S-TIMBER for Structural Timber Design and Analysis - by S-FRAME

Wood shrinks anisotropically as it loses hygroscopic moisture. While longitudinal shrinkage lumber products can be modeled best using the model of inc to the grain is nearly negligible in normal wood, transverse shrinkage across the grain is significant and characterized as tangential and radial shrinkage. The application of average tangential shrinkage values to a rectangular cross section results in errors, especially for boards cut from near the center of the log.

In addition, using a Cartesian coordinate system to calculate shrinkage cannot provide an estimate of cup. Calculating shrinkage and cup deformation using a previously developed model, this Excel model can provide a more realistic image of the final cross section and a more accurate estimate of shrinkage. The model is dependent on wood species, initial and final moisture contents, and location of the board within the log.

This paper describes and illustrates uses of the model. The utilization of sawn lumber generally requires that it be dried from its natural, high-moisture content condition. Wood shrinks by different amounts depending on the grain orientation, species, and by the decrease in moisture content MC. Shrinkage along the grain in normal wood is small enough to be ignored, while radial shrinkage the direction from pith to bark is about half that of tangential shrinkage the direction parallel to the growth rings and perpendicular to the radial direction.

This anisotropic shrinkage of wood often results in unwanted deformation of lumber, both during manufacture and while in service. It is the result of a much greater tangential shrinkage than radial shrinkage.

Larger tangential shrinkage than radial shrinkage causes flat-sawn boards boards in which the annual lumber products can be modeled best using the model of inc are approximately tangent to the wide face to cup toward the bark during drying, unless they are restrained. Flat-sawn lumber cut near the pith will tend to cup more than a similar board cut near the bark because the curvature of the growth rings is greater near the pith.

For the same reason, flat-sawn lumber from small-diameter trees will be more cup-prone than lumber from larger trees. Restraint to minimize deformation during kiln drying is commonly achieved by the weight of the lumber stacked above, and some operations place additional top weights to minimize warp in the upper layers of drying lumber. Using good lumber stacking practices is the best way to minimize cup during the kiln drying process.

Dry kiln schedules can also influence the development of cup by impacting the wood viscoelastic properties and having mechano-sorptive effects. Lumber with excessive cup may not completely achieve a smooth surface during planing, or the pressure of the planer rollers may split the severely cupped board. Additionally, cup can be reduced by not over drying the lumber during the kiln process.

These values are often used to calculate an estimate of the expected dimensional changes as wood moisture decreases or increases using the following equation Hoadley. This calculation assumes that the radial and tangential shrinkages occur parallel to the lumber surfaces. As a result, it has a built-in error in calculating the change in dimension, as it ignores the curvilinear nature of the growth rings. An additional deficiency is that this model of shrinkage is not able to predict cup.

Leavengood developed an Excel spreadsheet that estimates the dimensional change in wood with moisture loss or gain using a related approach, but does not provide an indication of cup magnitude.

Ormarsson et al. A model that estimates the amount of cup that develops in drying lumber was initially developed by Bookerand further modified and verified by Xiang et al. The objective of the current work was as follows: 1 develop a user-friendly version of the Booker-Xiang model; 2 demonstrate the application of the model; and 3 provide a graphic representation of the model results.

This was done using an Excel spreadsheet to calculate and graph the cross section distortion that occurs during moisture loss or gain because of the anisotropic shrinkage or swelling that potentially results in cup formation. This visualization will help manufacturers, lumber users, and consumers to better understand the possible development and magnitude of cup and dimension change.

As this approach does not consider visco-elastic and mechano-sorptive effects that would tend to reduce cup, the results represent a worst case scenario as if the wood were dried without external restraint.

To use this Excel spreadsheet model, the user needs to input seven pieces of information: 1 initial board width; 2 initial board thickness; 3 x-y Cartesian coordinates of the board center board centroid ; 4 initial moisture content; 5 final moisture content; 6 species of wood; and 7 diameter of log.

Based on this input, the model determines the perimeter points of the lumber and produces lumber products can be modeled best using the model of inc visual graphic of the lumber lumber products can be modeled best using the model of inc profile and placement within the log using an x-y coordinate grid that assumes Lumber Products Inc Tualatin Oregon Quest the origin is the log pith Fig.

The model uses the original size and position in the log which determines ring orientation to model the shrinkage. In modeling the lumber shrinkage, the following assumptions are made: 1 growth rings are circles that all have the same center, which coincides with the pith of the log; 2 radial shrinkage occurs toward the pith along a line from the pith to the outer circle, where the latter coincides with the outside of the log; and 3 tangential shrinkage is perpendicular to radial shrinkage and occurs toward the centroid of the lumber cross-section.

Species and their total green to oven-dry radial and tangential shrinkage values were obtained from the USDA Wood Handbook for the domestic and foreign wood species listed there. These were imported into the spreadsheet model, and the appropriate shrinkage values are lumber products can be modeled best using the model of inc based on the species selected by the user.

To account for the curvature of the growth rings and the imperfect estimations that result when tangential and radial shrinkage values are applied to rectangular dimension lumber, Booker et al. Modifications of that approach by Xiang et al. The current study uses the improved technique developed and described by Xiang et al.

Before perimeter points are adjusted, however, the amount of fractional radial and tangential shrinkage is calculated, based on the total amount of shrinkage possible for the species and the moisture content change that has occurred.

Equations 1 and 2 found in Table 1 describe this calculation. Next, tangential shrinkage along the growth rings is taken into account.

Whereas the previous radial shrinkage moves all points toward the pith, tangential shrinkage is toward the line drawn through the board centroid and the origin. Table 1. Consider the board shown in Fig. When the board is shrinking, tangential movement will occur along the growth rings toward OC by a value equal to the fractional tangential shrinkage, excluding the radial shrinkage previously applied isometrically.

The final step is to convert the polar coordinates given by Eqs. The new coordinates, showing the now distorted shape of the cupped or crowned lumber, are plotted along with the original shape.

Cross-section of board showing points on perimeter relative to the centroid of the board. The first two lines of output are the published percent total tangential The next two rows of output give the average board width 9. The output includes the actual board percent dimensional change for both width The former pair reflect the actual percent shrinkage based on the initial and final moisture content input, while the latter pair represent the total shrinkage if dried to the oven-dry condition.

This output pair can be compared to the published values for the total radial and tangential shrinkage for the modeled species, and are shown to differ because of the curvature of the growth rings and natural variability. Thus, they are in near agreement with either flatsawn or quartersawn boards annual rings are approximately perpendicular to the wide face of the board that are distant from the pith, as shown for the flatsawn board Table 2whose exhibited total average percent width shrinkage was From Table 2, for the flatsawn board, these values were 0.

Table 2. Because the model assumes that shrinkage occurs linearly with the loss of moisture below the FSP, in similar fashion, the model predicts that the resulting amount of cup as a function of decreasing moisture content is also linear. The model can be used to compare the magnitude of cup that develops depending on where it is sawn from the log.

Figure 2 shows four flatsawn overcup oak Quercus lyrata boards modeled as having their centroids at distances of 0. The predicted amount of cup increases more than threefold as the board center moves from near the bark inward toward the pith.

The relative amount of cup that will be developed depending on product size and location can be predicted by the model. The amount of cup versus the green width of dimension lumber was modeled for 1 flatsawn lumber near the pith; 2 flatsawn lumber near the bark; 3 quartersawn lumber; and 4 for the bastard sawn board that lies between the quartersawn and flatsawn boards.

Figure 3 illustrates that cup increases with increasing lumber width, that quartersawn lumber exhibits minimal cup, and that flatsawn lumber from near the pith was much more prone to cup than flatsawn lumber sawn from near the bark.

This has implications in lumber products can be modeled best using the Lumber Products Can Be Modeled Best Using The Model Of model of inc of being able to produce a dimension product that cleans up in the planer: severe cup may prevent the lumber from being planed on both sides. Boards that are cupped excessively might also split in the planer.

Different species of wood can also be modeled to predict the potential magnitude of cup that may develop in pieces that are located the same distance from the pith. As mentioned previously, many process factors will influence the development of cup; the model only predicts the potential of cup based on the magnitude and difference between the tangential Lumber Products Can Be Modeled Best Using The Model Of Online and radial shrinkages, board location, and moisture content change.

Species having a larger cup potential will require that good stacking practices are employed. The effects of swelling from the adsorption of moisture can also be estimated by the model.

Assuming that the top of the installed flatsawn board was the side nearest the bark, the result of moisture gain lumber products can be modeled best using the model of inc the accompanying swelling is the development of crown the top surface is convex.

Table 3. Booker, R. DOI: Forest Products Laboratory Hoadley, R. Leavengood, S. Ormarsson, S. Simpson, W. Xiang, Z. Article submitted: March 10, ; Peer review completed: May 22, ; Revised version received and accepted: June 2, ; Published: June 15, Modeling the cupping of lumber.

Mitchell, P. Abstract Wood shrinks anisotropically as it loses hygroscopic moisture. Use and Assumptions of the Booker-Xiang Shrinkage Model for Cupping To use this Excel spreadsheet model, the user needs to input seven pieces of information: 1 initial board width; 2 initial board thickness; 3 x-y Cartesian coordinates of the board center board centroid ; 4 initial moisture content; 5 final moisture content; 6 species of wood; and 7 diameter of log.

Methods To account for the curvature of the growth rings and the imperfect estimations that result when tangential and radial shrinkage values are applied to rectangular dimension lumber, Booker et al. Example of Model Input and Output Variables for Two Southern Red Oak Quercus falcata Boards Because the lumber products can be modeled best using the model of inc assumes that shrinkage occurs linearly with the loss of moisture below the FSP, in similar fashion, the model predicts that the resulting amount of cup as a function of decreasing moisture content is also linear.

Shrinkage actually varies between trees of the same species, within trees, and even within growth rings. Model results are therefore likely to differ from actual samples. The model approximates growth rings as being circular. Actual growth rings generally deviate from being perfect circles. Juvenile wood or abnormal compression and tension wood is not considered in the model.

Also, sloping grain or cross grain is not taken into account. A uniform moisture content is assumed throughout the wood, both in the initial and final states. Modeling of cup assumes that the wood is free of any restraint lumber products can be modeled best using the model of inc that the wood is completely an elastic material.

The calculated value of cup represents the potential maximum amount of cup if these forces are absent. It employs a polar coordinate system and thus produces a more accurate picture of shrinkage and shows the development of cup. The model has the ability to estimate and graphically illustrate shrinkage and cup as dependent on board location within the log, change in moisture content, change in product size, and differences between species.

The model was tested on a large log mill in British Columbia producing export products. It is shown that the model responds to market changes using sawing pattern selection and altered log. into lumber or other end products, as well as the cost of buying logs and sawing logs into lumber. It must be stressed that lumber yield from a log is secondary to lumber quality. Each log placed on the sawmill deck must be evaluated and sawn to produce the most valuable end products possible. Th is process starts by determining the bestCited by: 1. Use S-TIMBER to model and analyze mass timber and hybrid timber structures (Timber-Concrete-Steel models). Run a performance assessment on any timber design. Dimension Lumber; Glued-Laminated Timber (Glulam) Cross-Laminated timber (CLT) Timber Shearwalls; Timber Diaphragms systems.

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