METHOD FOR CONSTRUCTING A TRUSS FROM SELECTED COMPONENTS
The present disclosure includes a truss and a method for selecting components to construct a truss. The truss includes three or more chord elements (two or more upper chord elements and one or more lower chord elements) and one or more web elements. Embodiments of methods according to the disclosure include estimating a first change in length for each of the two or more upper chord elements and estimating a second change in length of each of the one or more lower chord elements, the first change in length and the second change in conditions to which the truss is exposed. The method may also include selecting the one or more web elements from the plurality of wood members such that it compensates for deformation caused by the first change in length and the second change in length.
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This application is a divisional application entitled to and claiming the benefit of priority from U.S. NONPROVISIONAL patent application Ser. No. 12/492,546 filed Jun. 26, 2009, and titled “METHOD FOR CONSTRUCTING A TRUSS FROM SELECTED COMPONENTS,” the contents of which are incorporated herein by reference.
TECHNICAL FIELDThe present disclosure is directed generally to trusses and methods for selecting components for constructing truss structures.
BACKGROUNDTrusses are pre-manufactured structural roof components which support the roofing and carry the top floor ceilings. Wood trusses are widely used in single and multi-family residential, institutional, agricultural and commercial construction. Their high strength-to-weight ratios permit long spans, offering greater flexibility in floor plan layouts. They can be designed in almost any shape or size, restricted only by manufacturing capabilities, shipping limitations and handling considerations.
A common problem associated with trusses made from wood is a phenomenon known as trust uplift. Truss uplift is a deformation of the truss structure, normally caused by a moisture differential between the lower chord element 106 and the upper chord elements 102. Because wood is a hygroscopic material, it can expand and contract due to changes in temperature and/or humidity, resulting in a change in length of the truss components.
Conditions contributing to uplift may include rain, wind, seasonal changes, or other factors influencing the moisture content of each truss component. In addition, components of truss structures may also be exposed to moisture changes during transportation or construction. Over time, the resulting dimensional changes of the truss components can lead to significant deformation of the overall truss structure. In a residential construction application, the lower chord element 106 often lifts in the winter and lowers again in the spring. When trusses arch up, they take the dry wall and ceiling with them, which can cause visible cracking. As the trusses dry out with the warm summer air, they can drop back down closing most of the cracks. This cracking is upsetting to a homeowner, as most homeowners might assume that there are structural problems with the house.
Both the wood products industry and the construction industry have taken steps to minimize truss uplift and other problems associated with the expansion or shrinkage of truss components. One solution is to avoid connecting the truss directly to the wall partitions. Instead the builder can connect the truss with an ‘L’ bracket (known as a “truss clip”) or strap, which allows vertical movement of the truss. An example of this solution is described in U.S. Pat. No. 5,560,156 and U.S. Pat. No. D318,359, which are hereby incorporated by reference. Another technique commonly practiced by wood products manufacturers is to grade lumber according to its strength and select only the strongest lumber to be sold as the upper chord elements 102 and the lower chord elements 106. Although the purpose of this lumber selection technique relates primarily to strength, selecting stronger chord elements may also reduce uplift.
One drawback of known solutions for truss uplift is that many of them involve alterations to the construction of the house. Additionally many are remedial in nature as opposed to preventative. Therefore, the wood product manufacturer has very little control over the perceived performance of the products sold for truss construction. Thus, there is a need to develop a new method that enables wood product manufacturers to select components for constructing trusses with minimized susceptibility to uplift.
SUMMARYThe following summary is provided for the benefit of the reader only and is not intended to limit in any way the invention as set forth by the claims. The present disclosure is directed generally towards truss structures and methods for constructing truss structures.
In one embodiment, a sample of lumber is provided and measurements are conducted to predict a value representing dimensional instability (e.g., predicted percent shrinkage rate, coefficient of hygroscopic expansion, coefficient of thermal expansion, estimated change in length) for each piece in the lumber sample. Accordingly, a distribution of the values representing dimensional instability for the sample of lumber is generated. The deformation of truss shape due to dimensional instability may be evaluated using models (e.g., finite element models, geometric models, static deflection analysis). Alternatively, empirical measurements can be made of truss deformation due to dimensional instability. Models according to embodiments of the disclosure may be used to determine a threshold for a value representing dimensional instability based on minimizing truss uplift. Lumber in the sample having a value representing dimensional instability below the threshold value is selected and lumber having a value representing dimensional instability above the threshold value is either diverted for use in other wood products or scrapped.
In other embodiments, lumber for the web elements may be selected using a model to determine an optimal value representing dimensional instability for the web elements based on the predicted change in length of the chord elements. In one embodiment, the distribution mentioned above is divided into three ranges: a first range, a second range, and a third range. Lumber within the second range generally has a higher value representing dimensional instability than lumber within the first range. Lumber within the third range generally has a higher value representing dimensional instability than lumber within the second range. In some embodiments, the web elements are selected from the lumber in the second range, the chord elements are selected from the lumber in the first range, and the lumber within the third range is scrapped or diverted. In some embodiments, the first range, the second range, and the third range are all different. In some embodiments, there may be some degree of overlap between the ranges.
In yet another embodiment, the distribution mentioned above is divided into four ranges: a first range, a second range, a third range, and a fourth range. Lumber within the first range generally has the lowest value representing dimensional instability and lumber within the fourth range generally has the highest value representing dimensional instability. Lumber within the third range generally has a higher value representing dimensional instability than lumber in the fourth range. In some embodiments, the web elements are selected from the lumber in the third range, the chord elements are selected from the lumber in the first range, and the lumber within the second and fourth ranges is scrapped or diverted. In some embodiments, the first range, the second range, the third range, and the fourth range are all different. In some embodiments, there may be some degree of overlap between the ranges.
Further aspects are directed towards trusses constructed using methods described in the disclosure. Embodiments of a truss structure according to the disclosure are enclosed structures made from two or more upper chord elements and one or more lower chord elements. The two or more upper chord elements and the one or more lower chord elements may be arranged in a single plane and connected end-on-end to form an inverted V structure. One or more web elements may be arranged inside the enclosed structure and connected to the chord elements. In embodiments according to the disclosure, the one or more web elements have values representing dimensional instability that are lower, on average, than the values representing dimensional instability for the two or more upper chord elements.
The present disclosure is better understood by reading the following description of non-limitative embodiments with reference to the attached drawings wherein like parts of each of the figures are identified by the same reference characters, and are briefly described as follows:
The present disclosure describes truss structures and methods for selecting elements for constructing truss structures. Certain specific details are set forth in the following description and
In this disclosure, the term “wood” is used to refer to any organic material produced from trees, shrubs, bushes, grasses or the like. The disclosure is not intended to be limited to a particular species or type of wood. The term “chord elements” is used to refer to the outer members forming an enclosed structure for any type of truss configuration. The term “web elements” is used to refer to inner members arranged within the truss. The term “coefficient of expansion” is used to refer to dimensional change (e.g., shrinking or expansion) of a wood member due to a change in a condition to which the wood member is exposed. The condition may relate, for example, to changes in moisture, changes in relative humidity, changes in temperature, or any other variable which may affect the dimensions of a wood member. Equation 1 represents an expansion coefficient (c) where L is the length of the wood member and V is a variable representing a condition to which the wood member is exposed.
As stated above, the variable V may relate to any condition which may affect the dimensions of the wood member. For example, if the variable is moisture, ε may be referred to as a hygroscopic expansion coefficient. If the variable is temperature, ε may be referred to as a thermal expansion coefficient.
Methods according to the disclosure involve strategies for selecting truss components (e.g., the upper chord elements 102, the web elements 104, and the lower chord element 106) from a sample of lumber pieces. According to embodiments of the disclosure, the first step involves predicting dimensional instability of each piece of lumber in the sample. Some methods for predicting dimensional instability are described, for example, in U.S. Pat. No. 6,305,224, U.S. Pat. No. 7,017,413, U.S. Pat. No. 7,324,904, and U.S. Pat. No. 7,383,730, which are hereby incorporated by reference. In addition, other methods for predicting dimensional instability known to those of ordinary skill in the art may be used. Dimensional instability may be quantified as change in length, percent shrinkage, coefficient of hygroscopic expansion, coefficient of thermal expansion, or any other measure of dimensional instability known to one of ordinary skill in the art.
In some embodiments of the disclosure, the next step involves constructing a model of truss deformation given the lengths or length-changes of each truss member under a set of conditions. Models according to the disclosure may be used to guide selection of the lumber pieces from the sample. There are many different shapes and configurations for truss structures, and models may vary based on the geometry of the truss being constructed. An example of truss configurations may be found in The Encyclopedia of Trusses published by Alpine Engineered Products Inc. and available at http://www.alpeng.com/images/stories/pdfs/EOT.pdf. In addition, models according to the disclosure may also be based on other truss configurations known to those of ordinary skill in the art.
According to embodiments of the disclosure, the uplift at various locations on the truss 300 can be calculated given the length of the truss components. In this example, truss uplift is calculated with respect to the center web element (the second web element 310); however, numerous other calculations are envisioned within the scope of this disclosure. Although this example illustrates a truss having a relatively simple geometry and a geometric model is used, models according to embodiments of the disclosure may also be constructed for more complicated truss structures. In addition, models according to embodiments of the disclosure may be modified to include dead loads and live loads acting as forces on the truss structure. Accordingly, many different types of models may be used to evaluate expansion. Geometric models, finite element analysis, static deflection analysis, or any other method known to those of ordinary skill in the art may be applied to create more sophisticated models according to the disclosure.
Referring back to
In Equation 2, θ is the first angle 314, L1 is the distance between the point first point 322 and the third point 326, L2 is the distance between the second point 324 and the third point 326, and L3 is the distance between the first point 322 and the second point 324. The second angle 316, the third angle 318, and the fourth angle 320 may be calculated according to the same procedure. The sum of the first angle 314, the second angle 316, the third angle 318, the fourth angle 320, and a fifth angle 332 (also known as the “lift angle”) around the second point 324 should equal 360 degrees. Thus, the fifth angle 332 can be calculated according to Equation 3:
λ=2π−(θ+φ+ψ+σ) Equation 3
In Equation 3, θ is the first angle 314, φ is the second angle 316, ψ is the third angle 318, σ is the fourth angle 320, and λ is the fifth angle 332. Once λ is known, the uplift at the second point 324 may be calculated according to Equation 4:
In Equation 4, λ is the fifth angle 332 and L2 is the distance between the point first point 324 and the third point 326. Using this model, the impact of changes in the lengths of various truss components resulting from a change in a condition affecting the dimensions of the truss 300 may be evaluated. If a wood products manufacturer has a sample of lumber with known or estimated expansion properties, models can be used to estimate the resulting uplift under a given set of conditions or a change in conditions for truss constructions using various configurations of different pieces of lumber. Accordingly, the wood manufacturer may select pieces of lumber for the web elements (308, 310, and 312) which compensate for the change in length of the chord elements (302, 304, and 306), thereby minimizing uplift of the truss 300.
Models according to the disclosure may be used to establish selection criteria for truss components from a given sample of lumber.
In this example, all lumber having a predicted percent shrinkage below a threshold value indicated by a line 500 is selected for truss construction. The lumber selected may be used for either the chord elements or the web elements of a truss. Generally half of the lumber may be selected while the other half is diverted or scrapped. Those of ordinary skill in the art will appreciate that the line 500 is merely an example of a threshold value and that other values may be used. The lumber pieces having a predicted percent shrinkage rate higher than the threshold value may be diverted for use in producing other wood products or scrapped. The threshold value is based on using models according to embodiments of the disclosure to predict uplift when components having varied predicted shrinkage rates within the population are selected.
In some embodiments, lumber for the web elements is selected based on its ability to compensate for the predicted shrinkage of lumber selected for the chord elements.
In Equation 5, ε2 is the coefficient of hygroscopic expansion for the first upper chord element 702, L1 is the length of the second lower chord element 708, L2,0 is the initial length of the first upper chord element 702, and L3,0 is the initial length of the web element 710. By repeating this method for numerous components of multiple trusses, one can derive a table showing the optimal coefficient of hygroscopic expansion for the web element 710 based on a given coefficient of hygroscopic expansion for the first upper chord element 702. Table 1 is an example of such a table.
Although Equation 5 and Table 1 illustrate methods according to embodiments of the disclosure with respect to a King Post truss, similar methods may be applied to the various other truss configurations. Thus, different optimal pairs may be obtained. In addition, pairings may be made with respect to coefficient of expansion other than the coefficient of hygroscopic expansion (e.g., coefficient of thermal expansion).
In addition to the methods described above, the disclosure also relates to trusses constructed using methods described in the disclosure. Embodiments of a truss structure according to the disclosure include enclosed structures made from two or more upper chord elements and one or more lower chord elements. The two or more upper chord elements and the one or more lower chord elements may be arranged in a single plane and connected end-on-end to form an inverted V structure. One or more web elements may be arranged inside the enclosed structure and connected to the chord elements. In embodiments according to the disclosure, the one or more web elements have values representing dimensional instability that are lower than the values representing dimensional instability for the two or more upper chord elements. The values representing dimensional instability may be, for example, a coefficient of expansion. In some embodiments, the one or more web elements have values representing dimensional instability that are higher than the values representing dimensional instability for the one or more lower chord elements.
In a roof structure made with trusses according to embodiments of the disclosure, the one or more web elements have values representing dimensional instability that are higher, on average, than the values representing dimensional instability for the two or more upper chord elements. In some embodiments, the one or more web elements have values representing dimensional instability that are higher, on average, than the values representing dimensional instability for the one or more lower chord elements. Roof structures made according to some embodiments of the disclosure are expected the exhibit less uplift than trusses made from randomly selected lumber. In addition, selecting lumber in accordance with some methods within the scope of the disclosure may improve truss stability while at the same time maximizing utilization of lumber having properties which are perceived to be undesirable for truss construction.
From the foregoing, it will be appreciated that the specific embodiments of the disclosure have been described herein for purposes of illustration, but that various modifications may be made without deviating from the disclosure. For example, methods according to embodiments of the disclosure may be used to construct truss configurations not explicitly illustrated in the disclosure. In addition, the ranges shown in
Aspects of the disclosure described in the context of particular embodiments may be combined or eliminated in other embodiments. For example, methods illustrated in
The following example will serve to illustrate aspects of the present disclosure. The examples are intended only as a means of illustration and should not be construed to limit the scope of the disclosure in any way. Those skilled in the art will recognize many variations that may be made without departing from the spirit of the disclosure.
ExampleA simulation study was conducted to compare the distribution of truss uplift calculations for four different truss member selection strategies. Strategy A simply involved random placement of mill-run lumber into the truss design. Strategies B, C, and D are all examples of methods according to embodiments of the disclosure.
The first step for the simulation study involved predicting the dimensional instability of a population of lumber pieces from which truss components will be selected. In this example, the lumber included 56 pieces having nominal dimensions of 2 inches by 4 inches by 16 inches from Plymouth, N.C. The dimensional instability of each piece of lumber was assessed by measuring the initial length, length change, and moisture content of each piece when moved from a 65% relative humidity equilibrium condition to a 20% relative humidity equilibrium condition. Equation 6 shows the formula used for calculating c, the linear coefficient of hygroscopic expansion:
In Equation 6, L65 is the length at 65% relative humidity. L20 is the length at 20% relative humidity. M65 is the moisture content at 65% relative humidity. M20 is the moisture content at 20% relative humidity.
Prediction models of dimensional instability were developed based on measures of acoustic velocity using methods known to those of ordinary skill in the art. Examples of methods used are described, for example, in U.S. Pat. No. 7,017,413.
The next step involved generating a distribution of computed truss uplifts based on selecting components for trusses using methods according to embodiments of the disclosure. Strategy B involved selecting truss components according to an example of embodiments described in
Strategies C and D involved evaluating models according to embodiments of the disclosure to determine the optimum placement of components in a modified Howe truss structure (see
Strategy D involved selecting truss components according to an example of embodiments described in
An algorithm was used to generate distribution plots of resulting truss uplifts for each strategy.
1. Randomly select linear hygroscopic expansion values, εi, from Fout for all chord elements.
2. Randomly select linear hygroscopic expansion values, εi, from Fin for all web elements.
3. Calculate the expanded length, Li=L0i+L0i·εi, of each truss component, where L0i is the initial length of component i.
4. Use the set of expanded lengths {Li} and the law of cosines to calculate the interior angles
5. Calculate the lift angle (e.g., λ=2π−(θ+φ+ψ+σ)
6. Calculate truss lift by:
7. Repeat steps 1-6 to generate a distribution of lift values.
Claims
1. A truss structure comprising:
- an enclosed structure, the enclosed structure comprising: two or more upper chord elements, the two or more upper chord elements being arranged in a single plane and connected end-on-end to form an inverted V structure, the inverted V structure having a first end, a second end, and a middle point located between the first end and the second end; and one or more lower chord elements, the one or more lower chord elements being arranged to connect the first end to the second end to form the enclosed structure; and
- one or more web elements arranged inside the enclosed structure, the one or more web elements connecting the two or more upper chord elements to the one or more lower chord elements;
- wherein the one or more web elements and the two or more upper chord elements each have values representing dimensional instability, the values representing dimensional instability of the one or more web elements being higher, on average, than the values representing dimensional instability for the two or more upper chord elements.
8. The truss of claim 1 wherein the one or more lower chord elements each have values representing dimensional instability, the one or more web elements values representing dimensional instability being higher, on average, than the values representing dimensional instability for the one or more lower chord elements.
9. The truss of claim 1 wherein the values representing dimensional instability are expansion coefficients.
10. The truss of claim 1 wherein the truss has a computed uplift between approximately 0.05 inches and approximately 0.60 inches.
11. The truss of claim 1 wherein the truss has a computed uplift that is less than about 0.10 inches.
12. The truss of claim 1 wherein the one or more web elements extend from the middle point to a middle point on one of the one or more lower chord elements or the one or more web elements extend from any point on the inverted V structure other than the middle point to any point on the one or more lower chord elements.
13. The truss of claim 1 wherein the two or more upper chord elements, the one or more lower chord elements, and the one or more web elements are lumber.
14. The truss of claim 1 wherein the truss has a shape, the shape being selected from the group consisting of a Howe truss, a King Post truss, a Queen Post truss, a Fink truss, a Double Fan truss, a Modified Queen truss, a Double Fink truss, a Double Howe truss, a Modified Fan truss, a Triple Fink truss, a Triple Howe truss, a Vault truss, a Coffer truss, a Cathedral truss, a Clear Story truss, Double Cantilever truss, a Tri-bearing truss, a Modified Queen Scissors truss, and a modified Howe Scissors truss.
Type: Application
Filed: Apr 5, 2013
Publication Date: Sep 12, 2013
Applicant: WEYERHAEUSER NR COMPANY (Federal Way, WA)
Inventor: John E. Jones, III (Seattle, WA)
Application Number: 13/857,845
International Classification: E04C 3/17 (20060101);