Patent Grant
7610732
This application claims priority to AU Application No. 2004900108, filed 09 Jan. 2004. The entire contents of this application are incorporated herein by reference.
1. Field of the Invention
The present invention relates to the cutting of segmented-end timber webs of the type used in manufacture of roof trusses by the “Turb-O-Web”™ method. In particular, the invention relates to a segmented end shape for the ends of a roof truss web with three or more straight facets to approximate a semi-circular or other part circular end.
2. Description of Related Art
The Turb-O-Web method of roof truss construction—which is the subject of U.S. Pat. Nos. 6,176,060, 6,249,972, 6,415,511 and 6,688,067—offers substantial efficiency gains in the construction of oblique roof trusses for building construction, by adapting the truss construction to use webs having standardised tapered end shapes and, usually, also predetermined incremental lengths. The contents of those patents are incorporated herein by reference.
The preferred end shapes for the Turb-O-Web method are semicircular, but it is possible to use webs having a segmented end shape which approximates a semicircle by a series of 3 or more, preferably at least 5, straight facets at successive angles (usually 5 facets for 70 mm wide webs or 7 facets for 90 mm wide webs). True semicircular ends give the greatest accuracy, but these require specialised cutting machines. Segmented ends consisting of regular (ie. equal angle) half polygons seeking to simulate a semicircular web end may cause an accumulation of small errors over a succession of webs, causing the web-to-chord joint locations to vary somewhat from the locations predicted by the design software which calculates on the basis of semicircular ends. Greater accuracy can be achieved by increasing the number of facets but this requires saws having more blades than is provided for on the most common types of saws.
The present invention relates to a segmented web end shape for use in the Turb-O-Web method, which seeks to result in an average accumulated error in joint location which is within acceptable tolerances.
The present invention provides an elongate, parallel-sided wooden web for a roof truss, said web having at least one end thereof shaped as series of three or more substantially straight facets to approximate a notional part circle having an origin, a radius and an endpoint substantially coincident with an endmost point of said web, wherein said end shape comprises an irregular part polygon having an end point substantially coincident with said endpoint of the notional part circle, and wherein junctions between one or more adjacent facets of said polygon lie outside said notional part circle and a part of one or more facets lie inside said notional part circle.
Preferably, the notional part circle is a semicircle.
Preferably, radius of the notional semicircle is substantially one half of the web width. Preferably also, said irregular part polygon is symmetrical about a centreline of said web.
Preferably, the junctions between said one or more adjacent facets lie substantially on a first semicircular locus concentric with and of greater radius than said notional semicircle, and one or more of said facets are substantially tangential to a second semicircular locus concentric with and of lesser radius than said notional semicircle. Preferably, the radii of said first and second semicircular loci differ substantially equally from the radius of the notional semicircle.
Preferably also, the parallel sides of the web extend beyond a perpendicular line passing through the origin of said notional semicircle to meet with respective adjacent facets of said polygon on said first semicircular locus.
In one form, the end shape has an odd number of facets, including an end facet tangential to the notional semicircle at said intersection point of said web centreline and said notional semicircle, and an even number of intermediate facets each meeting with adjacent facets on said first semicircular locus and being tangential to said second semicircular locus.
Preferably, said end shape with an odd number of facets has 5 or 7 facets, most preferably 5.
In an alternative form, the end shape has an even number of facets, including a pair of end facets meeting on the notional semicircle at said intersection point of said web centre line and said notional semicircle, and an even number of intermediate facets each meeting with adjacent facets on said first semicircular locus and being tangential to said second semicircular locus.
Preferably, said end shape with an even number of facets has 4 or 6 facets.
Further aspects of the invention include a roof truss including at least one of the webs, and a stock of webs including a plurality of said webs having a substantially identical end shape, said plurality of webs having discrete lengths at increments between minimum and maximum web lengths.
Further preferred embodiments will now be further described with reference to the accompanying figures and tables, in which:
Referring to
In the truss construction, the position of the end of one web determines the starting position for the next web (usually working outwards from the centre of the truss), and thus any differences in web length or end radius from that expected by the truss-design software may cause an accumulation of errors affecting the start and end positions and the angle of the webs of the truss.
The wooden roof truss webs 10 have parallel sides 12 and are typically rectangular in cross-section, of the cross-sectional dimensions typically used for roof truss webs, eg. 70 mm by 35 mm for Australia or a nominal 2″ by 4″ board (3½″ by 1½″) for USA. In trusses of the type made in accordance with U.S. Pat. No. 6,176,060, the ends of the webs are formed with a standardised tapered end shape, typically semicircular with a radius equal to the larger of the two cross-section dimensions.
With reference to
The angles and lengths of facets of the end shape are determined by circumscribing an irregular part polygon with the desired number of sides between an inner semicircle 22 of radius ri and an outer semicircle 24 of radius ro, concentric with and equally spaced from the notional semicircle 16.
The included angle at the origin 18 of semicircle 16 between the perpendicular line from the centre of the facet 26 to the origin 18 and the radius from origin to the intersection of the semicircle 16 and the facet 26 is designated as Angle A. The included angle at the origin 18 between the radius from origin to the intersection of the semicircle 16 and the facet 26 and the line from the origin 18 to the edge of the facet 26 is designated as Angle B. The included angle at the origin between both ends of the intermediate facet 26 is equal to 2A+2B.
Referring to
If there are an odd number of facets, as in
If there is an even number of facets, as in
In either configuration the endpoint of faceted end shape will coincide with the endpoint of the notional semicircular end 16. Thus, the overall length between the ends of the web will be the same as that of the equivalent web with true semicircular webs.
Between the end of the extension 12′ of each side 12 of the web and the respective outer edge of the end facet 28 or end facets 30 will be a number of intermediate facets 26 as shown in FIG. 2—ie. facets tangential to the inner semicircle 22 and with junctions between the facets lying on the outer semicircle 24. Each of these intermediate facets 26 will have a total angular extent (ie. the included angle at the origin) of 2A+2B. For a web end with a total of an odd number n of facets, not including the extensions 12′ of the web sides, there will be ½(n−1) of the intermediate facets 26 in each 90° quadrant of the web end. For an even number n of facets in the web end there will be ½(n−2) intermediate facets 26 in each 90° quadrant of the web end.
The angles A, B, and C defining the shape of the irregular polygonal end, and the radii ri and ro of the inner and outer circles from the notional semicircle—defining the maximum deviation of the end shape from the true semicircle—for a given number n of facets are thus determined by the solution to the following set of equations:
cos A=ri/r (1)
cos (A+B)=ri/ro (2)
cos C=r/ro (3)
ro+ri=2r (4)
and, if the number of facets n is odd:
(n−1)A+(n−1)B+2C=90° (5A)
or, if the number of facets n is even:
nA+(n−1)B+C=90° (5B)
where:
It is believed that for a given number of facets there is a unique solution to these equations, and hence a unique irregular polygonal shape satisfying the criteria.
It will be appreciated that the Figures and corresponding description are 2-dimensional representations of a 3-dimensional web end shape of constant shape across the narrow dimension of the web, so that for example each facet is a rectangular face and the junction points between facets are junction lines.
The web end is symmetrical about the centreline 20 of the web, so the other quadrant of the web end is a mirror of that shown. The far end of the web (not shown) will usually be a mirror image of the end shown.
The 5-faceted end shape of
Considering the top 90° quadrant of the faceted end shape of
Table 1 below is a portion of a spreadsheet table showing iterations for calculation of optimal facet angles for the web end of FIGS. 6 and 6A—a 5 facet end shape with a 45 mm (approx. 1¾ inch) radius—and Table 1A is an expanded iteration of a portion of Table 1.
Tables 1 and 1A solve for the facet angles and inner and outer radii for the end shape of
cos A=ri/r (1)
cos (A+B)=ri/ro (2)
cos C=r/ro (3)
ro+ri=2r, and (4)
(n−1)A+(n−1)B+2C=90°, where n=5 and r=45. (5A)
46.00
44.00
12.10
16.96
4.86
11.97
91.76
45.90
44.10
11.48
16.10
4.62
11.36
87.12
45.96
44.04
11.86
16.62
4.76
11.73
89.94
The rows of Tables 1 and 1A shown in bold give the closest fit.
It can be seen that the best solution for a 5-faceted end is found where Angle A is approximately 11.86 degrees, Angle B is approximately 4.76 degrees and Angle C is approximately 11.73 degrees, giving the 5-faceted web end a maximum deviation from the radius r of the semicircle of less than 1 mm for a 90 mm wide board. Even greater accuracy can be achieved if the angles of the cutting of the facets can be more closely controlled, but in practice this is well inside the allowable tolerances for cutting of the webs. Furthermore, the maximum deviations from the semicircular are of equal amounts either side of the true radius, and thus when assembling a roof truss with such webs the deviations will tend to average each other out, for example when a peak the end of one web abuts with the flat facet surface on the end of the adjacent web.
cos A=ri/r (1)
cos (A+B)=ri/ro (2)
cos C=r/ro (3)
ro+ri=2r, and (4)
nA+(n−1)B+C=90°, where n=6 and r=45. (5B)
45.70
44.30
10.12
14.22
4.10
10.04
95.35
45.60
44.40
9.37
13.17
3.81
9.30
88.34
45.68
44.32
9.97
14.02
4.04
9.90
89.87
The rows of Tables 2 and 2A shown in bold give the closest fit.
It will be noted that where there is in total an even number of facets employed, such as in
The following Table 3 is a summary table of the construction Angles A, B and C for a number of different faceted end configurations for a 90 mm wide web.
For a given number of facets n, the angles A,B and C defining the end shape will stay the same regardless of the radius r, with the maximum deviation from the semicircular varying proportionally to the radius r.
An advantage of the present invention is that it allows acceptable tolerance to be reached with as few cuts as possible, for example with 5 facets on the 3½ inch wide webs commonly used in USA. In conjunction with the Applicant's co-pending Australian Patent Application No 2004900109 filed 9 Jan. 2004—which teaches a 2-pass technique for cutting a 5-faceted end shape using a saw of the type conventionally employed by roof truss manufacturers to cut conventional custom angle cut webs, adoption of the Turb-O-Web system is further simplified. The contents of that patent application are incorporated herein by reference.
Furthermore, as the Turb-O-Web method uses a replicated end shape for the webs of the roof truss, once the number of facets to be used and width of timber are decided upon and the saw angles set accordingly, the saw angles need not be changed. This makes the web cutting task amenable to implementation by an older style saw, without electronic control, as a dedicated web cutting saw. Such saws are available cheaply as adjustment of the cutting angles of such saws is slow, but this is not a consideration in the present case, as the cutting angles may be set either permanently or by use of a template. Great accuracy can be attained, as the saw angles can be set permanently or semi-permanently and the length varied to cut batches of different length webs Web cutting according to the invention is also amenable to cutting by saws having limited electronic control capabilities, such as those having electronic control and adjustment of length but manual adjustment of the blade angle.
In this specification, the word “comprising” is to be understood in its “open” sense, that is, in the sense of “including”, and thus not limited to its “closed” sense, that is the sense of “consisting only of”. A corresponding meaning is to be attributed to the corresponding words “comprise, comprised and comprises where they appear.
While particular embodiments of this invention have been described, it will be evident to those skilled in the art that the present invention may be embodied in other specific forms without departing from the essential characteristics thereof. The present embodiments and examples are therefore to be considered in all respects as illustrative and not restrictive, the scope of the invention being indicated by the appended claims rather than the foregoing description, and all changes which come within the meaning and range of equivalency of the claims are therefore intended to be embraced therein. It will further be understood that any reference herein to known prior art does not, unless the contrary indication appears, constitute an admission that such prior art is commonly known by those skilled in the art to which the invention relates.
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| Number | Date | Country | |
|---|---|---|---|
| 20050166522 A1 | Aug 2005 | US |
