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Twist assessment and reduction in southern pine 2 by 4's.


As part of an ongoing research program aimed at warp reduction in Stud-grade lumber, 96 southern yellow pine 2 by 4s were high temperature kiln-dried. Following drying, torsional properties of 15 highly twisted boards were evaluated. Twisted boards were torqued until their ends were parallel, that is, free of twist. Inherent torsional stress and rigidity are reported. Correlation between torsional properties, i.e., stress and strain, and other predictors such as density and twist angle are also reported. After torsional measurements were taken, the 96 boards were repackaged, top weight restrained, and steam conditioned at approximately 215[degrees] F dry-bulb and 208[degrees] F wet-bulb temperature (EMC of approximately 12%) for approximately 6 hours. Weight restraint was a minimum of 100 lb./ft.[.sup.2] Differences in twist between completion of drying and completion of conditioning are reported. Results of the analysis presented herein may be used in studying the fundamental nature of twist in yellow pine, in optimizing remedial procedures, and in maximizing grade recovery.


For 2 by 4 southern yellow pine (SYP) lumber, the Stud-grade standard allows 0.375 inch of twist in 8-foot-long lumber (SPIB 1994). Currently, 2 by 4 lumber is sawn mainly from small-diameter stems that are grown under intensive forest management. Young, small-diameter stems that are mostly juvenile wood are highly prone to warpage, including twist. In commercial operations, twist accounts for a significant portion of lumber degrade from No. 2 and Better and Stud to No. 3 and No. 4. In the same lumber, the occurrence of knots that are of sufficient size or number to cause similar drops in grade are relatively rare. The small-diameter raw material does not generally have branches of sufficient size to produce grade-reducing knots. Twisted lumber results in loss in value, out-of-true walls and trusses, rejected material, etc. Previous research has attempted to alleviate some of this problem (Koch 1971, Mackay and Rumball 1972) but has not been widely commercially adopted. In two recent drying studies, the percentages of boards that missed Stud grade because of twist were 29 percent for SYP (Erickson and Shmulsky 2002a) and 49 percent for red pine (Erickson and Shmulsky 2002b). Those studies are being readied for publication. To produce twist-free lumber, boards must be adequately restrained during drying, heated to the point of plasticity, and set in the twist-free state.

As mechanical properties, torsional stress and elasticity are related to structural design and analysis. Buckling of narrow deep section beams is perhaps the most common instance of torsional importance. Literary references related to the importance of torsion are relatively few in number and contain minimal detail. The Wood Handbook states: "For solid wood members, torsional shear strength may be taken as shear strength parallel to grain" (FPL 1999). The average shear strength for clear specimens of loblolly pine is published as 1,390 psi at 12 percent moisture content (MC). The shear strength design value for Stud-grade SYP is 90 psi, kiln-dried to 19 percent MC. Torsional stress is not, however, generally associated with wood MC and drying.

Torsional stiffness or rigidity is a function of the elastic properties of the wood in shear parallel to grain. It has been shown (Brown et al. 1952) that the torsional rigidity modulus is approximately equal to 1/16 of the bending modulus of elasticity (MOE). For loblolly pine, the average MOE is 1.79 X [10.sup.6] for small clear specimens at 12 percent MC. The design value MOE is 1.4 X [10.sup.6] psi for Stud-grade 2 X 4's kiln-dried to 19 percent MC.

The general sentiment with respect to torsion in structural design is captured in the phrase "... it is recommended that the designer avoid those design situations which result in a twisting or rotation of the member, causing torsional stresses" (Faherty and Williamson 1995). Put simply, designers and engineers are cautioned against using wood in situations that cause axial torsion. This sentiment provides minimal assistance for the designer and no assistance for the lumber producer who might wish to remove twist from warped lumber. In only a small number of structural design cases are external forces evaluated with respect to their propensity for causing twist in structural members. This research investigates internal torsional stresses, which cause twist, and the directed external forces, which can be used for alleviation. Thus, this research application contrasts to traditional evaluation of torsional stress evaluation in structural design but the two fundamental concepts are fundamentally linked.

Materials and methods

Ninety-six pieces of green 2-by 4-inch SYP lumber were kiln-dried and measured for warp. Lumber was obtained from a sawmill in McDavid, Florida. The contributing sawmill produces a predominance of 2- by 4-inch lumber from small-diameter logs, averaging approximately 5 to 6 inches in diameter. As such, it was expected that the natural warp potential for the lumber was high.

For drying, lumber was stacked on 0.625-inch-thick stickers, spaced 2 feet apart. Boards were stacked tightly edge-to-edge. Kiln temperatures were 230[degrees]F dry bulb and 140[degrees]F wet bulb. After drying, the lumber was equalized at 190[degrees]F dry bulb and 170[degrees]F wet bulb to bring the lumber to its anticipated in-service average EMC of 8 percent. While this MC value is lower than the 19 percent value commonly specified in softwood grading rules, it seemed prudent for assessing potential warp behavior in service. Air velocity through the kiln package was approximately 600 ft./min. Because of this relatively slow air velocity, drying time was somewhat longer than that typical in the industry. Drying from green took approximately 20 hours. Then the equalization was run for approximately 20 hours. It is not believed that the lower air velocity and longer drying time had any impact on warp except as the warp relates to final MC. Upon completion of drying, the MC average and standard deviation were 8.4 and 2.0 percent, respectively. Next, boards were measured for warp in terms of crook, bow, and twist according to the following protocol:

1. With the board resting on a horizontal warp table, it was sequentially positioned in order to be visually examined for the presence of each warp form.

2. If the amount of warp appeared so small that a meaningful determination seemed implausible, a judgment of "no warp" was assigned.

3. When a measurement was judged to be required, it was made to the nearest 1/32-inch via insertion of an inclined plane wedge. With the wedge inserted to the point of mild refusal, the reading was read off the calibrated vertical face of the wedge.

Fifteen boards were then set aside for torsional assessment. Selection was based on boards that had sufficient twist to exclude them from Stud grade, but limited amounts of crook and bow.

For assessment of torsional properties, the wide face of each full-length board was placed on a rigid platen. One end of each board was then clamped to the rigid platen. Next, the amount of twist at the opposite end was measured with a digital caliper. To remove twist, a lever and weight system was devised such that torque was applied to the twisted end of each board. The amount of torque was increased until the twist was removed. At that point, the amount of torque was recorded. Some of the boards were then secured to the rigid platen at mid-length and the process was repeated. This procedure was done to test the uniformity of torsional stress through the length of the boards. Torsional properties were calculated based on the amount of twist, the torque, and the inherent board properties

To calculate the torsional stress in the boards, that is the torsion required to straighten the boards, an adaptation of the classical torsion formula was used. The classical torsion formula "[^.o.sub.max] = Tc/J is limited to torsion in cylindrical shafts.


[[tau].sub.max] = maximum shear stress

T = internal torque

c = shaft radius

J = polar moment of inertia

For rectangular members, the formula [[tau].sub.max] = [T (3a + 1.8b)]/8[a.sup.2][b.sup.2] calculates the maximum shear stress at the extreme surfaces (AITC 1994).


[[tau].sub.max] = shear stress (psi)

T = torque (lb. in.)

a = one-half the width of the board (in.)

b = one-half the thickness of the board (in.)

To calculate torsional rigidity, the following formula was employed:

G = 2T1/p[r.sup.4][theta]


G = torsional rigidity (psi)

T = torque (lb. in.)

1 = length (in.)

r = effective radius (in.)

[theta] = angle of twist (radians)

For calculation, an estimate of the radius was taken as that of a circular shaft with a sectional area equivalent to the sectional area of the rough-dry 2 by 4's. The rough-dry boards measured 1.7 by 3.7 inches; cross-sectional area equals 6.29 in. (2) An equivalent area circle has a radius of 1.42 inches.

After twist and torsion measurements were recorded on the 15 selected boards, all of the 96 boards were repackaged for conditioning. The kiln package consisted of 12 lumber courses, each 8 boards wide. Stickers were located every 2 feet. The pile was top weight restrained with approximately 1 ton of weight. This weight provided a minimum restraint pressure of approximately 100 lb./ft.[.sup.2] on the package. The lumber was then conditioned for approximately 6 hours at 215[degrees]F dry-bulb and 208[degrees]F wet-bulb temperature (EMC approximately 12%). After conditioning, the lumber was cooled for 24 hours, unstacked, and re-measured with respect to twist.

Results and discussion

First, it was noted that all the boards were twisted (or threaded) in the same direction, axially to the left. For reference, this is opposite to the twist direction of common metal fasteners such as nuts, bolts, and screws. Such behavior suggests that there are underlying fundamental causes such as tree genetics and wood ultrastructure that are responsible. If processing factors were causing the twist, a more even distribution of twist directions would be expected.

To determine the uniformity of stress along the lengths of the boards, 10 boards were selected and measured for torsion both at full length and at half length, that is from the midpoint to one end (4 ft.). For the 10 boards, mean torsional stress values were calculated as 294 psi for the 8-foot length and 274 psi for the 4-foot length. A paired t-test for differences indicated that there was no statistical difference in torsional stress for full-length versus half-length material (p-value = 0.31). These results were not unexpected because the mechanism for twist in this lumber seems to occur at the anatomical level. As such, the twist occurs throughout the wood and all along its length.

Summary statistics of torsional stress (reported as shear stress), torsional rigidity, twist, torque, and density are presented (Table 1). From the results, it is noted that the average shear stress that developed in the twisted boards (280 psi) is approximately three times higher than the design value shear stress (90 psi). This ratio suggests that to be made flat after drying, twisted boards must be torqued well above their design value for shear. As such, restraining such lumber in an attempt to keep it flat could cause shear failure in a portion of the lumber population.

The average torsional rigidity, 102 X [10.sup.3] psi, is about 1/16 of the design value MOE and about 1/17 that of clear wood. Generally, torsional rigidity is estimated as approximately 1/16 of MOE. This rigidity indicates that the inherent torsional stiffness within the twisted lumber tested herein is more or less exactly that which was expected.

Finally, correlations were run among the different variables. Torque was directly related to twist; r = 0.80 (p-value = 0.00). This suggests that boards with relatively high amounts of twist required relatively high amounts of torque to remove the warp. A weak but significant correlation was detected between torsional rigidity and density, r = 0.66 (p-value = 0.01). A significant correlation was not detected between maximum shear stress and torsional rigidity, r = 0.29 (p-value = 0.32).

Density varied substantially among the measured lumber. This variation is related mainly to the range of wood quality observed among the boards. Relatively clear boards with high amounts of juvenile wood and pith produced the lighter boards. Boards with more knots and higher proportions of latewood produced the denser boards.

The top-load restraint steam conditioning treatment proved effective at reducing twist. Prior to conditioning, average twist among the 15 selected boards was 0.645 inch. Because of excessive twist, none of the 15 boards qualified for Stud-grade after drying. Following the 6-hour steam conditioning treatment, the average twist dropped to 0.377 inch. Seven of the 15 boards were then up-graded from No. 3 to Stud-grade. Individual twist measurements for the 15 boards before and after steam conditioning were statistically compared with a paired t-test. Results indicated that the reduction in twist among the boards was highly statistically significant (p-value = 0.00).

It was suspected that MC increases might be a significant contributing factor to the observed reduction in twist. To investigate this factor, for the charge of 96 boards, 6 full-length sample boards were weighed prior to conditioning, randomly located in the kiln package, and re-weighed after conditioning. For the six sample boards, average initial and final board weights were 9.48 and 9.50 pounds, respectively. A paired t-test for differences indicated that these values were not statistically different (p-value = 0.55). Because no statistical difference in weight was detected in before-steam versus after-steam measurements, change in average MC was ruled out as a significant factor in the reduction in twist.

These results are not intended for structural-use applications; rather, they are intended to provide fundamental background that can be applied to remediation warp, specifically as twist, in wood drying. Based on the average and standard deviation values for torque at the board end, the minimum torque necessary to restrain 95 percent of these 8-foot long boards is 1,280 lb. in. The authors estimate that this torque value equates to a top load restraint of approximately 240 lb./ft.[.sup.2] During drying, torsional forces would be applied via the mechanical couple generated between sequential layers of stickers or by other means of restraint. Because the stickers provide multiple restraint points and the torsional stress in the boards is constant from end to end, each set of stickers would be responsible for only a fraction of the necessary total required torque. Also during drying, because the lumber is weakened from the high temperature and MC, the total torque necessary for restraint should be considerably lower. The employment of a steam conditioning treatment after drying is an effective means of "setting" boards in a minimal-twist state.
Table 1.--Summary statistics for twist in 15 8-foot long, kiln-dried
SYP 2 by 4's.

 Mean SD (a) Maximum Minimum

Torsional shear stress (psi) 280 90.4 481 137
Torsional rigidity
 (X [10.sup.3] psi) 102 24.5 156 64.5
Twist (in.) 0.645 0.210 1.05 0.384
Torque (lb. in.) 837 270 1,440 411
Density (lb. ft.[.sup.-3]) 30.2 4.22 38.1 23.0

(a) SD = standard deviation.

[c]Forest Products Society 2004.

Forest Prod. J. 54(4):66-68.

Literature cited

American Institute of Timber Construction (AITC). 1994. Timber Construction Manual. 4th ed. John Wiley & Sons, Inc., New York.

Brown, H.P., A.J. Panshin, and C.C. Forsaith. 1952. Textbook of Wood Technology, Vol. II. McGraw-Hill, Inc., New York.

Erickson, R.W. and R. Shmulsky. 2002a. Warp reduction of yellow pine 2 X 4s by restrained drying. Unpublished research results. Univ. of Minnesota, St. Paul, MN.

____________ and ____________. 2002b. Warp reduction of red pine 2 X 4s by restrained drying. Unpublished research results. Univ. of Minnesota, St. Paul, MN.

Faherty, K.F. and T.G. Williamson. 1995. Wood Engineering and Construction Handbook. 2nd ed. McGraw-Hill, Inc., New York.

Koch, P. 1971. Process for straightening and kiln-drying southern pine 2 X 4s in 24 hours. Forest Prod. J. 21(5):17-24.

Mackay J.F.G. and B.L. Rumball. 1972. Plasticizing distortion-prone softwood studs prior to high temperature seasoning. Forest Prod. J. 22(6):27-28.

Southern Pine Inspection Bureau. (SPIB). 1994. Grading rules. SPIB, Pensacola, FL.

USDA Forest Service, Forest Products Laboratory (FPL). 1999. Wood Handbook: Wood as an Engineering Material. FPL-GTR-113. Forest Prod. Soc., Madison, WI.

Rubin Shmulsky*

Robert W. Erickson*

The authors are, respectively, Assistant Professor and Professor Emeritus, Wood and Paper Science Dept., College of Natural Resources, Univ. of Minnesota, 2004 Folwell Avenue, St. Paul, MN 55108. Gracious thanks is extended to Carl Neels at International Paper, McDavid, FL. This paper was received for publication in September 2002. Article No. 9591.

*Forest Products Society Member.
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Author:Shmulsky, Rubin; Erickson, Robert W.
Publication:Forest Products Journal
Geographic Code:1USA
Date:Apr 1, 2004
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