U.S. patent application number 15/498564 was filed with the patent office on 2017-11-02 for asphalt roof shingle system.
The applicant listed for this patent is UNIVERSITY OF SOUTH CAROLINA. Invention is credited to Artem Aleshin, Brendan Croom, Michael A. Sutton.
Application Number | 20170314271 15/498564 |
Document ID | / |
Family ID | 60158801 |
Filed Date | 2017-11-02 |
United States Patent
Application |
20170314271 |
Kind Code |
A1 |
Sutton; Michael A. ; et
al. |
November 2, 2017 |
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.
Inventors: |
Sutton; Michael A.;
(Columbia, SC) ; Aleshin; Artem; (Columbia,
SC) ; Croom; Brendan; (Charlottesville, VA) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
UNIVERSITY OF SOUTH CAROLINA |
Columbia |
SC |
US |
|
|
Family ID: |
60158801 |
Appl. No.: |
15/498564 |
Filed: |
April 27, 2017 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
|
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62329478 |
Apr 29, 2016 |
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Current U.S.
Class: |
1/1 |
Current CPC
Class: |
E04D 1/26 20130101 |
International
Class: |
E04D 1/36 20060101
E04D001/36; E04D 1/20 20060101 E04D001/20; E04D 1/26 20060101
E04D001/26 |
Goverment Interests
STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT
[0002] This invention was made with government support under Grant
No. CBET-1321489 awarded by the National Science Foundation. The
government has certain rights in the invention.
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
CROSS REFERENCE TO RELATED APPLICATION
[0001] This application claims filing benefit of U.S. Provisional
Patent Application Ser. No. 62/329,478 having a filing date of Apr.
29, 2016, entitled "MULTI-SEALANT SYSTEM FOR IMPROVED SHINGLE
RESISTANCE TO SEPARATION" which is incorporated herein by
reference.
BACKGROUND
[0003] Asphalt roof shingles typically include fiber-reinforced
laminates that contain a chemical saturant to ensure sufficient
fire resistance. One self-sealing strip is also included and used
to adhesively bond the upper shingle to the one beneath (FIG. 1),
thereby providing uplift resistance. The inclusion of the single
self-sealing strip also aids in minimizing water penetration as
shingle delamination often results in water intrusion. In fact, it
has been estimated that interior losses due to water penetration
can be nine times higher in cost than those to the building
envelope.
[0004] Unfortunately, It has been documented that asphalt roof
shingles may delaminate at significantly lower wind speeds than
those for which they are rated, with major consequences on safety
and repair costs. For instance, it has been reported that recently
installed asphalt shingles that were rated for resistance against
177-km/h to 241-km/h 3-s gusts (ASTM 2009, 2011) delaminated when
subject to 185-km/h or less 3-s gusts produced by Hurricane Ike.
Durability of shingles is also of concern as wind resistance can be
impaired by aging effects.
[0005] Research is ongoing to develop standard test methods to
realistically simulate high wind loads for more accurate shingle
rating. For instance, Croom et al. (2015a, 2015b) have introduced a
beam-on-elastic-foundation (BOEF) model to simulate the uplift
response of conventional asphalt roof shingle-sealant structures
that include the single sealant strip. This model has been used in
numerical simulations to study the influence of salient geometric
parameters (e.g., sealant strip size and position) and material
properties (e.g., sealant out-of-plane stiffness). Through these
studies, it has been found that modern shingle systems are
approximately optimized to resist uplift pressures produced under
high winds and that uplift pressures produced under 150-mph winds
can induce delamination of typical asphalt roof shingles.
[0006] What are needed in the art are development of more resilient
material systems and more effective installation procedures that
can mitigate existing delamination problems with asphalt roof
shingles.
SUMMARY
[0007] According to one embodiment, disclosed is an asphalt roof
shingle system that includes multiple sealant strips between each
two overlaid shingles. More specifically, a system can include an
asphalt roof shingle, a first sealant strip and a second sealant
strip. In this system, both sealant strips are adhered to the same
side of the asphalt roof shingle, with the first sealant strip
being adhered to the asphalt roof shingle farther from an outer
edge of the roof shingle as compared to the second sealant
strip.
[0008] Also disclosed is a method for attaching roof shingles to a
roof, the method including attaching a first roof shingle to the
roof. Following, the method also includes attaching a second roof
shingle to the roof by use of a nail or other suitable fixed
support such as a screw, bolt, etc. along an attachment line such
that the second roof shingle partially overlays the first roof
shingle. Upon attachment, two sealant strips are located between
the first and second roof shingles, with a first sealant strip
adhered between the two asphalt roof shingles farther from the
outer edge of the second, upper roof shingle (and closer to the
attachment line of this shingle) as compared to the second sealant
strip.
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.times.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).
EI .differential. 4 w i .differential. x 4 = F i ( x ) , F i ( x )
= { p i ( x ) for i = 1 , 3 , 5 - Sw i ( t ) for i = 2 , 4 ( 1 )
##EQU00001##
[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):
w 1 ( x ) = 1 EI ( C 1 + C 2 x + C 3 x 2 2 + C 4 x 3 6 + p 1 x 4 24
) ( 2 ) w 2 ( x ) = C 5 e .alpha. x cos ( .alpha. x ) + C 6 e
.alpha. x sin ( .alpha. x ) + C 7 e - .alpha. x cos ( .alpha. x ) +
C 8 e - .alpha. x sin ( .alpha. x ) ( 3 ) w 3 ( x ) = 1 EI ( C 9 +
C 10 x + C 11 x 2 2 + C 12 x 3 6 + p 3 x 4 24 ) ( 4 ) w 4 ( x ) = C
13 e .alpha. x cos ( .alpha. x ) + C 14 e .alpha. x sin ( .alpha. x
) + C 15 e - .alpha. x cos ( .alpha. x ) + C 16 e - .alpha. x sin (
.alpha. x ) ( 5 ) w 5 ( x ) = 1 EI ( C 17 + C 18 x + C 19 x 2 2 + C
20 x 3 6 + p 5 x 4 24 ) ( 6 ) ##EQU00002##
where the parameter .alpha. 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).
M z ( x = 0 ) M w - .intg. 0 l 1 p 1 ( x ) x d x + .intg. l 1 l 1 +
l 2 w 2 ( x ) S x dx - .intg. l 1 + l 2 l 1 + l 2 + l 3 p 3 ( x ) x
dx + .intg. l 1 + l 2 + l 3 l 1 + l 2 + l 3 + l 4 w 4 ( x ) S xdx -
.intg. l 1 + l 2 + l 3 + l 4 l 1 + l 2 + l 3 + l 4 + l 5 p 5 ( x )
x dx = 0 ( 7 ) F y = 0 V w - .intg. 0 l 1 p 1 ( x ) d x + .intg. l
1 l 1 + l 2 w 2 ( x ) S dx - .intg. l 1 + l 2 l 1 + l 2 + l 3 p 3 (
x ) dx + .intg. l 1 + l 2 + l 3 l 1 + l 2 + l 3 + l 4 w 4 ( x ) S
dx - .intg. l 1 + l 2 + l 3 + l 4 l 1 + l 2 + l 3 + l 4 + l 5 p 5 (
x ) dx = 0 ( 8 ) ##EQU00003##
[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.ltoreq.x.ltoreq.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.ltoreq.x.ltoreq.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.ltoreq.x.ltoreq.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.ltoreq.x.ltoreq.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:
G ( x ) = .intg. Sw i ( x ) dw i = 1 2 S [ w i ( x ) ] 2 for i = 2
, 4 ( 10 ) ##EQU00004##
[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.ltoreq.l.sub.3.ltoreq.(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.ltoreq.l.sub.5.ltoreq.0.0154 m. [0062] Elastic stiffness of
sealant strip, 1.ltoreq.S.ltoreq.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.ltoreq.l.sub.3.ltoreq.0.ltoreq.m or
0.ltoreq.l.sub.1.ltoreq.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.ltoreq.l.sub.3.ltoreq.0 m or
0.ltoreq.l.sub.1.ltoreq.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.apprxeq.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.ltoreq.0.ltoreq.m or 0.ltoreq.l.sub.1.ltoreq.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.ltoreq.l.sub.5.ltoreq.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.ltoreq.S.ltoreq.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.ltoreq.S.ltoreq.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.
* * * * *