Distortion of Norway spruce timber

Part 3: Modelling bow and spring

R. Kliger, M. Johansson, M. Perstorper, G. Johansson

Abstract This paper clarifies the extent to which modelsbased on two- and three-dimensional material descrip-tions can predict bow and spring deformation. Changesin longitudinal shrinkage and swelling and their varia-tions over cross-sections of studs cause these studs todevelop distortion in terms of spring and/or bow. Radialvariation from pith to bark (two-dimensional) of thelongitudinal shrinkage in the cross-section is often as-sumed to be the only physical data needed to predictspring and bow in a stud. However, using measurementsfrom 240 studs of Norway spruce (fast-grown and oneslow-grown stand), it was found that there was nocorrelation between shrinkage gradients measured at onelongitudinal position and three-dimensional bendingdistortion (spring and bow). As a result, two studs, onewith large spring (and no bow or twist) and one withlarge bow (and no spring or twist), were cut longitudi-nally in sections 200 mm long. From these sections,sticks were cut and the longitudinal shrinkage wasmeasured twice on all sticks, when the climate was 90%relative humidity (RH) and 30% RH, in order to pro-duce data which correspond to changes in moisturecontent in the studs, roughly between 15% and 7.5%.The difference in the longitudinal shrinkage between twofaces of the studs explained spring or bow far betterwhen the variation in shrinkage along the stud wasconsidered. The longitudinal variation in shrinkage wasvery large; i.e. strains varied from 0.062% to 0.290%along one stud. Knowing the three-dimensional shrink-age variation, it appears to be possible to predictbending distortion with very good accuracy, as shown inthis paper. It is clearly demonstrated that knowledge ofthe three-dimensional variation in longitudinal shrinkage

is needed in order to predict bow and spring moreaccurately.

Verwerfung von FichtenschnittholzTeil 3: Modell der Langskrummung und -verwerfung

Zusammenfassung Dieses Manuskript klart ab, inwieweitModelle, die auf zwei- oder dreidimensionalen Material-beschreibungen basieren, Langskrummung und -ver-werfungsdeformation vorhersagen konnen. Anderungenin der Langsschrumpfung und ihre Variationen beiKantholzquerschnitten verursachen in diesen Kanthol-zern eine Deformation im Sinne von Langskrummungund -verwerfungen. Es wird angenommen, dass radialeVariationen vom Mark bis zur Rinde (zwei-dimensional)des Langsschrumpfungsquerschnitts oft die einzigenphysikalischen Daten sind, die benotigt werden, umLangskrummung und -verwerfung in Kantholz voraus-zusagen. Bei der Verwendung von Messungen von 240Kantholzern norwegischer Fichte (aus schnell gewachse-nem und einem langsam gewachsenen Bestand), fandman jedoch heraus, dass es keine Korrelation zwischenSchrumpfungsgradienten, gemessen in einer Langsposi-tion und dreidimensionaler Biegeverwerfung (Langsver-werfung und -krummung), gab. Als Ergebnis wurdenzwei Kantholzer, einer mit großer Verwerfung (und kei-ner Langskrummung und Verdrehung) und einer miteiner großen Langskrummung (und keiner Langsver-werfung oder Verdrehung) in Langsrichtung in 200 mmlange Abschnitte geteilt. Von diesen Abschnitten wurdenStabe geschnitten und die Langsschrumpfung an allenStocken zweimal gemessen, in einem Klima mit 90%relativer Feuchte (RH) und 30% RH, um Daten zuproduzieren, die sich auf Veranderungen des Feuchte-gehalts in den Kantholzern beziehen, ca. zwischen 15%und 7,5%. Der Unterschied in der Langsschrumpfungzwischen den beiden Flachen der Kantholzer erklarteLangsverwerfung und -krummung weitaus besser, wenndie Veranderung in der Schrumpfung entlang des Kant-holzes als Bezugsgroße genommen wurde. Die Langs-veranderung in der Schrumpfung war sehr groß; d.h. dieSpannung (Belastung) variierte von 0,062 bis 0,290%entlang eines Kantholzes. Ist die dreidimensionaleSchrumpfungsveranderung bekannt, ist es moglich, dieBiegeverwerfung mit ziemlicher Genauigkeit vorauszu-sagen, wie in diesem Manuskript gezeigt wird. Es wirdklar dargestellt, dass das Wissen um die dreidimensionaleVeranderung (Variation) bei der Langsschrumpfungbenotigt wird, um Langskrummung und -verwerfunggenauer vorherzusagen.

Holz als Roh- und Werkstoff 61 (2003) 241–250 � Springer-Verlag 2003

DOI 10.1007/s00107-003-0399-0

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Published online: 24 July 2003

R. Kliger (&), M. Johansson, M. Perstorper, G. JohanssonDepartment of Structural Engineering, Steel and Timber Structures,Chalmers University of Technology, 41296 Goteborg, SwedenE-mail: Robert.Kliger@ste.chalmers.seTel.: +46-31-7722016Fax: 46-31-7722260

The authors would like to express their gratitude to the SwedishCouncil for Building Research (BFR), project no. 950172-6, andthe Swedish Forestry and Agricultural Research Council (SJFR),reg. no. 20.0150/95, and the CF Lundstrom Foundation, for sup-porting this work.

Originalarbeiten Æ Originals

1Introduction

1.1BackgroundDistortion is a major obstacle for maintaining and expand-ing the market share of solid timber in the buildingindustry, see Johansson et al. (1994). Lack of straightnessprevents timber being used in modern, highly mechanizedcomponent manufacturing industry. In order to improvethe use of timber as part of refined elements with possiblefuture applications for industrial robots, it is essential tomanufacture straight sawn timber at a competitive price.

This paper deals with modelling distortion, primarilybow and spring, in full-size timber. Research, in which theforestry data, i.e. different stands, social position of trees,types of log and so on, was related to the amount of bowand spring in dried timber failed to produce any statisticalsignificance (Forsberg 1997). A literature study reveals thatthe input data for modelling distortion is usually based onmaterial parameters found in the literature and/or mea-sured on small, defect-free pieces of wood cut from discs.These discs and full-size timber (studs) are normally sawnfrom the same logs. The principal assumption is that thematerial parameters, such as shrinkage/swelling andmodulus of elasticity, which are needed to model bow andspring only vary in the radial direction (Mishiro et al. 1988,Perstorper et al. 1995, Ormarsson 1995, among others). It isoften assumed that two-dimensional variations in theseparameters measured at one longitudinal position on thelog are sufficient to model distortion. However, there are nolarge-scale experimental studies to verify this hypothesis.

1.2ObjectiveThe objective of the entire project was to measure andmodel moisture-related distortion in full-size timber.

The results are presented in a series of three papers. In thefirst paper in this series (Perstorper et al. 2001), adescription of the experimental set-up is presented, to-gether with the results for important material propertieswhich have some impact on distortion. The second paperby the authors (Johansson et al. 2001) focuses on model-ling twist. This paper is the third in the series and dealswith the formulation of a physical (analytical) explanationof moisture-related changes in bow and spring.

The main aim is to clarify the extent to which modelsbased on two- and three-dimensional material descrip-tions can predict bow and spring deformation.

The statistical comparisons to evaluate the statisticalsignificance of differences between groups of data wereproduced using the Mann-Whitney U-test rather than at-test, due to skewed data sets.

2Summary of the experimental set-upThe sawn timber came from two large-diameter stands, i.e.fast-grown and slow-grown Norway spruce from southernSweden. Logs were taken from the upper butt log (UBL) of40 trees, see Fig. 1. For an additional description of stands,see previous papers Perstorper et al. (1995 and 1998) andKliger et al. (1995).

The logs from 40 trees were sawn into 3·40 battens,70·290·2900 (in mm), before kiln drying to approximately12% moisture content. The centre batten from each logwas then ripped and planed to the final stud dimensions45·70·2900 (in mm). Six studs representing three studgroups with respect to radial location, outer, intermediateand core, were cut from the batten. In all, 240 studs wereobtained. From the top end of each stud, five sticks(dimension: 13·13·200) were sawn from a knot-free sec-tion: i.e. one from each corner and one in the middle.These sticks were used, among other things, to determinethe shrinkage/swelling properties in the longitudinal

Fig. 1. Log sampling, sawing patterns,definition of bow and spring and nota-tionsAbb. 1. Holzproben, Sagemuster, Defini-tion von Langskrummung und -verwer-fung sowie Bezeichnungen

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direction. The studs were hung vertically in the climatechamber to eliminate restraint on the material. Distortionin all the studs was measured four times during a moisturechange between approximately 85% RH and 30% RH, seePerstorper et al. (2001).

When the moisture content changes, the changes inlongitudinal shrinkage in the sticks taken from twoopposite faces should correspond to the changes in spring/bow in the studs. Two studs were cut longitudinally insections 200 mm long in order to study the 3-D variation.From the ‘‘spring’’ specimen, small sticks were cut fromeach 200 mm section from the edge faces; from the ‘‘bow’’specimen sticks were cut from each section, but from thewide faces. On these sticks the longitudinal shrinkage wasmeasured when the climate was changed from 90% RH to30% RH.

3Influence of moisture cyclingAll the studs were placed in the climate chamber andsubjected to four moisture stages, see Perstorper et al.(2001). These four moisture stages corresponded to anaverage moisture content in timber of 15.6%, 7.2%, 14.4%and 7.8%. Mean values, median and standard deviation forbow and spring measured at four moisture stages, areshown in Table 1. The changes in bow and spring appearto be reversible when moisture content is changed back toits original level. It appears that there is a linear rela-tionship between the magnitude of median spring (orbow) and moisture content, cf. Fig. 2. The same thingapplies to twist, cf. Johansson et al. (2001). Bow appears tobe the least linear of the three distortion cases. However,measurements of bow are most sensitive to the effect of theselfweight of each stud. The values for bow were notcompensated for this effect. The middle deflection causedby selfweight varied from 1 to 1.2 mm due to variations indensity, assuming the same MOE value of 10 GPa. How-ever, the variation in MOE can change substantially thedeflection mentioned above.

It is interesting to observe that the linear extrapolationof the regression lines appears to indicate that bow andspring should be zero well above fibre saturation point, i.e.45% moisture content for bow and 36% moisture contentfor spring. A similar regression line for spring measuredon loblolly pine was presented by Simpson and Tschernitz1998. This indicates that studs would have some distortionin terms of spring and bow even in ‘‘green’’ condition.

The correlation between the distortion measured at7.2% moisture content and 15.6% moisture content isgood for bow (R2=0.76) and for spring (R2=0.73), cf.

Fig. 3. The median value for bow increased by 25% and themean value increased by 58% when the average moisturecontent decreased from 15.6% to 7.2% (first step). Theincrease for spring was about the same, i.e. 40% for bothmedian and mean values for the same change in moisturecontent.

4Influence of growth characteristics on bow and spring

4.1Influence of stand typeThere is no statistically-significant difference betweenstands, both fast-grown and slow-grown, in terms of bowand spring measured on studs after being kiln-dried and

Table 1. Variations (in mm) in spring and bow at four different moisture stagesTabelle 1. Veranderungen (in mm) in Langsverwerfung und -krummung in vier unterschiedlichen Feuchtigkeitsstufen

Moisture stage Moisture content Count Bow Spring

(mean)[%] Mean Std dev Median Mean Std dev Median

1 15.6 240 2.65 2.51 2.09 2.35 1.88 1.942 7.2 240 4.45 5.04 2.76 3.33 2.74 2.803 14.4 237 2.75 2.74 1.98 2.41 1.90 2.004 7.8 226 2.91 4.43 2.46 3.17 2.61 2.58

Fig. 2a,b. The relationship between median moisture content andmedian bow (absolute values) and median spring (absolutevalues) at four moisture stages. The numbers represent fourconsecutive moisture stages: a Bow, b SpringAbb. 2a,b. Die Beziehung zwischen mittlerer Feuchte und mitt-lerer Langskrummung (absolute Werte) sowie mittlere Langs-verwerfung (absolute Werte) in vier Feuchtigkeitsstufen. DieZahlen reprasentieren vier konsekutive Feuchtigkeitsstadien: aLangskrummung, b Langsverwerfung

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conditioned at the first moisture stage, i.e. 15.6% moisturecontent. However, when all the studs were conditioned tothe ‘‘dry’’ moisture stage, i.e. 7.2% moisture content, dis-tortion increased significantly, as did the differences be-tween the two stands, see Table 2. Studs from the fast-grown stand displayed more distortion than studs fromthe slow-grown stand and the differences were statisticallysignificant, p<0.041 for bow and p<0.004 for spring. Whenall the studs were divided into three groups with respect totheir radial position, i.e. core, intermediate and outerstuds, the differences between the groups were less or notat all statistically significant. Only the outer studs differedbetween the two stands, p<0.069 for bow and p<0.024 forspring. The core studs displayed the same tendency as theouter studs. However, the differences between the stands

were not statistically significant (p�0.24 for bow andp�0.08 for spring). Spring and bow for studs from threedifferent radial positions were compared in order todetermine whether there was a difference between them.Studs nearest to the pith (core studs) displayed more bowthan the intermediate or outer studs, especially from fast-grown stand, cf. Fig. 4. However, these differences werenot statistically significant.

4.2Influence of radial positionThe median values for bow and spring measured at amoisture content of both 15.6% moisture content and7.2% moisture content decreases slightly from core to barkwhen all studs were divided into three stud groups and twostands, see Fig. 4. However, this tendency was not statis-tically significant. These findings distinguished themselvesfrom previous results (see Hallock 1965, for example),where the large spring was common for studs closest topith.

In general, there is a weak radial effect on the amountof bow or spring in the studs. This applies to both types ofstand, for both moisture conditions, i.e. 15.6% moisturecontent (‘‘wet’’) and 7.2% moisture content (‘‘dry’’) andfor the difference between ‘‘wet’’ and ‘‘dry’’ moisture levelin terms of the increase in the amount of bow or spring.

4.3Influence of material parametersIt is important to evaluate the influence of growthparameters on distortion, despite the fact that the mostcommon parameters used by wood technologists such asdensity, ring width or knot area ratio have shown verylittle or no effect on bow and spring in the past, Bendtsen(1978), Danborg (1994) and Perstorper et al. (1995),among others. The results obtained in this study fullyconfirm the previous findings. The same applies to thespiral grain angle which has no effect on bow and spring.

The effect of compression wood is confusing. Com-pression wood is expected to have a significant effect onbow and spring. The reason is that compression wooddisplays far higher longitudinal shrinkage than normalwood and this should therefore result in the more pro-nounced distortion of studs, such as bow and spring.However, there are two significant problems related tocompression wood. The first problem relates to how todecide, non-destructively, what is compression wood and

Fig. 3a,b. Relationships between bow/spring measured at 15.6%(‘‘wet’’) and at 7.2% (‘‘dry’’): a Bow, b SpringAbb. 3a,b. Verhaltnisse zwischen Langskrummung/-verwerfunggemessen bei 15,6% (‘‘nass’’) und bei 7,2% (‘‘trocken’’): aLangskrummung, b Langsverwerfung

Table 2. Influence of stand type, slow-grown (SG) and fast-grown (FG), on bow and spring during the first two moisture stagesTabelle 2. Einfluss des Holzbestandtyps, langsam gewachsen (SG) und schnell gewachsen (FG), auf Langskrummung und -verwerfungwahrend der ersten beiden Feuchtigkeitsstufen

Moisture Content Group Bow Spring

(%) (count) Mean (Std. Dev.) Median Mean (Std. Dev.) Median

15.6 All (240) 2.65 (2.5) 2.09 2.35 (1.9) 1.9415.6 SG (120) 2.45 (2.4) 1.86 2.42 (1.9) 1.8615.6 FG (120) 2.86 (2.6) 2.19 2.28 (1.8) 2.027.2 All (240) 4.45 (5.0) 2.76 3.33 (2.7) 2.807.2 SG (120) 3.52 (4.0) 2.52 2.88 (2.5) 2.307.2 FG (120) 5.38 (5.8) 3.54 3.78 (2.9) 3.37

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how to quantify and measure it. The second problem re-lates to the occurrence of compression wood in the cross-section of a stud. Equally distributed compression woodshould have no effect on bow or spring as all the sides of astud shrink equally and should therefore not bend a studin any direction.

In this study, compression wood was registered visuallyon the surface of each stud using three grades: no com-pression wood (0), a small amount of compression wood(1) and a lot of compression wood (2). The distributionbetween these three registered groups was very uneven, i.e.187 studs in group ‘‘0 ’’, 47 studs in group ‘‘1’’ and 4 studsin group ‘‘2’’. As a result, groups ‘‘1’’ and ‘‘2’’ were joinedtogether to make one group which represented studs withcompression wood. This rough registration gives noinformation of the amount of compression wood or itsdistribution in a stud. In the future, new techniques willhave to be developed to determine the position of com-pression wood in a log and then adjust the sawing patternto its occurrence when improving the straightness of studs.

The relationship between bow or spring measured at7.2% moisture content and the presence of compressionwood appeared to be very weak, see Fig. 5. The probablereason is the inadequate quantitative determination of thecompression wood. In the case of spring, there was nostatistically-significant difference between studs with andwithout compression wood. This applied to all the studs,to studs divided into fast-grown and slow-grown standsand to studs divided into three radial positions.

The statistical comparisons between compression woodand bow and between compression wood and changes inbow between two moisture stages were slightly differentfor the same groups of studs. For bow at 7.2% moisturecontent the presence of compression wood had a statisti-cally-significant effect, for all the studs (p<0.03) and for allthe outer studs (p<0.007).

A regression analysis was made to examine the extentto which the different measured parameters influenced themagnitude of bow and spring. Neither stepwise regressionanalysis nor multiple regression based on 12 variablesproduced large R2 values. The presumably independentvariables were: Dbow or Dspring, Dtwist, ring width, den-sity, compression wood, spiral grain angle, radial, tan-gential and longitudinal shrinkage, distance from pith andadjusted distance from pith (cf. Johansson et al. 2001).

Fig. 4a–d. Bow and spring (inabsolute values) at 15.6%moisture content and at 7.2%moisture content. Variationexpressed by three radial posi-tions and two stands: Bow a15.6%, b 7.2%, Spring c 15.6%,d 7.2%Abb. 4a–d. Langskrummungund -verwerfung (in absolutenWerten) bei 15,6% Feuchte undbei 7,2% Feuchte: Langskrum-mung a 15.6%, b 7.2%, Langs-verwerfung c 15.6%, d 7.2%

Fig. 5a,b. Influence of compression wood on bow and springmeasured at 7.2% moisture content for slow-grown and fast-grown stands: a Bow, b SpringAbb. 5a,b. Einfluss von Druckholz auf Langskrummungund -verwerfung, gemessen bei 7,2% Feuchte fur langsam undschnell gewachsene Baumbestande: a Langskrummung, b Langs-verwerfung

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5Prediction of bow and spring based on two-dimensionalvariation in longitudinal shrinkageThe difference in longitudinal shrinkage in the sticks takenfrom two opposite faces should correspond to the changesin spring/bow in the studs when the moisture contentchanges. For example, the positive bow should correspondto positive differences in longitudinal shrinkage strainbetween the two wide faces of a stud. This relationshipcould not generally be demonstrated with any statisticalsignificance, Fig. 6. The differences in shrinkage strainbetween the wide faces (for bow) and between the edgefaces (for spring) were calculated using Eq. 1.

Debl ¼ De14 � De23 and Des

l ¼ De12 � De34 ð1Þ

where:

Debl is the difference in the longitudinal shrinkage

strain between two wide faces (bow)Des

l is the difference in the longitudinal shrinkagestrain between two edge faces (spring)

Deij is the mean value for the longitudinal shrinkagestrain for sticks i and j

The relationship between changes in bow/spring andchanges in the longitudinal shrinkage strain between twofaces of a stud (Fig. 6) could not be improved by onlyincluding studs with corresponding shrinkage strainmeasured on sticks with no compression wood or knots,i.e. CW-0 and KAR-0. The distribution of all the sticks in

terms of the amount of compression wood and knots wasdiscussed by Perstorper et al. (2001).

6Prediction of bow and spring based on three-dimensionalvariation in longitudinal shrinkageThe results of the measurements of the shrinkage in thesticks taken from one longitudinal position did not revealany correlation with the measured bow and spring of thestuds. The conclusion was drawn that the shrinkage in thesticks taken from one end of the stud was not represen-tative for the whole stud. To test this hypothesis, two studswere chosen from the above-mentioned 240 studs. These

Fig. 6. The relationship betweenchanges in bow/spring (due tochanges in moisture content from15.6% to 7.2%) and changes in thelongitudinal shrinkage strain be-tween two faces of a stud (widefaces for bow and edge faces forspring)Abb. 6. Die Beziehung zwischenVeranderungen in Langskrum-mung/-verwerfung (gemaß Veran-derungen in der Feuchte von15,6% bis 7,2% sowie Verande-rungen in der Langsschrump-fungsspannung zwischen zweiKantholzflachen (weite Oberfla-chen fur Langskrummung undEckenflachen fur Langsverwerfung

Fig. 7. Cross-section of the two studs. The sticks sawn from thebow and spring stud. (The darker sticks are the ones which weremeasured)Abb. 7. Querschnitt der beiden Kantholzer. Die von derLangskrummung und -verwerfung des Kantholzes entnommeneStabe. (Die dunkleren Stabe wurden gemessen)

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two studs were chosen so that one of them had bow andalmost no spring or twist, and the other one had springand almost no bow or twist. The stud with large bow had achange in bow of 9.7 mm between moisture stage 1 (wet)and moisture stage 2 (dry) and the stud with large springhad a change in spring of 7.5 mm during the same changein moisture content. The stud with large bow was a studfrom the fast-grown stand and was cut near the bark of thelog. The stud with large spring came from a slow-grownstand and was cut at an intermediate position in the log.

These two studs were then cut longitudinally into 200-millimetre long sections. These sections were sawn into

sticks just like the ones taken from the ends of all thestuds; sections with large knots were not included. Fivesticks from each wide face were sawn (10 sticks from eachsection) from the sections from the stud with large bowand three sticks from each edge face were sawn (six sticksfrom each section) from the sections from the stud withlarge spring, see Fig. 7.

These sticks were then placed in a climate room with arelative humidity of 90% RH. After the equilibriummoisture content was obtained, the length of these stickswas measured. The same procedure was repeated after theequilibrium moisture content in the sticks at a relative

Fig. 8. Longitudinal shrinkagestrain in the sticks from thestud with large bow as a resultof changes in relative humidityfrom 90% RH to 30% RH.Sections marked with a starwere not included due to knotsin the cross-section of a studAbb. 8. Langsschrumpfungs-spannung in den Stabe desKantholzes mit großerLangskrummung als Ergebnisvon Anderungen der relativenFeuchte von 90% RH zu 30%RH. Die mit einem Sterngekennzeichneten Abschnittewurden aufgrund der Knoten ineinem Kantholzquerschnittnicht hinzugefugt

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humidity of 30% RH was obtained. From these measure-ments, the shrinkage strains could be calculated for eachstick.

There is a large variation in longitudinal shrinkagestrain along each stud, see Figs. 8 and 9. For more infor-mation about radial variations in longitudinal shrinkage,see Bengtsson et al. (1997). The shrinkage strain in thesticks from the stud with large bow varies between 0.06%and 0.32%, which produces a factor of 5 for the differencein longitudinal shrinkage within the stud. For the sticksfrom the stud with large spring, it can be observed that theshrinkage varied between 0.03% and 0.25%. For the sticks

from the stud with large spring, the shrinkage strains fromthe different faces of the sections varied a great deal. Inmost of the sections, it is the sticks with position 5 (5A–5C) that have the largest shrinkage strain and, in somesections, it is the shrinkage strains of the sticks fromposition 1 (1A–1C) that are the largest. Obviously, theshrinkage difference (gradient) varies a great deal alongthe studs. It is therefore not surprising that it is difficult topredict three-dimensional distortion from shrinkage datafrom one longitudinal position.

The shrinkage data can be represented as shrinkagestrain differences over the cross-section, see Eq. 2.

Fig. 9. Longitudinal shrinkagestrain in the sticks from thestud with large spring as aresult of changes in relativehumidity from 90% RH to 30%RH. Sections marked with astar were not included due toknots in the cross-section of astudAbb. 9. Langsschrumpfungs-spannung in den Staben desKantholzes mit großer Langs-verwerfung als Ergebnisvon Anderungen relativerFeuchte von 90% RH zu 30%RH. Die mit einem Sterngekennzeichneten Abschnittewurden aufgrund der Knoten ineinem Kantholzquerschnittnicht hinzugefugt

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Debl ¼

P5

i¼1

DeiA �P5

i¼1

DeiC

� �

5ð2Þ

where:

Debl is the difference in longitudinal strain between two

wide faces (bow)DeiA is the strain in stick i in row A.DeiC is the strain in stick i in row C.

The values of Desl for spring are calculated in a similar

way. The bow and spring distortion for the entire studsshould correspond to this difference in shrinkage.

The longitudinal variation in strain difference betweenthe two faces is shown in Fig. 10. The difference in strainchanges the signs from minus to plus for the spring stud.This shows that it can be very difficult to predict the dis-tortion on the basis of the shrinkage in only one of thesesections.

The difference in longitudinal shrinkage between twofaces of the stud should produce a physical explanation forbow and spring in that stud. There are at least two ways tocalculate bow and spring, based on measured differencesin longitudinal shrinkage. The first method is fairlyapproximate and the second is more precise.

The average difference in shrinkage for all sections iscalculated using the first method. It is then assumed thatthe stud deforms with an even curvature corresponding tothis average difference in shrinkage. Using this assump-tion as the starting point, bow and spring were predicted,see Table 3, Method B. In this table, a prediction based ondata from only one longitudinal position is also presented,Method A. This prediction is more a question of luck whenusing the input data from one section from one end of astud, see Fig. 10, for example. It is obvious that shrinkagedata from several longitudinal positions is needed for agood prediction.

The second and more precise method, Method C, takesaccount of the fact that the distortion curvature changesalong the stud. The difference in shrinkage strain distortseach section; from being a rectangle it becomes a paral-lelepiped.

The co-ordinates are calculated for the corners of thedistorted section from the shrinkage data. By ‘‘joining’’all the sections together, it is possible to calculate theco-ordinates for the rest of the section in relation to thefirst section, cf. Fig. 11. Using these co-ordinates, thebow and spring were calculated in the entire stud. Thecalculations show good correlation between themeasured and calculated distortion, see Table 3,Method C. The difference between the calculated

Fig. 10a,b. Shrinkage strain difference De1

between two opposite faces for differentsections of the stud: a Sections with largebow. b Sections with large spring. Thedarker columns are the mean DeAbb. 10a,b. Die Schrumpfungsspannungs-Differenz De1 zwischen zwei gegenuberliegenden Flachen fur verschiedene Ab-schnitte des Kantholzes: a Abschnitte mitgroßer Langskrummung, b Abschnitte mitgroßen Langsverwerfungen. Die dunkle-ren Spalten sind die mittlere De1

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and the measured distortion is close to the measuredvalue.

7ConclusionThere is a linear relationship between the magnitude ofmedian spring or bow and different levels of moisturecontent. The changes in bow and spring appear to bereversible when the moisture content level is changed.There is no statistically-significant difference betweenstands, either fast-grown or slow-grown, in terms of bowand spring measured on studs after they are kiln-dried andconditioned during the first moisture stage, i.e. 15.6%moisture content. However, when all studs were condi-tioned to the ‘‘dry’’ moisture stage, i.e. 7.2% moisturecontent, distortion increased significantly, as did the dif-ferences between the two stands in terms of bow andspring. Studs from the fast-grown stand displayed morebow and spring than studs from the slow-grown stand andthe differences were statistically significant. The medianvalues for bow and spring measured twice at approxi-mately 15% moisture content (mean value) and twice atapproximately 7.5% moisture content (mean value) de-creased slightly from core to bark when all the studs weredivided into three stud groups and two stands. However,this decrease was not statistically significant. The mostcommon parameters used by wood technologists, such asdensity, ring width or knot area ratio, showed no or verylittle effect on bow and spring. It was expected that com-pression wood would have a significant effect on bow andspring. However, this effect was also very weak. Theprobable reason was the insufficiently detailed and precisedetermination of the compression wood. In the future, anew technique is needed to determine three-dimensionalvariations in compression wood.

Using measurements from 240 studs of Norway spruce,it was found that there was no correlation betweenshrinkage gradients measured at one longitudinal positionand three-dimensional bending distortion (spring andbow). The difference in the longitudinal shrinkage between

two faces of the studs explained spring or bow far betterwhen account was taken of the variation in shrinkagealong the stud. The longitudinal variation in shrinkage wasvery large; i.e. strains varied from 0.06% to 0.32% alongone stud. Knowing the three-dimensional shrinkage vari-ation, it appears to be possible to predict the distortionwith a discrepancy of around 5%, as shown in this paper.The findings in this study clearly demonstrate that aknowledge of the three-dimensional variation in longitu-dinal shrinkage is needed in order to predict bow andspring more accurately.

ReferencesBengtsson C, Kliger IR, Johansson G (1997) The influence of woodraw material on moisture, shrinkage and swelling properties. Pro-ceedings COST Action E8, International Conference on Wood-WaterRelations, pp 213–228, Copenhagen, Denmark, June 16–17Danborg F (1994) Spiral grain in plantation trees of Picea abies. Can JFor Res 24:1662–1671Forsberg D (1997) Granvirkets formstabilitet kopplat till bestands-parametrar, ravarans egenskaper och byggbranschens krav. Rapportnr 45. Institutionen for Skog-Industri-Marknad Studier, SLU.. Upp-sala (in Swedish)Hallock H (1965) Sawing to reduce warp in plantation Loblolly pinestuds. USDA Forest Service, Forest Products Laboratory. Researchpaper FPL-51, Madison, USAJohansson G, Kliger R, Perstorper M (1994) Quality of structuraltimber—product specification system required by end-users. HolzRoh- Werkstoff 52(1):42–48Johansson M, Perstorper M, Kliger IR, Johansson G (2001) Distortionof Norway spruce timber—Part 2. Modelling of twist. Holz Roh-Werkstoff 59(2001):155–162Kliger IR, Perstorper M, Johansson G, Pellicane PJ (1995) Quality oftimber products from Norway spruce. Part 3: Influence of spatialposition and growth characteristics on bending stiffness and strength.Wood Sci Tech 29:397–410Mishiro A, Booker RE (1988) Warping in New Crop Radiata Pine100·50 mm (2 by 4) Boards. Bulletin of the Tokyo University Forests80, pp 37–68Ormarsson S (1995) A finite element study of the shape stability ofsawn timber subjected to moisture variations. Division of StructuralMechanics, Lund Institute of Technology, p 88Perstorper M, Pellicane PJ, Kliger IR, Johansson G (1995) Quality oftimber products from Norway spruce. Part 1: Optimization, keyvariables and experimental study. Wood Sci Tech 29:157–170Perstorper M, Pellicane PJ, Kliger IR, Johansson G (1995) Quality oftimber products from Norway spruce. Part 2: Influence of spatialposition and growth characteristics on warp. Wood Sci Tech 29:339–352Perstorper M, Johansson M, Kliger IR, Johansson G (2001) Distortionof Norway spruce timber—Part 1. Variation of relevant wood prop-erties. Holz Roh-Werkstoff 59(2001):94–103Simpson W, Tschernitz J (1998) Effect of thickness variation on warpin high-temperature drying plantation-grown Loblolly pine 2 by 4’S.Wood Fiber Sci 30(2):165–174

Table 3. Prediction of bow and spring (in mm) using various input data and comparison with measured valuesTabelle 3. Voraussage von Langskrummung und -verwerfung (in mm), in dem verschiedene Eingabedaten und der Vergleich mitden gemessenen Werten verwendet wurden

Specimen Calculated distortion MeasuredValues

Method A. Shrinkage diff. fromone section outside stud.

Method B. Averageshrinkage diff.from all sections.

Method C. Shrinkagediff. and curvaturefrom all sections

Bow 11.9 12.8 9.3 9.7Spring 0.6 8.8 7.1 7.5

Fig. 11. Diagrammatic sketch of the sections after shrinkageAbb. 11. Schematische Zeichnung der Abschnitte nach derSchrumpfung

250