its edgewise bending MOE by around 7%.

The same is true when the length of the board is shortened to half of its initial length, whereas the axial dynamic MOE revealed an increase of only 1% for both cases.

References

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Appendix

Table I: Initial measurement values for the 30 boards in Group 1

Board Width 1 [mm] Width 2 [mm] Width 3 [mm] Avg. width [mm] Height 1 [mm] Height 2 [mm] Height 3 [mm] Avg. height [mm] Length [mm] Weight [kg] Density FrequencyMOE [MPa] Moisture content [%]

1 45,5 46,3 45,4 45,7 147,9 146,9 147 147,3 4804 15,52 479,7 470,3 9794,2 13,5

2 45,7 45,6 46 45,8 146,8 146,9 145,5 146,4 4803 16,24 504,6 546,9 13927,9 13,8

3 45,9 45,9 45,9 45,9 147,2 147 148 147,4 4804 13,56 417,2 485,9 9093,0 12,8

4 46,4 46,3 45,9 46,2 147,3 147,2 148,3 147,6 4803 14,52 443,3 523,4 11206,7 13,1

5 46 46,5 45,9 46,1 147,1 147,1 142,9 145,7 4802 14,72 456,0 510,9 10979,6 12,9

6 46 45,7 46 45,9 148,1 147,2 146,2 147,2 4803 15,78 486,4 517,2 12005,3 13,5

7 46,2 46,3 44,6 45,7 147,1 146,7 148 147,3 4802 15,08 466,6 537,5 12434,3 13,6

8 46,2 46,2 45,7 46,0 147,6 146,2 146,5 146,8 4803 13,84 426,5 543,8 11638,2 13,1

9 46,3 46 46,2 46,2 147 147,1 147 147,0 4803 15,36 471,1 539,1 12634,5 13,8

10 45,6 45,8 45 45,5 147,8 145,4 148,3 147,2 4803 14,62 454,9 571,9 13729,6 13,4

11 46,4 46 46 46,1 146,9 146,3 146,4 146,5 4803 16 492,8 539,1 13215,4 13,9

12 45,7 45,8 45,6 45,7 147,7 147,5 147,5 147,6 4802 14,88 459,5 537,5 12244,4 13,9

13 45,9 46,1 44,9 45,6 144 146,6 146 145,5 4803 17,94 562,4 589,1 18010,6 14,4

14 46,3 46 45,6 46,0 147,5 146,9 147,3 147,2 4803 15,72 483,6 545,3 13269,3 14,1

15 46,4 46,1 46 46,2 147,2 146,6 147,5 147,1 4802 16,3 499,8 585,9 15826,2 14,3

16 46,6 46,3 45,2 46,0 147,6 147,3 148,3 147,7 4804 12,12 371,0 528,1 9551,0 11,9

17 46,7 46,3 45,1 46,0 147,9 148 148,3 148,1 4803 12,3 375,7 525 9555,8 14,1

18 45,6 46,4 46,3 46,1 147 146,1 148 147,0 4802 15,96 490,3 606,3 16625,5 14,3

19 45,6 46,2 46 45,9 148 147,1 147,8 147,6 4803 16,18 496,8 584,4 15655,2 14,3

20 45,9 46 45,6 45,8 147,6 147 147,8 147,5 4802 15,82 487,4 534,4 12839,4 13,7

21 45,4 46,1 45,1 45,5 144,3 147 147,1 146,1 4804 16,58 518,7 575 15830,9 13,6

22 46 46 45,7 45,9 148 146,9 147,2 147,4 4803 16,86 519,0 560,9 15065,7 14,1

23 45,7 45,9 45,6 45,7 146,9 147,4 148,1 147,5 4803 14,46 446,4 515,6 10950,7 12,9

24 46,2 46 46,1 46,1 147,9 146,5 147,1 147,2 4803 17,52 537,7 454,7 10257,6 13,8

25 46,3 46,2 46,4 46,3 148,1 146,8 146 147,0 4803 16,16 494,5 584,4 15582,4 14,2

26 46,5 46,4 44,8 45,9 148 147 149,1 148,0 4803 14,4 441,2 606,3 14967,1 13,2

27 44,8 46,2 45,7 45,6 148,6 146,5 148,2 147,8 4803 17,26 533,7 557,8 15323,1 14

28 45,3 46,1 45,4 45,6 147,9 146,8 147,3 147,3 4804 13,86 429,4 575 13106,8 13,2

29 46,2 46,2 45,6 46,0 147,4 146,8 148 147,4 4803 15,92 488,8 618,8 17272,7 13,7

30 44,6 45,7 45,8 45,4 146,2 147,2 147,8 147,1 4804 15,52 484,2 515,6 11883,1 13,7