This paper deals with the development of models for twist in structural timber. Twist was measured on 240 studs of Norway spruce (Picea abies). Several ...
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Holz als Roh- und Werkstoff 59 (2001) 155±162 Ó Springer-Verlag 2001
Distortion of Norway spruce timber Part 2. Modelling twist M. Johansson, M. Perstorper, R. Kliger, G. Johansson
This paper deals with the development of models for twist in structural timber. Twist was measured on 240 studs of Norway spruce (Picea abies). Several material parameters were also measured, such as spiral grain angle, shrinkage in all three directions, annual ring width and density. Twist in the studs was measured at four different times at different moisture contents. The amount of twist correlated well with the moisture content and was reversible throughout several moisture changes. When the moisture content decreased, the twist increased and vice versa. About 50% of the variation in twist could be explained by a single parameter, i.e. the average growth ring curvature. All studs with severe twist were cut with its centroid within a radius of 75 mm from the pith. A statistical analysis of the data shows that growth ring curvature and spiral grain angle together explained about 70% of the variation in twist. Other parameters, such as shrinkage strains, density and ring width, did not increase predictability. When using a model developed by Stevens and Johnston (1960), about 66% of the variation in twist could be explained. The model also explained twist quantitatively well. The model included curvature of the growth ring, spiral grain angle and the tangential shrinkage strain.
und umgekehrt. Rund 50% der Verdrehungswerte sind durch einen einzigen Parameter erklaÈrt, naÈmlich die JahrringkruÈmmung. Bei allen KanthoÈlzern mit starker Verdrehung lag die Mittelachse innerhalb eines Abstandes von 75 mm von der MarkroÈhre. Die statistische Analyse ergab, daû JahrringkruÈmmung und Faserwinkel zusammen ca. 70% der Variation der Verdrehung erklaÈren. Andere Parameter wie Schwindspannungen, Dichte und Jahrringbreite erhoÈhten die Vorhersagbarkeit nicht. Mit Hilfe des Modells von Stevens und Johnson (1960) konnten rund 66% der Verdrehung erklaÈrt werden. Dieses Modell lieferte auch zufriedenstellende quantitative Ergebnisse. BeruÈcksichtigt werden dabei JahrringkruÈmmung, Faserwinkel und tangentiale Schwindspannung.
1 Introduction
1.1 Background Twist is one of the main reasons for studs being rejected at the building site. It is widely known that the problems associated with distortion in timber (especially twist) are the main obstacle to the extended use of timber in the Verwerfung von Fichtenschnittholz. building industry, Sinclair (1992), Johansson et al. Teil 2. Simulation der Verdrehung (1994), among others. It is therefore crucial to develop Diese Arbeit behandalt dia Entwicklung von Modellon models, which would improve the understanding of how fuÈr die Verdrehung in Schnittholz. Die Verdrehung distortion varies. Modelling moisture-related distortion wurde gemessen an 240 FichtenkanthoÈlzern (Picea (twist, spring and bow) in full-size timber has been a abies). Mehrere Materialeigenschaften wurden ebenfalls challenge for many years. Twist of studs has been a gemessen, und zwar: Faserwinkel, Schwinden in drei subject for research during the last 40 years. Scientists Richtungen, Jahrringbreite und Dichte. Die Verdrehung have tried to ®nd out which parameters in¯uence twist der KanthoÈlzer wurde zu vier verschiedenen Zeitpunkten in studs. The most common way to predict twist is based bei unterschiedlichen Feuchtegraden gemessen. Das on statistical evaluation of measured data. A few trials Ausmaû der Verdrehung war gut korreliert mit der have been made to predict twist analytically and Feuchte. Mit abnehmender Feuchte stieg die Verdrehung numerically. The statistical method is the methodology that has been applied by the majority of scientists. Trials have been made to correlate the measured twist of the studs with Marie Johansson (&), Mikael Perstorper, Robert Kliger, measured material parameters, such as log diameter or Germund Johansson Chalmers University of Technology, distance from the stud to the pith, grain angle, knots and Department of Structural Engineering, compression wood. (Kloot and Page 1959, Brazier 1965, Steel and Timber Structures, 41296 GoÈteborg, Sweden Balodis 1972, Mishiro and Booker 1988, Woxblom 1993, Beard et al. 1993, Cown et al. 1996). The authors would like to express their gratitude to the Swedish In the mid-®fties Stevens and Johnston (1960) proposed Council for Building Research (BFR), project no. 950172±6, and the Swedish Forestry and Agricultural Research Council (SJFR), an analytical model of how a thin cylindrical shell of wood will twist. The experimental results showed that this model reg. no. 20.0150/95, and the CF LundstroÈm Foundation, for supporting this work. produced results that correlated rather well with twist of
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shells. Balodis (1972) con®rmed that this method was applicable to studs. In recent years a ®nite element approach has been used to model twist (see Ormarsson 1995, for example). In his model elastic properties, mechanosorptive creep coef®cients, spiral grain angle and shrinkage were used as parameters to predict twist of drying studs. A parametric study to investigate the in¯uence on twist using the ®nite element method showed that spiral grain angle and the distance from the stud to the pith had the largest in¯uence on twist (Ormarsson 1995). All these methods contribute to the understanding of twist in dried studs. However, some problems have been reported too. For example, to correlate the measured parameters to the measured values of twist may sometimes present a problem. All studs have often been dried and conditioned with external loads, to a smaller or larger extent. This external load is caused by studs stored at a higher position in the stack. As a result the external load has not been the same on all the measured studs. External load, large enough, can lower the twist of some studs substantially (Arganbright et al. 1978).
1.2 Objective The objective of the entire project was to measure and model moisture-related distortion in full-size timber. The results are presented in a series of three papers. In the ®rst paper in this series (Perstorper et al. 2001), a description of the experimental set-up is presented, together with the results for important material properties which have some impact on distortion. This paper is the second in the series and deals with the formulation of a physical (analytical) explanation of moisture-related changes in twist. The third paper by the authors (Kliger et al. 2001) focuses on modelling bow and spring.
The main aim of this paper is to clarify the in¯uence of material parameters on twist and to evaluate different modelling approaches.
2 Summary of the experimental set-up In the earlier paper in this series (Perstorper et al. 2001), an overall description of the research plan is presented; a short description of these issues is presented here. Trees from two large-diameter stands of Norway spruce, one fast-grown and one slow-grown were harvested in southern Sweden for this project. For an additional description of the stands, see Perstorper et al. (1995) and Kliger et al. (1995). The upper butt logs of 40 trees were sawn into 2.9 m long battens, 70 ´ 290 (in mm) before kiln drying, to approximately 12% moisture content. The members were then ripped and planed to the ®nal stud dimensions 45 ´ 70 ´ 2900 (in mm). Six studs were cut from each batten, in all 240 studs representing three stud groups with respect to radial location, outer, intermediate and core (Fig. 1). Each piece of timber was hung vertically in a conditioning room. Twist in all the studs was measured four times during moisture changes between approximately 85% relative humidity (RH) and 30% RH. Measurements of growth characteristics are described in detail in Perstorper et al. (2001). Spiral grain angle, shrinkage, ring width and density were measured on a 200 mm long more or less knot-free section taken at the top end of each stud. These properties were thus not measured on the actual stud. Stand characteristics like density and ring width for the two stands can be seen in Table 1. This 200 mm section was then cut in three slices, each 13 mm thick. Spiral grain angle was measured on the tangential face on all three 200 ´ 70 ´ 13 (in mm) slices (A, B, C), see Fig. 1. The slices were then cut to a total of
Fig. 1. Log sampling, sawing pattern and notations Bild 1. Probenahme, Einschnitt und Bezeichnung der Proben
Table 1. Density and ring width, mean values and standard deviation (). Density is obtained at volume and weight at 7.2% moisture content Tabelle 1. Mittelwerte und Standardabweichungen der Dichte und der Jahrringbreite. Die Dichte wurde bestimmt aus Volumen und Gewicht bei 7.2% rel. Feuchte
In order to model twist accurately it was necessary to know not only the magnitude of twist, but also the direction. Positive and negative directions are therefore de®ned, see Fig. 2. The de®nition is the same as used by Mishiro and Booker (1988).
3 Influence of moisture cycling on twist Density, [kg/m3] 373 (37.0) 427 (48.3) As expected, twist was very much in¯uenced by the surRing width, [mm] 5.72 (1.64) 3.18 (1.13) rounding climate. The twist deformation became considerably larger when the surrounding climate was changed from wet (85% RH) to dry (30% RH). The median value ®ve sticks 200 ´ 13 ´ 13 (in mm) from each stud. The for absolute twist increased from 1.5° to 3.6° (see Fig. 3). sticks from the B-layer, with a clear radial and tangential The original moisture content was not reached in the face, were used to determine tangential and radial second moisture cycle, see Table 2. This was due to the shrinkage properties. All ®ve sticks were used to determine hysteresis effect and to the fact that the relative humidity the longitudinal shrinkage. in the conditioning room was not exactly the same as at the starting point. However, the median values show a linear relationship between the moisture content level and the amount of twist in the studs, see Fig. 3. It is interesting to notice that an extrapolation of the regression equation indicates that twist should be zero at around the ®bre saturation point. This agrees well with the observations made on freshly cut timber in which twist has not yet developed or is very small. There is a strong correlation between twist at 15.6% moisture content and twist at 7.2% moisture content, see Fig. 4, the correlation is almost equally strong during other moisture stages (15.6% mc±7.2% mc Þ R2 0.92, 7.2% mc±14.4% mc Þ R2 0.85, 14.4% mc±7.8% mc Þ Fig. 2. De®nition of positive and negative direction of twist R2 0.95). In the third and fourth moisture stage some Bild 2. De®nition der positiven und negativen Verdrehung studs were used for other experiments (see, for example, Fast-grown
Slow-grown
Fig. 3. The relationship between median moisture content and median twist (absolute values) in degrees at the four moisture stages Bild 3. Beziehung zwischen mittlerer Feuchte und mittlerer Verdrehung (absolute Werte in Grad) bei vier Feuchtestufen Table 2. Variations (in degrees) in twist at four different moisture stages Tabelle 2. Variation der Verdrehung (in Grad) bei vier verschiedenen Feuchtestufen
Fig. 4. Relationship between twist measured at 15.6% moisture content and 7.2% moisture content Bild 4. Beziehung zwischen den bei 15,6% und 7,2% rel. Feuchte gemessenen Verdrehungen
Moisture stage
Relative humidity [%]
Moisture content (mean) [%]
Count
1 2 3 4
85 30 85 30
15.6 7.2 14.4 7.8
240 240 237 228
Twist (Absolute values) Mean [°]
Std Dev [°]
Median [°]
2.07 5.16 2.84 4.86
1.94 4.68 2.58 4.57
1.52 3.56 1.98 3.38
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Distance from pith to the centre-point of the crossKliger et al. 2001) which explains the differences in numsection of a stud (r) was also measured in order to deber in the different moisture stages. termine the average growth ring curvature (1/r). 4 In the following, twist is represented as the differInfluence of growth characteristics on twist ence between twist in degrees measured at moisture stage 1 (15.6% moisture content) and twist in degrees 4.1 measured at moisture stage 2 (7.2% moisture content). Influence of stand type and radial position This difference is called Dtwist in the following chapThere is no statistically-signi®cant difference between the ters. fast-grown and the slow-grown stand with respect to twist, see Fig. 5. This applies both at 15.6% moisture content and 4.3 at 7.2% moisture content. Growth ring curvature There is a very strong radial effect on the amount of The growth ring curvature is not a growth characteristic twist in the studs. Severe twist occurs only among studs but is nevertheless an important parameter. The growth cut closer to the pith than 70 mm, see Fig. 6. Johansson ring curvature for each stud is 1/distance from the pith to et al. (1994) proposed a limit for twist of wall studs at 18% the centre-point of the studs cross-section, see Fig. 7. moisture content, of 5 mm 3.8° on stud with a width of The numerical problem when predicted twist ap75 mm, based on the requirements related to assembly of a proaches in®nity (¥) as the radius approaches zero has to stud in a wall structure. Studs cut farther away from the be taken into account. In this paper this problem is solved pith than 70 mm, ful®ls requirements of 5 mm by almost by Eq. (1), which recalculates the distance from pith for 100% measured at 15% MC. studs cut closer to pith than 45 mm. The lowest value of 22.5 mm is a more representative 4.2 radius for a stud with the pith located in the centre of the Influence of material parameters cross-section, see Fig. 7b. One of the aims of this project was to clarify the in¯uence of relevant measurable material parameters on distortion. r 22:5 r 0 r 45
1 n 2 The material parameters that were measured within this project are, spiral grain angle (h), shrinkage strains (et, er, el), growth ring width (RW) and density (dens).
Fig. 5a, b. Twist in degrees (absolute values) obtained at a) moisture stage 1 (15.6% moisture content) and b) moisture stage 2 (7.2% moisture content) split by stand and by radial position Bild 5a, b. Verdrehung (absolute Werte in Grad): a) bei Feuchtestufe 1 (15,6%) und b) Feuchtestufe 2 (7,2%). Die Werte sind getrennt nach Standort und radialer Position
Fig. 6a, b. Twist in degrees (absolute values) versus distance from pith at different moisture stages Bild 6a, b. Verdrehung (absolute Werte in Grad) in AbhaÈngigkeit vom Abstand von der MarkroÈhre
Since both twist and spiral grain angle (h) are associated to radial position, it appears that the strong relationship between spiral grain angle and twist might be to some extent arti®cial. However, according to the stepwise regression analysis this relationship is only to some extent weakened (R2 0.26±0.24) after removing the variation explained by ring curvature (radial distance), see Table 3. In this study the spiral grain angle was measured on a 200 mm long piece cut from the top end. By this procedure it is to be noted that the normal longitudinal variation in spiral grain angle is not captured. It is therefore suggested for Fig. 7a, b, c. a) De®nition of radius (r). b) Equivalent radius for a future research to take several spiral grain angle readings stud with the pith located in the centre. c) Equation (1) for cal- along each specimen to obtain more representative values. culating a new radius for studs containing the pith Bild 7a, b, c. a) De®nition des Radius r; b) aÈquivalenter Radius fuÈr Kantholz mit zentrischer MarkroÈhre; c) Berechnung des neuen Radius (Gl. 1) fuÈr Kantholz mit Markanteil
4.5 Shrinkage According to Stevens and JohnstonÂs model (1960), see Eq. (3), twist should increase with increasing tangential shrinkage. On the contrary, the experimental results obTwist is strongly correlated to the curvature of the growth ring, R2 0.52. This relationship has been shown tained in this study indicate no correlation, see Fig. 9. theoretically by Steven and Johnston (1960) and is discussed in the following chapters. This relationship has also 4.6 Density and ring width been shown for conifer species in some experimental studies (Balodis 1972, Cown et al. 1996, Shelly et al. 1979, There is almost no correlation between density and 2 Kloot and Page 1959, Mishiro and Booker 1988). In a study twist, R 0.12. Some of this correlation is probably based on material from the same fast-grown stand, Perstorper et al. (1995), as in this study, an equally strong relationship between ring curvature and twist was found. Table 3. Stepwise regression of Dtwist and growth character4.4 Spiral grain angle Spiral grain angle (h) is the parameter that has the second strongest correlation with twist, R2 0.26. In this paper spiral grain angle is de®ned as the mean value of the three readings of the slices, cf. Perstorper et al. (2001). A similar level of correlation has been found in many other studies; Mishiro and Booker (1988) had a correlation of R2 0.31 for example, on Radiata Pine. Brazier (1965) found a stronger relationship (R2 » 0.5) between spiral grain and twist, on European larch. However, Brazier measured spiral grain angle and twist on approximately 0.6 m long specimens. It should be noted that the direction of the spirality apparently determines the direction of twist deformation. A left-handed spirality is associated with a left-handed twist deformation and vice versa, cf. Fig. 1 and 2. Spiral grain angle varies radially from a positive spirality to zero and sometimes also to a negative spirality, see Fig. 8b.
istics. Only studs for which tangential and radial shrinkage were correctly measured are included. (n = 185) Tabelle 3. Schrittweise Regression zwischen Dtwist und Wachstumscharakteristiken. Nur KanthoÈlzer, deren tangentiales und radiales Schwinden korrekt gemessen wurden, sind einbezogen (n = 185) Stepwise forward
Intercept 1/rn h et er el Dens RW
Step 0
Step 1
Step 2
Variables R in model
Variables R in model
Variables R in model
´ ± ± ± ± ± ± ± R2 = 0
´ ´ ± 0.49 ± 0.12 ± )0.09 ± 0.06 ± )0.13 ± 0.21 R2 = 0.52
´ ´ ´ ± 0.08 ± )0.08 ± 0.10 ± )0.05 ± 0.11 R2 = 0.63
0.72 0.51 )0.09 0.19 0.19 )0.34 0.45
Fig. 8a, b. Relationship between Dtwist, spiral grain angle (h) and distance from the pith (r). a) Dtwist versus spiral grain angle (h). b) Spiral grain angle (h) versus distance from the pith (r) Bild 8a, b. Beziehung zwischen Dtwist, Faserwinkel (h) und dem Abstand von der MarkroÈhre (r); a) Dtwist und Faserwinkel; b) Faserwinkel (h) und Abstand von der MarkroÈhre
159
Fig. 9a, b. Relationship between Dtwist, tangential shrinkage (et) and distance from the pith (r). a) Dtwist versus tangential shrinkage (et). b) tangential shrinkage (et) versus distance from the pith (r) Bild 9a, b. Beziehung zwischen Dtwist, tangentialem Schwinden (et) und Abstand von der MarkroÈhre (r); a) Dtwist und tangentiales Schwinden (et); b) tangentiales Schwinden (et) und Abstand von der MarkroÈhre (r)
160 due to the fact that both twist and density varies radially. The obtained result shows that ring width is associated with twist, R2 0.20. However, ring width is closely related with radial position and density. The observed association between ring width and twist is therefore a matter of common response to radial position rather than causation, see Fig. 10. After removing the twist variation, caused by growth ring curvature, the correlation between ring width and twist almost disapperard (R2 0.04).
5 Regression analysis A multiple regression analysis which included all parameters produced a coef®cient of determination of R2 0.65. A stepwise regression analysis was made in order to investigate to what extent the different parameters in¯uenced the magnitude of Dtwist. The stepwise regression analysis is a good tool since collinearity between parameters is taken into account. Using this method, 63% of the variation in Dtwist could be explained, see Table 3. The governing Equation (2) is a result of step 2 in the stepwise regression analysis. 1 DTwist 3:2 271:5 0:63 h
2 rn If a multiple regression analysis with only curvature of the growth ring (1/rn) and spiral grain angle (h) as independent variables is used to explain the Dtwist for all 232 studs, the coef®cient of determination R2 0.71. The difference between these two models is due to the fact that in the stepwise model the specimens with tangential and radial shrinkage were not correctly measured and therefore excluded. Most of these specimens were from positions close to the pith, which gives less variation in the measured data, see Fig. 11.
Fig. 11a, b. Twist versus distance from pith. a) All specimens included . b) Specimens where it was impossible to measure radial and tangential shrinkage are excluded Bild 11a, b. Verdrehung in AbhaÈngigkeit vom Abstand von der MarkroÈhre: a) Alle Proben; b) ohne die Proben deren radiales und tangentiales Schwinden nicht gemessen werden konnte
6 Modelling of twist using Stevens and Johnstons model Stevens and Johnston (1960) presented a model for twisting of cylindrical shells of wood during adsorption.
Fig. 10a, b. Relationship between Dtwist, growth ring width (RW) and distance from the pith (r). a) Dtwist versus growth ring width (RW). b) Growth ring width (RW) versus distance from the pith (r) Bild 10a, b. Beziehung zwischen Dtwist, Jahrringbreite (RW) und Abstand von der MarkroÈhre (r); a) Dtwist und Jahrringbreite (RW); b) Jahrringbreite (RW) und Abstand von der MarkroÈhre (r)
This model is built on a relationship between twist and shrinkage, grain angle and radius shown in Eq. (3).
l 2et h a r 1 et where:
3
a Twist [°] l Length [m] h Spiral grain angle [°] r Radius [m], distance from pith et Tangential shrinkage The model is only valid for small grain angles since it is assumed that tanh » h. The model also neglects longitudinal shrinkage strains. Balodis (1972) applied this model on the twist of studs cut parallel to the pith of a log. A simple geometrical construction shows that a chord formed by the intersection of a plane parallel to the central axis of the shell and the circular cross-section of the shell will undergo rotation a relative to the corresponding chord at the ®xed end. Such a plane could be considered to be a surface of a stud and the angle of rotation of the chord to be the angle of twist of the stud. Under the conditions that h r and et is constant throughout the stud, the rotation of the end of the plane and that of the actual stud will be the same and Eq. (3) should predict the angle of twist in the stud. To be able to use this equation both during adsorption and desorption signs must be used. Balodis found that data obtained using his model correlated well with his experimental data, however it did overestimate the magnitude of twist. Balodis presented three possible explanations to this difference: external restraint during seasoning, internal restraint or mistakes produced during the measurements of grain angle. External restraints during drying and conditioning gives a substantial reduction of twist according to many studies, especially when combined with high temperature drying (Arganbright et al. 1978). Another possible explanation of the discrepancy could be that the mathematical transformation from cylindrical shells to studs requires that the growth rings are almost parallel to the surface of the stud and that the stud is not thick. Balodis experimental set-up included almost no studs with growth rings parallel to the stud surface.
7 Computed twist in comparison with measured twist It appears that the model developed by Stevens and Johnston (1960) predicts twist with good accuracy, see Fig. 12. The coef®cient of determination is R2 0.66 for the relationship between predicted and actual twist. Furthermore, the model predicts the magnitude of twist with reasonable accuracy. It should be noted that the modi®ed expression for ring curvature according to Eq. (1) has been used (rn). The average tangential shrinkage for all studs was used in the prediction (et 0.028). When individual data for each stud was used, the prediction
161 Fig. 12. Twist predicted with Stevens and Johnston's model using rn, cf. Eq. (1) Bild 12. Verdrehung nach dem Modell von Stevens und Johnston (1960) unter Verwendung von rn, s. Gl. (1)
became considerably less accurate. One reason for this might be that the tangential shrinkage varies to a large extent in longitudinal direction. Thus, the data for the topend must not be representative for the whole stud.
8 Conclusions The twist in the studs more than doubled when the studs were dried from normal delivery moisture content (»15%) to in-service moisture content (»7%). Twist appears to be proportional to moisture content and is reversible throughout several moisture cycles. The effect of stand type, growth rate and density on twist is negligable. Thus, it is indicated that one cannot use silvicultural parameters in general to identify and reject twist-prone material. Site quality does not play a major role for twist. Twist is well correlated to growth ring curvature (R2 0.53) and spiral grain angle (R2 0.26). Growth ring curvature and spiral grain angle together explain about 70% of twist variation. Individual shrinkage data from the top end of each stud appears to be uncorrelated to twist. Knowledge of the variation in material properties along the stud may therefore be needed to further increase the twist prediction accuracy. Stevens and JohnstonÂs model is a good tool to predict twist both qualitatively and quantitatively. The model explained about 66% of the variation in twist. The easiest way to produce less twisted studs is to avoid using the central part of the log for studs. An area of 75 ´ 75 (in mm) containing pith should be avoided. References
Arganbright DG, Venturio JA, Gorvad M (1978) Warp reduction in young-growth ponderosa pine studs dried by different methods with top-load restraint. Forest Prod J 28: 47±52 Balodis V (1972) In¯uence of Grain Angle on Twist in Seasoned Boards. Wood Science 5: 44±50 Beard JS, Wagner FG, Taylor FW, Seale RD (1993) The in¯uence of growth characteristics on warp in two structural grades of southern pine lumber. Forest Prod J 43: 51±56 Brazier JD (1965) An Assessment of the Incidence and Signi®cance of Spiral Grain in Young Conifer Trees. Forest Prod J 15: 308±312
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Cown DJ, Haslett AN, Kimberly MO, McConchie DL (1996) The in¯uence of wood quality on lumber drying distortion. Annales des Sciences ForestieÁrer 53: 1177±1188 Johansson G, Kliger R, Perstorper M (1994) Quality of structural timber ± product speci®cation system required by end-users. Holz Roh- Werkstoff 52: 42±48 Kliger IR, Perstorper M, Johansson G, Pellicane PJ (1995) Quality of timber products from Norway spruce. Part 3: In¯uence of spatial position and growth characteristics on bending stiffness and strength. Wood Sci Technol 29: 397±410 Kliger IR, Johansson M, Perstorper M, Johansson G (2001) Distortion of Norway spruce ± Part 3. Modelling bow and spring. Holz Roh- Werkstoff 59: xxx±yyy Kloot NH, Page MW (1959) A study of distortion in radiata pine scantlings. Division of Forest Products, CSIRO, Technical Paper No. 7 Mishiro A, Booker RE (1988) Warping in New Crop Radiata Pine 100 ´ 50 mm (2 by 4) Boards. Bulletin of the Tokyo University Forests No. 80: 37±68 Ormarsson S (1995) A ®nite element study of the shape stability of sawn timber subjected to moisture variations. Division of
Structural Mechanics, Lund University of Technology, Sweden, p. 91 Perstorper M, Pellicane PJ, Kliger IR, Johansson G (1995) Quality of timber products from Norway spruce. Part 2. In¯uence of spatial position and growth characteristics on warp. Wood Sci Technol 29: 339±352 Perstorper M, Johansson M, Kliger IR, Johansson G (2001) Distortion of Norway spruce ± Part 1. Variation of relevant wood properties. Holz Roh- Werkstoff 59: xx±yy Shelly JR, Arganbright DG, Birnbach M (1979) Severe warp development in young-growth Ponderosa Pine studs. Wood and Fiber 11: 50±56 Sinclair SA (1992) Innovation in wood products: A result of market pull or properties push. Proc. IUFRO All-div. 5 Conference, Nancy, France. ARBOLOR: Vol. 1, p. 37 Stevens WC, Johnston DD (1960) Distortion caused by spiral grain. Timber Technology 68: 217±218 Woxblom L (1993) Quality variations in wall studs ± A study conducted at ®ve sawmills in southern Sweden. (In Swedish) Swedish Univ. of Agricultural Sciences, Dept. of Forest-IndustryMarket-Studies, Report No 28, Uppsala, Sweden
