Thiết kế kết cấu bê tông sử dụng cốt FRP thay cốt thép

Bank, Ph.D., P.E., FASCE* 25.1 Introduction ...25-125.2 Design of FRP-Reinforced Concrete Members ...25-2 Introduction • Properties of FRP Reinforcing Bars • Design Basis for FRP-Reinfor

25 Design of FRP Reinforced and Strengthened Concrete

Lawrence C Bank, Ph.D., P.E., FASCE*

25.1 Introduction 25-125.2 Design of FRP-Reinforced Concrete Members 25-2

Introduction • Properties of FRP Reinforcing Bars • Design Basis for FRP-Reinforced Concrete • Design of Flexural Members with FRP Reinforcing Bars

25.3 Design of FRP-Strengthened Concrete Members 25-9

Introduction • Properties of FRP Strengthening Systems • Design Basis for FRP Strengthening Systems for Concrete Members • Design of FRP Flexural Strengthening Systems • Design of FRP Shear Strengthening Systems • Design of FRP Axial Strengthening Systems

25.4 Summary 25-20References 25-20

25.1 Introduction

The design of concrete members either reinforced with FRP reinforcing bars or strengthened with strips

or sheets of FRP laminates or fabrics is discussed in this chapter The discussion in this chapter followsthe design recommendations of the most current versions of the design guidelines published by theAmerican Concrete Institute (ACI) that are used to design these concrete structures in the United States.The material presented is an updated and expanded version of portions of the chapter Fiber-Reinforced

Polymer Composites, which appeared in the Handbook of Structural Engineering (Bank, 2004) and was

based on ACI design guidelines in 2003 In addition, this chapter is intended to provide a brief overview

of topics covered in greater detail and accompanied by illustrative examples in Composites for Construction:

Structural Design with FRP Materials (Bank, 2006.) Research in the use of FRP reinforcements and FRP

strengthening systems for concrete structures has been the focus of intense international research activity

since the late 1980s A biannual series of symposia entitled Fiber-Reinforced Plastics in Reinforced Concrete

Structures (FRPRCS) has been the leading venue for reporting and disseminating these research results.

The most recent symposium, the seventh in the series dating back to 1993, was held in Patras, Greece,

in 2007 (Triantitillou, 2007)

* Professor, Civil and Environmental Engineering, at the University of Wisconsin, Madison; expert in the mechanics and design of composite material structures with an emphasis on applications to civil engineering.

25.2 Design of FRP-Reinforced Concrete Members

25.2.1 Introduction

Fiber-reinforced polymer (FRP) reinforcing bars and grids have been commercially produced for forcing concrete structures for over 30 years (ACI Committee 440, 1996; Bank, 2006; Nanni, 1993) FRPreinforcing bars have been developed for prestressed and non-prestressed (conventional) concrete rein-forcement This section considers only non-prestressed reinforcement for concrete structures and follows

rein-the procedures of ACI 440.1R-06, Guide for rein-the Design and Construction of Structural Concrete Reinforced

with FRP Bars (ACI Committee 440, 2006) Note that ACI 440.1R-06 does not cover reinforcing with

prefabricated FRP grids and mats Recommendations for the design of prestressed FRP-reinforced

con-crete can be found in ACI 440.4R-04, Prestressing Concon-crete with FRP Tendons (ACI Committee 440,

2004b) Current FRP reinforcing bars (referred to as FRP rebars in what follows) are commerciallyproduced using thermosetting polymer resins (commonly, polyester and vinylester) and glass, carbon,

or aramid reinforcing fibers The most common bars produced today are glass-fiber-reinforced vinylesterbars These are recommended for use in reinforcing applications for load-bearing concrete structures.The bars are primarily longitudinally reinforced with volume fractions of fibers in the range of 50 to60% FRP reinforcing bars are usually produced by a process similar to pultrusion (Starr, 2000) and have

a surface deformation or texture to develop the bond to concrete More information on the historicaldevelopment, constituent materials, and manufacturing processes of FRP rebars can be found in Bank(2006) A photograph of some typical FRP reinforcing bars is provided in Figure 25.1 In addition to theACI design guidelines, a number of other design guides have been published for FRP-reinforced concrete.These include Japanese (BRI, 1995: JSCE, 1997) and Canadian (ISIS, 2001; CSA, 2002) guides

25.2.2 Properties of FRP Reinforcing Bars

Glass-fiber-reinforced vinylester bars are available from a number of manufacturers in the United States,Europe, and Asia Bars are typically produced in sizes ranging from 3/8 in in diameter to 1-1/4 in indiameter (i.e., #3 to #10 bars.) FRP bars have a non-smooth surface, which is required for bond to theconcrete (see Figure 25.1) and is typically produced by a sand-coated external layer, molded deforma-tions, machined ribs, or a spiral wind The properties of FRP rebars are intended to be measured and

reported by FRP rebar manufacturers in accordance with ACI 440.3R-04, Guide Test Methods for

Fiber-Reinforced Polymers (FRP) for Reinforcing or Strengthening Concrete Structures (ACI Committee 440,

2004a) A standard product specification for FRP rebars has recently been approved for publication bythe Canadian Standards Organization (ISIS, 2006) The ACI is currently preparing a standard specification

FIGURE 25.1 Typical FRP reinforcing bars for concrete members.

for FRP bars For design, the key mechanical properties of interest are the longitudinal tensile strengthand longitudinal tensile modulus of the bar Most FRP bars are brittle and exhibit strongly linear andelastic axial stress–strain or axial load-deformation characteristics up to their failure loads They do notyield and have no plastic deformation capacity as do steel rebars It is also important to note that, unlikesteel rebars, the longitudinal strength (but not the longitudinal modulus) of FRP rebars decreases withthe diameter of the bar This is attributed to the relatively low in-plane shear modulus of FRP rebars(leading to shear lag effects), the additives used to produce larger diameter bars, and a statistical sizeeffect in brittle glass fibers Designers should always consult the manufacturer’s published propertiesfor use in design Typical properties for glass-fiber FRP rebars and carbon-fiber FRP bars are provided

in Table 25.1 It should be noted that the carbon-fiber bars are typically used as prestressing tendons

or near-surface-mounted (NSM) strengthening rods and not as conventional reinforcing bars due to

known as creep rupture or static fatigue Design guides therefore limit the amount of sustained load on

concrete structures reinforced with FRP rebars

Fiber-reinforced polymer rebars should only be used at service temperatures below the glass transition

temperature (T g ) of the polymer resin system used in the bar For typical vinylester polymers, this is

around 200°F The bond properties have been shown to be highly dependent on the glass transitiontemperature of the polymer In addition, it is important to note that the coefficients of thermal expansion

of FRP rebars are not the same in the transverse (radial) direction as in the longitudinal direction Thecoefficient of thermal expansion may be close to an order of magnitude higher in the transverse direction

TABLE 25.1 Properties of Typical Commercially Produced FRP Reinforcing Bars

Glass-Reinforced Vinylester Bar a,b,c (0.5-in Diameter)

Glass-Reinforced Vinylester Bar a (1-in Diameter)

Carbon-Reinforced Vinylester Bar a (0.375-in Diameter)

Carbon-Reinforced Epoxy Bar (0.5-in Diameter)

Fiber architecture Unidirectional Unidirectional Unidirectional Unidirectional

a Data for Aslan® (Hughes Brothers, Seward, Nebraska).

b Data for V-Rod™ (Pultrall, Quebec, Canada).

c Data for Leadline® (Mitsubishi, Tokyo, Japan).

Note: CTE, coefficient of thermal expansion; NR, not reported by the manufacturer.

of the bar due to its anisotropic properties (see typical properties in Table 25.1) This may cause tudinal splitting in the concrete due to temperature and shrinkage effects if sufficient cover is not provided.Fiber-reinforced polymer reinforcing bars made of thermosetting polymers cannot be bent in the fieldand must be produced by the FRP rebar manufacturer with bends for anchorages or for stirrups Thestrength of the FRP rebar at the bend is substantially reduced and must be considered in the design.According to ACI 440.1R-06, FRP rebars should not be used for carrying compressive stress in concretemembers (i.e., compression reinforcement in beams or columns) as this time, as insufficient research hasbeen conducted on this topic Where FRP bars are used in the compression zone they should be suitablyconfined to prevent local instability.

longi-25.2.3 Design Basis for FRP-Reinforced Concrete

The load and resistance factor design (LRFD) basis is stipulated by ACI 440.1R-06, which provides the

resistance factors (φ, or phi factors) for use with FRP rebars that are calibrated for the load factors requiredfor use in design with conventionally reinforced concrete structures by ACI 318-05 (e.g., 1.2 for deadload and 1.6 for live load) (ACI Committee 318, 2005) For the design of flexural members reinforcedwith FRP rebars, ACI 440.1R-06 provides the following resistance factors:

Flexural capacity (tensile reinforcement only):

φ = 0.55 for an under-reinforced beam section (ρf < ρfb)

φ = 0.65 for a substantially over-reinforced beam section (ρf > 1.4ρfb)

φ = 0.3 + 0.25ρf/ρfb for a lightly over-reinforced beam section (ρfb < ρ < 1.4ρfb)

Shear capacity (FRP shear reinforcement in the form of stirrups):

φ = 0.75 per ACI 318-05

where ρf is the FRP reinforcement ratio and ρfb is the balanced FRP reinforcement ratio The FRP

reinforcement ratio for an FRP-reinforced rectangular beam section (where the subscript f is used to

indicate FRP reinforcement to distinguish it from conventional reinforcement) is given as:

(25.1)and the balanced FRP reinforcement ratio is given as:

(25.2)

where A f is the area of FRP reinforcement, b is the beam width, d is the effective depth, β1 is a factor that

depends on concrete strength (e.g., 0.85 for 4000-psi concrete), f c′ is the cylinder compressive strength

of the concrete, E f is the longitudinal modulus of the FRP rebar, εcu is the nominal ultimate compressive

strain in the concrete (taken as 0.003), and f fu is the longitudinal design strength of the FRP rebar Figure25.2 shows the distribution of strains, stresses, and forces at the service condition and at the ultimatecondition for an FRP reinforced section

The design strength (f fu) and design failure strain (εfu) are obtained from the manufacturer-reported

guaranteed strength and guaranteed failure strain by multiplying them by an environmental reduction

factor (C E), which depends on the fiber type in the bar and the type of intended service of the structure

For example, for glass FRP rebars, C E is 0.7 for exterior concrete and 0.8 for interior concrete Theguaranteed strength and guaranteed strain to failure of FRP rebars are defined as the mean minus 3standard deviations of a minimum of 25 test samples (ACI Committee 440, 2006)

In addition to the strength criteria described above, the design basis for FRP-reinforced concrete bers also includes stipulations on the behavior and appearance of the FRP-reinforced member under service

mem-ρf f

A bd

f cu

f cu fu

f f

loads Maximum flexural crack widths are limited to 0.20 and 0.28 mils for exterior and interiors exposure,

and the stress in the main FRP reinforcing bars is limited to 0.2f fu , 0.3f fu , and 0.55f fu for glass, aramid, andcarbon bars, respectively, to prevent failure under sustained loads due to creep rupture or due to fatigue.Because FRP rebars typically have a lower modulus than steel rebars, the serviceability criteria (typically,deflections and crack widths) can often control the design of FRP-reinforced concrete sections

25.2.4 Design of Flexural Members with FRP Reinforcing Bars

25.2.4.1 Flexural Capacity with FRP Main Tension Bars

The nominal moment (or flexural) capacity of an FRP-reinforced concrete member (such as a beam or

a slab) is determined in a manner similar to that of a steel-reinforced section However, because FRPrebars do not yield, the ultimate strength of the bar replaces the yield strength of the steel rebar in thetraditional concrete beam design formula based on strain compatibility (assuming plane sections remainplane and bars are perfectly bonded to the concrete) and equilibrium of forces Both under-reinforcedsection design and over-reinforced section design are permitted; however, due to serviceability limits(primarily long-term deflections and crack widths), most glass FRP-reinforced flexural members will beover-reinforced

When ρf > ρfb, the over-reinforced section will fail due to concrete crushing, and the nominal momentcapacity is given in a manner similar to that for a section reinforced with steel rebars (where the rebarhas not reached its yield stress) The stress in the rebar therefore must be calculated to determine thecapacity of the section The nominal moment capacity is given as:

(25.3)where:

(25.4)

(25.5)

where f f is the stress in the FRP rebar at concrete compressive failure, and a is the depth of the equivalent

rectangular (Whitney) stress block in the concrete

FIGURE 25.2 Strains, stresses, and forces in the FRP-reinforced section at service and ultimate loads.

Stresses and forces at service loads Strains

4

0 85

0 5

When ρf < ρfb, the under-reinforced section will fail due to rupture of the FRP rebars in tension.Because the FRP reinforcement will not yield prior to its failure, the moment capacity of the sectioncannot be calculated assuming the concrete crushes when the bar ruptures (as in the case of a steel under-reinforced section) For this reason, the section capacity should be calculated using appropriate non-linear stress–strain relations of the concrete; however, this requires an iterative solution procedure, which

is not suited to design calculations To overcome this situation, ACI 440.1R-06 recommends computingthe approximate (and conservative) nominal flexural capacity as:

25.2.4.2 Shear Capacity with FRP Main Tension Bars and FRP Shear Reinforcement

The nominal shear capacity of an FRP-reinforced concrete member loaded in flexure is influenced bythe mechanical properties of the FRP main tension reinforcing bars and by FRP shear reinforcement,which is typically supplied in the form premanufactured stirrups The lower modulus of the FRP mainbars (assuming glass fibers) leads to a shallower compression zone and larger deflections at flexural failure

of FRP-reinforced flexural members than would be obtained in the same section reinforced with steelbars In addition, the strain in the FRP stirrups is limited to prevent large shear cracks from developing

in the FRP-reinforced concrete member Added to this, the strength of the FRP bar is reduced when it

is bent to form a stirrup due to the linear elastic material properties and the manufacturing process used

to manufacture bent FRP bars

The nominal shear capacity (V n) of an FRP-reinforced concrete beam is:

(25.9)

where V c is the nominal shear capacity of the concrete with FRP rebars used as main tension reinforcementand is given as:

(25.10)

where b w is the width of the beam web, and c is the depth of the neutral axis in the cracked elastic section

as defined for the serviceability calculations and is given as:

(25.11)(25.12)

E E

=

where ηf is the modular ratio, k is the depth ratio, and V f is the nominal shear capacity provided by theFRP stirrups For vertical FRP shear stirrups, it is given as:

(25.14)

where A fv is the total area of the stirrups that cross the shear crack, and f fv is the strength of the FRPstirrup, which is limited by the smaller of:

(25.15)and the strength of the FRP rebar at its bend:

(25.16)

where f fb is the strength of the FRP rebar at its bend, r b is the inside radius of the bend, and d b is thediameter of the FRP rebar Standard bend radii are reported by manufacturers and range from 4.25 to

6 in for typical FRP rebars The ratio of r b /d b may not be less than 3

25.2.4.3 Design for Serviceability

For serviceability design of concrete members with FRP bars three criteria, all calculated with respect tothe service loads on the member (with no load factors applied), must be checked against code-stipulatedlimits provided in ACI 440.1R-06: (1) maximum crack widths due to all loads, (2) maximum short-termand long-term deflections due to all loads accounting for long-term creep effects, and (3) maximumstresses in the FRP bars due exclusively to sustained loads and fatigue The width of a flexural crack in

an FRP-reinforced member is calculated from:

(25.17)

where w is the crack width (in inches), f f is the service load stress in the FRP reinforcement (in ksi), E f

is the modulus of the FRP rebars (in ksi), β is the ratio of the distance between the neutral axis and thebottom of the section (i.e., the tension surface) and the distance between the neutral axis and the centroid

of reinforcement, d c is the thickness of the concrete cover from the tension face to center of the closest

bar (in inches), s is the center-to-center bar spacing of the main FRP bars (in inches), and k b is a

bond-related coefficient k b is taken as 1.4 for commercially produced FRP rebars β is determined from:

(25.18)

where h is the section depth and d is the effective section depth The stress in the FRP bar at service loads

can be calculated from:

(25.19)

where m is the service load moment

V A f d s

b c

=2 +  

2

2 2

, = η 1( )−

To calculate maximum short-term and long-term deflections under service loads, a modified form ofthe Branson equation is used:

(25.20)

where I e is the effective second moment of area of the cracked section, I g is the second moment of the

gross section, M cr is the moment at cracking, M a is the applied service load moment, and βd is a reductioncoefficient for FRP reinforced beams that is given as:

or more as per ACI 318-05 (ACI Committee 318, 2005)

All FRP-reinforced concrete beams must be checked for possible failure due to creep rupture or fatigueunder service loads Creep rupture is checked with respect to all sustained service loads, whereas fatigue

is checked with respect to all sustained loads plus the maximum moment induced in a fatigue loading cycle:

The required development length (l d) for a straight FRP bar is given as:

(25.25)

where f fr is the stress in the FRP bar at failure which is the lesser of (1) the design strength of the bar for

under-reinforced beams (f fu ), (2) the actual stress in the bar for over-reinforced sections (f f), or (3) the

effective bond critical design stress in the bar for both over and under-reinforced sections (f fe), which isgiven as:

d g

cr a

, creep rupture= η 1( )−

d

fr c b b

f f C d

d

−+ ( )

13 6

(25.26)

where C is the lesser of (1) the distance from the center of the bar to the nearest outer concrete surface

in the tension zone, or (2) half the on-center spacing of the bars (side-by-side); α is the bar locationfactor, which is taken as 1.0 for bars that are in the bottom 12 in of the formwork when the concrete iscast and as 1.5 when the bars are more than 12 in above the bottom of formwork when the beam is cast

(known as top-bars) ACI 440.1R-06 further recommends that the term C/d b not be taken as larger than

3.5 and that the minimum embedment length (l e ) be at least 20 bar diameters, or 20d b

For hooked bars, the development length of the portion extending beyond the bend (the tail length)

is given as a function of the FRP rebar design strength For FRP rebars with design strengths in the range

of 75 to 150 ksi (typical of glass FRP rebars), the length of the hook (l bfh) is given as:

to the procedures of ACI 440.2R-02, Guide to the Design and Construction of Externally Bonded FRP

Systems for Strengthening Concrete Structures (ACI Committee 440, 2002) This guide is used for the

design of most FRP strengthening systems currently designed in the United States This guide is stillbased on ACI 318-99 load factors (e.g., 1.4 for deal loads and 1.7 for live loads) It is currently underrevision and, in addition to other changes, the next edition will be compatible with ACI 318-05 loadfactors (e.g., 1.2 for dead loads and 1.6 for live loads) The reader is advised to consult the new version

of this guide when it is released in 2008

The first FRP-strengthened concrete structures were beams strengthened to increase their flexuralcapacity using high-strength, lightweight, carbon-fiber-reinforced epoxy laminates that were bonded tothe undersides of the beams The method is a modification of one where epoxy-bonded steel plates areused to strengthen concrete beams which has been in use since the mid-1960s The FRP systems wereshown to provide significant benefits in constructability and durability over the steel plates Thereafter,significant work was conducted on strengthening of concrete columns to enhance their axial capacity,shear capacity, and ductility, primarily for seismic loadings This method is a modification of one usingsteel jackets to strengthen concrete columns This was followed closely by work on shear strengthening

of beams A review of the state of the art on the subject can be found Teng et al (2001), Hollaway andHead (2001), and Bank (2006) The method has also been used to strengthen masonry and timberstructures; however, applications of this type are not discussed in this chapter

Current FRP strengthening systems for concrete fall into two popular types: precured and

formed-in-place systems The precured systems consist of factory manufactured laminates (known as strips or plates)

of carbon-or glass-reinforced thermosetting polymers (typically epoxy or vinylester) that are bonded tothe surface of the concrete using an epoxy adhesive The manufactured precured laminates typically have

=

′

37 5

a volume fraction of fibers in the range of 55 to 65% and are cured at high temperatures (>300°F) but arebonded in the field at ambient temperatures The formed-in-place systems consist of layers of unidirectionalsheets or woven or stitched fabrics of dry fibers (usually glass, carbon, or aramid) that are saturated in thefield with a thermosetting polymer (e.g., epoxy or vinylester) which simultaneously produces and bonds

the FRP material to the concrete The process is often referred to as lay-up The formed-in-place FRP

systems typically have a fiber volume fraction of between 20 and 40% and are cured at ambient atures in the field Figure 25.3 shows a number of currently produced FRP strengthening systems

temper-A number of design guides and national standards are currently published that provide dations for the analysis, design, and construction of concrete structures strengthened with FRP materials(Concrete Society, 2004; CSA, 2002; FIB, 2001; ICC Evaluation Service, 1997; JSCE, 2001) In addition,manufacturers of FRP strengthening systems for concrete typically provide their own design and instal-lation guides for their proprietary systems Because the performance of the FRP strengthening system ishighly dependent on the adhesive or saturating polymer used, the preparation of the concrete surfaceprior to application of the FRP strengthening system, and the field installation and construction proce-

recommen-dures, manufacturers frequently certify approved contractors to ensure that their systems are designed

and installed correctly Guidance to ensure that FRP strengthening systems are appropriately installed,monitored, and inspected is provided in a number of guides (Concrete Society, 2003; ICC EvaluationService, 2001; TRB, 2004)

25.3.2 Properties of FRP Strengthening Systems

Carbon-fiber-reinforced epoxy laminates (or strips) are the most commonly used of the precured FRPstrengthening systems Depending on the type of carbon fiber used in the strip, different longitudinalstrengths and stiffness are produced Strips are typically thin (less than 0.100 in.) and are available in avariety of widths (typically 2 to 4 in.) Because the strips are reinforced with unidirectional fibers, theyare highly orthotropic with very low properties in the transverse and through the thickness directions.Manufacturers typically only report properties in the longitudinal directions and report very little data onphysical properties The strips are bonded to the concrete with an adhesive that is supplied by the stripmanufacturer Typical properties of strips are shown in Table 25.2 It is important to note that the propertiesshown for the strips are properties of the FRP composite and not the properties of the fibers alone

In the formed-in-place FRP strengthening systems, a greater array of products is available depending

on fiber type and sheet or fabric architecture In this group of products, a unidirectional, highly

ortho-tropic carbon-fiber tow sheet is produced by a number of manufacturers and is often used in strengthening

FIGURE 25.3 Typical FRP strengthening systems for concrete members.

applications The individual carbon tows in the sheet are held together by a polymeric binder (or a lightstitching) The sheet is often supplied on a wax paper backing Sheets are typically 10 to 40 inches wideand can be applied in multiple layers with different orientations The common fabric materials in theformed-in-place group are woven or stitched fiber fabrics having an areal density of 12 to 32 oz/yd2.Carbon-fiber fabrics and hybrid fabrics (with more than one fiber type) are also available Fabrics aretypically much thicker than tow sheets They are also used in multiple layers Because of the wide variety

of products available and their different thicknesses, it is not easy to compare their properties directly

In addition, the fibers must be used with a compatible resin system applied at a controlled volume fraction

to achieve a FRP composite with desirable properties In the case of sheet and fabric materials, facturers typically report the mechanical properties of the dry fibers and the thickness (or area) of thefibers It is important to note that when reported in this fashion the properties are not the properties ofthe FRP composite but of the fibers alone Properties of some commonly available fiber sheet and fabricmaterials are listed in Table 25.3

manu-The performance of the FRP strengthening system is highly influenced by the properties of the adhesivelayer in the case of the precured systems and by the properties of the saturating polymeric resin in thecase of formed-in-place systems The interface between the FRP composite and the concrete substratetransfers the loads from the concrete to the FRP composite In the case of flexural and shear (or axialtensile) strengthening, this load transfer is primarily in shear, and the strength and stiffness of the interface

layer between the FRP composite and the concrete are critical Such applications are termed bond critical.

In the case of axial compressive strengthening or lateral displacement ductility enhancement of columns,the role of the strengthening system is to confine the lateral expansion of the cracked concrete In thiscase, the interface bond is not as critical as long as the FRP system is in close contact with the concreteand is wrapped around the concrete continuously so as to provide a confining pressure with appropriate

hoop stiffness and strength Such applications are termed contact critical.

The FRP strengthening systems described above all depend on curing of the polymer adhesives or the

saturating resins at ambient temperature in the field; therefore, the glass transition temperature (T g) of thesesystems is typically quite low (120 to 180°F) The stiffness of the FRP strengthening system is decreased

TABLE 25.2 Properties of Typical Commercially Produced FRP Strengthening Strips

Standard-Modulus Carbon-Reinforced Epoxy Strip a,b,c

High-Modulus Carbon-Reinforced Epoxy Strip a

Glass-Reinforced Epoxy Strip b

Carbon-Reinforced Vinylester Strip d

Fiber architecture Unidirectional Unidirectional Unidirectional Unidirectional

a Data for CarboDur® (Sika Group; Zurich, Switzerland).

b Data for Tyfo® (Fyfe; San Diego, California).

c Data for MBrace® (BASF Construction Chemicals; Seven Hills, New South Wales, Australia).

d Data for Aslan® (Hughes Brothers; Seward, Nebraska).

Note: CTE, coefficient of thermal expansion; NR, not reported by the manufacturer All strips must be bonded with

manufacturer-supplied compatible adhesives.