BOWING IN ROOF JOISTS INDUCED BY MOISTURE GRADIENTS AND SLOPE OF GRAIN

Transcription

1 BOWING IN ROOF JOISTS INDUCED BY MOISTURE GRADIENTS AND SLOPE OF GRAIN USDA FOREST SERVICE RESEARCH PAPER FPL U.S. DEPARTMENT OF AGRICULTURE FOREST SERVICE FOREST PRODUCTS LABORATORY MADISON, WIS.

2 ABSTRACT During winter months many houses constructed with flat or low-pitched roofs have exhibited upward bowing deflections of 5/8 to 3/4 inch at midspan causing a separation between ceiling and partitions. Where the problems exist, a definite moisture gradient across the depth of the roof joist has been measured in the field. Wood has a very low shrinkage coefficient in the longitudinal direction which is essentially parallel to the axis of the lumber. Its magnitude is far too low to account for the bowing deflections recorded in actual houses. However, shrinkage values in the radial or tangential direction are 50 to 80 times greater than the longitudinal. Any significant slope of grain produces shrinkage components from the tangential and radial direction relative to the axis of the member. Twenty-six specimens of three different species were cut with varying slopes of grain. A moisture gradient was created across the depth of the specimen and bowing deflections were observed. Relationships between bowing deflection and grain angle were established. The magnitudes of observed deflections agreed with those measured in the field.

3 BOWING IN ROOF JOISTS INDUCED BY MOISTURE GRADIENTS AND SLOPE OF GRAIN By ROGER L. TUOMI, Engineer and DARREL M. TEMPLE, Engineer 1 Forest Products Laboratory, 2 Forest Service U.S. Department of Agriculture INTRODUCTION Certain house designs use flat or lowpitched roofs with floating ceilings. Ceiling coverings are attached directly to the roof joists. with no positive connection to the interior partitions. This is a popular design, particularly for factory-built homes with panel-type construction. Upon heating of the structure in moderately cold climates, some of these units exhibit an upward bowing of the roof joists resulting in a separation of the ceiling from the interior partitions. A moisture gradient is created by the temperature differential between top and bottom surfaces of the member. Water vapor migrates toward the cold surface causing the upper fibers to elongate which results in an upward bowing of the member. In cases investigated by the Forest Products Laboratory (fig. 1), deflections were measured at a maximum of 5/8 to 3/4 inch at the midspan of nominal 2- by 6-inch joists over a 12-foot span. Moisture content measurements showed the existence of a moisture gradient within the joist ranging from about 8 percent near the ceiling to approximately 12 percent 1 inch down from the roof, resulting in a more than 4 percent differential between the top and bottom surfaces. It was hypothesized that the observed bowing was a result of differential shrinkage caused by the moisture gradient. However, normal shrinkage parallel to the grain could not account for deflections of the magnitude recorded. Wood is an anisotropic material in shrinkage characteristics. Longitudinal shrinkage (parallel to the grain) is quite small, averaging about 0.1 percent for green to ovendry. But shrinkage values in the tangential or radial directions (across the grain) are 50 to 80 times greater. When lumber is cut, its longitudinal axis is not necessarily parallel to the fiber direction. The relationship between fiber direction to the edges of a piece is called slope of grain. The maximum permissible slope of grain values vary with the grade of lumber. For example, the maximum slope of grain permitted for No. 2 stress-graded lumber is 1:8 (4.8 ) (9). 3 The effective longitudinal shrinkage value for a member with significant slope of grain is probably the resultant of longitudinal, tangential, and radial values relative to the axis of the piece. Although knots and compression wood are known to cause crook and bowing in lumber, it seems unlikely that these factors could be present with enough consistency to account for the joist bowing problem as observed. Also, the direction of bowing would depend upon the location of the above defects. 1 Graduate Student, Department of Civil Engineering, Colorado State University, Fort Collins, Colo. 2 Maintained at Madison, Wis., in cooperation with the University of Wisconsin. 3 Underlined numbers in parentheses refer to Literature Cited at the end of this report. 1

4 Three species of lumber were studied to determine the relationship of average slope of grain to the magnitude of bowing which might occur in a member under conditions that create a moisture gradient across the piece. Twenty-six specimens, with varying slope of grain, were subjected to environments that produced different moisture gradients through the depth of each specimen. Deflection readings were taken periodically during the exposure period. Figure 1. Upward bowing of low-pitched roof produced a 3/4-inch gap between ceiling and partition wall during winter. (M ) PAST AND CURRENT WORK Many data have been obtained on the behavior of wood with reference to dimensional changes associated with changes in moisture content (e.g., 2,3). A procedure for establishing shrinkage values is contained in American Society for Testing and Materials standards (1). However, no work has been located which relates dimensional changes to bowing deflections in structural members. 2

5 Forest Products Laboratory reports (4,7) discuss longitudinal shrinkage of wood and indicate shrinkage in any plane should be calculable by trigonometric relations. No data to either prove or disprove this assumption were presented. Roberts (5) conducted a study in 1944 in which he charted the moisture content gradient through a plank in contact with water on one side and free air on the other. No attempt was made, however, to measure internal stresses or deformation resulting from this gradient. Tables are available (8) showing the equilibrium moisture content of wood when exposed to air at a given temperature and relative humidity. Also, much work has been done on predicting the movement of moisture through wood both as hygroscopic moisture and free water. TEST MATERIALS A total of 26 specimens of Douglas-fir, southern pine, and white pine were tested in two groups. The first group (large scale) was made up of nominal 2- by 6-inch by 8-foot members, five Douglas-fir and eight southern pine. The Douglas-fir specimens were planks which had been seasoned prior to selection for use in the test. They were placed in a treating retort and water was introduced under pressure to raise the moisture content above fiber saturation. The pine specimens were cut from green logs immediately prior to testing. Specimens were cut to have a wide range of slope of grain, with one Douglas-fir and two pine specimens selected to have a significant number of knots. All other specimens were cut from relatively clear wood. The second group of specimens (small scale) was made up of Douglas-fir and white pine. Members were 40 inches long, 2 inches deep, and cut from nominal 1-inch board stock to have a varying slope of grain. Five of the Douglas-fir specimens were cut from a single board to attain grain slopes ranging from 1:80 (0.72 ) to 1:4.5 (12.5 ). Three additional specimens, relatively straight-grained, were cut from another board to attain desired knot locations. All five white pine specimens were cut from one board. All members were free of knots and had grain slopes ranging from 1:60 (0.95 ) to 1:4.25 (13.2 ). TEST METHOD The tests were designed to create a moisture content differential across the depth of the test specimen. This differential could then be measured along with the corresponding midspan deflection of the member. The deflection measured could then be compared with the predicted deflection computed from theoretical considerations. At the time of selection for use in the test, the average grain slope on two faces and growth ring orientation (fig. 2) of each member were measured and recorded. Measurements were made with a scribe. The angle relative to the wide face, α, lies in the vertical or bowing plane, while β, is in the horizontal plane. The angle on the end of the specimen, γ, is the direction of growth rings relative to the wide face or vertical axis of the member. Figure 2. Deviation of grain direction relative to the axes of a wood member. (M ) 3

6 Large-Scale Specimens In the large-scale test involving the nominal 2- by 6-inch specimens, the moisture content differential was created by drying. The southern pine specimens were in a green condition initially. The Douglas-fir specimens were first brought to a moisture content well above fiber saturation by pressure treatment with water. After treatment they were wrapped in plastic and allowed to stand for a period of 1 week to allow the moisture content within each member to become relatively constant. The specimens were then covered with three coats of aluminum paint, conforming to Federal Specification TT-P-320a, type I, on three faces and the ends, leaving one of Figure 3. Large-scale specimens supported on stands within a dry kiln. (M ) 4

7 the narrow faces uncoated. The paint served as a vapor barrier during the test, forcing desorption to occur only through the exposed surface. The efficiency of the paint as a vapor barrier was estimated at 80 percent (6). After the paint had cured for a period of approximately 48 hours, the specimens were placed in a dry kiln (fig. 3) with a drybulb temperature of 140 F and an equilibrium moisture content for the wood of 5 percent. The specimens remained in the kiln for a period of 40 days with the moisture gradient and deflection at midspan being recorded at intervals. It was necessary to move the specimens to an outdoor location after this period. The specimens were damaged during a storm after a total of 55 days when the study was terminated. The moisture content within the member was monitored using an electrical resistance moisture meter attached to probes set prior to placing the specimens into the kiln. The probes consisted of No. 6 wood screws which penetrated approximately 3/8 inch into the wood. The holes into which the probes were inserted had been filled previously with a conducting silver paint to prevent resistance buildup at the metal-wood interface. The moisture content was measured at three levels within each member, two readings at each level. The average of the two readings was taken as the representative moisture content at that level. Temperature and species corrections were applied to each reading. Deflections were measured to the nearest 1/100 inch by means of a wire stretched along the original neutral axis of the member and a scale attached to the specimen at midspan. Constant tension was maintained in the wire throughout the test using an 8-ounce weight. Small-Scale Specimens In the test involving the smaller specimens, the moisture differential was created by wetting one of the uncoated narrow faces of the specimen (fig. 4) and leaving the opposite uncoated face open to the air. The wide faces of the specimen were coated with aluminum paint. The specimens were supported in a container with their lower surfaces submersed in water. A fan above the specimens accelerated drying of the upper surface. Moisture content within these specimens was monitored as previously described. Deflection to the nearest 1/1,000 inch was measured using a dial gage mounted on a bar with a span equal to that of the test specimens. The upper surface of the specimens was the reference datum for measurement. Figure 4. Small-scale test specimens with bottom surface in contact with water. (M ) 5

8 METHOD OF ANALYSIS Analysis of the problem is based on the premise that strain-and therefore bowinginduced by a moisture content differential is analogous to that which will occur in a member subjected to a constant moment (fig. 5). The basic relations applying to a member under moment stress are where δ is the maximum bending stress at top or bottom, E is the modulus of elasticity, I is the member moment of inertia, ε/2 is the strain at either the top or bottom surface, is bowing deflection, x is a position measured along the piece length, and M is the magnitude of the moment. Figure 5. Model of specimen where bowing is caused by differential strain due to change in fiber length from a moisture differential across the depth of member. (M ) The first relation is valid only for a symmetrical member with a constant modulus of elasticity. If these conditions are satisfied, the c of the second relation becomes equal to one-half the depth of the member. Since under a constant moment the maximum deflection will occur at x equal to one-half the length of the member, the basic relations may be combined in the form (1) where is the maximum vertical deflection of the member, L is the length of the member, and d is the depth. If free strain is allowed to occur under changing moisture content, the amount of strain may be defined by the shrinkage which occurs when the wood is dried below 30 percent moisture content (fiber saturation). Shrinkage values have been established over the range of 30 to 0 percent moisture content (8) for various wood species. The strain then becomes or from equation (1) where K is the shrinkage coefficient parallel to the member axis, and MC is the difference in moisture content between the top and bottom surfaces. Examination of this equation shows it to be made up of three principal parts: is (2) (3) defined by the dimensions of the member; is a function primarily of the environment surrounding the member; and K is a function of the wood properties and internal geometry of the member. The strain that causes bowing is that which occurs parallel to the longitudinal axis of the member. Average shrinkage values (8) have been established for shrinkage in the three planes; i.e., K L (longitudinal), K R (radial), and K T (tangential). It is assumed that the resultant shrinkage coefficient, K, can be computed for any given direction by trigonometric relations. The resultant shrinkage factor has a component relative to the longitudinal axis of the member and therefore controls bowing strain. Theoretically the resultant of the three shrinkage deformations can be determined by successive rotations of the three vectors into the bowing plane using space analytical geometry. The component of the resultant vector relative to the longitudinal axis in the vertical plane would then become the effective shrinkage coefficient. 6

9 This approach produced only limited success. One major obstacle was that the magnitudes of the three shrinkage coefficients were not accurately known. Also, since the moisture profiles were nonlinear the effective moisture gradient could not be determined directly. The moisture profiles for the small specimens (fig. 6) took the form of compound S curves. They resembled closely the moisture gradient found in Roberts study (5) for 2- inch-thick Douglas-fir specimens after 13 months of conditioning. Maximum deflections and maximum moisture differences were observed after 7 and 11 days for the Douglas-fir and white pine specimens, respectively. The apparent profiles for the large specimens were parabolic (fig. 7). The term apparent is used because electric moisture meters are not highly accurate at moisture contents above fiber saturation. The reverse procedure, drying rather than wetting, was employed to create a gradient. When testing was terminated, about two-thirds of the wood volume was still above fiber saturation. In both cases, the moisture profiles were nonlinear and the effective gradient had to be estimated by some weighted procedure. The member stiffness, or modulus of elasticity, is also known to vary with moisture content (8). Its magnitude is slightly greater than 1 percent for each percent change in moisture content. A method of handling both variables simultaneously was not apparent. The procedure that was finally adopted is partially theoretical and partially empirical. It considers only the slope of grain on the wide face, α, which lies in the bowing plane. Rather than separating the two factors, i.e., the shrinkage value K and the effective moisture gradient MC only the product of the two or total (between top and bottom) strain ε (eq. 2) was used. In this analysis, actual strain measurements were not taken, but were related to observed deflections. Since the magnitudes of the tangential and radial shrinkage coefficients are reasonably close relative to the longitudinal shrinkage, this simplification should not significantly alter results. Figure 7. Apparent moisture profile of large specimens undergoing drying from fiber saturation. (M ) Figure 6. Moisture profile of small specimens with lower surface in contact with water. (M ) 7

10 Since shrinkage is a minimum in the longitudinal direction (α=0) and a maximum in the orthogonal direction (α=90 ), shrinkage and grain direction may be related by basic trigonometric functions. Shifting the axes (abscissa 180 and ordinate -1), and changing the frequency and amplitude to correspond with the above shrinkage limits, suggests relating strain, ε, to slope of grain on the wide face, α, by: or Equation (5) is a functional identity which is a simplified form of equation (4). Regression analyses of test data then related deflection to slope of grain by: = a sin 2 α+ b (6) where is bowing deflection, a is coefficient from least squares analysis (4) b is bowing deflection for straight-grain material, and α is slope of grain on the wide face in (5) degrees. RESULTS AND DISCUSSION Results are presented in table 1. The average slopes of grain for the three faces are given along with the maximum observed bowing deflections. The influence of knots on four specimens was not evident. Large-Scale Specimens The maximum deflection of 0.46 inch on the Douglas-fir 2 by 6 material was measured on the specimen with the greatest slope of grain on the wide face, 9.46 (fig. 8). This corresponds to a slope of 1:6 which is only slightly steeper than that permitted for No. 2 stress-graded lumber. The correlation coefficient, r, between equation (6) and the measured data was quite good, 0.974, but the number of data points was limited. However, extrapolating the equation to α=90 and applying the bowing equation (eq. (1)) yields a shrinkage coefficient of 7.3 percent which agrees with the tangential shrinkage coefficient for Douglasfir listed in the Wood Handbook (8). Bowing is a function of the span length squared, and the maximum observed deflection would have exceeded 1 inch over a 12- foot span. The southern pine specimens did not adapt well to the method of analysis used for the other species. However, there was a definite trend toward an increase in bowing deflection with increase in slope of grain. The maximum observed deflection was in excess of 5/8 inch. The reason for the different behavior for the southern pine specimens is not known. They were the only specimens cut from green logs and were undergoing initial drying. The logs were of relatively small diameter and specimens were cut from an area close to the pith. The effectiveness of the aluminum paint vapor barrier was underestimated. After 55 days of drying, about two-thirds of the wood volume was still above fiber saturation. Small-Scale Specimens Correlation coefficients from the regression curves for the two species of small-scale tests were extremely good (figs. 9 and 10). Data were available to maximum grain angles of only 12.5 and 13.2 for Douglasfir and white pine, respectively. Extrapolating the regression equation, as before, produced shrinkage values of 3.5 percent for Douglas-fir and 4.7 percent for white pine. This agreed quite well with typical moisture content-shrinkage curves for softwoods dried from fiber saturation to about 10 percent moisture content. The absolute moisture contents at times of maximum deflections ranged from about 8.4 percent at the upper surface to fiber saturation at the bottom for all small specimens. The time to maximum deflection with this wetting procedure was 7 days for Douglas-fir and 11 days for white pine. Beyond that time, the specimens continued to absorb additional moisture, but the upper surface also had an increase in moisture content, thus reducing the absolute moisture differential. 8

11 The observed shrinkage coefficients for the small-scale specimens would produce bowing deflections of nearly 1-1/2 inches in nominal 2 by 6 lumber over a 12-foot span. Table 1. Relationship between slope of grain and bowing deflection Specimen No. Average slope of grain Bowing deflection In. Douglas-fir 1-A A A A A Southern pine 5-A A A A A A A A White pine LARGE-SCALE SPECIMENS!, SMALL-SCALE SPECIMENS 1 1-B B B B B Douglas-fir 6-B 7-B 8-B 9-B 10-B 11-B2 12-B2 13-B Large specimens were 2 x 6 in. x 8 ft., over a 92-in. span; small specimens were 1 x 2 x 40 in., over a in. span. 2 Specimens contained significant number of knots.

12 Figure 8. Relationship between slope of grain and bowing deflection for large Douglas-fir specimens. Figure 10. Relationship between slope of grain and bowing deflection for small Douglas-fir specimens. (M ) (M ) Figure 9. Relationship between slope of grain and bowing deflection for small white pine specimens. (M ) 10

13 CONCLUSIONS AND RECOMMENDATIONS A moisture gradient across the depth of a structural member with significant slope of grain will produce undesirable bowing deflections in houses constructed with flat or low-pitched roofs. Three corrective measures would probably minimize the problem; reducing the moisture gradient, selecting straight-grain lumber, and mechanically fastening the ceiling joists to interior partition. Reducing the moisture gradient may be the most difficult. A good ceiling vapor barrier and adequate ventilation should help. This is good construction practice in any event, and should be done to achieve optimum insulation performance. Selecting joists on the basis of slope of grain for this application would not be difficult. The grain angle on the wide face can be determined with a scribe. A maximum slope of grain might be set at 1:16 for flatroof joists, rather than 1:8. Theoretically this would reduce the maximum bowing by a factor of about 4. Mechanically securing the ceiling joists can be accomplished by conventional methods. The magnitude of the tiedown force can be calculated by statics if the span, member size and stiffness, and probable deflection are known. A restraint of about 200 pounds would be adequate for most situations. DEFINITION OF TERMS = regression constants = depth of member (in.) = modulus of elasticity (Ib/in. 2 ) = member moment of inertia (in. 4 ) = resultant shrinkage coefficient parallel to member axis = shrinkage coefficient parallel to grain direction = shrinkage coefficient in radial direction = shrinkage coefficient in tangential direction = length of member (in.) = bending moment (in.-lb) = change in moisture content across depth of member (pct) = slope of grain on wide face (deg.) = slope of grain on narrow face (deg.) = angle of growth rings relative to wide face (deg.) = deflection of member at midspan (in.) = total differential strain between upper and lower surfaces of member (in./in.) 11

14 LITERATURE CITED (1) American Society for Testing & Materials Standard methods for testing small clear specimens of timber. ASTM Standard Desig. D Philadelphia, Pa. (2) Barkas, W. W Recent work on the moisture in wood in relation to strength and shrinkage. For. Prod. Spec. Rep. No. 4 (England). (3) Barkas, W. W The swelling wood under stress. Her Majesty s Stationery Office, London, England. (4) MacLean, J. D Effect of direction of growth rings on the relative amount of shrinkage in width and thickness of lumber and effect of radial and tangential shrinkage on dimensions of round timbers. U.S. For. Prod. Rep. No. R1473. Madison, Wis. (5) Roberts, H. D The moisture content distribution in wood used as a partition between water and air. Div. of For. Prod. Rep. No. 84 (Australia). (6) U.S. Forest Products Laboratory Aluminum coatings for moisture proofing wood. U.S. For. Prod. Lab. Tech. Note No Madison, Wis. (7) U.S. Forest Products Laboratory Longitudinal shrinkage of wood. U.S. For. Prod. Lab. Rep. No Madison, Wis. (8) U.S. Forest Products Laboratory Wood handbook: Wood as an engineering material. USDA Ag. Handb. 72. Rev. Sup. Doc., U.S. Gov. Print. Off., Washington, D.C (9) West Coast Lumber Inspection Bureau Standard grading for West Coast Lumber. WCLIB, Portland, Oreg. * U.S. GOVERNMENT PRINTING OFFICE /