Method of designing a corrugated sheet and corregated sheet obtained

Abstract

Method for designing a corrugated roofing sheet made of natural fibers, impregnated with bitumen including a uniform pattern of mutually parallel alternating corrugations borne by a mid-plane, the corrugations defining rounded crests each separated from the next by a rounded trough, the crests and trough being connected by alternately inclined portions, the transverse offset between two successive crests being equal to the transverse offset between two successive troughs and defining the pitch P of the corrugations, the sheet having a thickness E of material substantially constant over its extent, and a height H being twice the distance between the mid-plane and the exterior surface of a crest or twice the distance between the mid-plane and the exterior surface of a trough, these two distances being identical. The height, thickness and pitch values are determined by Fi<H.sup.3/(8?E?(H+P))<Fs, where Fi=25 mm and Fs=35 mm.

Claims

1. A method of designing a bitumen-impregnated natural-fiber corrugated roofing (1) sheet, where said sheet has a uniform pattern of mutually parallel alternating corrugations borne by a mid-plane (4), and said alternating corrugations are defined, in the vertical and cross section of the sheet, as rounded crests (2) each separated from the next one by a rounded trough (3), the crests and troughs being connected by alternately inclined portions (5, 5), the crests (2) being above the mid-plane (4) and the troughs (3) below the mid-plane (4), the inclined portions (5, 5) cutting the mid-plane (4) at the middle thereof by having a part above the mid-plane and a part below the mid-plane, the transverse spacing between two successive crests (2) being equal to the transverse spacing between two successive troughs (3) and defining the pitch P of the corrugations, the sheet (1) having a thickness E of material substantially constant over its extent, the sheet having a height H defined as being twice a first distance between the mid-pane (4) and the external surface of a crest (2) or twice a second distance between the mid-plane (4) and the external surface of a trough (3), said first and second distances being identical, said method comprising the steps of: determining the height H, thickness E and pitch P values by solving an inequation:
Fi<H.sup.3/(8?E?(H+P))<Fs where Fi=25 mm and Fs=35 mm, Fi and Fs being limits of the inequation; and calculating at least one parameter selected from inertia per sheet width unit and volume per sheet width unit, said calculation of the parameter of inertia per sheet width unit being a function of the height H, the thickness E, the pitch P and the radii R1 and R2 of the crests and troughs of the corrugations, said calculation of the parameter of volume per sheet width unit being a function of the height H, the thickness E, the pitch P and the radii R1 and R2 of the crests and troughs of the corrugations, and the height H, thickness E and pitch P values being determined by solving the inequation for a determined value of the parameter of inertia per sheet width unit and/or a determined value of the parameter of volume per sheet width unit, said determined value being either a constant of respectively inertia per width unit or volume per sheet width unit defined a priori, or at least one value respectively higher than a threshold of inertia per width unit or lower than a threshold of volume per sheet width unit determined a priori.

2. The method according to claim 1, wherein, in said determining step, the limits used for the inequation are: Fi=29 mm, and Fs=31 mm.

3. The method according to claim 1, wherein the method is applied to a non-optimized corrugated sheet having thickness, height and pitch measurements determined in order to optimize at least one parameter selected from the inertia per width unit and the volume per sheet width unit by modifying one or several of said thickness, height and pitch measurements, and wherein the method further comprises, for said measurements and according to the parameter(s) to be optimized: calculating the inertia per width unit and/or the volume per sheet width unit of the non-optimized corrugated sheet; then using the result(s) of the inertia per width unit and/or volume per sheet width unit of the non-optimized corrugated sheet as the constant defined a priori or as the threshold determined a priori for the determined value(s) of the parameter(s); then determining the height H, thickness E and pitch P values by solving the inequation for the determined value(s) of the parameter(s), respectively inertia per sheet width unit and/or volume per sheet width unit.

4. The method according to claim 3, wherein the rounds of the crests (2) and troughs (3) are arcs of a circle with identical radius values, and wherein the same radius value is kept between the non-optimized corrugated sheet and the optimized corrugated sheet.

5. The method according to claim 1, wherein the inclined portions are substantially straight.

6. The method according to claim 1, wherein the volume per sheet width unit parameter is replaced by a weight per sheet width unit parameter in the method.

7. The method according to claim 3, wherein the volume per sheet width unit parameter is replaced by a weight per sheet width unit parameter in the method.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) The present invention will now be exemplified, without being limited thereby, by the following description in relation with the following figures:

(2) FIG. 1, which is a perspective view of a bitumen-impregnated cellulose corrugated sheet,

(3) FIG. 2, which is a cross-sectional view (or end view) of a part of a bitumen-impregnated cellulose corrugated sheet,

(4) FIG. 3, which is a cross-sectional view (or end view) of a first example of corrugated sheet optimization, and

(5) FIG. 4, which is a cross-sectional view (or end view) of a second example of corrugated sheet optimization.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

(6) Generally, the formula obtained allows determining ex nihilo the dimensions of a corrugated sheet that shows an interesting inertia/volume (or, which is equivalent, inertia/weight) compromise or optimizing the dimensions of an already-known sheet by modifying a least one of the parameters among the height, the corrugation pitch and/or the sheet thickness in relation with the inertia and the volume (or the weight, which is equivalent). It is hence also applicable to existing industrial facilities that allow some adjustments, for example of the corrugation pitch or of the thickness of material, without thereby having to construct a new facility.

(7) The application of the formula may also be made as a function of imposed constraints relating to the value of the desired inertia, in particular equal to a constant or higher than a threshold, and/or relating to the value of the desired volume of material, in particular equal to a constant or lower than a threshold, wherein the values can correspond to values chosen a priori, ex nihilo, or depend on values obtained on other sheets to be optimized. Furthermore, the constraints may also relate to one or two of the three height, pitch and thickness parameters for which is/are attributed one/two value(s) a priori or equal to that/those of a sheet to be optimized. The application of constraints being however limited by the fact that it must be possible to obtain a result satisfying the inequation, as the increase of the number of constrained parameters may lead to an impossibility to produce a height, pitch and thickness result satisfying the inequation. It is also possible to obtain several results of height, pitch and thickness values satisfying the inequation and it is the most advantageous one according to determined criteria, for example simplicity of implementation, that will be chosen.

(8) The bitumen-impregnated cellule corrugated sheets that are schematized in FIGS. 2 to 3 are seen in cross-section or, which is equivalent, from the edge or from the longitudinal end if considering that the length is parallel to the crests or to the troughs, and hence to the corrugations, of the sheet.

(9) In FIG. 2, a part of corrugated sheet 1 is shown in relation with the dimensional parameters that are more particularly concerned. The sheet 1 includes a uniform pattern of mutually parallel alternating corrugations borne by a mid-plane 4 that cuts virtually the sheet into two parts, an upper one and a bottom one. The alternating corrugations define, in vertical and cross section of the sheet, rounded crests 2, each separated from the next one by a rounded trough 3. The crests and the troughs are connected by alternatively inclined portions 5, 5. The crests 2 are above the mid-plane 4 and the troughs 3 are under the mid-plane 4. The inclined portions 5, 5 cut the mid-plane 4 at the middle thereof by having a part above the mid-plane 4 and a part below the mid-plane 4. The corrugations of these two parts are mirror-symmetrical with respect to the mid-plane 4 if considering a virtual offset of half a pitch between the two parts. In other alternative embodiments, it is not the case, in particular in the case where the radii R1 and R2 are different from each other.

(10) Transversally, the spacing between two successive crests 2 is equal to the spacing between two successive troughs 3 and this spacing defines the pitch P of the corrugations. The sheet has a thickness E of material substantially constant over its extent. The sheet has a height H defined as being twice the distance between the mid-plane 4 and the external surface of a crest 2 or twice the distance between the mid-plane 4 and the external surface of a trough 3, these two distances being identical. In other words, the height H of the sheet 1 is its overall height.

(11) The crests and the troughs are rounded as arcs of a circle and have preferably the same value of radius R1 (for the crest 2) and R2 (for the trough 3) to ensure the topbottom symmetry of half a pitch P of the alternating corrugations. Preferably, the inclined portions 5, 5 include a linear part at least at the level of the mid-plane 4 and that is more or less extended upward and downward as a function of the height H of the sheet. Hence, it may exist, in the case of an inclined portion with a linear part, a transitional part of the inclined portion 5, 5 that is neither linear nor in an arc of a circle in the area that meets the crest, or the trough respectively (the transition is made between a straight area and an arc-of-a-circle area). In other cases, it is the whole inclined portion 5, 5 that is neither linear nor in an arc of a circle and that forms a transitional part (the transition is made between two arc-of-a-circle areas).

(12) These dimensional parameters being now clarified, the application of the inequality making it possible to determine the dimensions of a sheet having an interesting inertia-to-volume (or inertia-to-weight, which is equivalent) characteristic can be explained. This inequality is the following one:
Fi<H.sup.3/(8?E?(H+P))<Fs

(13) where Fi=25 mm and Fs=35 mm.

(14) In its simplest application, height H, pitch P and thickness E values are chosen a priori, and it is verified by calculation whether they verify the inequality. However, this method may be tedious.

(15) In more advanced applications, a software is implemented, which allows scanning height H, pitch P and thickness E values, and the software calculates for each value of the scanning whether their verify the inequality. The scanning of the values may be continuous or, preferably, step-based, with for example a step of 0.5 mm or 1 mm between each value. Preferably, min and max limits are set for the scanning of the values, for example a scanning of the thickness between 1.5 mm and 5 mm with a scanning step of 0.2 mm. It is possible, in some cases, to set/constrain one or two of the three H, P, E parameters, the two other ones or the other one been scanned. These scanning methods (with or without constraint(s) on the only H, P, E parameters) may give many combinations of H, P, E values that satisfy the inequality.

(16) It is possible to limit even more the H, P, E results satisfying the inequality by imposing other constraints in addition to the direct ones on H, P, E indicated hereinabove. These other constraints are in particular the inertia and/or the volume or the weight. The inertia and the volume or weight also depend on the H, P, E, R1 and R2 parameters. Other constraints may also be considered as, for example, the width of the sheet and the number of corrugations over the width, the fact that the sheet is laterally ended by a trough or another part of the corrugation.

(17) In the following, the inertia per width unit and the volume per width unit will be considered. In a simple mode, this/these other constraint(s) consist(s) in imposing a defined value of inertia and/or of volume or weight. In other modes, a range of values of inertia and/or volume or weight may be defined and the determination of the parameters is made, preferably, also by scanning of the range(s) of values. These values are defined a priori.

(18) These two constraints may be used together with the inequality, or only one of the two constraints, and a system with three (in)equations, or two (in)equations respectively, is then obtained.

(19) The application to the optimization of the dimensions of a sheet is deduced from the previous applications under constraint. Indeed, the constraint(s) is(are) this time not defined a priori but are directly in relation with the dimensions and/or characteristics of the sheet to be optimized. For example, the inertia of the sheet to be optimized is calculated or measured, and H, P, E results satisfying the inequality and producing an optimized sheet with the same inertia, or a better inertia, are determined. It is the same for the volume or the weight that is calculated or measured on the sheet to be optimized, and H, P, E results satisfying the inequality and producing an optimized sheet with the same volume or weight, or a lower volume or weight, are determined. It is possible to combine both of them, for example for searching for an optimized sheet with a better inertia for a similar or lower weight. It is also possible to search for an optimized sheet with a lower weight for a similar or better inertia. The term similar is to be understood herein within the meaning of identical or close. It is understood that any searches are possible as, in particular, a better inertia for a lower weight. This optimization may impose constraints on H, P, E that come from the H, P, E values of the sheet to be so optimized: for example, it may be imposed as a constraint to keep the same thickness E of matter. Conversely, the constraint that the same pitch P and possibly the same H, may be imposed as this/these latter constraints can be required for reasons of compatibility between roof covering elements.

(20) In any cases, in particular optimization or not, constraint or not, at least the indicated inequality must be applied to determine the H, P, E values of the sheet that is desired to be obtained. The obtained sheets have a particularly interesting inertia-to-volume (or weight) characteristic: they have an interesting mechanical strength for a relatively reduced quantity of material, hence a saving of material.

(21) As seen, simple or complex solving tools may be used to determine the H, P, E dimensions of sheets satisfying the inequality of the invention. For example, with a raw method by scanning of values, in continuous or by discrete values, for the height and/or the pitch and/or the thickness and/or the inertia and/or the volume in order to search for height, pitch and thickness values satisfying the inequality. A more advanced method may include a step of creating a function based on the inequation and taking into account the possible constraints on the height and/or the pitch and/or the thickness and/or the inertia and/or the volume, then studying the function. Preferably, computer-based calculation and decision tools are implemented for that purpose.

(22) FIGS. 3 and 4 relate to an optimization of a known bitumen-impregnated cellulose corrugated sheet (not shown) having the following dimensions: width 950 mm, thickness E 3 mm, height H 38 mm, pitch P 95 mm and radii R1 and R2 of the rounds of the crests and troughs 16 mm. This non-optimized sheet has ten crests. The inertia per width unit of this known sheet is of 54.4 cm.sup.4/m. The volume per width unit of this known sheet is of 0.007719 m.sup.3/m. If the inequality formula is applied to this known sheet, it is obtained 17.19 mm, which is outside the limits Fi=25 mm and Fs=35 mm of the inequality. In FIGS. 3 and 4, CDG denotes the centre of gravity of the sheet.

(23) In FIG. 3, the constraint has been imposed to have the same inertia per width unit as the known sheet for a lower weight per width unit, hence for a lower volume per width unit. One of the results of the application of the inequality with this constraint gives a sheet whose dimensions are the following ones: pitch P=143 mm, height H=47 mm, thickness E=2.3 mm. For the optimized sheet obtained, it has been desired to have a width close to that of the non-optimized sheet and that ends at the bottom of a trough at its two ends (or at the top point of a crest if the sheet is turned upside down). It results therefrom that the optimized sheet obtained, as shown in FIG. 2, has seven crests and a width of 1001 mm, the radii of the arc-of-a-circle rounds of the crests and troughs being kept at R1=R2=16 mm. If the inequality formula is applied to these H, P, E values, it is obtained 29.70 mm.

(24) In FIG. 4, the constraint has been imposed to have an increased inertia per width unit with respect to that of the known sheet for a same weight per width unit, hence for a same volume per width unit. One of the results of the application of the inequality with this constraint gives a sheet whose dimensions are the following ones: pitch P=127 mm, height H=49 mm, thickness E=2.8 mm. For the optimized sheet obtained, it has been desired to have a width close to that of the non-optimized sheet and that ends at the bottom of a trough at its two ends (or at the top point of a crest if the sheet is turned upside down). It results therefrom that the optimized sheet obtained, as shown in FIG. 4, has eight crests and a width of 1016 mm, the radii of the arc-of-a-circle rounds of the crests and troughs being kept at R1=R2=16 mm. If the inequality formula is applied to these H, P, E values, it is obtained 29.84 mm.

(25) It is also possible to optimize the known sheet according to the following modes. If it is searched for an optimized sheet with a decrease of the volume per width unit and a better inertia per width unit, the application of the inequality formula may give an optimized sheet with P=143 mm, H=48 mm, E=2.4 mm. This optimized sheet has an inertia per width unit of 61.7 cm.sup.4/m and a volume per width unit of 0.00578 m.sup.3/m. If the inequality formula is applied to this optimized sheet, it is obtained 30.16 mm, which is well inside the limits Fi=25 mm and Fs=35 mm of the inequality, the H, P, E values hence effectively satisfying the inequality. It is to be noted that the radii of the arc-of-a-circle rounds of the crests and troughs has been kept at R1=R2=16 mm.

(26) If it is still searched for an optimized sheet with a decrease of the volume per width unit and a better inertia per width unit, the application of the inequality formula may give an optimized sheet with P=127 mm, H=47 mm, E=2.5 mm. This optimized sheet has an inertia per width unit of 65.5 cm.sup.4/m and a volume per width unit of 0.00633 m.sup.3/m, lower than that of the non-optimized sheet. If the inequality formula is applied to this optimized sheet, it is obtained 29.83 mm, which is well inside the limits Fi=25 mm and Fs=35 mm of the inequality, the H, P, E values hence effectively satisfying the inequality. It is to be noted that the radii of the arc-of-a-circle rounds of the crests and troughs has been kept at R1=R2=16 mm.

(27) It is understood that the application of the inequality may provide several sets of H, P, E values that satisfy the inequality. It is hence possible, in order to limit the number of possible results, to choose to increase the constraints when applying the inequality, by constraining the inertia and/or the weight or even other dimensional characteristics and for example H, P, E and/or I (the width of the corrugated sheet). In applications more advanced than the simple scanning of the H, P, E values to search, possibly under constraint(s), for results satisfying the inequality, it is possible to study potential curves of progression of the inequality formula H.sup.3/(8?E?(H+P)) and those of the inertia per width unit and of the volume per width unit, and to determine by a linear combination a formula or curve of which a singular point will be searched for as a function of H, P, E, in particular a maximum or a minimum according to the choice that has been made for the linear combination. In any cases, the inequality will have to be respected.