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**An Introduction to FRP-Strengthening of Concrete Structures**

ISIS Educational Module 4: An Introduction to FRP-Strengthening of Concrete Structures Updated October 2010 for ISIS Canada ISIS EC Module 4

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Module Objectives The use of FRPs in civil infrastructure is steadily increasing in Canada and around the world. This module is directed mainly to students to: Provide a background and general awareness of FRP materials, their properties , their behaviour and their potential uses Introduce the philosophies and procedures for strengthening structures with FRPs Familiarize the students with designing using the Canadian Highway Bridge Design Code (CHBDC) ISIS EC Module 4

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**Evaluation of Existing Structures Flexural Strengthening **

Overview Introduction FRP Materials Evaluation of Existing Structures Flexural Strengthening Shear Strengthening Column Strengthening Installation of FRP strengthening systems Quality control and quality assurance Additional applications Field applications ISIS EC Module 4

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**Global Infrastructure Crisis**

1 - Introduction The world’s population depends on an extensive infrastructure system Roads, sewers, highways, buildings The system has suffered in past years Neglect, deterioration, lack of funding Global Infrastructure Crisis ISIS EC Module 4

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**Why is strengthening needed?**

1 - Introduction Why is strengthening needed? Many structures, including bridges and parking garages, have become structurally deficient due to deterioration. In Canada, more than 40% of the bridges currently in use were built more than 40 years ago. Many structures are also becoming functionally obsolete due to increased loading. ISIS EC Module 4

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**Why repair with the same materials? Why repeat the cycle?**

2 - FRP Materials Why repair with the same materials? Why repeat the cycle? Light weight High Strength FRP Materials Easy to install 5x steel Corrosion resistant Highly versatile Durable structures Suits many projects ISIS EC Module 4

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**FRP is a composite consisting of fibres and matrix. Fibres: **

2 - FRP Materials FRP is a composite consisting of fibres and matrix. Fibres: Provide strength and stiffness Their quality, orientation and shape affect the final product Matrix (resin): Coats the fibres Protects the fibres from abrasion Transfers stresses between the fibres Strain [%] 2-8 50-90 Stress [MPa] Fibres FRP Matrix ISIS EC Module 4

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**FRP material properties are a function of: **

2 - FRP Materials FRP material properties are a function of: Fibre quality, orientation and shape Fibre volumetric ratio Adhesion to the matrix Manufacturing process (additives and fillers) ISIS EC Module 4

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**Wide range of FRP products are available: Plates (Rigid strips) **

2 - FRP Materials Wide range of FRP products are available: Plates (Rigid strips) Sheets (Flexible fabric) Rods The fibres could be: Carbon Glass Aramid FRP sheet ISIS EC Module 4

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**FRP advantages: Disadvantage: 2 - FRP Materials Does not corrode**

High strength to weight ratio Reduced installation time and cost Non-conductive and non-metallic Low maintenance requirements Disadvantage: High temperature is a serious concern ISIS EC Module 4

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**FRP properties versus steel: Linear elastic behaviour to failure **

3 - FRP Materials FRP properties versus steel: Linear elastic behaviour to failure No yielding Higher ultimate strength Lower strain at failure Strain [%] 1 2 3 500 1000 1500 2000 2500 Stress [MPa] CFRP GFRP Steel ISIS EC Module 4

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**2 - FRP Materials ISIS EC Module 4 FRP System Fiber Type Weight [g/m2]**

Thickness [mm] Tensile Strength [MPa] Tensile Elastic Modulus [GPa] Strain at Failure [%] Fyfe Co. LLC [www.fyfeco.com] Tyfo SEH51A Glass 915 1.3 460 20.9 1.8 Tyfo SEH25A 505 0.5 417 Tyfo SCH41 Carbon 644 1.0 834 82 0.9 Hughes Brothers Inc. [www.hughesbros.com] Aslan 200 -- 124 Aslan 500 #2 2.0 2068 1.7 Aslan 500 #3 4.5 1965 1.5 Aslan 400 CFRP Laminates 1.4 2400 131 1.9 Sika Canada Inc. [www.sika.ca] SikaWrap 430G 430 504 24.6 SikaWrap 100G 558 24.4 2.2 SikaWrap 230C 230 0.4 715 61.0 1.1 SikaWrap 103C 610 717 65.1 CarboDur S 2800 165 CarboDur M 210 1.2 CarboDur H 1300 300 BASF Building Systems Inc. [www.BASFBuildingSystems.com] MBrace S&P Laminate 2700 159 MBrace EG 900 900 0.37 1517 72.4 2.1 MBrace CF 130 0.17 3800 227 MBrace CF 160 600 0.33 MBrace CF 530 3500 373 0.94 MBrace AK 60 Aramid 0.28 2000 120 1.6 ISIS EC Module 4

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**Installation: 1) Wet lay-up system: 2 - FRP Materials**

- The system is installed on the surface of the concrete element while the resin matrix is still “wet”, and the polymerization occurs on site - Saturate sheets with epoxy adhesive, then place on the concrete surface and press with a roller - Used with flexible sheets - Multiple layers can be used Epoxy Roller ISIS EC Module 4

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**2) Pre-cured system: 2 - FRP Materials**

- Used with FRP plates or laminates - Used for surface bonded plates or near surface mounted reinforcements - Not as flexible for variable structural shapes - The pre-cured laminates should be placed on or into the wet adhesive - Place on the concrete surface - Multiple layers can not be used ISIS EC Module 4

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**3- Near Surface Mounted (NSM)**

2 - FRP Materials 3- Near Surface Mounted (NSM) It is a newer class of FRP strengthening technique. Un-strengthened concrete T-beam Longitudinal grooves cut into soffit FRP strips placed in grooves Grooves filled with epoxy grout Research indicates that NSM reinforcement is effective and efficient for strengthening. ISIS EC Module 4

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**FRP-Strengthening Applications :**

2 - FRP Materials FRP-Strengthening Applications : Type Application Fibre Dir. Schematic Flexural face of the beam Tension and/or side axis of the beam Along long. Section Shear Side face of the beam (U or closed wrap) Perpendicular to long. axis of the beam Section Confinement Around the column Circumferential Section ISIS EC Module 4

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**3 - Evaluation of Existing Structures**

Repair process includes: Evaluation of the existing structure Understanding the cause and the effect of the deterioration Determining if repair is required and its extent (quantify) Analysis and design Introducing a repair strategy ISIS EC Module 4

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**3 - Evaluation of Existing Structures**

Fixing the effect without understanding the cause is likely to result in premature failure of repair. Proper repair requires an understanding of the cause to eliminate the effect. Evaluation is important to: Determine concrete condition Identify the cause of the deficiency Establish the current load capacity Evaluate the feasibility of FRP strengthening ISIS EC Module 4

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**3 - Evaluation of Existing Structures**

Evaluation should include: All past modifications Actual size of elements Actual material properties Location, size and cause of cracks and spalling Location and extent of corrosion Quantity and location of rebar ISIS EC Module 4

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**3 - Evaluation of Existing Structures**

Problems in a structure could be due to: Defects: In design or material or during construction Damage: Due to overloading, earthquake or fire Deterioration: Due to corrosion or sulphate attack ISIS EC Module 4

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**3 - Evaluation of Existing Structures**

Examples of some deficiencies: 1. Environmental effects Wet-Dry Chloride Ingress Freeze-Thaw ISIS EC Module 4

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**2. Corrosion 3 - Evaluation of Existing Structures**

A primary factor leading to extensive degradation….. 2. Corrosion End result Concrete Reinforcing Steel Moisture, oxygen and chlorides penetrate Corrosion products form Volume expansion occurs Through concrete More cracking Through cracks Corrosion propagation ISIS EC Module 4

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**3 - Evaluation of Existing Structures**

Deficiencies could be due to: Updated design loads Updated design code procedures Increase in traffic loads Now Then ISIS EC Module 4

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**3 - Evaluation of Existing Structures**

Deficiencies could be due to: Fire damage Earthquakes ISIS EC Module 4

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**4 - Flexural Strengthening**

Material resistance factors (CHBDC): - Concrete c = 0.75 - Steel reinforcement: - Reinforcing bars s = 0.90 - Prestressing strands p = 0.95 - Base FRP for pultruded FRP: - AFRP FRP = (for externally bonded applications) - AFRP FRP = (for NSMR) - CFRP FRP = (for externally bonded applications and NSMR) - GFRP FRP = (for externally bonded applications and NSMR) - Non-pultruded FRP made by wet lay-up: 0.75 times base FRP ISIS EC Module 4

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**4 - Flexural Strengthening**

Failure Modes The analysis of the flexural strength of FRP strengthened elements is based on the following assumptions: 1) The internal stresses are in equilibrium with the applied loads. 2) Plane sections remain plane. 3) Strain compatibility exists between adjacent materials. (ie. Perfect bond between: concrete and steel, concrete and FRP) 4) The maximum tensile strain of the FRP (eFRPt ) is 5) The maximum compressive strain in the concrete (ecu ) is 6) The contributions of FRPs in compression and of the concrete in tension are neglected. ISIS EC Module 4

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**4 - Flexural Strengthening**

Failure Modes The potential modes of failure are: 1) Concrete crushing before steel yielding or rupture of the FRP. 2) Steel yielding followed by concrete crushing before rupture of the FRP. 3) Steel yielding followed by rupture of the FRP. 4) Peeling, debonding, delamination or anchorage failure of the FRP (considered premature tension failures to avoid). ISIS EC Module 4

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**4 - Flexural Strengthening**

Rectangular section without compression steel: b d Cross Section As Strain Distribution eFRP ec h bFRP es c Stress Distribution fs ffrp Equiv. Stress Distribution a = b1c a1Φcf’c Ts Tfrp Cc Ts = fsAsfs TFRP = fFRPAFRPEFRPeFRP Cc = fca1f’cb1bc ISIS EC Module 4

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**4 - Flexural Strengthening**

The equilibrium equations are: 1) Force equilibrium in the section: Compression forces =Tension forces 2) Moment equilibrium in the section: External applied moment= Internal moment Cc = Ts + TFRP a a Mapplied = Ts d - + TFRP h - 2 2 ISIS EC Module 4

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**4 - Flexural Strengthening**

Rectangular section with compression steel : b ecu a1Φcf’c d’ e’s Cs f’s c a = b1c A’s Cc d h As es fs Ts eFRP ffrp Tfrp bFRP Cross Section Strain Distribution Stress Distribution Equiv. Stress Distribution Add a compressive stress resultant Cs = fsf’sA’s a a a Mr = Ts d- +TFRP h- - d′ +Cs 2 2 2 ISIS EC Module 4

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**4 - Flexural Strengthening**

Iterative design procedure: Assume initial strains Select FRP material and AFRP Assume a failure mode If concrete crushing before steel yields, then: ecu = and esteel < eyield If concrete crushing after steel yields, then: ecu = and esteel > eyield If FRP ruptures after steel yields, then: efrp = efrpt and esteel > eyield b ec c d h As es efrp bfrp ISIS EC Module 4

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**4 - Flexural Strengthening**

Determine the compressive stress block factors (a1, b1) b a1Φcf’c a = b1c d Cc h As Ts TFRP bfrp b1 = 0.97 – f’c > 0.67 a1 = 0.85 – f’c > 0.67 ISIS EC Module 4

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**4 - Flexural Strengthening**

Calculate c (neutral axis position) Using equilibrium equation the following equations can be derived and used: - Concrete crushing before steel yields (es and e’s < ey ) -Steel yielding followed by concrete crushing (es and e’s > ey ) - Steel yielding followed by FRP rupture (es and e’s > ey ) a1fc f’cb1bc2 + fsEs ecu (As’+As)+ fFRPEFRP (ecu+efi)AFRP c - fsEs ecu (As'd'+Asd)+ fFRPEFRP ecuAFRP h = 0 a1fc f’cb1bc2 + fsfy(As’-As)+ fFRPEFRP (ecu+efi)AFRP c- fFRPEFRP ecuAFRP h = 0 fsfy(As-As’)+ fFRPEFRP eFRPtAFRP c = a1fc f’cb1b ISIS EC Module 4

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**4 - Flexural Strengthening**

Check failure mode assumption with the material strains If failure is initiated by: Concrete crushing: FRP rupture: - If the assumption is proven to be false, go back to step 3 and make another assumption - If the assumption is correct, proceed to the next step ecu= es= ecu eFRP = eFRPu ≤ eFRPt (efi+eFRPu) ≤ es'= (efi+eFRPt) (efi+eFRPu) ≤ es= (efi+eFRPt) (efi+eFRPu) ≤ ec= (efi+eFRPt) d - c c-d' c-d' h-c h-c c d-c d-c h - c eFRP= ecu - efi h-c h-c c c c c - d' es'= ecu h-c h-c c ISIS EC Module 4

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**4 - Flexural Strengthening**

Compute internal forces Calculate the section moment resistance (Mr) Compare Mr to the applied moment (Mapplied) If Mr < Mapplied, go to step 2 and change AFRP If Mr > Mapplied, then the design is safe Cs = fsfsA's Ts = fsAsfs Tfrp = ffrpAFRPEFRPeFRP a a a - d′ Mr = Ts d- +TFRP h- +Cs 2 2 2 ISIS EC Module 4

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**4 - Flexural Strengthening**

Optimized determination of AFRP Assuming: All the steel has yielded and combining the equilibrium equations: Determine c using the following equation Determine strain in FRP a1fc f’cbwb12c2 -a 1 fc f’cbwhb1c- Cs(h-d′)+Ts(ds-h) - Mf = 0 2 h - c eFRP = ecu - efi ≤ ≤ eFRPu c ISIS EC Module 4

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**4 - Flexural Strengthening**

Determine successively: Optimize value of AFRP Use this AFRP as an input for the iterative design method Cc = fca1f’cb1bc TFRP = Cc + Cs - Ts TFRP AFRP = fFRPEFRP eFRP ISIS EC Module 4

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**4 - Flexural Strengthening**

T-section: If the neutral axis lies in the web (c < hf), then treat it as a rectangular section with a compression zone width = be. If the neutral axis lies outside the web (c > hf), then treat it as a T-section. Geometric parameters ISIS EC Module 4

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**4 - Flexural Strengthening**

= + Geometric parameters Factored moment subdivision The section is treated as the summation of: flange (Mrf) and web (Mrw). - Flange (Mrf) a1fc f’c(be-bw)hf hf Asf = Mrf = fs fy Asf d - fsfy 2 - Web (Mrw) a a Asw = As –Asf Mrw = fs fy Asw d - +TFRP h - 2 2 ISIS EC Module 4

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**4 - Flexural Strengthening**

Design procedure: Select FRP material and AFRP Determine behaviour of the section ( Rect. or T) If Then, it is rectangular behaviour Else, it is a T-section Determine Asf and Mrf Determine AFRP to obtain required Mrw fsfyAs+fFRP EFRP eFRP A FRP hf ≥ a1fc f’c b1be ISIS EC Module 4

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**4 - Flexural Strengthening**

Example: Calculate the moment resistance (Mr) for an FRP-strengthened rectangular concrete section Section information: b = 125 mm h = 360 mm 2-15M bars d = 320 mm CFRP f’c = 40 MPa efrpu = 1.26 % AFRP = 110 mm2 fy = 400 MPa Es = 200 GPa EFRP = 210 GPa ISIS EC Module 4

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**4 - Flexural Strengthening**

Solution: Step 1: Assume failure mode Assume failure of beam due to crushing of concrete in compression after yielding of internal steel reinforcement Thus, ecu= and esteel > eyield ISIS EC Module 4

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**4 - Flexural Strengthening**

Step 2: Calculate concrete stress block factors a1 = 0.85 – f’c > 0.67 a a1 = 0.85 – (40) = 0.79 b1 = 0.97 – f’c > 0.67 a b1 = 0.97 – (40) = 0.87 ISIS EC Module 4

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**4 - Flexural Strengthening**

Step 3: Find depth of neutral axis, c Steel yielding followed by concrete crushing a1fc f’cb1bc2 + fsfy(As’-As) + fFRPEFRP (ecu+efi)AFRP c - fFRPEFRP ecuAFRP h = 0 0.79(0.75)40(0.87) 125(c2) + 0.9(400) (0-400)+ 0.80(210000)( )110 c - 0.80(210000) (0.0035)(110)360 = 0 (c2)-79320(c) = 0 c = mm or c = mm (rejected) ISIS EC Module 4

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**4 - Flexural Strengthening**

Step 4: Check mode of failure Steel yielding followed by concrete crushing ecu= es= ecu ds-c = = > 0.002(ey) c 111.7 h-c eFRP= ecu = = > 0.006 not O.K. c 111.7 Trial 2, assume the steel yields and the strain in the FRP is 0.006 ISIS EC Module 4

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**4 - Flexural Strengthening**

Step 5: Trial 2 Compression in concrete = Tension in ( Steel + FRP) a1fc f’cbb1c = fsfy As + fFRPEFRP eFRPAFRP 0.79(0.75)40(0.87)125(c) = 0.9(400) (210000)0.006(110) c = 98.9 mm ISIS EC Module 4

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**4 - Flexural Strengthening**

Step 6: Check mode of failure eFRP = 0.006 es= eFRP ds-c = > 0.002(ey) = 0.006 h-c c 98.9 ecu= eFRP = 0.006 = < O.K. h-c The assumed mode of failure is correct ISIS EC Module 4

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**4 - Flexural Strengthening**

Step 7: Moment Resistance b1c b1c Mr = Ts ds- +TFRP h- 2 2 b1c b1c = fsfy As fFRPEFRP eFRPAFRP ds- h- 2 2 0.87 (98.9) = 0.9(400)400 +0.80(210000)0.006(110) 320- 2 0.87 (98.9) 360- 2 Mr = 75 106 N.mm = 75 kN.m ISIS EC Module 4

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**4 - Flexural Strengthening**

Example: The T-beam requires strengthening to upgrade its moment capacity to 600 kN-m. Calculate the required area of FRP (Afrp). Section information: f’c = 30 MPa efrpu = 1.26 % As = 8 x 300 mm2 fy = 400 MPa Es = 200 GPa Efrp = 155 GPa ISIS EC Module 4

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**4 - Flexural Strengthening**

Step 1: Calculate concrete stress block factors a1 = 0.85 – f’c > 0.67 a a1 = 0.85 – (30) = 0.805 b1 = 0.97 – f’c > 0.67 a b1 = 0.97 – (30) = 0.895 ISIS EC Module 4

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**4 - Flexural Strengthening**

Step 2: Evaluating the moment capacity of the existing section Assume neutral axis is inside the flange (c < hf) Compression in concrete = Tension in steel a1fc f’cbb1c = fsfy As 0.805(0.75)30(0.895)650(c) = 0.9(400)(300× 8) c = 82mm > hf The assumption (c < hf) is wrong. ISIS EC Module 4

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**4 - Flexural Strengthening**

Step 2: Evaluating the moment capacity of the existing section Assume neutral axis is outside the flange (c > hf) a1fc f’c(be-bw)hf Asf = fsfy 0.805(0.75)30( )70 =1409 mm2 Asf = 0.9(400) Asw = As –Asf = = 991 mm2 70 Mrf = 0.9 (400)1409 (510 - ) = ×106 N.mm = kN.m 2 ISIS EC Module 4

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**4 - Flexural Strengthening**

Step 2: Evaluating the moment capacity of the existing section Compression in concrete = Tension in steel (Asw) a1fc f’cbb1c = fsfy Asw 0.805(0.75)30(0.895)250(c) = 0.9(400)(991) c = 88.03mm > hf 0.895 (88.03) Mrw= 0.9 (400)991(510 - ) = ×106 N.mm = kN.m 2 Mr= =408.8 kN.m Moment resistance of the section ISIS EC Module 4

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**4 - Flexural Strengthening**

Step 3: Optimized determination of AFRP 1) Determine c using the following equation: a1fc f’cbwb12c2 - a1fc f’cbwhb1c - Cs(h-d′)+fsfy Asw(ds-h)-(Mf -Mrf ) = 0 2 0.805(0.75)30(250)(0.895)2c2 (0.75)30(250)600(0.895)c 2 - 0.9(400)991( ) + ( )x106 = 0 c c = 0 c= (rejected) or 187mm (accepted) ISIS EC Module 4

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**4 - Flexural Strengthening**

Step 3: Optimized determination of AFRP 2) Strain in FRP h-c eFRP = ecu = = > 0.006 c 187 eFRP = 0.006 TFRP = a1fc f’cbwb1c - fsfy Asw =0.805(0.75)30(250)0.895(187) - 400(0.9)991= N TFRP AFRP = = = mm2 fFRPEFRP eFRP 0.75x0.8×155×103×0.006 Select: 2 layers b = 250mm and tFRP = 1.5mm, AFRP = 750mm2 ISIS EC Module 4

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**4 - Flexural Strengthening**

Step 4: Check the design Assume tension failure of the FRP and yielding of steel 1) Neutral axis location TFRP + fsfy Asw 0.75(0.8)(155000)0.006(750)+ 0.9(400)991 c = = a1fc f’cbb1 0.805(250)0.75(30)0.895 = mm >hf …………O.K 2) Check strains c 191.3 ec= eFRP = 0.006 = < h-c ds-c es= eFRP = 0.006 = > ey ………….O.K h-c ISIS EC Module 4

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**4 - Flexural Strengthening**

Step 4: Check the design 3) Moment resistance of the section b1 c b1 c Mrw = Ts ds - +TFRP h - = 2 2 0.895(191.3) Mrw = 0.9(400)991 510 - × 10-6+ 2 0.895(191.3) 0.75(155000)0.006(600) 600 - × 10-6 2 = kN.m 70 Mrf = 0.9(400)1409(510 - ) = ×106 N.mm = kN.m 2 Mrt = Mrw + Mrf = = kN.m ISIS EC Module 4

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**FRP sheets can be applied to increase shear resistance. **

5 - Shear Strengthening The shear resistance of the concrete element depends on the interaction between the concrete and the reinforcement. FRP sheets can be applied to increase shear resistance. The sheets are placed perpendicular or at an angle to the beam’s longitudinal axis. The shear capacity from the FRP stirrups is related to the angle of the cracks in the concrete, the direction and the effective strain of the FRP. ISIS EC Module 4

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**dfrp is the effective shear depth for FRP **

5 - Shear Strengthening dfrp is the effective shear depth for FRP sfrp is the spacing of the FRP stirrups wFRP is the width of the FRP stirrup is the angle of inclination of diagonal cracks in the concrete. b is the angle of the FRP stirrups ISIS EC Module 4

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**Many different possible configurations: **

5 - Shear Strengthening Many different possible configurations: 1) Continuous wraps or finite width sheets (width and spacing) 2) Angle between the sheet and the beam’s axis 3) Wrap configuration with respect to the cross section Continuous Finite b = 90 b 90 U-Wrap Fully Wrapped ISIS EC Module 4

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**Shear resistance of a beam (Vr ): 1) Existing capacity **

5 - Shear Strengthening Shear resistance of a beam (Vr ): 1) Existing capacity - Resistance from concrete (Vc) - Resistance from steel (Vs) 2) Additional capacity - Resistance from FRP wraps (Vfrp) Vr = Vc Vs Vfrp + ISIS EC Module 4

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**fs fyAv dv(cotq+cota)sina**

5 - Shear Strengthening Shear resistance of a beam (Vr ): 1) Resistance provided by concrete (Vc) dv ≥ (0.72h, 0.9d) 2) Resistance provided by steel (Vs) Vc = 2.5bvfcfcr bvdv Vs = fs fyAv dv(cotq+cota)sina s ISIS EC Module 4

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**fFRP AFRP EFRP eFRPe dFRP (cotq + cotb) sinb**

5 - Shear Strengthening 3) Resistance provided by FRP: Vfrp = fFRP AFRP EFRP eFRPe dFRP (cotq + cotb) sinb sFRP Afrp = 2 tfrp wfrp efrpe is the effective strain in the FRP stirrups dfrp is the effective depth sfrp is the spacing of the FRP stirrups ISIS EC Module 4

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**Tension FRP for flexure**

5 - Shear Strengthening Effective depth of FRP, dfrp: a d Closed wrap shear FRP No flexural FRP Closed wrap shear FRP Tension FRP for flexure dfrp ≥ (0.9d, 0.72h) dfrp ≥ 0.9h ISIS EC Module 4

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**Tension FRP for flexure**

5-Shear Strengthening Effective depth of FRP, dfrp: a hfrp U-Shaped FRP stirrup No flexural FRP U-Shaped FRP stirrup Tension FRP for flexure dfrp ≥ (0.9hfrp, 0.72h) dfrp ≥ (0.72h,hfrp) ISIS EC Module 4

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**Effective strain in FRP, eFRPe:**

5 - Shear Strengthening Effective strain in FRP, eFRPe: a efrpe = ≤ 0.75 efrpu (For completely wrapped sections) efrpe = Kvefrpu ≤ (For other configurations) where: Kv= K1= K1K2Le ≤ 0.75 11900 efrpu 2/3 fc’ dfrp-Le 23300 K2 = Le= 27 dfrp (tfrpEfrp)0.58 ISIS EC Module 4

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**- Spacing of strips, sFRP:**

5 - Shear Strengthening Checks: - Spacing of strips, sFRP: sfrp ≤ wfrp + d frp 4 - Maximum allowable shear strengthening, Vfrp : Vc+ Vs+ Vfrp ≤ 0.25fcf’c bvdv ISIS EC Module 4

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**Example: Section information**

5 - Shear Strengthening Shear Strengthening Example: Example Calculate the shear capacity (Vr) for an FRP-strengthened concrete section Section information f’c = 45 MPa efrpu = 1.5% fy = 400 MPa (re-bar & stirrup) Steel used is 10M Efrp = 230GPa s = 225 mm c/c tfrp = 1.02 mm wfrp = 100 mm sfrp = 200 mm Section b = 150 mm hfrp = 450 mm ds =550mm CFRP wrap 150mm Elevation h=600 mm ISIS EC Module 4

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**Solution: 1) Resistance provided by concrete (Vc) Vc = 2.5bvfcfcr bvdv**

5 - Shear Strengthening Solution: 1) Resistance provided by concrete (Vc) Vc = 2.5bvfcfcr bvdv fcr = 0.4* √ f’c = 0.4* √45=2.68 dv ≥ (0.72h and 0.9d) ≥ (0.72*600 and 0.9*550) ≥ (432 and 495) = 495mm Vc = 2.5*0.18*0.75*2.68*150*495*10-3 = kN ISIS EC Module 4

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**fs fyAv dv(cotq + cota)sina**

5 - Shear Strengthening 2) Resistance provided by steel (Vs) Vs = fs fyAv dv(cotq + cota)sina s Vs = (0.9)400(200)495(cot42 + cot90)sin90 225 Vs = 175,921 N = kN ISIS EC Module 4

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**ffrp Afrp Efrp efrpe dfrp (cotq + cotb) sinb**

5 - Shear Strengthening 3) Resistance provided by GFRP (Vfrp) Vfrp= ffrp Afrp Efrp efrpe dfrp (cotq + cotb) sinb sfrp dfrp ≥ (0.9 hfrp,0.72h) ≥ (0.9 × 450, 0.72 × 600) ≥ (405,432) = 432mm Afrp = 2 tfrp wfrp = 2(1.02)(100) = 204 mm2 ISIS EC Module 4

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**3) Resistance provided by FRP:**

5 - Shear Strengthening 3) Resistance provided by FRP: fc’ 2/3 K1= 45 2/3 = = 1.406 27 27 23300 23300 = 17.888mm Le= = (tfrpEfrp)0.58 (1.02 x )0.58 dfrp-Le K2= 0.959 = = dfrp 432 K1K2Le (1.406)(0.959)(17.888) 0.135 < 0.75 =0.135 Kv= = = 11900 efrpu 11900 (1.5)(10-2) ISIS EC Module 4

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**fFRP AFRP EFRPeFRPe dFRP (cotq + cotb) sinb**

5 - Shear Strengthening Effective strain in FRP, efrpe: a efrpe ≤ 0.004 efrpe ≤ Kvefrpu = (1.5)(10-2)= efrpe= VFRP = fFRP AFRP EFRPeFRPe dFRP (cotq + cotb) sinb sFRP VFRP = 0.6(204)(230000)( )(432)(cot42) 200(1000) =136.8 kN ISIS EC Module 4

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**Total resistance of the section (Vr):**

5 - Shear Strengthening Total resistance of the section (Vr): Vr = Vc Vs VFRP + Vr = = kN ISIS EC Module 4

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**1) Maximum allowable shear strengthening, VFRP :**

Checks: 1) Maximum allowable shear strengthening, VFRP : Vc + Vs + VFRP ≤ 0.25fcf’c bvdv 379.9 ≤ 0.25(0.75)(45)(150)(495)(10-3) 379.9 ≤ kN…………………………O.K. ISIS EC Module 4

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**2) Spacing of strips, sFRP:**

5 - Shear Strengthening Checks: 2) Spacing of strips, sFRP: sFRP ≤ wFRP + d FRP 4 200 ≤ 100 + 432 4 200 ≤ 208 mm…………………….O.K ISIS EC Module 4

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**FRP sheets can be wrapped around concrete columns to increase strength **

6 - Column Strengthening FRP sheets can be wrapped around concrete columns to increase strength How it works: Internal reinforcing steel Concrete FRP wrap flfrp …FRP confines the concrete… Concrete shortens… …and places it in triaxial stress… …and dilates… ISIS EC Module 4

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**6 - Column Strengthening**

The result: Increased load capacity Increased deformation capability ISIS EC Module 4

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**6 - Column Strengthening**

Confinement efficiency Best: circular cross-section Worst: rectangular section Areas of concrete unconfined by the small bending stiffness of FRP system Stress concentration at corners confined unconfined Uniform stress distribution in circular section Stress distribution in rectangular section ISIS EC Module 4

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**6 - Column Strengthening**

Slenderness of the column If the column is not slender, then the column is designed and analyzed for axial load only (short column). If the column is slender, then the column is designed and analyzed for combined axial load and bending moment. ISIS EC Module 4

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**6 - Column Strengthening**

Slenderness of the column Slenderness could be ignored if: klu r < M1 M2 Braced columns klu r < 22 Un-braced columns Where: k is the effective length factor for the column lu is the unsupported length of the column r is the radius of gyration of the section M1 is the smaller end moment at ULS due to factored loads M2 is the larger end moment at ULS due to factored loads ISIS EC Module 4

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**1 - Short column (axial load only)**

6 - Column Strengthening 1 - Short column (axial load only) ISIS EC Module 4

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**6 - Column Strengthening**

1) Confinement Pressure (flFRP): 2tFRPfFRPfFRPu flFRP= …………………………Eq 6-2 Dg Where: flFRP is the confinement pressure tFRP is the thickness of the FRP confining system Dg is the external diameter of the circular section or the diagonal of the rectangular section ISIS EC Module 4

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**6 - Column Strengthening**

Confinement Limits: To ensure adequate ductility of column Minimum confinement pressure Why? Limit flfrp ≥ 0.1fc ′ To prevent excessive deformations of column Maximum confinement pressure Why? Limit flfrp ≤ 0.33 fc ′ ISIS EC Module 4

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**6 - Column Strengthening**

2) Confined concrete strength (fcc): ′ The benefit of the confining pressure is to increase the confined compressive concrete strength, fcc ′ fcc= fc+ 2 flFRP ′ ′ …………………………Eq 6-3 Where: fc is the unconfined specified concrete strength ′ ISIS EC Module 4

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**6 - Column Strengthening**

3) Axial Load capacity (Pr): The factored axial load resistance for an FRP-confined reinforced concrete column, Pr is given by: ′ Pr= 0.8 a1fc fcc(Ag-As)+ fs fyAs …………………………Eq 6-5 Where: Ag is the gross area of the cross section As is the total cross- sectional area of the longitudinal steel reinforcing bars ISIS EC Module 4

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**6 - Column Strengthening**

Design steps for short column (axial load only): 1) Determine the required confined concrete (fcc) strength according to Equation 6-5. 2) Determine the required confinement pressure (flFRP) from Equation 6-3. 3) Using the properties of the selected FRP system, determine a minimal thickness for the FRP (tFRP) from Equation 6-2. 4) Check for the confinement limits. ′ ISIS EC Module 4

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**2 - Slender Column (axial load + moment)**

6 - Column Strengthening 2 - Slender Column (axial load + moment) ISIS EC Module 4

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**6 - Column Strengthening**

Section analysis is based on stress and strain compatibility Axial strain distribution Cross section FRP Steel bars Equivalent stress distribution confined concrete unconfined concrete Internal forces side FRP tension face FRP ec c ec c ′ es c-d ′ esj dsj-c es d-c eFRP h-c = = = = = …………………Eq 6-6 ′ ′ ′ ecc ′ fcc Ccc+ Cc+ Cs – Fsj – Ts - TFRP,side - TFRP,face = Pr ≥ Pf = 5 -1 +1 ′ ec ′ fc ISIS EC Module 4

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**6 - Column Strengthening**

1) Assuming concrete crushing Internal force Distance from the centre of the section ′ ′ ′ ′ h c 2fc+fcc fc+fcc c ec ′ - c - ec ′ Ccc fc b c- ecc ′ 3fc+3fcc ′ ′ 2 ecc 2 h b1 c c Cc ′ ec ′ ec ′ fca1 fc b b 1 - c + 1- ecc ′ ecc ′ 2 2 Cs ′ fs fy A s ′ h /2 -d ecc ′ h fs (dsj-c) dsj - Fsj Es Asj ≤ fs fy A sj c 2 Ts fs fy A s or fs es Es A s if es < ey d – h/2 ecc ′ h (h-c) TFRP,side fFRP (h-c) EFRP (h-c) tFRP - c 2 3 ecc ′ h TFRP,face fFRP (h-c) EFRP btFRP c 2 ISIS EC Module 4

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**6 - Column Strengthening**

′ ′ ec-ec ′ 2) Assuming maximum FRP tension (eFRP = eFRPt ): Dfc= (fcc-fc) ecc - ec ′ ′ Internal force Distance from the centre of the section ′ ′ fc+Dfc h-c ′ h h-c 3fc+Dfc Ccc fc b c- ec c - ec ′ eFRPt eFRPt 6fc+3Dfc ′ 2 2 h-c h b1 h-c ′ ec ′ ec ′ Cc fca1 fc b b1 - c + 1- eFRPt eFRPt 2 2 h ′ - d Cs fs fy A s or fs es Es A s if es < ey ′ ′ ′ ′ 2 eFRPt h Fsj fs (dsj-c) Es Asj ≤ fs fy A sj dsj - h-c 2 Ts fs fy A s d-h/2 h (h-c) TFRP,side fFRP fFRPu (h-c) tFRP ≤ fFRP EFRPeFRPt (h-c) tFRP - 2 3 TFRP,face fFRP fFRPu b tFRP ≤fFRP EFRPeFRPt b tFRP h 2 ISIS EC Module 4

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**6 - Column Strengthening**

Design steps for slender column: 1) Assuming a linear distribution of strain, identify the relationship of strain in the various materials as a function of the assumed failure strain. 2) Determine the resultant force for each material. 3) Calculate the position of the neutral axis using equilibrium of forces. 4) Check the validity of the assumptions of strains and stresses for all materials. ISIS EC Module 4

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**6 - Column Strengthening**

Design steps for slender column: 5) Determine Pr as the sum of the resultant force from each material. 6) Determine Mr as the sum of the internal resultant forces multiplied by their respective distances to the centroid of the section. ISIS EC Module 4

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**6 - Column Strengthening**

Rectangular Columns External FRP wrapping may be used with rectangular columns. However, strengthening is not as effective and is more complex. Confinement only in some areas Confinement all around ISIS EC Module 4

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**6 - Column Strengthening**

Some geometrical limitations are imposed: Sharp edge concrete should be rounded to promote an intimate and continuous contact of the FRP with the concrete. - minimum radius is 35 mm The aspect ratio of the section (h/b) ≤ 1.5 The smaller cross section dimension (b) ≤ 600 mm The equations used are the same. Dg is taken as the diagonal of the cross section. 2tFRPfFRPFFRPu flFRP= Dg =√ h2+b2 ISIS EC Module 4

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**6 - Column Strengthening**

Additional Considerations External FRP wrapping may also be used with circular and rectangular RC columns to strengthen for shear. Particularly useful in seismic upgrade situations where increased lateral loads are a concern. ISIS EC Module 4

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**6 - Column Strengthening**

The confining effects of FRP wraps are not activated until significant radial expansion of concrete occurs. Therefore, ensure service loads are kept low enough to prevent failure by creep and fatigue To avoid creep failure: PD ≤ 0.85 0.8a1fc f`c (Ag-As)+ fsAs fs ≤ Es ≤ 0.8fy Where: PD is the dead load fs is the stress in the axial steel reinforcement ISIS EC Module 4

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**6 - Column Strengthening**

Example Example: Determine the number of layers of GFRP wrap that are required to increase the factored axial load capacity of the column to 3450 kN. Information RC column factored axial resistance (after strengthening) = 3450 kN lu = 2500 mm Dg = 450 mm Ag = mm2 As = 2500 mm2 fy = 400 MPa f’c = 30 MPa ffrpu = 600 MPa tfrp = 1 mm ffrp = 0.70*0.75 ISIS EC Module 4

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**6 - Column Strengthening**

Solution: Step 1: Check for the slenderness effect klu r < M1 M2 k =1.0, M1=0 and M2=0 2500 112.5 = 22.2 < 34 Thus, the slenderness effect can be ignored ISIS EC Module 4

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**6 - Column Strengthening**

Step 2: Determine the required confined concrete strength, fcc ′ Pr = 0.8 a1fc fcc(Ag-As)+ fs fyAs ′ a1 = 0.85 – f’c > 0.67 a1 = 0.85 – (30) = 0.81 = 0.8 0.81(0.75) fcc( )+ 0.9(400)2500 ′ ′ fcc= 35.9 MPa ISIS EC Module 4

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**6 - Column Strengthening**

Step 3: Determine the required confinement pressure (flFRP) fcc= fc+ 2 flFRP ′ ′ 35.9 = flFRP flFRP = 2.95 MPa Step 4: Check for the confinement limits flfrp ≥ 0.1fc =0.1(30) = 3 MPa ′ flfrp ≤ 0.33 fc =0.33(30) = 9.9 MPa ′ flFRP = 3 MPa ISIS EC Module 4

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**6 - Column Strengthening**

Step 5: Determine the minimal thickness for the FRP (tFRP) and number of layers 2tFRPfFRPFFRPu flFRP = Dg 2tFRP(0.70×0.75)600 3 = 450 tFRP = 2.14 mm Since tGFRP = 1.0 mm, 3 layers of GFRP are required. ISIS EC Module 4

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**6 - Column Strengthening**

Example Example: Check the design of the following column. It is required to resist a factored axial load of 6000 kN and a factored moment of 1600 kN.m. Information 75 325 800 600 Axial FRP 2 layers Hoop FRP 6 layers Steel bars Ast = 4000 mm2 fy = 400 MPa f’c = 30 MPa ffrpu = 3450MPa tfrp = mm efrpu = 0.015 ISIS EC Module 4

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**6 - Column Strengthening**

Step 1: Determine the properties of the confined concrete Equivalent diameter: h = 1.25 ≤ 1.5 b < 800 b Dg=√ b2+h2 =√ = 1000 mm Confining pressure: 2tFRPfFRPfFRPu 2(6 × 0.167)(0.75 ×0.70)3450 flFRP = = = 3.63 MPa Dg 1000 Confinement limits: 0.33 fc ≥ flfrp ≥ 0.1fc 10 ≥ flfrp ≥ 3………………….O.K ′ ′ ISIS EC Module 4

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**6 - Column Strengthening**

Step 1: Determine the properties of the confined concrete Confined concrete strength: fcc = fc+ 2 flFRP ′ ′ fcc= 30+2×3.63 = MPa ′ Concrete strain: ′ ′ ecc fcc = 5 -1 +1 ec ′ fc ′ 37.26 ecc ′ = ( ) = 30 ISIS EC Module 4

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**6 - Column Strengthening**

Step 2: Determine the equations of the resultant forces The following assumptions were made: - Compression failure (concrete crushing) - fc varies linearly from f’c to fcc - Yielding of both tension and compression steel - Intermediate steel in elastic domain ′ a1 = 0.85 – f’c > 0.67 a1 = 0.85 – (30) = 0.805 b1 = 0.97 – f’c > 0.67 b1 = 0.97 – (30) = 0.895 ISIS EC Module 4

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**6 - Column Strengthening**

Assuming concrete crushing: ′ ′ fc+fcc c c × 0.0035 ′ Ccc= fc b c- ec = 0.75 600 c - ecc ′ 2 2 0.0077 c × 0.0035 c - = 0.0077 c ′ ′ ec c × 0.0035 Cc= fca1 fc b b 1 ecc ′ = 0.75(0.805)30(600)0.895 0.0077 c × 0.0035 = 0.0077 ′ Cs=fs fy A s = 0.9(400)1500 = N ISIS EC Module 4

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**6 - Column Strengthening**

ecc ′ 0.0077 Fsj = fs (dsj-c) Es Asj = 0.9 (400-c) ×1000 c c 0.0077 (400-c) =180 × 106 c Ts= fs fy A s = 0.9 (400) 1500 = N ecc ′ 0.0077 TFRP,side= fFRP (h-c) EFRP (h-c) tFRP = 0.75×0.70 (800-c) 2 × 0.334 c c 0.0077 = (800-c) 2 c ecc ′ 0.0077 TFRP,face= fFRP (h-c) EFRP btFRP= 0.75×0.70 (800-c) ×600 ×0.334 c c 0.0077 = (800-c) c ISIS EC Module 4

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**6 - Column Strengthening**

Step 3: Determine the position of the neutral axis, c: Ccc+Cc+Cs-Fsj-Ts-TFRP,side-TFRP,face= Pr c × 0.0035 c × 0.0035 c - 0.0077 0.0077 0.0077 0.0077 (400-c) -180 × 106 (800-c) 2 c c 0.0077 (800-c) = 6000 × 103 c c = 472 mm ISIS EC Module 4

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**6 - Column Strengthening**

Step 4: Check the assumptions for strains: ecc c ′ 472-75 472 ′ es ′ (c-d ) = × = > OK = ecc c ′ 472 esj (dsj-c) = × = < ± OK = 472 ecc c ′ es (d-c ) = × = > OK = ecc c ′ 472 (h-c ) eFRP = × = < OK = c ec ecc ′ 472 0.0077 c ′ = × = mm = ′ ISIS EC Module 4

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**6 - Column Strengthening**

Step 5: Determine Pr: Pr = Ccc+Cc+Cs-Fsj-Ts-TFRP,side-TFRP,face = 214.5 -180 × 106 0.0077 ( ) 2 472 0.0077 ( ) = 5997 × 103 N 472 ISIS EC Module 4

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**6 - Column Strengthening**

Step 6: Determine Mr: h c 2fc+fcc ′ ′ Ccc - c - ec ′ ecc ′ ′ ′ 3fc+3fcc 2 800 2X 3X30+3X37.3 = 1075 X 106 N.mm = 2 h b1 c Cc ec ′ - c + 1- ecc ′ 2 2 800 0.895 = 1- X 214.5 = 97 X 106 N.mm 2 2 h 800 ′ Cs - d = -75 = 176 X 106 N.mm 2 2 ISIS EC Module 4

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**6 - Column Strengthening**

Step 6: Determine Mr: h Fsj dsj - = 0 N.mm 2 h 800 Ts d - = = 176 X 106 N.mm 2 2 h (h-c) 800 ( ) TFRP,side = 71400 = 21 X 106 N.mm - - 2 3 2 3 h 800 TFRP,face = = 52 X 106 N.mm 2 2 Total = 1597 X 106 N.mm The flexural resistance is adequate Mr = 1597 kN.m ≈1600 kN.m ISIS EC Module 4

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**7 - Installation of FRP Strengthening Systems**

Includes: 1) Approval of FRP materials 2) Handling and storage of FRP materials 3) Staff and contractor qualifications 4) Concrete surface preparation 5) Installation of FRP systems 6) Curing the FRP system 7) Protection and finishing for FRP system ISIS EC Module 4

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**7 - Installation of FRP Strengthening Systems**

1) Approval of FRP materials: The use of certified FRP materials is recommended. Qualification testing can be used for the approval of the FRP materials. 2) Handling and storage of FRP materials: - Must be carried out in accordance with manufacturer specifications. - Contractor and supplier must ensure that FRP materials are shipped in adequate conditions. Do not use opened or damaged containers. - FRP components must be stored in clean & dry area, sheltered from sun rays. - Do not use material that has exceeded its shelf life. - Material safety data sheet for all FRP materials and components should be obtained from the manufacturer and should be accessible at the job site. ISIS EC Module 4

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**7 - Installation of FRP Strengthening Systems**

3) Staff and contractor qualifications: The workers must have a basic knowledge of all stages of the installation of the FRP systems. The minimum required knowledge includes: An understanding of the security instructions Mixing proportions of resins Application rates Pot life and curing times Installation techniques ISIS EC Module 4

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**7 - Installation of FRP Strengthening Systems**

4) Concrete surface preparation: Repair of existing substrate: - The concrete surfaces must be free of particles and pieces that no longer adhere to the structure. - The surface must be cleaned from oil residuals or contaminants. - Rough surface should be smoothed. - Sections with sharp edges must be rounded. - Surface preparation for contact critical applications - A continuous contact between the concrete and the FRP confinement system should be guaranteed. - Rounding of corners, filling holes and elimination of depression are of prime importance. ISIS EC Module 4

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**7 - Installation of FRP Strengthening Systems**

5) Installation of FRP systems: - Primer, putty, saturating resin and fibres should be a part of the same system. - All equipment should be clean and in good operating condition - Ambient air and concrete surface temperature should be 10°C or more - The mixing of resins should be done in accordance with the FRP system manufacturer recommended procedure. All components should be mixed at a proper temperature and in the correct ratio until there is a uniform mix, free from trapped air. - The installation of FRP is either hand wet applied system or precured system. ISIS EC Module 4

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**7 - Installation of FRP Strengthening Systems**

6) Curing the FRP system FRP materials should be cured according to the recommendations of the manufacturer unless the curing process is accelerated by heating, chemical reactant or other external supply. The curing time should not be less than 24 hours before further work is done on the repaired surface. Chemical contamination from gases, dust or liquid must be prevented during the cure of all materials. ISIS EC Module 4

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**7 - Installation of FRP Strengthening Systems**

7) Protection and finishing for FRP system When the surface of the FRP materials is sufficiently dry or hard, a protection system and/or paint compatible with the installed reinforcement can be added. The coating must dry for a minimum of 24 hours . A certificate of compatibility of the protection system with the selected type of FRP reinforcement must be obtained from the manufacturer of the FRP materials. ISIS EC Module 4

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**8 - Quality Control and Quality Assurance**

The FRP material suppliers, the FRP installation contractors and all others associated with the FRP strengthening project should maintain a comprehensive quality assurance and quality control program. 1) Material qualification and acceptance: The FRP manufacturer, distributor or their agent should provide information demonstrating that the proposed FRP meets all mechanical, physical and chemical design requirements. Tensile strength, type of fibres, resins, durability, etc. 2) Qualification of contractor personnel: The selection of contractors should be based on evidence regarding their qualifications and experience for FRP strengthening projects. ISIS EC Module 4

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**8 - Quality Control and Quality Assurance**

3) Inspection of concrete substrate: - The concrete surface should be inspected and tested before application of FRP. The inspection should include: - Smoothness or roughness of the surface - Holes and cracks - Corners radius - Cleanliness - Pull-off tests should be performed to determine the tensile strength of the concrete for bond-critical applications. ISIS EC Module 4

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**8 - Quality Control and Quality Assurance**

4) FRP material inspection: Inspection of the FRP materials shall be conducted before, during and after their installation. - Before Construction The FRP supplier should submit certification & identification of all the FRP materials to be used. The installation procedure should be submitted as well. - During Construction Keep records for: - Quantity and mixture proportions of resin - The date and time of mixing - Ambient temperature & humidity - All other useful information Visual inspection of fibres orientation and waviness should be carried out. ISIS EC Module 4

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**8 - Quality Control and Quality Assurance**

4) FRP material inspection: - At completion of the project: A record of all final inspection and test results related to the FRP material should be retained. Samples of the cured FRP materials should be retained as well. 5)Testing: - Qualification testing: It is a specification for the product certification of FRPs used for rehabilitation. It includes some guidelines as: - FRP systems whose properties have not been fully established should not be considered - Constituent materials, fibres, matrices and adhesives, should be acceptable by the applicable code and known for their good performance. ISIS EC Module 4

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**8 - Quality Control and Quality Assurance**

5) Testing: - Field testing: Confirmatory test samples of the FRP material systems should be prepared at the construction site and tested at an approved laboratory. In-place load testing can be used to confirm the behaviour of the FRP strengthened member. ISIS EC Module 4

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**9 - Additional Applications**

Prestressed FRP Sheets One way to improve FRP effectiveness is to apply prestress to the sheet prior to bonding This allows the FRP to contribute to both service and ultimate load-bearing situations It can also help close existing cracks, and delay the formation of new cracks Prestressing FRP sheets is a promising technique, but is still under development ISIS EC Module 4

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**Maryland Bridge - Winnipeg, Manitoba - Constructed in 1969**

10 - Field Applications Maryland Bridge - Winnipeg, Manitoba - Constructed in 1969 - Twin five-span continuous precast prestressed girders - CFRP sheets to upgrade shear capacity ISIS EC Module 4

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**John Hart Bridge - Prince George, BC**

10 - Field Applications John Hart Bridge - Prince George, BC - 84 girder ends were shear strengthened with CFRP Locations for FRP shear reinforcement - Increase in shear capacity of 15-20% - Upgrade completed in 6 weeks ISIS EC Module 4

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**Country Hills Boulevard Bridge**

10 - Field Applications Country Hills Boulevard Bridge - Calgary, AB - Deck strengthened in negative bending with CFRP strips - New wearing surface placed on top of FRP strips ISIS EC Module 4

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**(Currently under revision)**

Design Guidance CAN/CSA-S806-02: Design and Construction of Building Components with Fibre Reinforced Polymers (Currently under revision) A Canadian code exists for the design of FRP-strengthened concrete members CAN/CSA-S6-10: Canadian Highway Bridge Design Code ISIS EC Module 4

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**Additional Information**

Available from ISIS EC Module 1: Mechanics Examples Incorporating FRP Materials ISIS EC Module 2: An Introduction to FRP Composites for Construction ISIS EC Module 3: An Introduction to FRP-Reinforced Concrete ISIS EC Module 5: Introduction to Structural Health Monitoring ISIS EC Module 6: Application & Handling of FRP Reinforcements for Concrete ISIS EC Module 7: Introduction to Life Cycle Engineering & Costing for Innovative Infrastructure ISIS EC Module 8: Durability of FRP Composites for Construction ISIS EC Module 9: Prestressing Concrete Structures with Fibre Reinforced Polymers ISIS EC Module 4

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CM 197 Mechanics of Materials Chap 14: Stresses in Beams

CM 197 Mechanics of Materials Chap 14: Stresses in Beams

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