The Design of Fiber Reinforced Polymers for Structural .... guide for the design and construction of externally bonded frp systems for strengthening concrete structures aci document
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The Design of Fiber Reinforced Polymers for Structural Strengthening An Overview of ACI 440 Guidelines Sarah Witt Fyfe Company November 7, 2008 1
The Design of Fiber Reinforced Polymers for Structural
StrengtheningAn Overview of ACI 440
Guidelines
Sarah WittFyfe Company
November 7, 2008
1
Presenter
Presentation Notes
Good Morning – thank you all for getting here early and coming to my presentation of the Design of Fiber Reinforced Polymers, also referred to as FRP or composites, for structural strengthening.
2
GUIDE FOR THE DESIGN AND CONSTRUCTION OF EXTERNALLY
BONDED FRP SYSTEMS FOR STRENGTHENING CONCRETE
STRUCTURES
ACI Document 440.2R-08Printed July 2008
Presenter
Presentation Notes
This presentation gives you an overview of the design recommendations provided by the ACI 440.2R document, just republished this past summer. This document improves upon the last version, published in 2002. How many of you have attended other design presentations on the ACI 440.2R document? Great – I’m glad to see people with continued interest in the design of FRP. My presentation will focus on the new parts of the document so as not to repeat too much of what you might already have heard while still touching on some of the most common design issues. So what’s new in the document? The latest version has new sections on Near Surface Mounting FRP, strengthening prestressed member with FRP, and has a lot of improved guidelines for bond and general detailing.
3
OutlineStrengthening Concrete Structures
Reasons for strengtheningTypes of FRP strengthening systemsMaterials and properties of FRP strengthening systems
Substrate Preparation/FRP ApplicationRepairProper detailing and installation methodsQuality control
Reinforcement DetailsBond and delaminationDetailing of laps and splices
Design Examples and Case Studies
Presenter
Presentation Notes
Here is a brief outline of what I will be discussing today. There is a lot of information to cover is an short time so please feel free to stop me and ask questions – I’m trying to condense a lot of information into just a short time. I will be going over why we use FRP for strengthening and then have a brief discussion on surface preparation and quality control. Then I will get into the design process. If we still have some time, I will go over a quick example for flexural strengthening.
4
Reasons for Strengthening
Change in useConstruction or design defectsCode changesSeismic retrofitDeterioration
Presenter
Presentation Notes
To start – why would you want to use FRP for strengthening an existing structure? There are many reasons why you as engineers might want to do this. Some of the most common reasons are listed here. Change in use describes an application in which a structure is required to carry additional loads, beyond which it was originally designed. This could be a new planter on a parking deck or office space changing to high density file storage. In an industrial environment, it could describe a situation in which a structure is having additional load applied to it via new equipment. The next category we wish wouldn’t happen, but does on occasion. Poor workmanship or design defects can cause a structure to have inadequate load-bearing capacity. FRP can be used to bring the structure back to the performance level for which it was designed. Code changes or bringing a structure up to a newer, stricter code requires a reevaluation and potential strengthening of the structure. This is another great opportunity to utilize FRP. Seismic Retrofit was one of the very first applications of FRP. Much of the initial research in this area was retrofitting of bridge columns to better perform in a seismic event. Finally we have structural repair to members that have deteriorated due to aggressive environments, general wear and tear of other factors that cause deterioration
5
Excessive Loading
Presenter
Presentation Notes
And since a picture speaks a thousand words a few shots of what that might cause you to look to FRP to increase the load carrying capacity of your structure – excessive snow loading.
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Flexural Cracking
Presenter
Presentation Notes
Cracking from shear or flexure
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Overloading
Presenter
Presentation Notes
One of my favorite – over loading in front of the warning sign
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Seismic Loads
Presenter
Presentation Notes
Prevent damage from earthquakes so your structure doesn’t end up looking like this
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Improper Steel Placement
Presenter
Presentation Notes
Improper steel placement or also inadequate steel cover. FRP can used if the rebar ended up right next to the formwork with inadequate cover.
10
Impact Damage
Presenter
Presentation Notes
And impact damage – although in a case as bad as this, a new girder will be required…..
Precured systemsUnidirectional laminatesMultidirectional gridsShell elements
Other forms not covered
Section 3.2, Guide:
Presenter
Presentation Notes
So now you have determined that your structure needs help, how can FRP provide a solution? Fiber Reinforced Polymers, referred to as FRP, are a combination of high strength fibers in a polymer matrix. This composite material is applied to a structural member to add additional tension capacity. The two most common methods to install FRP are the wet lay up system and precured systems.
12
Typical FRP Systems forStrengthening Structures
Presenter
Presentation Notes
The wet lay up system uses rolls of dry fiber that are saturated with epoxy at the job site. The fibers may be saturated with the use of a machine or by hand. Then the material cures in place on the structural member.
13
Typical FRP Systems forStrengthening Structures
Presenter
Presentation Notes
In precured systems, the fibers are saturated with epoxy and cured in the manufacturing plant. They are then shipped to the job site and adhesively bonded to the structural member. The most common types are precured strips and reinforcing bars.
14
Typical Fiber Properties
Carbon
Aramid
E-Glass
Presenter
Presentation Notes
With either the wet lay up or precured system, there are three common types of fiber – carbon , glass and aramid. Aramid is the generic term for Kevlar, which is a trademarked name. You can see their comparative properties in this chart. With any of the fiber types, the material behavior is linearly-elastic. These materials exhibit no yielding or strain softening. This important aspect must be closely considered when using these materials for reinforcing and strengthening concrete to avoid a brittle failure. The design portion of this presentation will look at this issue in more detail.
Substrate Preparation / RepairBond vs. Contact Critical
Contact CriticalRequires intimate contact between the FRP System and the concrete
Confinement of columns
Bond CriticalRequires an adhesive bond between the FRP system and the concrete
Beam, slab and wall strengthening
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Presenter
Presentation Notes
The first step in any FRP installation is to properly prepare the substrate – that is the surface of the member you want to strengthen. There are two types of applications for FRP that require two different levels of surface preparation. Contact critical applications require only intimate contact between the FRP System and the concrete. For this type of application, you generally need clean, sound, dry concrete. In some cases, paint can even be left on the member. The most classic application that is contact critical is the wrapping of columns. Bond critical applications require an adhesive bond between the FRP and the concrete. The surface preparation for this type of application is more involved. Beam, slab and wall applications are all bond critical.
For these applications it is recommended that the tensile strength of the substrate be a minimum of 200-psi in order to sustain the bond stresses that will be induced by the FRP and the concrete needs a minimum compressive strength of 2500 psi. All unsound concrete needs to be removed and replaced.
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Substrate Preparation
Preparation of concrete surface
Section 6.4, Guide:
Minimum ICRI CSP 3
Presenter
Presentation Notes
The concrete surface is mechanically abraded to achieve an ICRI concrete surface profile of 3. More information on the CSP 3 profile can be found in ICRI Publication No. 03732.
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Epoxy Injection
Cracks wider than 0.010 in (0.3 mm) should be injected prior to application of the FRP system.
ACI 224.1
Smaller cracks in aggressive environments may require sealing
Section 6.4, Guide:
Presenter
Presentation Notes
…and finally cracks wider than 0.01 inch need to be injected
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Quality Control & Assurance
Bond testingACI 503RASTM D4541Tension adhesion strengths should exceed 200 psi (1.4 MPa), exhibit failure of the concrete substrate.
Cured thicknessExtract small core samples less than 0.5 in (13 mm) diameterAvoid sampling in high stress areas if possibleRepair using overlapping sheets on filled core.
During-construction:
Presenter
Presentation Notes
As with any construction project, it is important to ensure good quality control. In-field bond testing can be used on bond critical applications to ensure the minimum 200 psi bond strength. On all applications, core sampling can be used to ensure the proper number of layers have been installed.
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Quality Control & Assurance
General Acceptance Criteria for DelaminationsWet Layup
Delaminations less than 2 in2 (1300 mm2) each are permissible:No more than 10 delaminations per 10 ft2 of laminate areaTotal delamination area less than 5% of total laminate area
Delaminations less than 25 in2 (16,000 mm2) may be repaired by resin injection or ply replacement, depending upon the size, number and location of delaminations.Delaminations greater than 25 in2 (16,000 mm2) should be repaired by selectively cutting away the affected sheet and applying an overlapping sheet patch of equivalent plies.
Precured systemsEach delamination must be inspected and repaired in accordance with the engineer’s direction
Post-construction:
Presenter
Presentation Notes
After installation, the whole system should be inspected for material delaminations. Delaminations, or bubbles, are the most common problem with FRP installation. The ACI 440 document provides guidelines on allowable delamination size and proper repair.
FRP materials can be used to provide additional flexural strength, shear strength and axial enhancement to existing structural members.
2323
Strengthening Limits
Limited by strength of other structural componentsColumns, footings, etc.
Limited by other failure mechanismsPunching shear
Loss of FRP should not result in immediate collapse
( ) ( )newLLDLexistingn SSR 75.01.1 +≥φ (9-1)
Section 9.2, Guide:
Presenter
Presentation Notes
In any design situation, there is a limit to how much additional strength may be added. ACI 440.2R provides guidelines on theses limits to ensure that another, less desirable failure is not induced, and to ensure that loss of the FRP will not result in immediate collapse of the structure. This equation was updated in the latest version.
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Structural Fire Endurance
Glass Transition Temperatures of most FRP systems is typically in the range of 140 - 180oF (60 - 80oC)Use of an insulation system can improve the overall fire rating of the strengthened reinforced concrete memberInsulation system can delay strength degradation of concrete and steel, increasing the fire rating of the memberThe contribution of the FRP system can be considered if it is demonstrated that the FRP temperature remains below a critical temperature
Presenter
Presentation Notes
Another strengthening limit on the use of FRP is fire. The polymer resins used in FRP have glass transition temperatures in the range of 140 – 180 degrees Fahrenheit. At these temperatures, the epoxies begin to soften and you can no longer count on the full design strength. However, there has been research in this area and the new ACI document reflects changes in the philosophy based on this additional information. This includes the recognition that the use of an insulation system can improve the overall fire rating of a strengthened reinforced concrete member. Also, the contribution of the FRP system can be considered during the fire event if it can be demonstrated that the FRP temperature will remain below a critical temperature during the fire. The critical temperature is defined as the temperature at which significant deterioration of the FRP properties has occurred.
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Rational Fire Endurance Check
Given cover and fire endurance requirementFind the temperature of the steel & concreteFind a reduced steel & concrete material strengthFind the associated reduced section strengthReduced strength > Unfactored demandNo phi factors or load factors
ACI 216R:
Presenter
Presentation Notes
The general fire philosophy comes from the ACI 216 document, that analyzes the behavior of a structure during a fire. Many of you have probably already used this document for a non FRP project. There are no phi or load factors, and reduced concrete and steel strengths are determined based on degradation in a fire. These values are used to compute a design strength of the member during a fire.
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Rational Fire Endurance Check
From ACI 216R - Reduce material strengths at elevated temperature:
( ) ( )LLDLexistingn SSR +≥
Steel: θyy ff →
Concrete: θcc ff '' →
FRP: *0→fuf
Section 9.2.1, Guide:
(9-2)
Presenter
Presentation Notes
This same philosophy is applied to the analysis of an FRP strengthened structure. The steel and concrete are given appropriately reduced properties and the FRP is discounted. The remaining design strength of the member must satisfy equation 9.2 as shown. However, as mentioned before, the use of coatings will allow higher properties to be used for the concrete and steel. Or the use of coatings and/or special epoxies with higher glass transition temperatures can allow the strength of the FRP to be included, if the temperature of the FRP remains below a critical temperature.
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Maximum Service Temperature
Typical glass transition temperature (Tg) for epoxy 140 -
180oF (60 - 80oC)
Above Tg mechanical properties start to degrade
Service temperature should not exceed Tg - 27°F (Tg – 15°C)
Section 1.3.3, Guide:
Presenter
Presentation Notes
Not to be confused with fire design, the service temperature, that is the ambient temperature that the structural members will see, must be limited to the glass transition temperature minus 27 degrees Fahrenheit.
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Flexural StrengtheningChapter 10, Guide
Typical flexural strength increases up to 40%This limit is based on the Guide’s requirements
Positive and negative moment strengtheningAdd strength to RC and PC membersReduce crack widthsSeismic loadings not covered
un MM >φ (10-1)
Presenter
Presentation Notes
FRP is commonly used for both positive and negative moment strengthening. The goal is to have the design flexural strength be greater than the factored moment.
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Assumptions
Design calculations are based on actual dimensions and material properties.Plane sections remain plane (including FRP).Maximum compressive strainTensile strength of concrete is ignored.FRP has linear-elastic relation to failure.Perfect bond between FRP and concrete (no slip).The shear deformation within the adhesive layer is neglected.
003.0=cuε
Section 10.2.1, Guide:
Presenter
Presentation Notes
The design assumptions used for calculating the flexural strength are very straight forward. They include the assumptions from reinforced concrete analysis along with a few particular to FRP such as: the FRP has a linear elastic relation to failure, there is a perfect bond between the concrete and FRP and the shear deformation within the adhesive layer is neglected.
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Verification of Shear Capacity
Section shear capacity must be sufficient to handle shear forces associated with increased flexural capacity.
Section 10.2.1, Guide:
Presenter
Presentation Notes
The designer must also ensure that the section should have adequate shear strength to handle the increased flexural capacity. Meaning that the increase in flexural capacity should not induce the shear failure.
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Failure Modes
1. crushing of concrete prior to steel yield2. yield of steel followed by concrete crushing3. yield of steel followed by FRP failure4. shear / tension delamination in concrete cover5. FRP debonding from substrate
The desired mode of failure is usually mode 2 or 3.
Section 10.1.1, Guide:
Presenter
Presentation Notes
In addition to the failure modes associated with reinforced concrete, the addition of FRP adds two more failure modes – shear/tension delamination in the concrete cover and FRP debonding. The desired failure mode, even after addition of FRP, is to have the steel yield – since this is the ductile failure mode. Following steel yielding, the concrete can crush or the FRP can fail.
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Effective Strain in FRP
0
100
200
300
400
500
600
0 0.005 0.01 0.015 0.02Strain (in/in)
Stre
ss (k
si)
Effective Strain
Rupture Strain
Presenter
Presentation Notes
As mentioned earlier, fiber reinforced polymer materials are linear elastic to failure. To ensure a margin of safety in the design, the full ultimate strength of the FRP will rarely be realized. The concept of “effective strain” is introduced in the ACI 440.2R guideline. The “effective strain” is the strain level achieved in the FRP when the section fails (due to concrete crushing, FRP debonding, etc.). Note that since FRP materials are 100% linearly elastic, the effective strain is linearly proportional to the stress developed in the FRP material as well.
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Limitation on Strain in FRP
fuff
cfd tnE
f εε 9.0083.0'
≤= (10-2) US
To prevent debonding in regions away from FRP Termination
(10-2) SI
fdbicufe cch εεεε ≤−⎟⎠⎞
⎜⎝⎛ −
= (10-3)
fuff
cfd tnE
f εε 9.041.0'
≤=
Presenter
Presentation Notes
In the latest document, new limitations have been provided to ensure that the FRP does not debond in regions away from the termination points. I don’t expect you remember these equations, but know that they are there as guidelines.
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Calculation Procedure
Estimated c = c for Equilibrium?
Estimate neutral axis, c
Determine initial strain in substrate
Determine failure mode
Calculate material strain
Calculate stresses and forces
Check Equilibrium (Calculate c)
Compute Moment Capacity
Check service conditions
YesNo
Presenter
Presentation Notes
So here is an overview of the calculation procedure for flexural strengthening which is an iterative process– First you determine the initial strain in the substrate. This is important because the strain in the FRP is only the strain caused by loads after the installation of the FRP. Any initial strains in the member prior to FRP installation are not counted in the design strain. Then an estimate is made for the neutral axis. A failure mode is determined, and the FRP design strain is calculated. Then the stresses and forces are calculated based on the assumed neutral axis. Equilibrium is checked which calculates a value for c. If this value is the same as the initial assumption – great. Chances are though that the initial c value needs to be adjusted, and the process reiterated until it matches the final value. This may take a few iterations. Once they match, you can compute the section moment capacity and check services conditions.
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Estimate the Neutral Axis DepthNo closed form solution existsMust find depth to the neutral axis by trial and errorAs a starting point, a good rule of thumb is 20% of the effective section depth
dc 20.0≈
c
εs
εfe εbiεb
εc
Presenter
Presentation Notes
So – to go over that step by step – after first determining the initial strains in the substrate, you estimate a value for c. A good starting point is 0.20d.
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Determine Mode of Failure
Concrete Crushing Controls
FRP Rupture Controls
(10-3)fdbicufe cch εεεε ≤−⎟⎠⎞
⎜⎝⎛ −
=
fdbicufe cch εεεε ≤−⎟⎠⎞
⎜⎝⎛ −
=
fdbicufe cch εεεε ≥−⎟⎠⎞
⎜⎝⎛ −
=
Presenter
Presentation Notes
Then you determine the failure mode. If the design strain, based on the assumed c, is smaller than the rupture strain, debonding of the FRP controls. If the design strain is larger, concrete crushing controls. This is important because….
37
Concrete Stress Block
Whitney stress block is valid only when concrete crushing governs failure (i.e., εc=0.003)If FRP rupture controls, a stress block appropriate for the concrete strain level should be used
ActualStress
Distribution
EquivalentStress
Distribution
γf 'c
β1cc
Presenter
Presentation Notes
ACI 318 uses the Whitney stress block model for estimating the compressive stress distribution. This model is only valid when concrete crushing is governing failure. If FRP failure governs failure, the strain level in the concrete may be substantially lower than 0.003-in/in. The Whitney stress block will not give an equivalent stress distribution for this condition. The actual non-linear stress distribution in the concrete must be considered or an alternative equivalent stress block model must be employed.
38
Concrete Stress Block
( ) ( )[ ]( ) ( )22
1
1 1ln tan42
cccc
cccc
εεεεεεεεβ′+′′−′
−=−
( )cc1
2c
2c1900
ε′εβε′ε+
=γ ln.
c
cc E
f711 ′=ε′
.
εc < 0.003
γf'c
β1c
Presenter
Presentation Notes
One equivalent stress block model, for concrete strains less than 0.003-in/in, is shown here. Once again, don’t worry about the whole equation, just know remember the general design process.
39
Calculation of Flexural StrainAssume strain compatibilityBased on failure modeCalculate the strain in each material by similar triangles
( ) ⎟⎟⎠
⎞⎜⎜⎝
⎛
−−
+=cdcd
fbifes εεε (10-10)
c
εs
εfe εbiεb
εc
Presenter
Presentation Notes
With the strain in the FRP determined, the strain level in the steel reinforcement and concrete can be determined.
40
Calculation Of Stress
ysss fEf ≤= ε
Steel – Elastic / Plastic:
fesfe Ef ε=FRP – Elastic:
(10-11)
(10-9)
StrainSt
ress FRP
Steel
Presenter
Presentation Notes
With the strain level in each material, the stresses in each material can be determined as well. For the steel reinforcement (which is idealized as elastic-perfectly plastic), Eqn 10-9 will indicate the stress level in the steel. For the FRP (which is idealized as perfectly elastic), the stress level can be determined from Eqn 10-9.
41
Check Force EquilibriumSum forces in the horizontal directionIf forces do not equilibrate, revise “c”Repeat previous steps
bffAfA
cc
fefssest ′
+=
11αβ Asfs
α1f'cβ1c
Afff
Presenter
Presentation Notes
With all of the material stresses determined, internal force equilibrium may be checked. If the neutral axis depth, c, determined by the equation shown is different from the estimated neutral axis depth, then force equilibrium is not satisfied. The neutral axis depth must then be revised and the iterative process repeated until force equilibrium is satisfied. You can see that this analysis is the same as used for reinforced concrete, with the addition of the FRP force at the bottom of the section.
42
Ultimate Strength Model
εfe εbiAf = n tf wfffe = Ef εfe
fsεs
εc
c
⎟⎠⎞
⎜⎝⎛ −+⎟
⎠⎞
⎜⎝⎛ −=
2211 chfAcdfAM feffssnβψβ
(10-13)
Presenter
Presentation Notes
With strain compatibility and force equilibrium satisfied, the nominal moment strength of the reinforced/strengthened concrete section may be determined.
43
Loss in Ductility
( )
⎪⎪⎩
⎪⎪⎨
⎧
≤
<<−
−+
≥
=
syt
tsysy
syt
t
for
for
for
εε
εεεεε
ε
φ
65.0
005.0005.0
25.065.0
005.090.0
ACI 318 :A section with lower ductility should compensate with a higher reserve of strength
(10-5)
0.90
0.65
φ
Steel Strain at Ultimate
εsy 0.005
ρb
≈0.75ρb
Presenter
Presentation Notes
Following the philosophy of ACI 318, guidelines are given for appropriate phi factors based on section ductility.
44
Design Flexural Strength
⎥⎦
⎤⎢⎣
⎡⎟⎠⎞
⎜⎝⎛ −+⎟
⎠⎞
⎜⎝⎛ −=
2211 chfAcdfAM fefssnβψβφφ
Reduction factor for FRP contribution: 85.0=ψ
(10-13)
(10-1)un MM >φ
Presenter
Presentation Notes
With the strength reduction factor, phi, computed based on ductility, the design moment strength may be computed. Please note that there is also a reduction factor for the FRP contribution. This partial reduction factor is used in recognition of the fact that FRP reinforcement is not as statistically reliable as internal steel reinforcement.
45
ServiceabilityAt service, stress in steel should be limited to 80% of yield strength:
yss ff 80., ≤ (10-6)
Curvature
Mom
ent
Unstrengthened
FRP Strengthened
Ms
My
Mu
Presenter
Presentation Notes
A final check for serviceability should be made to ensure that at service, the stress in the steel is below 80% of the yield strength.
46
Prestressed Concrete MembersAssumptions
Assumptions for concrete members applystrain compatibility for strain or change in strain in the prestressing steel prestressing steel rupture mode should be investigatedwhere prestressing steel is draped several sections should be evaluated
Presenter
Presentation Notes
This same design philosophy can be extended to prestressed members. A few more assumptions are made in the design process – there is strain compatibility in the prestressing steel and in the case of draped steel, several sections along the length of the member should be checked. Note that the design equations in the latest ACI 440.2R can be applied to bonded prestressed members. The design for unbonded prestressed members is still being evaluated.
47
Prestressed Concrete MembersFailure Modes
1. Strain level in FRP governed by strain limitations due:1. concrete crushing2. FRP rupture3. FRP debonding4. Prestressing steel failure
Presenter
Presentation Notes
Adding on to the evaluation of failure modes, you must also consider prestressing steel failure
48
To maintain a sufficient ductility the nominal strain in the prestressing steel should be higher than 0.013. If this strain is not achieved a lower strength factor should be used
As with non prestressed sections, appropriate phi factors are chosen based on ductility.
49
In service stress in the prestressing steel should be prevented from yielding:
Prestressed Concrete MembersServiceability
pysps ff 82.0, ≤
pusps ff 74.0, ≤
(10-20a)
(10-20b)
Presenter
Presentation Notes
And serviceability must be checked.
50
•The calculation procedure for nominal strength:• satisfy should strain compatibility•satisfy force equilibrium•consider mode of failure•similar to method for reinforced members
Prestressed Concrete MembersNominal Strength
Presenter
Presentation Notes
The nominal strength is calculated in a similar method to reinforced sections
51
For a given value of the neutral axis, c:
Prestressed Concrete MembersNominal Strength
feffe Ef ε=
035.01 2
2
≤+⎟⎟⎠
⎞⎜⎜⎝
⎛++= pnet
cc
epeps r
eEA
P εεε
Stress level in the FRP
Strain in the tendon
(10-21)
(10-22)
Presenter
Presentation Notes
The appropriate stress and strain values are computed
52
The value of enet depends on the mode of failure
Prestressed Concrete MembersNominal Strength
⎟⎟⎠
⎞⎜⎜⎝
⎛ −≤
ccd p
pnet 003.0εconcrete crushing
FRP rupture or debonding ( ) ⎟
⎟⎠
⎞⎜⎜⎝
⎛
−−
+≤cdcd
f
Pbifepnet εεε
(10-23a)
(10-23b)
Presenter
Presentation Notes
Modes of failure are evaluated
53
Force equilibrium can be checked by satisfying:
Prestressed Concrete MembersNominal Strength
bffAfA
cc
fefpsp
1'
1 βα+
= (10-25)
Presenter
Presentation Notes
And equilibrium is satisfied
54
Case Study – Slab Upgrade
P/T flat slab live load increase:
50 – 100 psf
Presenter
Presentation Notes
And just to give you a break from looking at slides with equations, a picture of a slab strengthening project using FRP. A change of use in the garage resulted in an increase in the required loading from 50 to 100 psf. FRP was used to add additional moment capacity.
55
Case Study – Slab Upgrade
Positive moment upgrade to column strip
Presenter
Presentation Notes
Another case of positive moment strengthening.
56
Shear StrengtheningChapter 11, Guide
un VV >φ
Increase shear capacity of beams or columnsAmount of increase depends on section geometry, existing reinforcement, and a variety of additional factors.
Change failure mode to flexuralTypically results in a more ductile failure
(11-1)
Presenter
Presentation Notes
On to shear strengthening. Similar to flexural strengthening, the nominal shear strength must be greater than the design shear strength.
57
Wrapping Schemes
Fully Wrapped “U-wrap” Two sides bonded
Overlap
Presenter
Presentation Notes
The FRP material can be wrapped around the entire cross section, in a “U” wrap configuration, or simply bonded to two sides of the member. Fully wrapped sections are often impractical for beams as it is necessary to penetrate through the adjoining slab or flange. However, this is quite common and practical for shear strengthening of concrete columns.
58
Effective Strain in FRP
Maximum strain that can be achieved in the FRP system at the ultimate load stageGoverned by the failure mode of the FRP system and the strengthened member.
memberswrappedcompletelyforfufe εε 75.0004.0 ≤=
pliesfaceorwrapsUbondedforfuvfe −≤= 004.0εκε
(11-6a)
(11-6b)
Presenter
Presentation Notes
And with FRP shear reinforcement, the concept of strain limitations or effective strain is again employed. For completely wrapped members, loss of aggregate typically controls the failure. This is assumed to occur at a strain level of 0.004-in/in. Thus the effective strain in these applications is assumed to be 0.004-in/in. For applications where the material is wrapped on three sides or just bonded on the two faces of the beam, the strain value is a percentage of the ultimate strain, calculated as kv.
59
Effective Strain Limitations for FRPDetermination of bond-reduction coefficient κv:
75.0468
Lkk
fu
e21v ≤
ε=κ (11-7) US
75.0900,11
21 ≤=fu
ev
Lkkε
κ
3/2'c
1 4000f
k ⎟⎟⎠
⎞⎜⎜⎝
⎛= (11-9) US
3/2'c
1 27f
k ⎟⎟⎠
⎞⎜⎜⎝
⎛=
⎪⎪⎩
⎪⎪⎨
⎧
−−
−
=bondedsidestwofor
dLd
wrapsUford
Ld
k
f
ef
f
ef
22
(11-7) SI(11-9) SI
(11-10)
Presenter
Presentation Notes
The percentage, kv, is a function of the strength of the concrete and wrapping scheme used. This is evident in the series of equations shown. Note also that the effective strain is limited to 75% of the ultimate elongation to account for the less common FRP rupture failure mode. Kv is a function of factors k1 and k2 and an active bond length Le.
60
Effective Strain Limitations for FRPDetermination of active bond length Le:
(11-8) US( ) 58.0ff
e Etn2500L = ( ) 58.0
ffe
Etn300,23L = (11-8) SI
Le
Presenter
Presentation Notes
It has been observed that when FRP bonded to concrete is in direct tension the majority of bond stresses are carried over a relatively small length of the FRP. This length is shown as Le.
61
Effective Strain Limitations for FRPDetermination of bond-reduction coefficient κv:
75.0468
Lkk
fu
e21v ≤
ε=κ (11-7) US
75.0900,11
21 ≤=fu
ev
Lkkε
κ
3/2'c
1 4000f
k ⎟⎟⎠
⎞⎜⎜⎝
⎛= (11-9) US
3/2'c
1 27f
k ⎟⎟⎠
⎞⎜⎜⎝
⎛=
⎪⎪⎩
⎪⎪⎨
⎧
−−
−
=bondedsidestwofor
dLd
wrapsUford
Ld
k
f
ef
f
ef
22
(11-7) SI(11-9) SI
(11-10)004.0≤= fuvfe εκε
Presenter
Presentation Notes
So going back to the formulas for kv, you insert the correct values for k1, k2 and Le and determine the effective strain
62
Pertinent Shear Dimensions
df
wf
sf
wf
sf
β
( )f
ffefvf s
dcossinfAV
α+α=
fffv wnt2A =
ffefe Ef ε=
(11-3)
(11-4)
(11-5)
α
Presenter
Presentation Notes
With the effective strain computed, the shear contribution of the FRP reinforcement can be simply calculated by the equations shown, working from the bottom up. Note that these equations are very similar to the equations used to compute the contribution of internal steel stirrups to the shear strength.
63
Design Shear Capacity
( )ffscn VVVV ψφφ ++=
( )
)(85.0
)(95.0)318(85.0
pliesfaceorwrapsUbonded
wrappedfullyACI
VVVV
f
f
fscn
−=
==
++=
ψ
ψφ
ψφφ
(11-2)
Presenter
Presentation Notes
The overall design shear capacity can be obtained from summing the contribution of the concrete, steel, and FRP as shown in Eqn 11-2 with the appropriate strength reduction factors. Note that the overall strength reduction factor, phi, is the same as for regular steel reinforced concrete and that a reduction factor is again applied to the FRP. This reduction factor on the FRP is 0.85 for bonded applications and 0.95 for fully wrapped applications. This is done in recognition of the fact that fully wrapped applications are more statistically reliable than bonded applications.
64
Spacing, Reinforcing Limits
4max,dws ff +=
dbfVV wcfs '8≤+
bdf66.0VV cfs ′≤+
(11-11) US
Section 11.1, Guide:
Based on ACI 318-05, Section 11.5.6.9:
(11-11) SI
Presenter
Presentation Notes
A final note on shear strengthening that has been added in the latest ACI version. It is important to maintain reasonable spacing of FRP stirrups just as with steel stirrups. The maximum spacing that will ensure that the FRP reinforcement crosses a potential shear crack is given in the equation shown. There is also an upper limit on the total amount of shear reinforcement that can be provided given by Eqn (11-11). This criteria is similar to the criteria given by ACI 318 to prevent crushing of the compression strut developed in the concrete under shear loads.
65
Case Study – Precast Garage
Installed FRP “U” Wraps
Presenter
Presentation Notes
And finally another picture of an installed FRP strengthening system for beam shear. This picture shows one of the major advantages of FRP in that you only have to install the material where it is needed. This makes it a very cost effective repair solution.
66
ConfinementChapter 12, Guide
Increase in member axial compressive strengthEnhance the ductility of members subjected to combined axial and bending forcesIncrease the strength of members subjected to combined axial and bending forces
Presenter
Presentation Notes
In the latest version of ACI, there has been improvements to the section on confinement.
67
Axial Compression
Fibers oriented transverse to the longitudinal axis of the member
Contribution of any longitudinal fibers to axial strength is negligible
Results in an increase in the apparent strength of the concrete and in the maximum usable compressive strain in the concretePassive confinement
Intimate contact between FRP system and member is critical
Presenter
Presentation Notes
The analysis is based on orienting the fibers transverse to the longitudinal axis of the member. This results in an increase in the apparent strength of the concrete and the maximum usable compressive strain in the concrete. This is an example of a contact critical application, that we discussed earlier.
Confinement
Confining Pressure
Presenter
Presentation Notes
Confinement of a circular section is well understood. The FRP material, shown in blue, provides a confining pressure around the column.
69
FRP Confined Concrete Behavior
ccf ′
ccuε
cf ′
Longitudinal StrainTransverse Strain (Dilation)
Stre
ss
Unconfined Concrete
FRP Confined Concrete
εL
εT
Longitudinal Strain
Transverse Strain
cf ′85.0
cε ′ 003.0=cuεfuε feε
Presenter
Presentation Notes
This chart shows the improvement of the behavior of confined concrete
70
FRP Confined Concrete
Strain Limitation
fufe εκε ε≤= 004.0
Longitudinal StrainTransverse Strain (Dilation)
fufe εκε ε= (12-5)
(12-12)
For pure axial loading:
For combined axial + bending:
55.0=εκ Recommended value (accounts for premature failure strain of FRP)
Limit to maintain shear integrity of concrete
Presenter
Presentation Notes
Designing FRP confined concrete is also, like shear and flexure, based on limiting the design strain. This is to account for premature failure strain of the FRP and to maintain shear integrity of the concrete.
71
FRP Confinement Model
ccu
ccc ffEε
′−′=2
( )
⎪⎩
⎪⎨⎧
≤≤′+′
′≤≤′
−−=
ccuctcc
tccc
ccc
c
forEf
forfEEEf
εεεε
εεεε
2
22
2 04
2
2EE
f
c
ct −
′=′ε
Longitudinal StrainTransverse Strain (Dilation)
Where,
Stre
ss
Unconfined Concrete
FRP Confined Concrete
Ec
E2
Strain
ccf ′
cf ′
tε ′cε ′ ccuε
(12-2a)
(12-2b)
(12-2c)
Presenter
Presentation Notes
The confinement model used by ACI 440.2R is based on the stress and strain model by Lam and Teng.
72
FRP Confinement Model
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛⎟⎟⎠
⎞⎜⎜⎝
⎛′′
+′=45.0
1250.1c
fe
c
lbcccu f
fεε
κεε
lafccc fff κψ 3.3+′=′
Longitudinal StrainTransverse Strain (Dilation)
Where,
fl is the confining pressure exerted by the FRP jacket
κa and κb are shape factors
Stre
ss
Unconfined Concrete
FRP Confined Concrete
Ec
E2
Strain
ccf ′
cf ′
tε ′cε ′ ccuε
(12-3)
(12-6)
Presenter
Presentation Notes
Here are the equations used – they include a shape factor Ka and Kb…
73
Circular Sections
Ef εfe
FRP Jacket
fl
flEf εfe
fl
Concrete0.1== ba κκ
Shape factors:
DtnE
f feffl
ε2= (12-4)
Confining pressure:
Presenter
Presentation Notes
Which are 1 for circular sections.
74
Rectangular Sections
b
h
D 22 hbD +=
DtnE
f feffl
ε2= (12-4)
Confining pressure:
Equivalent circular column
Presenter
Presentation Notes
The confining pressure equations for rectangular sections are limited to those columns with an aspect ratios of less than 2 and face dimension less than 36 inches. Of course, as with most design cases, if testing can be used to demonstrate the effectiveness for other dimensions, FRP can be used.
75
Rectangular Sections
2
⎟⎠⎞
⎜⎝⎛=
hb
AA
c
eaκ
b
h
Effective confinement area, Ae
5.0
⎟⎠⎞
⎜⎝⎛=
bh
AA
c
ebκ
Shape factors:
(12-9)
(12-10)
Confining stress concentrated at corners
Presenter
Presentation Notes
This shows the effective confinement area and the equations for the shape factors for rectangular columns.
76
Rectangular Sections
Ratio of effective confinement area to total area of concrete
( ) ( )
g
gg
cc
c
e A
rbbhrh
hb
AA
ρ
ρ
−
−⎥⎦
⎤⎢⎣
⎡−⎟
⎠⎞
⎜⎝⎛+−⎟
⎠⎞
⎜⎝⎛
−=
13
221
22
(12-11)
Presenter
Presentation Notes
The ratio of effective confinement area to total area is calculated using this rather large equation. It is interesting to note that is based on corner radius (Rc). The larger the radius of your corners, the more effective the FRP wrap, as the confinement is provided in from the corners.
77
Using the Confinement Model
( )[ ]stystgccn AfAAfP +−= '85.085.0 φφ
with existing steel spiral reinforcing
with existing steel-tie reinforcing:
( )[ ]stystgccn AfAAfP +−= '85.080.0 φφ
Compressive Strength:
(12-1a)
(12-1b)
Use the confined concrete compressive strength in ACI 318 equations
Presenter
Presentation Notes
The calculated increased compressive strength of the concrete is used in the axial load equations from ACI 318.
78
Serviceability Considerations-Axial Compression
To ensure radial cracking will not occur under service loads,
'65.0 cc ff ≤
To avoid plastic deformation under sustained or cyclic loads,
ys ff 60.0≤
Section 12.1.3, Guide:
Presenter
Presentation Notes
And serviceability must be checked for axial compression as well.
79
Reinforcement DetailsChapter 13, Guide
General Guidelines:Do not turn inside corners;Provide a minimum 1/2 in. (13 mm) radius when the sheet is wrapped around outside cornersProvide adequate development length
Provide sufficient overlap when splicing FRP plies.
Presenter
Presentation Notes
So the last section for design is reinforcement details. You all have been great for sticking with me through the technical parts of this presentation. Reinforcement details are very important for FRP design and they have been improved in the latest version of 440.2R. I will highlight these quickly just to give you an idea of what to look for that is unique for FRP. Well, let me start with what is not unique. FRP must have sufficient bond length and properly detailed splices, just like with rebar.
Plies should extend a distance equal at least to ldfpast the point along the span corresponding to the cracking moment, Mcr, If Vu > 0.67Vc at the termination point the FRP laminate should be anchored with transverse (“clamping”) reinforcement
Section 13.1.2, Guide
Presenter
Presentation Notes
Successive layers of the material must be staggered at the ends. Each layer should extend 6” past the previous layer.
81
Bond and DelaminationTransverse (“clamping”) reinfocement
Area of transverse (“clamping”) FRP U-Wrap reinforcement to prevent concrete cover layer from splitting:
( )( )
anchorfuvf
allongitudinfufanchorf E
fAA
εκ= (13-1)
Presenter
Presentation Notes
FRP u-wraps may be used at the ends of the beam to prevent the concrete cover layer from splitting. This detail should be used when the factored shear at the termination point is greater than 2/3 of the concrete shear strength. Basically, its an extra anchor for the flexural strengthening in areas of high shear.
82
Development Length
The bond capacity of FRP is developed over a critical length:
'057.0
c
ffdf
f
tEnl =
(13-2)
'c
ffdf
f
tEnl =
in in.-lb units
in SI units
Presenter
Presentation Notes
Equations for development length of externally bonded material
83
Detailing of NSM bars
groove dimensions shall be at least 1.5 times the diameter of the barFor a rectangular bar the minimum groove size shall be 3ab x 1.5bb
Presenter
Presentation Notes
And finally, a few details for NSM. I have not specifically mentioned near surface mounting as the equations I have talked about are all applicable, but to finish I will just mention for those of you who are not familiar with this technology. Near Surface mounting involves taking bars or rods made from FRP and placing them in grooves at the surface of the member. This picture shows a picture of both options. It is important to properly detail the groove dimensions.
84
Development Length of NSM bars
Development length of NSM bar:
( ) fdb
db fdlmax5.04 τ
=
( )( ) fdbb
bbdb f
badal
max5.02 τ+=
Development length of NSM bar:
for rectangular bars
for circular bars (13-3)
(13-4)
Presenter
Presentation Notes
And calculate the development length. So with that….
QUESTIONS?
Thank You
85
Presenter
Presentation Notes
I will ask if there are any questions.
86
Design Example
Flexural Strengthening of Interior Beam
87
Manufacturer’s reported FRP-system properties
24’-0”
w
DL,wLL
ELEVATION SECTION
12”
21.5”
24”f’c=5000 psi
3-#9 barsfy=60 ksi
FRP
2-12”x 23’-0” FRP pliesφMn=266 k-ft
(w/o FRP)
Thickness per ply, 0.040 in. 1.016 mm
Ultimate tensile strength 90 ksi 0.62 kN/mm2
Rupture strain, 0.015 0.015
Modulus of elasticity of FRP laminates, 5360 ksi 37 kN/mm2
Design Example: Flexural Strengthening of an Interior Beam
88
Loadings and corresponding moments
Two, 12 in. wide by 23 ft. long plies are to be bonded to the soffit of the beam using the wet-lay-up technique.
Design Example: Flexural Strengthening of an Interior Beam
89
• Step 1 - Compute the FRP-system design material properties
*fuEfu fCf =
*fuEfu C εε =
For an interior beam, an environmental-reduction factor (CE ) of 0.95 is suggested.
85ksiksi)(0.95)(90 ==fuf
in.0.0142in./15in./in.)(0.95)(0.0 ==fuε
Design Example: Flexural Strengthening of an Interior Beam
90
• Step 2 - Preliminary calculations
Properties of the concrete:
β1 from ACI 318-05, Section 10.2.7.3.
1'1.05 0.05 0.80
1000cfβ = − =
psi4,030,000psi500057,000 ==cE
Design Example: Flexural Strengthening of an Interior Beam
91
Properties of existing reinforcing steel:
bdAs
s ≡ρ
22 in.3.00)in.3(1.00 ==sA
( )( ) 0.0116in.21.5in.12
in.3.00 2
==ρ s
Design Example: Flexural Strengthening of an Interior Beam
• Step 2 - Preliminary calculations
92
• Step 2 - Preliminary calculations
Properties of the externally bonded FRP reinforcement:
fff wntA =
bdAf
f ≡ρ
( )( )( ) 2ply
in. 0.96in.in. 120.040plies 2 ==fA
( )( ) 0.00372in. 21.5in. 12
in. 0.96 2
==fρ
Design Example: Flexural Strengthening of an Interior Beam
93
• Step 3 - Determine the existing state of the strain on the soffit
The existing state of strain is calculated assuming the beam is cracked and the only loads acting on the beam at the time of the FRP installation are dead loads. A cracked section analysis of the existing beam gives k=0.334 and Icr=5937 in.4
ccr
DLbi EI
kdhM )( −=ε
( ) ( )( )[ ]( )( )
0.00061ksi4,030in.5,937
in.21.50.334in.24in.k8644
=
−⋅=
bi
bi
ε
ε
Design Example: Flexural Strengthening of an Interior Beam
94
0128.0)0142.0(9.00113.0 =≤=fdε
• Step 4 – Determine the design strain of the FRP System
( ) ( ) fufd inpsipsi εε 9.0
04.0000536025000083.0 ≤=
Design Example: Flexural Strengthening of an Interior Beam
95
• Step 5 - Estimate c, the depth to the neutral axis
A reasonable initial estimate of c is 0.20d. The value of c is adjusted after checking equilibrium.
dc 20.0= ( )( ) in. 4.30in. 21.50.20 ==c
Design Example: Flexural Strengthening of an Interior Beam
96
• Step 6 - Determine the effective level of strain in the FRP reinforcement
fdbif
fe ccd
εεε ≤−⎟⎟⎠
⎞⎜⎜⎝
⎛ −= 003.0
009.000061.03.4
3.424003.0 ≤−⎟⎠⎞
⎜⎝⎛ −
=feε
009.00131.0 ≤=feε
009.0=feε
Design Example: Flexural Strengthening of an Interior Beam
97
Since FRP controls the section failure, the concrete strain is less than 0.003:
( ) ⎟⎟⎠
⎞⎜⎜⎝
⎛
−+=
cdc
fbiefc εεε
( ) 0021.03.424
3.400061.0009.0 =⎟⎠⎞
⎜⎝⎛
−+=cε
Design Example: Flexural Strengthening of an Interior Beam
98
• Step 7 - Calculate the strain in the existing reinforcing steel
( ) ⎟⎟⎠
⎞⎜⎜⎝
⎛
−−
+=cdcd
fbifes εεε
( ) 0084.030.42430.45.2100061.0009.0 =⎟
⎠⎞
⎜⎝⎛
−−
+=sε
Design Example: Flexural Strengthening of an Interior Beam
99
• Step 8 - Calculate the stress level in the reinforcing steel and FRP
ysss fEf ≤ε=
feffe Ef ε=
ksi60ksi348ksi60)0084.0)(ksi000,29(s
≤=≤=
sff
( )( ) ksi.2840.009ksi5,360 ==fef
Design Example: Flexural Strengthening of an Interior Beam
100
• Step 9a - Calculate the internal force resultants
Approximate stress block factors may be calculated using the parabolic stress-strain relationship of concrete as follows:
0021.010030,4
)000,5(7.17.16
'' =
×==
c
cc E
fε
Design Example: Flexural Strengthening of an Interior Beam
749.0)0021.0(2)0021.0(6
0021.0)0021.0(426
4'
'
1 =−−
=−−
=cc
cc
εεεεβ
886.0)0021.0()749.0(3)0021.0()0021.0(3
33
22'
2'
1 ==−
=c
ccc
γεεεεα
101
• Step 9b – Check equilibrium
Force equilibrium is verified by checking the initial estimate of the neutral axis, c
Design Example: Flexural Strengthening of an Interior Beam
