Asphalt Roof Shingle System

Abstract

Asphalt roofing systems including multiple sealing strips between two overlaid asphalt roof shingles are described. Additional sealing strips can enhance wind and water resistance of a roof. Simulations are carried out with three tab asphalt roofing shingles to determine desirable locations for multiple sealing strips between overlaid shingles.

Claims

1. An asphalt roof shingle system comprising: an asphalt roof shingle comprising an outer edge; a first sealant strip adhered to a surface of the asphalt roof shingle; a second sealant strip adhered to the surface of the asphalt roof shingle, wherein the first sealant strip is farther from the outer edge as compared to the second sealant strip.

2. The asphalt roof shingle system of claim 1, wherein the first sealant strip and the second sealant strip are on an upper surface of the asphalt roof shingle.

3. The asphalt roof shingle system of claim 1, further comprising a release liner covering the first sealant strip and the second sealant strip.

4. The asphalt roof shingle system of claim 1, wherein the asphalt roof shingle is a three tab asphalt roof shingle.

5. The asphalt roof shingle system of claim 1, wherein the first sealant strip and the second sealant strip are each about 0.5 inches in length.

6. The asphalt roof shingle system of claim 1, wherein the first sealant strip and the second sealant strip are separated from one another by a distance of about 2.2 inches or less.

7. The asphalt roof shingle system of claim 1, wherein the first sealant strip and the second sealant strip are separated from one another by a distance of about 0.5 inches or more.

8. The asphalt shingle system of claim 1, wherein the second sealant strip is a distance from the outer edge of the asphalt shingle, the distance being the sum of an exposure length of the shingle and about 0.6 inches.

9. The asphalt shingle of claim 8, wherein the exposure length is about 5 inches.

10. A method for attaching roof shingles to a roof, comprising: attaching a first asphalt roof shingle to the roof; following, attaching a second asphalt roof shingle to the roof along an attachment line by use of a fixed support such that the second asphalt roof shingle partially overlays the first asphalt roof shingle, wherein upon attachment, a first sealant strip and a second sealant strip are located between the first and second asphalt roof shingles, with the first sealant strip being located farther from an outer edge of the second asphalt roof shingle than the second sealant strip.

11. The method of claim 10, wherein the fixed support comprises a nail.

12. The method of claim 10, wherein the first and second asphalt roof shingles are three tab asphalt roof shingles.

13. The method of claim 10, wherein the ratio of the distance from the second sealant strip to an outer edge of the second asphalt shingle to the distance from the attachment line to the outer edge of the second asphalt shingle is about 0.11 or less.

14. The method of claim 13, wherein the distance from the second sealant strip to the outer edge of the second asphalt shingle is about 0.6 inches or less.

15. The method of claim 10, wherein the ratio of the distance from the attachment line to the first sealant strip to the distance from the attachment line to the outer edge of the second asphalt shingle is about 0.42 or less.

16. The method of claim 15, wherein the distance from the attachment line to the first sealant strip is about 2.2 inches or less.

17. The method of claim 10, wherein the first sealant strip is about half way between the attachment line and the second sealant strip.

18. The method of claim 10, wherein following attachment of the second asphalt roof shingle, an exposure length of the first asphalt roof shingle extends beyond the outer edge of the second asphalt roof shingle.

19. The method of claim 18, wherein the exposure length is about 5 inches.

Description

BRIEF DESCRIPTION OF THE FIGURES

[0009] A full and enabling disclosure of the present subject matter, including the best mode thereof to one of ordinary skill in the art, is set forth more particularly in the remainder of the specification, including reference to the accompanying figures in which:

[0010] FIG. 1 is a photograph of a mock-up prior art asphalt roof shingle with one self-sealing adhesive strip.

[0011] FIG. 2 is a side view of an asphalt roof shingle-sealant system including two sealant strips between overlaid shingles.

[0012] FIG. 3 is an exploded top view of an asphalt roof shingle-sealant system including two sealant strips between overlaid shingles.

[0013] FIG. 4 illustrates loading and boundary conditions for a two sealant strip system.

[0014] FIG. 5 schematically illustrates the structural model used in the parametric study described in the Examples section, with p.sub.1=p.sub.3=507 Pa and p.sub.5=2028 Pa.

[0015] FIG. 6A illustrates the change in the applied energy release rate (G) at the inner and outer edges of the inner sealant strip as a function of the clear spacing between the two sealant strips as this distances changes by varying the distance from the nail line to the inner edge of the inner sealant strip (shingle lip length of 0.0154 m).

[0016] FIG. 6B illustrates the change in G at the inner and outer edges of the outer sealant strip as a function of the clear spacing between the two sealant strips as this distance changes by varying the distance from the nail line to the inner edge of the inner sealant strip (shingle lip length of 0.0154 m).

[0017] FIG. 7A illustrates the change in G at the inner and outer edges of the inner sealant strip as function of clear spacing between the two sealant strips as this distance changes by varying the distance from the nail line to the inner edge of the inner sealant strip (shingle lip length of 0 m).

[0018] FIG. 7B illustrates the change in G at the inner and outer edges of the outer sealant strip as function of clear spacing between the two sealant strips as this distance changes by varying the distance from the nail line to the inner edge of the inner sealant strip (shingle lip length of 0 m).

[0019] FIG. 8 illustrates the change in G at the sealant strip edges as function of clear spacing between the two sealant strips as this distance changes by varying the distance from the nail line to the inner edge of the inner sealant strip (shingle lip length of 0.008 m.

[0020] FIG. 9 illustrates the change in G at all sealant strip edges for selected shingle lip length values, and associated G.sub.min for one optimal configuration as described in the Examples section.

[0021] Repeat use of reference characters in the present specification and drawings is intended to represent the same or analogous features or elements of the present invention.

DETAILED DESCRIPTION

[0022] Reference will now be made in detail to various embodiments of the disclosed subject matter, one or more examples of which are set forth below. Each embodiment is provided by way of explanation of the subject matter, not limitation thereof. In fact, it will be apparent to those skilled in the art that various modifications and variations may be made in the present disclosure without departing from the scope or spirit of the subject matter. For instance, features illustrated or described as part of one embodiment, may be used in another embodiment to yield a still further embodiment.

[0023] In general, the present disclosure is directed to the utilization of multiple sealing strips between two overlaid asphalt roof shingles. The addition of a second sealing strip between each pair of shingles in a roofing system can lead to enhancement in shingle uplift resistance and durability that can justify the additional materials and manufacturing cost.

[0024] Upon assembly, disclosed roofing systems include individual roofing shingles attached to overlaid shingles with two (or more) sealant strips. The introduction of an additional sealant strip compared to conventional one-strip configurations can increase effectiveness in the shingle capability to resist high wind loads (e.g., Category 4 hurricanes). For instance, a standard three-tab shingle attached in a roof by use of two sealant strips on each side can result in maximum energy release rate (G) values that are almost 14 times smaller than those in conventional one-sealant strip counterparts. Moreover, by use of a two sealant strip system, the maximum G values can be far less sensitive to changes in sealant stiffness due to, e.g., aging.

[0025] A side view of a one-layer asphalt roof shingle system that includes two adhesive sealant strips between overlaid shingles is shown in FIG. 2. As shown, an upper asphalt shingle 20 is attached to the underlying shingle 22 (alternatively roof panels, etc.) by use of a nail 10 or other suitable fixed support (e.g., a screw, bolt, etc.). In addition, the roofing system can adhere the asphalt shingle 20 to the underlying shingle 22 with an inner sealant strip 12, and an outer sealant strip 14.

[0026] FIG. 3 illustrates an exploded view of a system including the lower shingle 22 and the upper shingle 20. As shown, the system includes a first, inner sealant strip 12 and a second, outer sealant strip 14. In FIG. 3, the same sealant strips 12, 14 are shown on the upper surface of the lower shingle 22 and in relief on the lower surface of upper shingle 20 so as to demonstrate their location between the two shingles 20, 22 following assembly.

[0027] The system can incorporate any asphalt shingles as are generally known in the art including three-tab shingles or architectural shingles. In particular, while the following discussion is primarily directed to a system that incorporates standard three tab asphalt shingles that include two sealant strips between overlaid shingles, it should be understood that the system is not limited to three tab shingles or two sealant strips, and other types of shingles can be utilized as well as greater numbers of sealant strips between pairs of shingles. In the illustrated embodiments, a system includes standard three tab shingle having cross sectional dimensions as are generally known in the art, i.e., about 12 inches in length (x-direction on the illustrations) by about 36 inches in width (z-direction on the illustrations).

[0028] Asphalt roof shingles generally include an organic base or a fiberglass base. In either case, the shingle can include asphalt or a modified asphalt applied to one or both sides of the saturated base. This laminate can then be covered with granules formed of slate, schist, quartz, vitrified brick, stone, ceramic granules, mixtures of different materials, or the like that can serve to block ultra-violet light, provide some physical protection of the asphalt and can give the shingles their color. In general, the lower side (i.e., the side of the shingle that will be facing the structure) can be treated with sand, talc mica, or the like to prevent the shingles from sticking to each other before use. The shingles can incorporate additives as are generally known in the art. For example, the shingles can include copper or other materials added to the surface to help prevent algae growth, mineral fillers (e.g., as a component of the asphalt layer) that can improve water repellency, fire resistance improvement materials, etc.

[0029] The sealing strips 12, 14 can be typical strips as are known in single-sealant strip systems. For instance, the sealing strips 12, 14, can be self-sealing strips as are known that are typically made of limestone- or fly ash-modified resins, or polymer-modified bitumen. By way of example, the sealing strips 12, 14, can include a self-adhesive compound that can include a pressure-sensitive adhesive, a heat-sensitive adhesive, or a combination thereof as is known in the art.

[0030] FIG. 3 presents a top view of a system including a lower shingle 22, an inner sealing strip 12, and an outer sealing strip 14 located on the upper surface of the shingle 22. In general, the sealing strips 12, 14 can be pre-applied to an upper surface of a shingle 22 during formation and can be temporarily covered with a release liner 29 that can protect the adhesive properties during production, transportation and storage of the shingle 22. Of course, this is not a requirement of a system and in other embodiments, the sealing strips can be pre-applied to a lower surface of a shingle (e.g., shingle 20 in the figures) or applied at the time of installation.

[0031] The release liner 29 is typically a polyester, polypropylene or polyethylene film that is siliconized on the surface that contacts the sealing strips 12, 14 for removal during application to a roof. For instance, each sealing strip 12, 14 can be applied by print wheels or the like, that can pick up hot liquid sealant and print it on an upper surface of the shingle 22 in a solid or broken line pattern, as is known. Each sealant strip 12, 14, can generally be of the same basic length dimension (i.e., in the x-direction on the figures) as is known for single strip sealant systems. For instance the sealant strips 12, 14, can be about 0.5 inches (e.g., about 0.013 m) in length l.sub.2 and l.sub.4, respectively, on FIG. 3. In addition, each sealant strip 12, 14 can be a continuous strip or a broken strip as is known. For instance, each strip 12, 14 can be provided as a series of individual stripes that can be broken in one or both of the x- and z-directions, but with a clear space between the two such that the length of l.sub.3 is about 0.5 inches (about 0.013 m) or greater.

[0032] To utilize the system, a first, lower shingle 22 can be attached to a roof. Following a release liner 29 can be removed 1 from the upper surface of the shingle 22 thereby exposing the sealant strips 12, 14. The second shingle 20 can then be overlaid on the first shingle 2 and attached to the roof via a series of nails or other suitable fixed supports along an attachment line 19. The two shingles 20, 22 can be overlaid according to standard practice, i.e., offset from one another in the z-direction and partially overlaid in the x-direction such that the lower shingle 22 has an exposure length, e.g., of about 5 inches (about 0.127 m). Upon this attachment, the sealant strips 12, 14 can adhere between the two shingles 20, 22.

[0033] The locations of the two sealant strips can vary depending upon the particular types and sizes of shingles used. For instance, when considering a three tab shingle system, the sealant strips can be located such that the leading edge length l.sub.5 of the upper shingle 20 that extends from the outer edge 18 of the shingle 20 to the outer edge of the outer sealant strip 14 can be about 0.6 inches (about 0.015 m, e.g., 0.0154 m) or less. For instance, the leading edge length l.sub.5 can be about 0.3 inches (about 8 mm) or less in some embodiments.

[0034] The total distance from the attachment line 19 to the outer edge 18 of the upper shingle 20 (i.e., l.sub.1+l.sub.2+l.sub.3+l.sub.4+l.sub.5) can generally be the same as or similar to that of single sealant strip systems, e.g., about 5.25 inches (about 0.1334 m). Thus, and independent of the particular shingle or lengths involved, the ratio of the leading edge length l.sub.5 to that of the entire length from the attachment line 19 to the outer edge 18 can be about 0.11 or less (i.e., about 0.015/0.1334 or less), or about 0.06 or less (i.e., about 0.008/0.1334 or less) in some embodiments.

[0035] In one embodiment, the inner sealant strip 12 can be located such that it is about half way between the attachment line 19 and the outer sealant strip 14. For example, the length of l.sub.1 (the distance from the attachment line 19 to the inner edge of the inner sealant strip 12) can be about equal to that of l.sub.2 (the distance from the outer edge of the inner sealant strip 12 to the inner edge of the outer sealant strip 14). This is not a requirement however, and these two distances are not necessarily about equal to each other. In various embodiments, the length of l.sub.1 can be about 2.2 inches (about 0.056 m) or less, about 2.1 inches (about 0.052 m), or less or about 1.9 inches (about 0.049 m) or less. Thus, and independent of the particular shingle or lengths involved, the ratio of l.sub.1 to the entire length from the attachment line 19 to the outer edge 18 can be about 0.42 or less, about 0.39 or less, or about 0.37 or less in some embodiments.

[0036] When considering a system in which the sealant strips 12, 14 are pre-applied to the upper surface of the lower shingle 22, the locations of the sealant strips can be configured such that the above relationships can hold and the lower shingle 22 can have the desired exposure length following attachment beneath the upper shingle 20. For instance, a typical exposure length (i.e., that portion of the shingle that is exposed following overlaying of the upper shingle) for an asphalt roof shingle is about 5 inches (about 0.127 m). Thus, the length l.sub.6 on shingle 22 of FIG. 3 can be the desired exposure length plus the desired leading edge length l.sub.5 of the upper shingle, e.g., about 5 inches (0.127 m) plus about 0.6 inches (0.015 m), or about 5.6 inches (about 0.142 m) or less in some embodiments.

[0037] The addition of a second sealing strip between pairs of asphalt shingles in a roofing system can provide an efficient approach to increase roof resiliency against high wind loads and offset detrimental aging effects.

[0038] The present disclosure may be better understood with reference to the Examples set forth below.

Example

[0039] A beam-on-elastic-foundation (BOEF) mechanical model as illustrated in FIG. 4 was used to examine the viability and design parameters for a two sealant strip asphalt shingle system. In the simulations, the attachment line 19 was approximated as a fixed end and it was assumed that a “unit width” in the z-direction (orthogonal to x and y in FIG. 4) experiences a uniform response and that the inner 12 and outer 14 adhesive sealant strips had a uniform width in the z-direction along their entire length in the x-direction, that is, the gaps found in “intermittent” strips (FIG. 1) were not specifically modeled.

[0040] Table 1 provides a list of the BOEF model parameters, notations, and dimensional units as used in this Example.

TABLE-US-00001 TABLE 1 Dimensional Notation Parameter unit* l Length of shingle (along axis x) L l.sub.1 Distance between nail line and inner edge of L inner sealant strip l.sub.2 Length of inner sealant strip (along axis x) L l.sub.3 Distance between outer edge of L inner sealant strip and inner edge of outer sealant strip (along axis x) l.sub.4 Length of outer sealant strip (along axis x) L l.sub.5 Length of leading edge L of shingle (along axis x) W Width of shingle element (along axis z) L E Elastic modulus of shingle FL.sup.−2 material (along axis x) S Stiffness of elastic foundation FL.sup.−3 (sealant strip) per unit thickness I Shingle cross-sectional area moment L.sup.4 of inertia (with respect to axis z) EI Flexural stiffness of shingle FL.sup.2 cross section (with respect to p.sub.1 Out-of-plane surface pressure FL.sup.−2 on shingle surface between nail line and inner edge of inner sealant strip p.sub.3 Out-of-plane surface pressure on FL.sup.−2 shingle surface between outer edge of inner sealant strip and inner edge of outer p.sub.5 Out-of-plane surface pressure FL.sup.−2 on shingle leading edge G Applied energy release rate at sealant strip edge FL.sup.−1 *F = force; L = length.

[0041] As illustrated in FIG. 4, the portion of shingle 20 of length l=l.sub.1+l.sub.2+l.sub.3+l.sub.4+l.sub.5 was modeled as a beam with flexural stiffness EI, and the inner sealant strip 12 and outer sealant strip 14 having length l.sub.2 and l.sub.4, respectively, were modeled as elastic foundations having similar axial stiffness, S (units FL.sup.−3). The constant uplift pressures p.sub.1 and p.sub.3 (units FL.sup.−2) applied between the attachment line 19 and the inner edge 9 of the inner sealant strip 12, and between the outer edge 11 of the inner sealant strip 12 and the inner edge 13 of the outer sealant strip 14, respectively, are assumed to be independent loading parameters over the lengths l.sub.1 and l.sub.3, respectively, on the shingle 20. It is noted that while line loads (units FL.sup.−1) are typically used in beam problems, pressure loads (units FL.sup.−2) were used to ensure consistency with uplift pressure values; a beam with unit width of 1 m was assumed, which made these two load types functionally equivalent based on the relation line load=pressure×width. In the mechanical model, both the location and length of each sealant strip 12, 14 along the shingle edge (axis x) were varied to quantify their influence on the resistance to delamination.

Mathematical Formulation

[0042] Based on Euler-Bernoulli beam theory, the out-of-plane deflection (y-direction in FIG. 4) of the shingle 20 was modeled based on the formulation presented in Eq. (1).

[00001]$\begin{array}{cc}\mathrm{EI}.Math.\frac{{\partial }^4.Math.w_i}{\partial x^4}=F_i\left(x\right),.Math.F_i\left(x\right)=.Math.\{\begin{array}{cc}{p}_i\left(x\right)& \mathrm{for}.Math..Math.i=1,3,5\\ -{\mathrm{Sw}}_i\left(t\right)& \mathrm{for}.Math..Math.i=2,4.Math.\end{array}& \left(1\right)\end{array}$

[0043] The analytical solutions for the deflections w.sub.i(x) in Eq. (1) where i=1, 2, 3, 4 and 5 were associated with Region 1, 2, 3, 4 and 5, respectively, along the shingle 20 (FIG. 4), and can be expressed by means of Eq. (2) through Eq. (6):

[00002]$\begin{array}{cc}.Math.w_1\left(x\right)=\frac{1}{\mathrm{EI}}.Math.\left(C_1+C_2.Math.x+\frac{C_3.Math.x^2}{2}+\frac{C_4.Math.x^3}{6}+\frac{p_1.Math.x^4}{24}\right)& \left(2\right)\\ w_2\left(x\right)=C_5.Math.e^{\alpha .Math..Math.x}.Math.\cos \left(\alpha .Math..Math.x\right)+C_6.Math.e^{\alpha .Math..Math.x}.Math.\sin \left(\alpha .Math..Math.x\right)+C_7.Math.e^{-\alpha .Math..Math.x}.Math.\cos \left(\alpha .Math..Math.x\right)+C_8.Math.e^{-\alpha .Math..Math.x}.Math.\sin \left(\alpha .Math..Math.x\right)& \left(3\right)\\ .Math.w_3\left(x\right)=\frac{1}{\mathrm{EI}}.Math.\left(C_9+C_{10}.Math.x+\frac{C_{11}.Math.x^2}{2}+\frac{C_{12}.Math.x^3}{6}+\frac{p_3.Math.x^4}{24}\right)& \left(4\right)\\ w_4\left(x\right)=C_{13}.Math.e^{\alpha .Math..Math.x}.Math.\cos \left(\alpha .Math..Math.x\right)+C_{14}.Math.e^{\alpha .Math..Math.x}.Math.\sin \left(\alpha .Math..Math.x\right)+C_{15}.Math.e^{-\alpha .Math..Math.x}.Math.\cos \left(\alpha .Math..Math.x\right)+C_{16}.Math.e^{-\alpha .Math..Math.x}.Math.\sin \left(\alpha .Math..Math.x\right)& \left(5\right)\\ .Math.w_5\left(x\right)=\frac{1}{\mathrm{EI}}.Math.\left(C_{17}+C_{18}.Math.x+\frac{C_{19}.Math.x^2}{2}+\frac{C_{20}.Math.x^3}{6}+\frac{p_5.Math.x^4}{24}\right)& \left(6\right)\end{array}$

where the parameter α is equal to (S/EI).sup.0.25. The boundary conditions at x=0, x=l.sub.1, x=l.sub.1+l.sub.2, x=l.sub.1+l.sub.2+l.sub.3, x=l.sub.1+l.sub.2+l.sub.3+l.sub.4 (FIG. 4) are presented in Table 2.

TABLE-US-00002 TABLE 2 Parameter x = 0 x = l.sub.1 x = l.sub.1 + l.sub.2 x = l.sub.1 + l.sub.2 + l.sub.3 x = l.sub.1 + l.sub.2 + l.sub.3 + l.sub.4 Out-of-plane w.sub.1 = 0 w.sub.1 = w.sub.2 w.sub.2 = w.sub.3 w.sub.3 = w.sub.4 w.sub.4 = w.sub.5 deflection Slope of deflected w.sub.1′ = 0 w.sub.1′ = w.sub.2′ w.sub.2′ = w.sub.3′ w.sub.3′ = w.sub.4′ w.sub.4′ = w.sub.5′ shape Bending moment Elw.sub.1″ = M.sub.w Elw.sub.1″ = Elw.sub.2″ Elw.sub.2″ = Elw.sub.3″ Elw.sub.3″ = Elw.sub.4″ Elw.sub.4″ = Elw.sub.5″ Shear force Elw.sub.1′″ = −V.sub.w Elw.sub.1′″ = Elw.sub.2′″ Elw.sub.2′″ = Elw.sub.3′″ Elw.sub.3′″ = Elw.sub.4′″ Elw.sub.4′″ = Elw.sub.5′″

[0044] It was assumed that the uplift displacement and uplift slope at the nail 10 (x=0) were equal to zero, thereby representing a fixed support. These continuity equations were then used in conjunction with the static equilibrium equations in Eq. (7) and Eq. (8) to calculate the values for the reaction bending moment and shear force (M.sub.w and V.sub.w at x=0), and the constants of integration in Eq. (2) and Eq. (6) (C.sub.1 through C.sub.20).

[00003]$\begin{array}{cc}.Math..Math.M_z\left(x=0\right).Math..Math.M_w-{\int }_0^{l_1}.Math.p_1\left(x\right).Math.x.Math..Math.d.Math..Math.x+{\int }_{l_1}^{l_1+l_2}.Math.w_2\left(x\right).Math.S.Math..Math.x.Math..Math.\mathrm{dx}-{\int }_{l_1+l_2}^{l_1+l_2+l_3}.Math.p_3\left(x\right).Math.x.Math..Math.\mathrm{dx}+{\int }_{l_1+l_2+l_3}^{l_1+l_2+l_3+l_4}.Math.w_4\left(x\right).Math.S.Math..Math.\mathrm{xdx}-{\int }_{l_1+l_2+l_3+l_4}^{l_1+l_2+l_3+l_4+l_5}.Math.p_5\left(x\right).Math.x.Math..Math.\mathrm{dx}=0& \left(7\right)\\ .Math..Math.F_y=0.Math..Math.V_w-{\int }_0^{l_1}.Math.p_1\left(x\right).Math..Math.d.Math..Math.x+{\int }_{l_1}^{l_1+l_2}.Math.w_2\left(x\right).Math.S.Math..Math.\mathrm{dx}-{\int }_{l_1+l_2}^{l_1+l_2+l_3}.Math.p_3\left(x\right).Math.\mathrm{dx}+{\int }_{l_1+l_2+l_3}^{l_1+l_2+l_3+l_4}.Math.w_4\left(x\right).Math.S.Math..Math.\mathrm{dx}-{\int }_{l_1+l_2+l_3+l_4}^{l_1+l_2+l_3+l_4+l_5}.Math.p_5\left(x\right).Math..Math.\mathrm{dx}=0& \left(8\right)\end{array}$

[0045] In Eq. (7) and Eq. (8), the bending moment and shear force at x=l.sub.1, x=l.sub.1+l.sub.2, x=l.sub.1+l.sub.2+l.sub.3 and x=l.sub.1+l.sub.2+l.sub.3+l.sub.4 were functions of unknown coefficients in the free body diagram developed for the region of interest along the shingle. For example, for a free body diagram of Region 1 (0≦x≦l.sub.1 in FIG. 4), M(x=l.sub.1) is a function of M.sub.w, V.sub.w, and C.sub.1 through C.sub.4. The constants of integration C.sub.1 through C.sub.20 were obtained using 20 equations that are representative of the boundary conditions defined in Table 2.

[0046] This set of equations can be solved as a system of linear equations by means of Eq. (9):

[B]{C}={b}  (9)

as demonstrated previously (Croom et al. (2015a)) for the case of shingle tabs with one sealant strip. In Eq. (9) the rows in matrix [8] include the coefficients obtained from the integration and differentiation of Eq. (2) through Eq. (6) for specific beam coordinates (x in FIG. 4), and accounting for the boundary conditions presented in Table 2; vector {C} includes the constants of integration (C.sub.1 through C.sub.20); and vector {b} includes factors obtained from the integration of applicable loading and geometry parameters.

Shingle-Sealant Bond Energy Release Rate

[0047] The energy release rate, G, was used as a measure of shingle-sealant bond strength, and the uplift displacement of the shingle was calculated at any location (0≦x≦l.sub.1+l.sub.2+l.sub.3+l.sub.4+l.sub.5 in FIG. 4) based on the methodology described in Eq. (1) through Eq. (8). Therefore, simulations provided a direct means to determine the applied G values along the inner and outer edge of both sealant strips 12, 14. The uplift force per unit area at an arbitrary position x along the two sealant strips (i.e., Region 2 in the domain l.sub.1≦x≦l.sub.1+l.sub.2 for the inner strip 12, and Region 4 in the domain l.sub.1+l.sub.2+l.sub.3≦x≦l.sub.1+l.sub.2+l.sub.3+l.sub.4 for the outer strip 14, in FIG. 4) is given as S w.sub.i(x), where w.sub.i(x) is the uplift displacement of the sealant material, with i=2 and i=4 corresponding to the inner and outer sealant strips, respectively. Thus, G was determined at an arbitrary position x for either sealant strip (along Region 2 and Region 4 in FIG. 4) using the following expression:

[00004]$\begin{array}{cc}G\left(x\right)=\int {\mathrm{Sw}}_i\left(x\right).Math.{\mathrm{dw}}_i=\frac{1}{2}.Math.{S\left[w_i\left(x\right)\right]}^2.Math..Math.\mathrm{for}.Math..Math.i=2,4& \left(10\right)\end{array}$

[0048] The applied G values at the inner and outer edges of both sealant strips were used to identify potential initiation sites for peeling-type failure of asphalt roof shingles.

Parametric Study of Shingle-Sealant Structural Response

[0049] The analytical model presented above was used to predict the uplift response of a roof asphalt shingle having two sealant strips. Then, the applied energy release rate, G, at the inner and outer edges of both sealant strips (Region 2 and Region 4 in FIG. 4) was calculated using Eq. (10).

[0050] The nominal dimensions used in the representative shingle-sealant structural model include (Table 2 and FIG. 4) included the following:

[0051] sealant strip thickness, t=0.0028 m (y-direction);

[0052] shingle flexural stiffness, EI=0.234 N-m.sup.2;

[0053] sealant elastic stiffness, S=4.53 GPa/m;

[0054] sealant strip length, l.sub.2=l.sub.4=0.0127 m (x-direction, mimicking typical values in commercially available self-sealing strips);

[0055] shingle length, l.sub.1+l.sub.2+l.sub.3+l.sub.4+l.sub.5=0.1334 m (x-direction);

[0056] distance between the attachment line 19 and the inner edge of the outer strip, l.sub.1+l.sub.2+l.sub.3=0.105 m (x-direction, i.e., assuming a length for the leading edge portion,

[0057] l.sub.5=0.0154 m (mimicking typical values in commercially available three-tab asphalt roof shingles).

[0058] Assuming a nominally elastic response of both the sealant and shingle substrate, two material properties are required to model the shingle-sealant uplift response: the modulus of elasticity of the shingle material in the x-direction, E; and the elastic stiffness of the sealant per unit thickness, S, in the y-direction (Table 1, FIG. 4). In this parametric study, these parameters were E=280 MPa and S=4.53 GPa/m as derived through physical experiments on representative shingle and sealant materials reported by Croom et al. (2015a).

[0059] A mechanical model originally formulated and validated by Peterka et al. (1997, 1999) was used to estimate the uplift pressures along the shingle length. The introduction of an additional sealing strip was accounted for by assuming a similar uplift pressure in Region 1 and Region 3 (i.e., p.sub.1=p.sub.3), as shown in FIG. 5. For a wind height of 9.24 m and mean roof height of 4.62 m, assuming a 3-s peak gust of 241 km/h associated with a “H-rating” for asphalt roof shingles (ASTM 2011), the resulting constant uplift pressures were p.sub.1=p.sub.3=507 Pa, and p.sub.5=2028 Pa. These pressure values were input in the analytical model to perform a parametric study for the following significant variables and ranges: [0060] Distance between outer edge 11 of inner sealant strip 12 and inner edge 13 of outer sealant strip 14 (i.e., clear spacing between the inner and outer strip shown as Region 3 in FIG. 5), 0≦l.sub.3≦(0.1334−l.sub.2−l.sub.4−l.sub.5) where the upper bound in associated with l.sub.1=0. [0061] Distance between outer edge 15 of outer sealant strip 14 and leading edge 18 of the shingle 20 (i.e., length of shingle lip shown as Region 5 in FIG. 5), 0≦l.sub.5≦0.0154 m. [0062] Elastic stiffness of sealant strip, 1≦S≦10 GPa/m to reflect the potential for physical changes due to temperature effects and aging.

[0063] The forward method for the analytical shingle-sealant structural model was implemented in Python v3.3 using the numerical package NumPy (Oliphant 2006), performing all calculations with double-floating point precision.

Assumptions and Limitations of Mechanical Model

[0064] The salient assumptions and limitations of the mechanical model were identified in a previous study for the case of shingles with one sealant strip (Croom et al. 2015a, 2015b), and are summarized as follows. [0065] Shingle uplift is constant along the entire width of a given shingle tab, i.e., w.sub.i(x) does not change along the width direction, z. [0066] Shingle and sealant materials deform elastically. [0067] Sealant strip is continuous across its width, i.e., effects associated with possible premature local delamination along intermittent sealant strips (e.g., FIG. 1) are neglected.

[0068] Another potential limitation was represented by the assumption that p.sub.1=p.sub.3 for a two-sealant strip configuration, though to the best of the inventors' knowledge no experimental evidence is available regarding actual pressures.

Results

Influence of Sealant Strip Location on Applied G at Sealant Strip Edges

[0069] In FIG. 6A and FIG. 6B, the applied G at the inner and outer edge of both sealant strips is presented as a function of the clear spacing between the sealant strips, assuming a constant length for the shingle tab (l.sub.1+l.sub.2+l.sub.3+l.sub.4+l.sub.5=0.1334 m), sealant strips (l.sub.2=l.sub.4=0.0127 m), and shingle lip (l.sub.5=0.0154 m), i.e., for 0.0926 m≦l.sub.3≦0≦m or 0≦l.sub.1≦0.0926 m. The applied G at the inner edge 9 of the inner sealant strip 12 (x=l.sub.1) increased nonlinearly with increasing values of l.sub.1 (i.e., as the inner sealant strip 12 is positioned away from the shingle nail line 10, x=0, and l.sub.3 is reduced) as illustrated in FIG. 6A. This trend was reversed for the outer edge 11 of the inner sealant strip 12 (x=l.sub.1+l.sub.2) as the applied G rapidly decreased with increasing values of l.sub.1, and was similar to the trend of the applied G at the inner edge 13 of the outer sealant strip 14 (x=l.sub.1+l.sub.2+l.sub.3) as shown in FIG. 6B, reflecting the fact that both edges are subject to an approximately symmetric loading condition as produced by the uplift pressure p.sub.3 along l.sub.3, irrespective of the l.sub.1 value (FIG. 5). Instead, for the constant shingle lip length l.sub.5=0.0154 m, the position of the inner sealant strip 12 has minor effects on the applied G at the outer edge 15 of the outer sealant strip 14, which lies within the range 0.27-0.28 J/m.sup.2 (FIG. 6B), reflecting the fact that this edge 18 is directly exposed to wind loads (FIG. 2). Otherwise, the maximum applied G was minimized for l.sub.1=0.049 m (G=0.025 J/m.sup.2).

[0070] Theoretically, it was possible to minimize the maximum applied G at this sensitive location (outer edge 15 of the outer sealant strip 14) by using zero-lip shingle tabs. This is illustrated in FIG. 7A and FIG. 7B where the applied G at the inner and outer edge of both sealant strips is presented as a function of the clear spacing between the sealant strips, assuming a constant length for the shingle tab (l.sub.1+l.sub.2+l.sub.3+l.sub.4+l.sub.5=0.1334 m) and sealant strips (l.sub.2=l.sub.4=0.0127 m), and a zero-length shingle lip (l.sub.5=0 m), i.e., for 0.108 m≦l.sub.3≦0 m or 0≦l.sub.1≦0.108 m. As expected, the trend for the applied G at the inner 9 and outer 11 edge of the inner sealant strip 12 (FIG. 7A) mimicked that for the case of l.sub.5=0.0154 m (FIG. 6A). Here, higher peak values of applied G were attained due to the larger maximum length of either Region 3 (l.sub.3) or Region 1 (l.sub.1) subject to the uplift pressure p.sub.1=p.sub.3=507 Pa. The same applied to the applied G at the inner edge 13 of the outer sealant strip 14 (FIG. 7B) compared to the case where l.sub.5=0.0154 m (FIG. 6B) whereas G≈0 J/m.sup.2 at the outer edge 15 since l.sub.5=0 m. If this configuration was considered while disregarding the practical difficulty of manufacturing and effectively installing shingles with zero-length lips, then failure due to delamination would be governed by the applied G at all other sealant strip edges. In fact, G.sub.min, defined as the greatest lower bound of G for all four sealant strip edges, would be minimized for l.sub.1=0.056 m (G.sub.min=0.046 J/m.sup.2).

[0071] This analysis shows that as the inner sealant strip 12 is moved away from the nail line 10 and toward the outer sealant strip 14 (by increasing l.sub.1), the applied G increases at the inner edge 9 of the inner sealant strip 12, decreases with a similar gradient at the outer edge 11 of the inner sealant strip 12 and at the inner edge 13 of the outer sealant strip 14, and remains nearly constant at the outer edge 15 of the outer sealant strip 14. Therefore, for a nominal sealant strip length (l.sub.2=l.sub.4=0.0127 m in FIG. 5), there exists a shingle-sealant configuration (i.e., position for the two sealant strips given by x=l.sub.1 and x=l.sub.1+l.sub.2+l.sub.3, respectively) where the maximum energy release rate at any of the sealant strip edges can be minimized.

[0072] Based on the simulation results, for a set of given shingle lip length values (l.sub.5), Table 3 summarizes the G.sub.min values and the associated position of the inner sealant strip (l.sub.1). The optimal G.sub.min (i.e., lower-bound G for all sealant strip edges) was attained for a shingle configuration where l.sub.5=0.008 m. This is illustrated in FIG. 8 where the applied G at the inner and outer edge of both sealant strips is presented as a function of the clear spacing between the sealant strips, assuming a constant length for the shingle tab (l.sub.1+l.sub.2+l.sub.3+l.sub.4+l.sub.5=0.1334 m), sealant strips (l.sub.2=l.sub.4=0.0127 m), and shingle lip (l.sub.5=0.008 m), i.e., for 0.1 m≦0≦m or 0≦l.sub.1≦0.1 m. For l.sub.1=0.052 m and l.sub.3=0.0479 m, the applied G was similar for all edges of both sealant strips, resulting in a minimized G.sub.min=0.034 J/m.sup.2 (FIG. 8 and Table 3).

TABLE-US-00003 TABLE 3 l.sub.5 [m] G.sub.min [J/m.sup.2] l.sub.1 [m] 0 0.0460 0.0562 0.0035 0.0408 0.0544 0.0063 0.0360 0.0528 0.0080 0.0341 0.0521 0.0095 0.0580 0.0596 0.0127 0.1450 0.0719 0.0154* 0.2741 0.0690
Comparison with Standard Asphalt-Shingle Systems with One Sealant Strip

[0073] Simulations of conventional asphalt roof shingles with one sealant strip have estimated that the optimal value of G.sub.min under 241-km/h 3-s gusts is approximately 0.47 J/m.sup.2 (Croom et al. 2015a, 2015b). This applied energy release rate value lies in the upper bound of the range 0.10-0.51 J/m.sup.2 for peeling-type failures, which was estimated based on reported “T-pull” test data for one-layer asphalt roof shingles. For the simulated system, the introduction of a second sealant strip at l.sub.1=0.0521 m (FIG. 5), in conjunction with the use of a lip length l.sub.5=0.008 m, and sealant strip length l.sub.2=l.sub.4=0.0127 m, increases the uplift resistance of the shingle-sealant system subject to 241-km/h 3-s gusts (i.e., “H-rated” per ASTM 2011). In fact, the resulting G.sub.min=0.034 J/m.sup.2 (FIG. 8 and Table 3) for a standard 0.1334-m long shingle tab was found to be almost 14 times smaller than that that of one-sealant strip counterparts.

[0074] G.sub.min for optimized configurations was in the range 0.034-0.046 J/m.sup.2 for 0≦l.sub.5≦0.008 m, as illustrated in FIG. 9. However, it became more sensitive to increases in the shingle lip length past l.sub.5=0.008 m (i.e., as the outer sealant strip 14 was shifted toward the nail line 10), reaching values that were one order of magnitude higher, up to 0.14 J/m.sup.2 for l.sub.5=0.0127 m, and 0.27 J/m.sup.2 for l.sub.5=0.0154 m. The latter value was still nearly half of that for optimized one-sealant strip systems. Nonetheless, from a practical standpoint, positioning the outer sealant strip 14 closer to the leading edge 18 compared to an optimized one-sealant strip configuration can take better advantage of a two-sealant strip configuration.

Influence of Sealant Stiffness on Applied G at Sealant Strip Edges

[0075] The material properties of modern asphalt roof shingle-sealant systems are susceptible to changes due to environmental exposure (e.g., temperature). Therefore, it was of interest to assess the influence of stiffness changes in the sealant strip on the applied energy release rate, G, when using two-sealant strip configurations. To this end, based on the mechanical model shown in FIG. 5, simulations were performed to estimate G.sub.min for selected values of Sin the range 1-10 GPa/m, assuming a shingle lip length of l.sub.5=0.008 m, and uplift pressures p.sub.1=p.sub.3=507 Pa and p.sub.5=2028 Pa from 241-km/h 3-s gusts. While S=4.53 GPa/m was estimated as a representative value for commercially available sealant materials based on physical tests (Croom et al. 2015a), analyzing results for the range 1-10 GPa/m was intended to account for realistic scenarios of either softening or embrittlement of the sealant material.

[0076] The simulation results for S=1, 2, 4.53, 7 and 10 GPa/m are presented in Table 4, including G.sub.min values and the position of this sealant strip (l.sub.1). These results indicate that G.sub.min and the optimal positioning of both sealant strips are weak functions of the sealant stiffness for 1≦S≦10 GPa/m. These results are important since they confirm that, by selecting the position of both sealant strips based on the minimization of G.sub.min, significant softening or embrittlement of the sealant material produces negligible changes in G.sub.min, which remains in the range 0.029-0.040 J/m.sup.2 (Table 3).

TABLE-US-00004 TABLE 4 S [GPa/m] G.sub.min [J/m.sup.2] l.sub.1 [m] 1.00 0.0295 0.0504 2.00 0.0325 0.0508 4.53* 0.0341 0.0521 7.00 0.0353 0.0517 10.0 0.0397 0.0534 *Representative sealant stiffness per unit thickness for commercially available asphalt roof shingles.

[0077] Data mining of the simulation results demonstrates that for a given shingle tab length and sealant strip length, there exists a geometric configuration that minimizes the applied energy release rate associated with peeling-type failure at the sealant strip edges. In addition, the minimized applied energy release rate is strongly dependent on the position of the sealant strips. To radically enhance uplift resistance (and, in turn, longevity), modern one-layer asphalt roof shingle systems with one sealant strip can be modified by shifting the existing sealant strip closer to the free edge to reduce the applied G at the outer edge near the leading edge of the shingle and adding a second sealant strip approximately half way between the outer sealant strip and the nail line, thereby ensuring that similar applied G values are attained at both edges of the inner sealant strip and the inner edge of the outer sealant strip.

[0078] Uplift resistance is insensitive to changes in the elastic stiffness of the sealant material (1≦S≦10 GPa/m) by one order of magnitude. Thus, significant softening or embrittlement of the two strips of sealant material will have negligible effects on the applied G values. In addition, though the applied G values were not appreciably affected by changes in the elastic stiffness of the sealant material, long-term exposure to the environment may reduce the strength of the shingle-sealant bond (which can be quantified by a reduction in the critical applied energy release rate). If environmental degradation is of concern, an additional advantage of incorporating a second sealant strip is that it will take a longer exposure time and continuing reductions in the critical applied energy release rate before bond failure takes place, thereby increasing the design life of the shingle.

[0079] While certain embodiments of the disclosed subject matter have been described using specific terms, such description is for illustrative purposes only, and it is to be understood that changes and variations may be made without departing from the spirit or scope of the subject matter.