U.S. patent application number 11/227902 was filed with the patent office on 2006-04-06 for shape modification and reinforcement of columns confined with frp composites.
Invention is credited to Chris P. Pantelides, Lawrence D. Reaveley.
Application Number | 20060070338 11/227902 |
Document ID | / |
Family ID | 36060731 |
Filed Date | 2006-04-06 |
United States Patent
Application |
20060070338 |
Kind Code |
A1 |
Pantelides; Chris P. ; et
al. |
April 6, 2006 |
Shape modification and reinforcement of columns confined with FRP
composites
Abstract
Strengthening reinforced concrete columns by using Fiber
Reinforced Polymer (FRP) composites can be an effective method of
retrofitting existing columns. FRP composites have a number of
advantages over steel, including their high strength-to-weight
ratio and excellent durability. The confinement effectiveness of
FRP materials for rectangular sections can be improved by
performing shape modification such that a rectangular column
section is modified into a shape that does not have 90 degree
comers such as an elliptical, oval or circular column. An expansive
concrete can be advantageously used between the FRP material and
the existing concrete in order to post-tension the FRP material
circumferentially and improve confinement of the concrete. A finite
element analytical model is also disclosed which model describes
the stress-strain relationship for the FRP-confined columns after
shape modification.
Inventors: |
Pantelides; Chris P.; (Salt
Lake City, UT) ; Reaveley; Lawrence D.; (Salt Lake
City, UT) |
Correspondence
Address: |
THORPE NORTH & WESTERN, LLP.
8180 SOUTH 700 EAST, SUITE 200
SANDY
UT
84070
US
|
Family ID: |
36060731 |
Appl. No.: |
11/227902 |
Filed: |
September 14, 2005 |
Related U.S. Patent Documents
|
|
|
|
|
|
Application
Number |
Filing Date |
Patent Number |
|
|
60610265 |
Sep 15, 2004 |
|
|
|
60640545 |
Dec 30, 2004 |
|
|
|
Current U.S.
Class: |
52/847 |
Current CPC
Class: |
E04C 3/34 20130101 |
Class at
Publication: |
052/721.3 |
International
Class: |
E04C 3/34 20060101
E04C003/34 |
Claims
1. A fiber reinforced polymer composite structure, comprising: a) a
core including an inner cement structure at least partially
surrounded by an outer cement structure, said outer cement
structure including a non-shrink cement or an expansive cement; and
b) a fiber reinforced polymer material at least partially
surrounding said core.
2. The composite structure of claim 1, wherein the inner cement
structure has a cross-sectional shape which is different than a
cross sectional shape of the core.
3. The composite structure of claim 2, wherein the inner cement
structure has a rectangular shape and the core has a circular
shape.
4. The composite structure of claim 1, wherein the outer cement
structure consists essentially of an expansive cement.
5. The composite structure of claim 1, wherein the core is
post-tensioned and has a hoop stress along the fiber reinforced
polymer material.
6. The composite structure of claim 1, wherein the fiber reinforced
polymer material comprises a fiber and a polymeric matrix.
7. The composite structure of claim 6, wherein the fiber is
selected from the group consisting of glass fiber, carbon fiber,
aramid fiber, and combinations thereof.
8. The composite structure of claim 7, wherein the fiber is carbon
fiber.
9. A method of reinforcing structural columns, comprising the steps
of: a) placing a fiber reinforced polymer outer shell around an
existing column, said outer shell being configured to leave an open
space between the existing column and the outer shell; b) filling
the open space with expansive cement or non-shrink cement.
10. The method of claim 9, wherein the existing column has a
cross-sectional shape which is different than a cross-sectional
shape of the outer shell.
11. The method of claim 9, wherein the fiber reinforced polymer
outer shell comprises a fiber and a polymeric matrix.
12. The method of claim 11, wherein the fiber is selected from the
group consisting of glass fiber, carbon fiber, aramid fiber, and
combinations thereof.
13. The method of claim 9, wherein the outer shell comprises at
least two pieces which are placed around the existing column to
form the outer shell.
14. The method of claim 13, wherein at least one additional layer
of fiber reinforced polymer material is wrapped around the outer
shell after placing the fiber reinforced polymer outer shell around
the existing column.
15. The method of claim 13, further comprising the step of splicing
the at least two pieces with a vertical fiber reinforced polymer
composite strip along each seam between the at least two
pieces.
16. The method of claim 9, further comprising the step of reshaping
the existing column prior to placing the fiber reinforced polymer
outer shell such that edges of the existing column having an angle
of about 90 degrees are rounded.
17. The method of claim 9, further comprising the steps of: a)
preparing a mold b) wrapping the mold with at least one layer of
fiber reinforced polymer material to form the outer shell; c)
dividing the outer shell longitudinally into at least two
pieces;
18. The method of claim 9, further comprising the step of designing
the fiber reinforced outer shell prior to the step of placing the
fiber reinforce outer shell around the existing column, said step
of designing including: a) defining a core finite element model in
three dimensions corresponding to the core of the composite
structure; b) defining a jacket finite element model along an outer
surface of the core finite element model; c) defining boundary
conditions for each of the core and jacket finite element models;
d) post-tensioning the jacket finite element model by applying an
equivalent thermal gradient; and e) performing finite element
analysis by incremental application of a simulated load and
subsequent iteration calculate force and displacement of each node
within each finite element model to form a stress-strain curve; and
f) comparing the stress-strain curve to a desired performance and
redefining the jacket finite element model and the boundary
conditions when the stress-strain curve does not meet the desired
performance.
19. A method of preparing fiber reinforced polymer shells for
reinforcing structural columns, comprising the steps of: a)
preparing a mold; b) wrapping the mold with at least one layer of
fiber reinforced polymer material to form an outer shell; and c)
dividing the outer shell longitudinally into at least two
pieces.
20. The method of claim 19, wherein the step of wrapping the mold
includes a wet layup of resin coated fibers followed by curing of
the resin.
21. The method of claim 19, wherein the fiber reinforced polymer
material comprises a fiber and a polymeric matrix.
22. The method of claim 21, wherein the fiber is selected from the
group consisting of glass fiber, carbon fiber, aramid fiber, and
combinations thereof.
23. The method of claim 21, wherein the fiber is in the form of a
sheet or a strand.
Description
RELATED APPLICATIONS
[0001] This application claims benefit of U.S. Provisional Patent
Application No. 60/610,265 filed on Sep. 15, 2004, and U.S.
Provisional Patent Application No. 60/640,545 filed on Dec. 30,
2004, each of which are incorporated herein by reference.
BACKGROUND OF THE INVENTION
[0002] In recent years, fiber reinforced polymer (FRP) composites
have emerged as an alternative to traditional materials for
strengthening and rehabilitation of structures. The light weight of
FRP, high-strength to weight ratio, corrosion resistance, and high
efficiency of construction are among many of the advantages which
encourage civil engineers to use this material. FRP composites have
been used in the retrofit of bridge columns due to insufficient
capacity or displacement ductility. FRP jackets can provide lateral
confinement to the concrete columns that can substantially enhance
their compressive strength and ultimate axial strain. One of the
most significant problems which concerns civil engineers is the
constitutive law of FRP-confined concrete. Due to the increasing
need for repair of structures, research has been carried out to
investigate the behavior of FRP-confined concrete columns.
[0003] Many researchers have introduced stress-strain models to
replicate compressive behavior of FRP-confined concrete. Some
studies describe the behavior of the FRP concrete in terms of the
properties of the concrete core and the confining FRP jacket. Other
studies are governed by prior constitutive models and models for
steel confined concrete.
[0004] Recently, some researchers proposed a confinement model,
which is based on the concept of a variable strain ductility ratio.
The researchers suggested that the compressive behavior of
FRP-confined concrete can be separated into a strain-softening and
a bilinear strain hardening component. Such a model shows agreement
with experimental results for circular columns.
[0005] Researchers have also presented a simple design-oriented
stress-strain model for FRP-confined rectangular columns based
largely on a database of existing test results. In this model the
concept of the equivalent circular column is introduced.
[0006] Most of the models mentioned above only refer to circular
sections; moreover, test results are largely based on the standard
6 in..times.12 in. concrete cylinder tests. However, for
FRP-confined rectangular columns, FRP jackets provide a non-uniform
confinement over the cross-section and only a portion of the
concrete section is effectively confined. For this reason, much
less is known about the behavior of FRP-confined rectangular
sections.
[0007] Unfortunately, current efforts tend to have limited value
when reinforcing rectangular columns. Further, although many
reinforcing methods result in moderate improvements in mechanical
properties, the costs of such methods tends to outweigh the
benefits and increase in strength. Therefore, materials and methods
for further enhancing mechanical properties of structural columns
and members continue to be sought.
SUMMARY OF THE INVENTION
[0008] It has been recognized that development of improved
materials and methods for strengthening structural columns which
avoid many of the above deficiencies would be a significant
advancement in the industry. Accordingly, the present invention
provides fiber reinforced polymer (FRP) composite structures which
include a core and a fiber reinforced polymer material at least
partially surrounding the core. The core includes an inner cement
structure at least partially surrounded by an outer cement
structure. The outer cement structure comprises or consists
essentially of expansive cement or non-shrink cement. Typically,
this is the result of applying the principles of the present
invention to reinforce existing structures. Frequently, the inner
cement structure of non-expansive cement can include steel
reinforcements. However, the materials and methods of the present
invention can significantly reduce or even eliminate the need for
steel reinforcement in cement structures.
[0009] In another aspect of the present invention, the inner cement
structure can have a cross-sectional shape which is different than
a cross-sectional shape of the core. This results in a composite
structure having a non-uniform gap thickness or non-uniform
thickness of the non-shrink or expansive portion of the core. Thus,
a pre-existing structure having, for example, a rectangular
cross-section can be modified into a structure having a circular,
oval or elliptical cross-section. Modification of the
cross-sectional shape can have multiple advantages. The elimination
of corners can reduce stress concentration and early failure of the
FRP jacket. Typically, the FRP shell is cured before the grout is
poured in the space between the existing column and the FRP shell.
Therefore, the effect on the FRP shell is a post-tensioning, and
the effect on the existing column is radial compression. For
example, the FRP materials and post-tensioning of the FRP jacket
can provide improved mechanical properties as described in more
detail below. Additionally, elliptical, oval and circular shapes
can provide a greater degree of strength under asymmetric loads
than comparable rectangular configurations.
[0010] In accordance with an embodiment of the present invention,
the FRP jacket can be post-tensioned and have a hoop stress along
the FRP material. In one aspect, post-tensioning of the FRP jacket
can be readily accomplished by using expansive concrete. The
post-tensioning induced in the present invention can be in the form
of tensile stress along the FRP fibers, i.e. circumferential rather
than axial.
[0011] In yet another aspect of the present invention, the FRP
material can include a fiber and a polymeric matrix. Typical fibers
can include, but are not limited to, glass fiber, carbon fiber,
aramid fiber, and combinations thereof. Glass and carbon fibers
tend to be cost effective and provide good mechanical properties.
Aramid fibers are light, durable and are known to have high
tenacity. The selection of the fiber can be based on factors such
as cost, strength, rigidity, and long-term stability. Additionally,
each type of fiber offers different performance characteristics and
suitability for various applications. For example, aramids may come
in low, high, and very high modulus configurations. Carbon fibers
are also available with a large range of moduli; with upper limits
nearly four times that of steel. Of the several glass fiber types,
glass-based FRP reinforcement is least expensive and generally uses
either E-glass or S-glass fibers. The fiber material for use in FRP
can be provided as sheets which can be cut to a desired size or as
lengths of fiber which can be wrapped and/or laid as desired to
form a particular shape.
[0012] The polymeric resins used as the matrix for the fiber are
usually thermosetting resins. Most available FRP materials are
provided with polymeric resins such as polyesters, vinylesters, or
epoxies, although other polymeric materials can also be used.
Additionally, the fibers and the FRP composites are heterogeneous
and anisotropic which can make characterization and prediction of
properties somewhat difficult.
[0013] The above described FRP composite structures can be produced
in accordance with a number of optional embodiments of the present
invention. In one embodiment, existing structural columns can be
reinforced. This is accomplished by placing a FRP outer shell
around the existing column such that there is an open space between
the existing column and the outer shell. Typically, this can be
accomplished by placing two pieces of a shell around the column.
Once the outer shell is in place, at least one additional layer of
FRP material is wrapped around the outer shell to secure the two
pieces together. Optionally, the outer shell can be formed and
cured around the column while leaving an open space. The open space
between the existing column and the outer shell can then be filled
with expansive or non-shrink cement.
[0014] In one embodiment of the present invention, the existing
column has a cross sectional shape which is different than a
cross-sectional shape of the outer shell. For example, the existing
column may be rectangular in shape while the outer shell is
circular or elliptical in shape.
[0015] Thus, there has thus been outlined, rather broadly, the more
important features of the invention so that the detailed
description thereof that follows may be better understood, and so
that the present contribution to the art may be better appreciated.
Other features of the present invention will become clearer from
the following detailed description of the invention, taken with the
accompanying drawings and claims, or may be learned by the practice
of the invention.
BRIEF DESCRIPTION OF THE DRAWINGS
[0016] Additional features and advantages of the invention will be
apparent from the detailed description which follows, taken in
conjunction with the accompanying drawings, which together
illustrate, by way of example, features of the invention; and,
wherein:
[0017] FIG. 1 is a perspective view of an exemplary FRP composite
structure according to one embodiment of the present invention.
[0018] FIG. 2 is a cross sectional view of a FRP composite
structure according to one embodiment of the present invention.
[0019] FIG. 3A is a cross sectional view of a FRP composite
structure in accordance with one embodiment of the present
invention wherein the inner cement structure has a circular
cross-sectional shape and the core has a circular cross-sectional
shape.
[0020] FIG. 3B is a cross sectional view of a FRP composite
structure in accordance with one embodiment of the present
invention wherein the inner cement structure has a square
cross-sectional shape and the core has a circular cross sectional
shape.
[0021] FIG. 3C is a cross sectional view of a FRP composite
structure in accordance with one embodiment of the present
invention wherein the inner cement structure has a rectangular
cross sectional shape and the core has an elliptical cross
sectional shape.
[0022] FIG. 4 is a perspective view of a FRP outer shell around an
existing column, with outer shell being configured to leave an open
space between the existing column and outer shell so that the open
space may be filled with expansive or non-shrink cement in
accordance with one embodiment of the present invention.
[0023] FIG. 5 is a perspective view of a FRP composite outer shell
which has been divided into two pieces and place around an existing
column in accordance with one embodiment of the present
invention.
[0024] FIG. 6 is a perspective view of two pieces of a FRP
composite outer shell that have been spliced with a vertical FRP
composite strip along the seams between the two pieces in
accordance with one embodiment of the present invention.
[0025] FIG. 7A is a perspective view of a mold used for forming a
FRP composite outer shell in accordance with one embodiment of the
present invention.
[0026] FIG. 7B is a perspective view of a mold that has been
partially wrapped with at least one layer of fiber reinforced
composite material to form an outer shell in accordance with one
embodiment of the present invention.
[0027] FIG. 7C is a perspective view of an outer shell which has
been divided into two pieces so that it can be used in applications
requiring retrofitting existing columns in accordance with one
embodiment of the present invention.
[0028] FIG. 8 is a graph of concrete strength vs. aging time in
accordance with one embodiment of the present invention.
[0029] FIG. 9 is a graph of expansion hoop strain for expansive
cement in accordance with one embodiment of the present
invention.
[0030] FIG. 10A is a graph of the expansion history of 12''
circular columns in accordance with one embodiment of the present
invention.
[0031] FIG. 10B is a graph of expansion history of 16'' circular
columns in accordance with one embodiment of the present
invention.
[0032] FIG. 10C is a graph of expansion history of elliptical (1:2)
columns in accordance with one embodiment of the present
invention.
[0033] FIG. 10D is a graph of expansion history of elliptical (1:3)
columns in accordance with one embodiment of the present
invention.
[0034] FIG. 11A is a perspective view for a wrapping method of a
circular column in accordance with one embodiment of the present
invention.
[0035] FIG. 11B is a cross sectional view of a circular column
without a fiber reinforced polymer wrap.
[0036] FIG. 11C is a cross sectional view of a circular column with
a fiber reinforced polymer wrap.
[0037] FIG. 11D is a cross sectional view of a circular column with
a fiber reinforced polymer wrap.
[0038] FIG. 11E is a perspective view for a wrapping method of a
circular column in accordance with one embodiment of the present
invention.
[0039] FIG. 11F is a cross sectional view of a circular column of
expansive concrete with a fiber reinforced polymer wrap.
[0040] FIG. 11G is a cross sectional view of a circular column of
expansive concrete with a fiber reinforced polymer wrap.
[0041] FIG. 11H is a perspective view for a wrapping method of a
circular column in accordance with one embodiment of the present
invention.
[0042] FIG. 11I is a cross sectional view of a circular column with
a fiber reinforced polymer wrap.
[0043] FIG. 11J is a cross sectional view of a circular column with
a fiber reinforced polymer wrap.
[0044] FIG. 12A is a perspective view for a wrapping method of a
square column in accordance with one embodiment of the present
invention.
[0045] FIG. 12B is a cross sectional view of a square column
without a fiber reinforced polymer wrap.
[0046] FIG. 12C is a cross sectional view of a square column with a
fiber reinforced polymer wrap.
[0047] FIG. 12D is a cross sectional view of a square column
encircled by regular concrete and a fiber reinforced polymer
wrap.
[0048] FIG. 12E is a cross sectional view of a square column with a
fiber reinforced polymer wrap.
[0049] FIG. 12F is a cross sectional view of square column
encircled by regular concrete and a fiber reinforced polymer
wrap.
[0050] FIG. 12G is a perspective view for a wrapping method of a in
accordance with one embodiment of the present invention.
[0051] FIG. 12H is a cross sectional view of a square column
encircled by expansive concrete and a fiber reinforced polymer wrap
in accordance with one embodiment of the present invention.
[0052] FIG. 12I is a cross sectional view of a square column
encircled by expansive concrete and a fiber reinforced polymer wrap
in accordance with one embodiment of the present invention.
[0053] FIG. 12J is a perspective view for a wrapping method of a
square column in accordance with one embodiment of the present
invention.
[0054] FIG. 12K is a cross sectional view of a square column with a
fiber reinforced polymer wrap.
[0055] FIG. 12L is a cross sectional view of a square column with a
fiber reinforced polymer wrap.
[0056] FIG. 13A is a perspective view for a wrapping method of a
rectangular column in accordance with one embodiment of the present
invention.
[0057] FIG. 13B is a cross sectional view of a rectangular column
without a fiber reinforced polymer wrap.
[0058] FIG. 13C is a cross sectional view of a rectangular column
with a fiber reinforced polymer wrap.
[0059] FIG. 13D is a cross sectional view of a rectangular column
encircled by regular concrete and a fiber reinforced polymer
wrap.
[0060] FIG. 13E is a cross sectional view of a rectangular column
with a fiber reinforced polymer wrap.
[0061] FIG. 13F is a cross sectional view of a rectangular column
encircled by regular concrete and a fiber reinforced polymer
wrap.
[0062] FIG. 13G is a perspective view for a wrapping method of a
rectangular column in accordance with one embodiment of the present
invention.
[0063] FIG. 13H is a cross sectional view of a rectangular column
encircled by regular concrete and a fiber reinforced polymer
wrap.
[0064] FIG. 13I is a cross sectional view of a rectangular column
encircled by regular concrete and a fiber reinforced polymer
wrap.
[0065] FIG. 14A is a perspective view for a wrapping method of a
rectangular column in accordance with one embodiment of the present
invention.
[0066] FIG. 14B is a cross sectional view of a rectangular column
without a fiber reinforced polymer wrap.
[0067] FIG. 14C is a cross sectional view of a rectangular column
with a fiber reinforced polymer wrap.
[0068] FIG. 14D is a cross sectional view of a rectangular column
encircled with regular concrete and a fiber reinforced polymer
wrap.
[0069] FIG. 14E is a cross sectional view of a rectangular column
with a fiber reinforced polymer wrap.
[0070] FIG. 14F is a cross sectional view of a rectangular column
encircled by regular concrete and a fiber reinforced polymer
wrap.
[0071] FIG. 14G is a perspective view for a wrapping method of a
rectangular column in accordance with one embodiment of the present
invention.
[0072] FIG. 14H is a cross sectional view of a rectangular column
encircled by expansive concrete and a fiber reinforced polymer wrap
in accordance with one embodiment of the present invention.
[0073] FIG. 14I is a cross sectional view of a rectangular column
encircled by expansive concrete and a fiber reinforced polymer wrap
in accordance with one embodiment of the present invention.
[0074] FIG. 15 is a side perspective view illustrating the
placement of specimens in a compression machine in accordance with
one embodiment of the present invention.
[0075] FIG. 16A is a cross sectional view illustrating placement of
LVDT devices in accordance with one embodiment of the present
invention.
[0076] FIG. 16B is a cross sectional view illustrating placement of
LVDT devices in accordance with one embodiment of the present
invention.
[0077] FIG. 16C is a cross sectional view illustrating placement of
LVDT devices in accordance with one embodiment of the present
invention.
[0078] FIG. 17 is a perspective view of a column compression
machine used in testing the specimens in accordance with one
embodiment of the present invention.
[0079] FIG. 18 is a graph of load versus displacement behavior of
circular specimens.
[0080] FIG. 19 is a graph of stress versus strain relation for
specimens with regular concrete.
[0081] FIG. 20 is a graph of stress versus strain relation for
specimens with expansive cement concrete.
[0082] FIG. 21 is a graph of stress versus strain for several
specimens in accordance with embodiments of the present
invention.
[0083] FIG. 22 is a graph of stress versus strain for several
specimens in accordance with embodiments of the present
invention.
[0084] FIG. 23 is a graph of finite element results for
CFRP-confined square and rectangular columns.
[0085] FIG. 24 is a graph of finite element results for
CFRP-confined elliptical columns.
[0086] The above figures are provided for illustration purposes and
variations in dimensions, shapes, materials and the like can be
made without departing from the claimed scope of the invention.
[0087] Reference will now be made to the exemplary embodiments
illustrated, and specific language will be used herein to describe
the same. It will nevertheless be understood that no limitation of
the scope of the invention is thereby intended.
DETAILED DESCRIPTION
[0088] Before the present invention is disclosed and described, it
is to be understood that this invention is not limited to the
particular structures, process steps, or materials disclosed
herein, but is extended to equivalents thereof as would be
recognized by those ordinarily skilled in the relevant arts. It
should also be understood that terminology employed herein is used
for the purpose of describing particular embodiments only and is
not intended to be limiting.
[0089] It must be noted that, as used in this specification and the
appended claims, the singular forms "a," and "the" include plural
referents unless the context clearly dictates otherwise. Thus, for
example, reference to "a layer" includes one or more of such
layers, reference to "a column" includes reference to one or more
of such structures, and reference to "a lay-up process" includes
reference to one or more of such processes.
[0090] Definitions
[0091] In describing and claiming the present invention, the
following terminology will be used in accordance with the
definitions set forth below.
[0092] As used herein, "cement" as any material which can be used
to bind. For example, concrete can include crushed stone, sand, and
a cement. Portland cement is a fired mixture of limestone and clay
which, when hydrated, forms interlocking crystals which bind to the
sand, stone, and one another. Cements can generally be classified
as shrink, non-shrink, or expansive cements. The most commonly used
cement for general construction is shrink cement.
[0093] As used herein, "post-tension" refers to tension created or
induced in a material subsequent to formation. For example,
post-tensioning of FRP shells occurs after curing of the FRP shell
to create a post-tensioned shell having circumferential, or hoop
stress.
[0094] As used herein with respect to an identified property or
circumstance, "substantially" refers to a degree of deviation that
is sufficiently small so as to not measurably detract from the
identified property or circumstance. The exact degree of deviation
allowable may in some cases depend on the specific context.
[0095] As used herein, a plurality of items, structural elements,
compositional elements, and/or materials may be presented in a
common list for convenience. However, these lists should be
construed as though each member of the list is individually
identified as a separate and unique member. Thus, no individual
member of such list should be construed as a de facto equivalent of
any other member of the same list solely based on their
presentation in a common group without indications to the contrary.
For example, glass fiber and carbon fiber are listed in a common
group. However, those skilled in the art will recognize that glass
fiber may be more or less suitable than carbon fiber for a specific
application depending on cost restrictions, strength requirements,
and other factors.
[0096] Concentrations, amounts, and other numerical data may be
expressed or presented herein in a range format. It is to be
understood that such a range format is used merely for convenience
and brevity and thus should be interpreted flexibly to include not
only the numerical values explicitly recited as the limits of the
range, but also to include all the individual numerical values or
sub-ranges encompassed within that range as if each numerical value
and sub-range is explicitly recited.
[0097] As an illustration, a numerical range of "about 1 inch to
about 5 inches" should be interpreted to include not only the
explicitly recited values of about 1 inch to about 5 inches, but
also include individual values and sub-ranges within the indicated
range. Thus, included in this numerical range are individual values
such as 2, 3, and 4 and sub-ranges such as from 1-3, from 2-4, and
from 3-5, etc. This same principle applies to ranges reciting only
one numerical value. Furthermore, such an interpretation should
apply regardless of the breadth of the range or the characteristics
being described.
[0098] Invention
[0099] Due to the increasing need for repair of existing support
structures, research has been carried out to investigate the
behavior of FRP-confined concrete columns. The compressive
stress-strain behavior of FRP confined concrete cylinders is
generally nonlinear and the initial portion of the stress-strain
response typically follows that of the unconfined concrete.
Moreover, after reaching the peak unconfined concrete stress level,
the response of the FRP-confined concrete softens. This softening
can occur with either a localized descending branch that may
stabilize as the dilation of the concrete core progresses, or the
concrete may exhibit a somewhat linear behavior until the FRP
composite jacket fails.
[0100] In accordance with the present invention, FRP materials can
be used to either reinforce existing structures regardless of
shape, or form new structures with improved mechanical, structural
and aesthetic properties.
[0101] Referring now to FIG. 1, a fiber reinforced composite
structure 10 is shown comprising a core 14 including an inner
cement structure 18 at least partially surrounded by an outer
cement structure 22. The inner cement structure can have steel
reinforcements therein; however, the present invention reduces the
need for steel reinforcements. The outer cement structure 22 may
include a non-shrink cement or an expansive cement. Alternatively,
the outer cement structure 22 may consist exclusively of expansive
cement. Encircling the core 14 is an FRP material 26, which makes
up an FRP outer shell 30. The FRP material 26 preferably comprises
a fiber and polymeric matrix. Traditionally, the fiber is selected
from the group consisting of glass fiber, carbon fiber, aramid
fiber, and combinations thereof, although other FRP materials can
also be used.
[0102] The composite structure 10 is shown in FIG. 2 with a core 14
having a cross sectional shape that is different from the cross
sectional shape of inner cement structure 18. Alternatively, the
core 14 may have a cross sectional shape similar to the cross
sectional shape of the inner cement structure 18, as shown in FIG.
3A. The composite structure 10 is shown in FIGS. 3B and 3C having a
core 14 with a cross sectional shape that is different from the
cross sectional shape of the inner cement structure 18.
Specifically, FIG. 3B shows the composite structure 10 having a
core 14 with a circular cross sectional shape and an inner cement
structure 18 with a square cross-sectional shape, and FIG. 3C shows
the composite structure 10 wherein the inner cement structure 18
has a rectangular cross sectional shape and the core 14 has an
elliptical cross sectional shape.
[0103] Now referring to FIG. 4, a FRP outer shell 30 is shown
around an existing column 34. The existing column can have steel
reinforcements therein; however, the present invention reduces the
need for steel reinforcements. The outer shell 30 is configured
such that there is an open space 38 between the existing column 34
and the outer shell 30. The open space 38 can then be filled with
cement 42. The cement 42 may be either expansive cement or
non-shrink cement or a combination thereof. In a preferred
embodiment of the present invention, as shown in FIG. 1, pegs 15
can be placed between the inner cement structure and the FRP outer
shell to secure the positioning of the outer column and existing
column prior to filling the open space with cement.
[0104] FIG. 5 illustrates one embodiment of the present invention
wherein the outer shell 30 comprises at least two pieces which can
be placed around the existing column 34 to form the outer shell 30.
This can be achieved by separating the FRP outer shell 30 into two
pieces and placing the two pieces around the existing column to
form the outer shell. To reinforce an existing column 34 it is
typically necessary to separate the outer shell 30 longitudinally
into a first piece 46 and a second piece 48. The first piece 46 and
second piece 48 can then be placed around the existing column 34 to
reform the outer shell 30. In most cases, the outer shell 30 is
designed and shaped to leave an open space 38 between the existing
column 34 and the outer shell 30. Thus, the outer shell 30 provides
a convenient avenue for shape modification of existing structures.
Shape modification is particularly relevant with respect to
retrofitting existing structures. An existing column 34 with a
square or rectangular cross-section may be modified such that the
resulting composite structure 10 has a circular or elliptical
cross-section. Typically, FRP composite jackets subjected to
membrane loading in accordance with the present invention are
stronger than rectangular column sections having long flat sides.
This is largely because of the dominant bending action of the flat
sides. Therefore, shape modification of an existing column 34 using
the present invention can be readily accomplished to provide
improved structural and mechanical properties to the composite
structure 10.
[0105] Once the first piece 46 and second piece 48 have been placed
around the existing structure 34 they can be spliced, as shown in
FIG. 6, with a vertical FRP composite strip 56 along each seam 58
between the first piece 46 and second piece 48 so as to form a
unitary outer shell 52. In a preferred embodiment of the present
invention, after the first and second piece of the outer shell have
been spliced with a vertical FRP composite strip, additional FRP
material may be wrapped around the outer shell. Typically the
wrapping can be done with a single continuous sheet; however,
multiple sheets can be wrapped in a wet lay-up process followed by
curing of the polymer resin. Most often, the number of layers can
range from 1 to about 14 additional layers.
[0106] In yet another preferred embodiment of the present
invention, prior to placing the first piece 46 and second piece 48
around the existing column 34, the existing column may be reshaped
such that the edges of the existing column having an angle of about
90 degrees are rounded. One important consideration in forming
FRP-confined rectangular columns in accordance with the present
invention is the issue of effectiveness of FRP confinement, which
may significantly decrease due to the presence of 90.degree.
corners or abrupt change of direction around the perimeter.
Small-scale tests illustrate the effect of rounding the column
comers on confinement efficiency. The rounding of corners on
concrete columns has been shown to have an effect in ultimate
strength as high as an 80% increase with respect to square columns
without rounding the corners. In addition to higher strengths,
higher ultimate compressive strains can be achieved for columns
with rounded comers, which is more important for seismic
applications than strength. Typical ultimate strain increases range
from 200% to 300%. While the effectiveness of confinement increases
with the corner radius, the rounding of corners cannot always be
made in practice as large as ideally desired because of the
presence of the hoop steel reinforcement, typically about 1.5-2.5
in. from the exterior concrete surface.
[0107] In one embodiment of the invention, FRP materials can be
placed along the longitudinal axis of the existing column in direct
contact with the existing column, either during or after formation
of the FRP shell, for increased flexural resistance of the column,
if required.
[0108] Many applications will call for a FRP outer shell that is
pre-manufactured. However, many applications will require
manufacture of the outer shell. In these applications, a mold can
be prepared in order to form the FRP outer shell. A mold can be
prepared to correspond with a desired final shape of the column. A
mold is not necessarily the same shape as the existing column.
Frequently, an existing rectangular or square column can be
modified to produce a circular or elliptical column of slightly
larger width.
[0109] In one embodiment of the present invention as illustrated in
FIGS. 7A, 7B and 7C, a mold 60 is prepared. The mold 60 is then
wrapped with at least one layer of FRP material 64 to form an outer
shell 72. The mold can then be removed leaving the outer shell as
an independent structure. Typically, the wrapping can be done with
a single continuous sheet; however, multiple sheets can be wrapped
in a wet lay-up process followed by curing of the polymer resin.
The sheets may be cut to a desired size or as lengths of fiber
strands, as shown in FIG. 7B, which can be wrapped and/or laid as
desired to form a particular shape. Most often, the number of
layers can range from 1 to about 14 additional layers.
[0110] In a preferred embodiment of the present invention, the FRP
material 64 comprises a fiber and a polymeric matrix. Typical
fibers can include, but are not limited to, glass fiber, carbon
fiber, aramid fiber, and combinations thereof. Any suitable FRP
material can be used which includes a fiber material and a
polymeric matrix. Non-limiting examples of commercial products can
include SikaWrap, Aquawrap, and the like.
[0111] Wrapping of the mold 60 may include a wet layup of resin
coated fibers followed by a curing of the resin. Once the resin has
cured, the outer shell 72 can be divided longitudinally into at
least a first piece 76 and a second piece 78 so that it can be used
in applications that require retrofitting existing columns.
[0112] For purposes of designing FRP structures for existing
columns, those persons skilled in the art will recognize that it is
possible to use finite element analysis to prepare the design of
the FRP structure prior to retrofitting the existing column.
EXAMPLES
[0113] The following examples illustrate exemplary embodiments of
the invention. However, it is to be understood that the following
is only exemplary or illustrative of the application of the
principles of the present invention. Numerous modifications and
alternative compositions, methods, and systems may be devised by
those skilled in the art without departing from the spirit and
scope of the present invention. The appended claims are intended to
cover such modifications and arrangements. Thus, while the present
invention has been described above with particularity, the
following examples provide further detail in connection with what
is presently deemed to be practical embodiments of the
invention.
[0114] In the following examples, the radii of curvature for the 90
degree corners of the square and rectangular columns were designed
to be 3/4 in. This would allow modification of existing columns,
taking into account typical existing steel reinforcement at 90
degree corners. Expansive cement was used for some examples,
whereas non-shrink cement was used for other examples to fill the
space between the outer shell and existing column.
[0115] Further, regular shrink concrete was used to prepare a
number of test samples which were then compared to samples using
expansive and non-shrink concrete. All columns were cast in one
batch to eliminate variations between them; 6''.times.12'' and
4''.times.8'' standard cylinders were made along with these
specimens. The compressive strength was obtained from the tests of
cylinders at 28 days after casting the concrete. The concrete
strength versus time relationship is shown in FIG. 8. FIG. 8
illustrates that the concrete strength increased during the first 6
months and after six months approaches a constant value of 2600
psi.
[0116] Expansive Cement
[0117] Unstressed FRP composite jackets do not participate in the
confinement of concrete until the concrete starts expanding.
Typically, this involves at least partial failure of the concrete
and/or softening of the concrete. In accordance with the present
invention, expansive concrete can post-tension the FRP composites
jacket in the hoop direction prior to application of vertical or
axial loading to the column.
[0118] The expansive cement used in the following examples includes
Type-K and KOMPONENT cements, manufactured by CTS Company, Cypress,
Calif. The two principal constituents of KOMPONENT are calcium
sulfoaluminate and gypsum (calcium sulfate). The formation of
ettringite crystals, which results from the hydration of the two
ingredients, causes an expansion of the cement. When expansion is
restrained by FRP composite jackets in accordance with the present
invention, the expansive cement induces tensile stress in the FRP
composite jackets along the circumference of the FRP jackets.
[0119] To determine the optimal mixing ratio of Type-K cement and
KOMPONENT, a preliminary test was conducted. In this test, four
types of expansive cements were investigated:
[0120] (1) MIX 1: 100% Expansive KOMPONENT
[0121] (2) MIX 2: 75% Expansive KOMPONENT+25% Portland Cement
[0122] (3) MIX 3: 50% Expansive KOMPONENT+50% Portland Cement
[0123] (4) MIX 4: 15% Expansive KOMPONENT+85% Portland Cement
[0124] Each of the four mixtures was prepared and cast in
prefabricated CFRP cylinder shells (6''.times.12''). Strain gauges
were placed at the middle height of the CFRP cylinders to monitor
the expansion history over time. The resulting strain curves are
shown in FIG. 9, which shows that both mix (2) and mix (3) gave the
largest hoop strain for the FRP jacket compared to the other two
mixes. Data from accompanying cylinder tests show that the
compressive strength of mix (3) was 920 psi compared to 850 psi for
mix (2). Mix (3) was selected since it contained less expansive
cement. Thus, it appears that for this particular expansive cement,
volume percents of expansive cement from about 30 to about 85 can
be suitable. The final mix design (based on mix (3)) for the
expansive concrete is shown in Table 1. TABLE-US-00001 TABLE 1 Mix
Design for the Expansive Concrete COMPONENT DETAILS Gals/% lbs C.F.
Cement Type K 10% 351 1.79 Expansive Cement Komponent 5% 166 0.84
Water U.S. Gallons 45 gall 375 6.00 Air % Entrained 7% +/- 1% 1.89
Air Target Rock ASTM C-33 520 3.22 (SSD) 3/8s Pea Gravel Sand ASTM
C-33 2143 13.26 (SSD) Total 3555 25.3.00
[0125] Several specimens with 12 in. diameter circular, 16 in.
diameter circular and elliptical (aspect ratio 1:2 and 1:3) with
CFRP and GFRP jackets, were cast and then cured at an indoor
temperature around 70.degree. F. The details of construction are
described below in more detail. A data acquisition system was used
to monitor the hoop expansion of the FRP composite jacket for each
specimen. FIGS. 10A-10D show the hoop expansion strain of the
circular and elliptical columns for about 70 days.
[0126] Non-Shrinkage Concrete
[0127] As an alternative to expansive cement, a shrinkage
compensated cement was also used to compare the differences between
the expansive cement FRP jackets and the non-shrinkage FRP jackets.
In this case, the non-shrinkage concrete was used to modify the
rectangular or square sections to elliptical or circular sections
as detailed below. Once the aging of the concrete was stable, the
FRP jackets were wrapped using a wet lay-up process. A structural
grout, Sika Grout 212 was selected as the grout to make non-shrink
concrete.
[0128] Fiber Reinforced Polymer
[0129] Two FRP composite materials were used to confine the
concrete columns. One was SikaWrap Hex 103C (available from Sika
Canada Inc.), which is a high strength, unidirectional carbon fiber
fabric. The second FRP material was Aquawrap G-06 by Air Logistics,
which is a unidirectional pre-impregnated glass fiber fabric. The
primary material properties determined in this study are shown in
Table 2. TABLE-US-00002 TABLE 2 Material Properties of CFRP and
GFRP Composites* FRP Tensile Tensile Tensile Ply Thick- Composite
Strength (ksi) Modulus (Msi) Strain (%) ness (in.) CFRP 177 12.6
1.4 0.038 GFRP 33 2.45 1.4 0.064 *Determined at University of Utah,
following ASTM D3039 after curing at room temperature.
Construction of Specimens and Sample Preparation
[0130] A total of 30 test structures were prepared such that each
had nearly the same cross-sectional area prior to shape
modification and the same height of 3 feet. Thus, comparisons were
made for different cross sections and aspect ratios. Molds for
specimens were made out of plywood and sonatubes.
[0131] In addition, both CFRP and GFRP composites-confined
specimens were tested and compared with baseline specimens without
FRP composites. A breakdown of the test matrix is presented in
Tables 3-6. FIGS. 11A through 11J, 12A through 12L, 13A-13I, and
14A-14I show details of the wrapping methods for each specimen.
Regardless of the number of FRP layers, the entire bonded jackets
were made of one continuous sheet of FRP fabric that was cut to the
proper length and width. An additional 3'' of overlap splice was
provided. To expansive cement concrete specimens, the following
steps were followed:
[0132] (a) Preparation of circular and elliptical forms.
[0133] (b) Build 1.sup.st layer of FRP shell and cut the shell into
two halves.
[0134] (c) Make stay-in-place FRP forms by lap splicing with one
FRP layer and applying the other remaining layers.
[0135] (d) Pour expansive cement concrete to fill the open space
between the FRP shell and the standard concrete column.
TABLE-US-00003 TABLE 3 Matrix of Test Specimens: Circular Columns
COLUMN INI- INI- DESIG- TIAL TIAL NO. NATION TYPE LENGTH SIZE FRP
TYPE Note 1 C-0-0 Circular 36'' 12'' None 2 C-C1-0 Circular 36''
12'' Carbon 1 Layer 3 C-G3-0 Circular 36'' 12'' Glass 3 Layers 4
C-CT-E Circular 36'' 12'' Carbon expansive Fiber concrete Tube (1
layer) 5 C-GT-E Circular 36'' 12'' Glass expansive Fiber concrete
Tube (3 layers) 6 C-CS-0 Circular 36'' 12'' Carbon 2 Layers Fiber
of CFRP Strip 7 C-GS-0 Circular 36'' 12'' Glass 6 Layers Fiber of
GFRP Strip
[0136] TABLE-US-00004 TABLE 4 Matrix of Test Specimens: Square
Columns COLUMN INITIAL INITIAL NO. DESIGNATION TYPE LENGTH SIZE FRP
TYPE Note 8 S-0-0 Square 36'' 11'' .times. 11'' None 9 S-C2-0
Square 36'' 11'' .times. 11'' carbon 2 layers 3/4'' radii at
90.degree. corners 10 S-C2-F Square 36'' 11'' .times. 11'' carbon 2
layers 11 S-G6-0 Square 36'' 11'' .times. 11'' Glass 6 layers 3/4''
radii at 90.degree. corners 12 S-G6-F Square 36'' 11'' .times. 11''
Glass 6 layers 13 S-CT-E Square 36'' 11'' .times. 11'' Carbon fiber
tube (2 layers) 14 S-GT-E Square 36'' 11'' .times. 11'' Glass fiber
tube (6 layers) 15 S-CS-0 Square 36'' 11'' .times. 11'' Carbon
fiber 3/4'' radii strip at 90.degree. corners 16 S-GS-0 Square 36''
11'' .times. 11'' Glass fiber 3/4'' radii strip at 90.degree.
corners
[0137] TABLE-US-00005 TABLE 5 Matrix of Test Specimens: Rectangular
Columns (1) COLUMN INITIAL INITIAL NO. DESIGNATION TYPE Length SIZE
FRP TYPE Note 17 R2-0-0 Rectangular 36'' 8'' .times. 15'' None 18
R2-C2-0 Rectangular 36'' 8'' .times. 15'' carbon 2 layers 3/4''
radii at 90.degree. corners 19 R2-C2-F Rectangular 36'' 8'' .times.
15'' carbon 2 layers 20 R2-G6-0 Rectangular 36'' 8'' .times. 15''
Glass 6 layers 3/4'' radii at 90.degree. corners 21 R2-G6-F
Rectangular 36'' 8'' .times. 15'' Glass 6 layers 22 R2-CT-E
Rectangular 36'' 8'' .times. 15'' Carbon fiber tube (2 layers) 23
R2-GT-E Rectangular 36'' 8'' .times. 15'' Glass fiber tube (6
layers) Note: For the elliptical columns, the longer axis is 21.2
in. and the shorter axis is 11.4 in.
[0138] TABLE-US-00006 TABLE 6 Matrix of Test Specimens: Rectangular
Columns (2) COLUMN INITIAL INITIAL NO. DESIGNATION TYPE Length SIZE
FRP TYPE Note 24 R3-0-0 Rectangular 36'' 6'' .times. 18'' None 25
R3-C2-0 Rectangular 36'' 6'' .times. 18'' carbon 2 layers 3/4''
radii at 90.degree. corners 26 R3-C2-F Rectangular 36'' 6'' .times.
18'' carbon 2 layers 27 R3-G6-0 Rectangular 36'' 6'' .times. 18''
Glass 6 layers 3/4'' radii at 90.degree. corners 28 R3-G6-F
Rectangular 36'' 6'' .times. 18'' Glass 6 layers 29 R3-CT-E
Rectangular 36'' 6'' .times. 18'' Carbon fiber tube (2 layers) 30
R3-GT-E Rectangular 36'' 6'' .times. 18'' Glass fiber tube (6
layers) Note: For the elliptical columns, the longer axis is 25.4
in. and the shorter axis is 8.4 in.
[0139] Testing of Specimens
[0140] The strain gauges employed in this testing program were
manufactured by measurements Group, Inc. with model designation as
EA-06-125BZ-350. The resistance of these gauges at normal
temperature (75.degree. F.) is 350.+-.0.15% ohms. In order to
measure the transverse strain on the FRP jacket during loading,
strain gauges were placed on fibers in the hoop direction, at about
the mid-height of the specimens. Special care was taken during the
installation to avoid damage of the strain gauges. Considering the
geometry of the cross sections, the layout of strain gauges was
varied for each shape.
[0141] Linear variable differential transducers (LVDTs) are used to
measure average strains when the use of strain gauges is
impossible. In these tests, LVDTs are employed to measure the
vertical and lateral strains. The data from LVDTs can be used to
calculate the average axial and transverse strains over the column
height and width. LVDTs are installed using aluminum angles with
threaded rods at their ends. The angles must be solidly clamped to
the specimen for accurate readings. FIG. 15 shows the LVDT
configuration. Two types of LVDTs used for experiments are MVL7C
and MVL7, manufactured by Sensotec Company. They can measure a
displacement in the range of .+-.0.500 in. and .+-.2.000 in.,
respectively, with high accuracy. For the square and rectangular
columns, additional LVDTs are installed on the two sides of the
cross section to measure the transverse strain in both directions
as shown in FIGS. 16A-16C.
[0142] The specimens were tested using a structural load frame
having an actuator manufactured by Geneva Hydraulics, Inc. This
actuator can impose a compression load up to 2000 kips and is
capable of a 24 in. stroke. FIG. 17 illustrates the setup of the
column compression tests. All of the specimens were loaded
monotonically under a displacement control mode with a constant
loading rate of 0.05 in. per minute.
[0143] A data acquisition system was used to record the values of
the strain gauges and LVDTs. The data acquisition system used in
this testing program consisted of scanners, WIN5100 (manufactured
by Measurements Group) with interface cards and the STRAINSMART
software. The scanners can read electrical signals from the sensors
and send this information to a computer via the interface cards.
The software then converts these signals into the desired digital
output. Prior to the start of testing, a configuration file had to
be written in the software to assign the measured quantities to
input and output channels. In addition, the calibration values of
strain gauges and LVDTs were input into this configuration file.
After the setup of the configuration file and immediately before
testing, all of the initial values were set to zero to prepare for
recording.
[0144] Experimental Results
[0145] In early tests, a group of 7 circular columns were tested.
All of the FRP strengthened specimens showed significant increases
in axial stress and axial strain capacity. As seen in Table 7, the
increase in ultimate strength (f'.sub.cc/f'.sub.co) ranges from 138
to 238 percent for regular concrete specimens and 545 to 676
percent for expansive cement concrete specimens. In addition,
compared with the baseline column without any reinforcement, FRP
composite jackets improve the confinement of the columns which
results in a significant increase in axial strain as presented in
Table 7. The increases in ultimate strain
(.epsilon.'.sub.cc/.epsilon.'.sub.co) ranges from 848 to 1421
percent for the FRP reinforced specimens. TABLE-US-00007 TABLE 7
Results of Circular Column Tests Wrapping f'.sub.cc/ Specimen No.
FRP Type Layers Method f'.sub.co
.epsilon.'.sub.cc/.epsilon.'.sub.co C-0-0* NO FRP 1.00 1.00 C-C1-0*
CFRP 1 Continuous 2.20 8.48 (wet-layup) C-G3-0* GFRP 3 Continuous
2.38 12.06 (wet-layup) C-CS-0* CFRP 2 5 in. Strips 1.38 9.36
(wet-layup) (5 in. spacing) C-GS-0* GFRP 6 5 in. Strips 1.82 14.21
(wet-layup) (5 in. spacing) C-CT-E** CFRP 1 Continuous 5.45 11.74
(prestressed) C-GT-E** GFRP 3 Continuous 6.76 13.71 (prestressed)
*Regular concrete, **Expansive cement concrete
[0146] The specimens in this testing group exhibited several
failure modes. The governing failure mode was determined by the
mechanical properties of the FRP composite material and the
reinforcement scheme. It was observed from the tests that the most
typical failure mechanism was crushing of concrete followed by the
tensile failure of the FRP at or near the mid-height of the
specimens. Because the fabric was unidirectional and oriented at 0
degrees, a band or ring was typically formed as a result of the
shearing off, and separation of, the fabric in the hoop
direction.
[0147] The load-versus-displacement graphs for each specimen are
presented in FIG. 18. As well as the increased axial strain, this
increased deflection is also believed to be a result of the greater
energy absorption capacity of the specimens provided by the FRP
composites. These results indicate that application of high
performance FRP composites to a concrete member does not promote
brittle failure. Therefore, the ductility of FRP-confined specimens
can be described by using the principle of energy absorption by
comparing the area under the load-displacement curves.
[0148] The stress-strain curves for regular concrete specimens and
specimens with expansive cement concrete are shown in FIG. 19 and
20, respectively. As seen from FIG. 19, the loading behavior of the
FRP-confined specimens with regular concrete can be divided into
three phases. The first phase is from the origin to point A. Point
A corresponds to an axial stress f=0.8f.sub.co' (where f.sub.co' is
the strength of the baseline specimen C-0-0). In this phase where
the behavior for all specimens (in FIG. 19) is almost the same,
lateral expansion was very small and the FRP stresses were very low
(about 16%-33% of their ultimate strength as observed from the
tests). When the load exceeded point A, the FRP stress and strain
started to increase quickly. Cracking noises were heard once the
loading approached f.sub.co' which marked the FRP being put into
tension. In the second phase, from A to B, the FRP composite
participated in confinement which resulted in the small axial
strain (displacement) as seen from stress-versus-strain and
load-versus-displacement curves. After point B, which marked the
turning point on the stress-strain curves, the loading went into
the third phase. In this phase, the FRP strain increased very
quickly and the specimen stiffness decreased as observed form the
tests. The specimens deformed largely in the axial direction and
the fabric was deformed on the surface of the FRP composite.
Finally, the concrete in the specimens crushed followed by the
fracture of FRP.
[0149] These three phases represent the typical behavior of the
axially loaded FRP-confined concrete specimens. In the beginning
phase, the concrete has a small expansion and the FRP jacket does
not participate. However, in phase AB, the concrete expands and FRP
composite jacket is put into tension. Therefore, the FRP material
provides partial confinement against expansion. In the last phase
after B, the concrete goes into a flowing state until FRP fracture
and the failure is very brittle. The behavior of the specimens with
expansive cement concrete was somewhat different. Specifically, the
initial slope of the stress-strain curve is lower than that of the
regular concrete specimens, but the later slope after the turning
point is similar to that of the regular concrete specimens. The
comparisons show that the axial stress capacity was equivalent to
the FRP-confined regular concrete specimens and the axial strain
capacity was much larger.
[0150] Testing results for several square columns are shown in
FIGS. 21 and 22. In each figure S-0-0 shows results for an 11 in.
square column without FRP composites, S-G6-0 shows results for an
11 in. square column with 6 layers of glass FRP composite directly
wrapped thereon, and S-GT-E shows results for an 11 in. square
column with expansive concrete modified into a 16 in. diameter
circle with 6 layers of glass FRP composite in accordance with the
present invention. FIG. 21 illustrates that the GFRP expansive
composite column has a strength of about 3.3 times that of the
unwrapped column and about 2.3 times that of the directly wrapped
column. Likewise, FIG. 22 illustrates that strain, i.e. ductility,
for the GFRP expansive composite column is about 8 times that of
the unwrapped column.
[0151] Thus, the above discussion illustrates that FRP composites
are very effective in increasing the load-carrying capacity and
deformation ability of existing columns. Significant increases in
both ultimate stress and strain are observed from the tests. When
compared to the regular concrete specimens, the specimens with
expansive cement concrete show more deformation ability and
ductility at failure. In addition, they have a higher increase in
the ultimate strength. With the same volumetric FRP ratio, the
confinement effectiveness for specimens confined by FRP strips
decreases if compared to those confined with continuous FRP.
Therefore, the strengthening method with FRP strips should be used
with caution for the normal retrofit of bridge columns. Otherwise,
the maximum spacing of FRP strips should be limited. However,
strengthening with FRP strips offers the advantage of easy
inspection. The FRP composites can significantly improve the axial
behavior of the columns. It is recommended that at least two layers
of FRP composites be used for the retrofit of existing columns.
[0152] Finite Element Analysis
[0153] To validate the results obtained from the experimental
research, a nonlinear finite analysis was conducted by using the
finite element software package: ANSYS6.0 (ANSYS 2000). Four types
of models were developed according to the geometric characteristics
of the specimens. SOLID65, which is an eight-node brick element
with 3 DOFs at each node, was used to model concrete. SHELL181 is a
four-noded element that is well-suited to model FRP composite
materials. The material properties for the unconfined concrete and
FRP composites were obtained from compression cylinder and tensile
coupon tests, respectively. Considering the symmetry of each
column, only one-quarter of the column section along its
longitudinal direction was modeled; symmetrical boundary conditions
were applied at the symmetrical borders along the X and Y axes. To
model the pre-tensioning effect of the expansive cement concrete on
the FRP jackets, an equivalent thermal gradient was applied on the
FRP composite jacket to obtain the pre-stressed hoop strain prior
to applying the axial loading. For each model, a nonlinear analysis
was conducted considering both material and geometric nonlinear
behavior. The loading process was divided into many incremental
steps, in which an incremental axial displacement was applied.
Every increment was iterated until convergence was met with respect
to the criteria of force and displacement. To optimize the
calculation, each load step was divided into 20 sub-steps to
expedite the process of convergence.
[0154] Analysis Results
[0155] The output of ANSYS results consists of the nodal
displacement, element stress, element strain and other information.
For the axial stress in each loading step, a mean value was
calculated by taking the average of the longitudinal 6 elements
along the central line of the model. By entering this value into
the element result tables, circumferential or hoop strain was
obtained. Then, the curves of axial stress versus axial strain and
hoop strain were developed by joining a series of data for each
loading step.
[0156] The results of finite element analysis for some
rectangular/square specimens are summarized in the stress-strain
curves in FIGS. 23 and 24. It is noted from FIG. 23 that the
confinement provided was not sufficient to significantly increase
the axial stress for the square and rectangular sections. Both the
square and rectangular models demonstrated a typical softening
behavior which is characterized by a sudden drop from the peak
stress (as seen from FIG. 23). Observations from the results of the
normal elliptical models (as shown in FIG. 24) also demonstrated
the softening behavior. However, this softening is not as much as
that of the rectangular columns. This result illustrates that the
confinement effect is directly related to the shape of the section
and that the confinement efficiency of circular columns is much
better than the sections with 90 degree corner radius. Another
important result can be observed from the comparison of bonded and
pre-stressed FRP jackets of the present invention, as shown in FIG.
24, that the effectiveness of prestressing on the FRP also has a
significant contribution to the confinement efficiency. This type
of finite element analysis can also be used to design a retrofit to
suit a specific project by choosing the desired increase in
strength and efficiency and varying parameters such as shape and
number of layers to balance results with cost effectiveness.
[0157] Of course, it is to be understood that the above-described
arrangements are only illustrative of the application of the
principles of the present invention. Numerous modifications and
alternative arrangements may be devised by those skilled in the art
without departing from the spirit and scope of the present
invention and the appended claims are intended to cover such
modifications and arrangements. Thus, while the present invention
has been described above with particularity and detail in
connection with what is presently deemed to be the most practical
and preferred embodiments of the invention, it will be apparent to
those of ordinary skill in the art that numerous modifications,
including, but not limited to, variations in size, materials,
shape, form, function and manner of operation, assembly and use may
be made without departing from the principles and concepts set
forth herein.
* * * * *