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

ISIS Educational Module 4: An Introduction to FRP-Strengthening of Concrete Structures Produced by ISIS Canada

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FRP Repair with reinforcement Module Objectives To provide students with a general awareness of FRP materials and their potential uses To introduce students to the general philosophies and procedures for strengthening structures with FRPs ISIS EC Module 4

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**Overview Additional Info Introduction Field Applications FRP Materials**

Repair with reinforcement Overview Additional Info Introduction Field Applications FRP Materials Advanced Applications Evaluation of Existing Structures Specifications & Quality Control Beam & One-Way Slab Strengthening Column Strengthening ISIS EC Module 4

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**Global Infrastructure Crisis**

FRP Repair with reinforcement Introduction Section: 1 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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**A primary factor leading to extensive degradation…**

FRP Repair with reinforcement Introduction Section: 1 A primary factor leading to extensive degradation… 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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**Why repair with the same materials? Why repeat the cycle?**

FRP Repair with reinforcement Introduction Section: 1 Why repair with the same materials? Why repeat the cycle? Lightweight High Strength Easy to install FRP Materials 5x steel Corrosion resistant Highly versatile Durable structures Suit any project ISIS EC Module 4

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**FRP-Strengthening Applications**

Repair with reinforcement FRP Materials Section: 1 FRP-Strengthening Applications Type Application Fibre Dir. Schematic Flexural side face of Tension and/or beam axis of beam Along long. Section Shear Side face of beam (u-wrap) Perpendicular to long. axis of beam Section Confinement Around column Circumferential Section ISIS EC Module 4

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**Longstanding reputation in automotive and aerospace industries**

FRP Repair with reinforcement FRP Materials Section: 2 General Longstanding reputation in automotive and aerospace industries Over the past 15 years have FRP materials been increasingly considered for civil infrastructure applications FRP costs have decreased New, innovative solutions needed! ISIS EC Module 4

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**Wide range of FRP products available: Plates**

Repair with reinforcement FRP Materials Section: 2 General Wide range of FRP products available: Plates Rigid strips Formed through pultrusion Sheets Flexible fabric Carbon FRP sheet ISIS EC Module 4

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**Creates a material with attributes superior to either component alone!**

FRP Repair with reinforcement FRP Materials Section: 2 Constituents What is FRP? Fibres Matrix Provide strength and stiffness Protects and transfers load between fibres Carbon, glass, aramid Epoxy, polyester, vinyl ester Fibre Composite Matrix Creates a material with attributes superior to either component alone! ISIS EC Module 4

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**Typical FRP stress-strain behaviour**

Repair with reinforcement FRP Materials Section: 2 Properties Typical FRP stress-strain behaviour Strain [%] >10 34-130 Stress [MPa] Fibres FRP Matrix ISIS EC Module 4

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**Resin acts as adhesive AND matrix**

FRP Repair with reinforcement FRP Materials Section: 2 Installation Techniques uWet lay-up Used with flexible sheets Resin acts as adhesive AND matrix Saturate sheets with epoxy adhesive Place on concrete surface Epoxy Roller ISIS EC Module 4

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**Resin acts as adhesive AND matrix**

FRP Repair with reinforcement FRP Materials Section: 2 Installation Techniques vPre-cured Used with rigid, pre-cured strips Resin acts as adhesive AND matrix Apply adhesive to strip backing Place on concrete surface Not as flexible for variable structural shapes ISIS EC Module 4

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**Linear elastic behaviour to failure No yielding **

FRP Repair with reinforcement FRP Materials Section: 2 Properties 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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**FRP material properties are a function of:**

Repair with reinforcement FRP Materials Section: 2 Properties Type of fibre and matrix FRP material properties are a function of: Fibre volume content Orientation of fibres ISIS EC Module 4

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**High strength-to-weight ratio Electromagnetically inert**

FRP Repair with reinforcement FRP Materials Section: 2 Pro/Con FRP advantages Will not corrode High strength-to-weight ratio Electromagnetically inert FRP disadvantages High initial material cost But not when life-cycle costs are considered ISIS EC Module 4

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**Evaluation of Existing Structures**

FRP Repair with reinforcement Evaluation of Existing Structures Section: 3 Deficiencies Deficiencies due to: Wet-Dry Chloride Ingress Freeze-Thaw uEnvironmental Effects ISIS EC Module 4

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**Evaluation of Existing Structures**

FRP Repair with reinforcement Evaluation of Existing Structures Section: 3 Deficiencies Deficiencies due to: Then Now v Updated Design Loads w Updated design code procedures ISIS EC Module 4

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**Evaluation of Existing Structures**

FRP Repair with reinforcement Evaluation of Existing Structures Section: 3 Deficiencies Deficiencies due to: Then Now xIncrease in Traffic Loads ISIS EC Module 4

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**Evaluation of Existing Structures**

FRP Repair with reinforcement Evaluation of Existing Structures Section: 3 Evaluation 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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**Evaluation of Existing Structures**

FRP Repair with reinforcement Evaluation of Existing Structures Section: 3 Evaluation Evaluation should include: All past modifications Actual size of elements Actual material properties Location, size and cause of cracks, spalling Location, extent of corrosion Quantity, location of rebar ISIS EC Module 4

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**Evaluation of Existing Structures**

FRP Repair with reinforcement Evaluation of Existing Structures Section: 3 Concrete Surface One of the key aspects of strengthening: State of concrete substrate Concrete must transfer load from the elements to the FRPs through shear in the adhesive Surface modification required where surface flaws exist ISIS EC Module 4

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**Beam/One-Way Slab Strengthening**

FRP Repair with reinforcement Beam/One-Way Slab Strengthening Section: 4 Flexural Strengthening FRP rupture Assumptions uFailure caused by: Concrete crushing vPlane sections remain plane wPerfect bond between steel/concrete, FRP/concrete Adequate anchorage & development length provided for FRPs FRPs are linear elastic to failure Concrete compressive stress-strain curve is parabolic, no strength in tension Initial strains in FRPs can be ignored ISIS EC Module 4

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**Beam/One-Way Slab Strengthening**

FRP Repair with reinforcement Beam/One-Way Slab Strengthening Section: 4 Resistance Factors Material Bridge Building Steel fS =0.90 fS =0.85 Concrete fC =0.75 fC =0.6 FRP ffrp = 0.75 ffrp = 0. 50 Carbon Glass ISIS EC Module 4

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**Beam/One-Way Slab Strengthening**

FRP Repair with reinforcement Beam/One-Way Slab Strengthening Section: 4 Failure Modes Four potential failure modes: Concrete crushing before steel yields Steel yielding followed by concrete crushing Steel yielding followed by FRP rupture Debonding of FRP reinforcement Debonding is prevented through special end anchorages Assume failure mode Perform analysis Check failure mode *** Assume initial strains at the time of strengthening are zero *** *** Refer to EC Module 4 Notes *** ISIS EC Module 4

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**Beam/One-Way Slab Strengthening**

FRP Repair with reinforcement Beam/One-Way Slab Strengthening Section: 4 General Design 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 • Force equilibrium in section: Ts + Tfrp = Cc Eq. 4-1 Ts = fsAsfs Tfrp = ffrpAfrpEfrpefrp Cc = fca1f’cb1bc ISIS EC Module 4

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**Beam/One-Way Slab Strengthening**

FRP Repair with reinforcement Beam/One-Way Slab Strengthening Section: 4 General Design b ec a1Φcf’c c a = b1c d Cc h As es fs Ts efrp ffrp Tfrp bfrp Equiv. Stress Distribution Cross Section Strain Distribution Stress Distribution • Apply strain compatibility and use these equations to solve for neutral axis depth, c • Section capacity: Mr = Ts d - a 2 Eq. 4-5 + Tfrp h - ISIS EC Module 4

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**Beam/One-Way Slab Strengthening**

FRP Repair with reinforcement Beam/One-Way Slab Strengthening Section: 4 Analysis Procedure b ecu c d h As es efrp bfrp Cross Section Strain Distribution Step1: Assume failure mode Assume that section fails by concrete crushing after steel yields efrp = ecu Eq. 4-6 ec = ecu = (h-c)/c es = ecu (d-c)/c Eq. 4-7 Thus: ISIS EC Module 4

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**Beam/One-Way Slab Strengthening**

FRP Repair with reinforcement Beam/One-Way Slab Strengthening Section: 4 Analysis Procedure b ecu a1Φcf’c c a = b1c d Cc h As es fs Ts ffrp Tfrp efrp bfrp Equiv. Stress Distribution Cross Section Strain Distribution Stress Distribution Step 2: Determine compressive stress block factors Eq. 4-8 a1 = f’c > 0.67 Eq. 4-9 b1 = f’c > 0.67 ISIS EC Module 4

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**Beam/One-Way Slab Strengthening**

FRP Repair with reinforcement Beam/One-Way Slab Strengthening Section: 4 Analysis Procedure b ecu a1Φcf’c c a = b1c d Cc h As es fs Ts ffrp Tfrp efrp bfrp Equiv. Stress Distribution Cross Section Strain Distribution Stress Distribution Step 3: Determine neutral axis depth, c Eq. 4-10 fca1f’cb1bc ffrpAfrpEfrpefrp = fsAsfs + ISIS EC Module 4

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**Beam/One-Way Slab Strengthening**

FRP Repair with reinforcement Beam/One-Way Slab Strengthening Section: 4 Analysis Procedure b ecu a1Φcf’c c a = b1c d Cc h As es fs Ts Tfrp efrp ffrp bfrp Equiv. Stress Distribution Cross Section Strain Distribution Stress Distribution Step 4: Check if assumed failure mode is correct > efrp = ecu (h-c)/c efrpu Eq. 4-11 ? If true, go to Step 6 If false, go to Step 5 ISIS EC Module 4

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**Beam/One-Way Slab Strengthening**

FRP Repair with reinforcement Beam/One-Way Slab Strengthening Section: 4 Analysis Procedure b ecu a1Φcf’c c a = b1c d Cc h As es fs Ts ffrp Tfrp efrp bfrp Equiv. Stress Distribution Cross Section Strain Distribution Stress Distribution Step 5: Calculate factored moment resistance Mr = fsAsfy d - a 2 Eq. 4-12 + h - ffrpAfrpEfrpefrp ISIS EC Module 4

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**Beam/One-Way Slab Strengthening**

FRP Repair with reinforcement Beam/One-Way Slab Strengthening Section: 4 Analysis Procedure b ecu a1Φcf’c c a = b1c d Cc h As es fs Ts ffrp Tfrp efrp bfrp Equiv. Stress Distribution Cross Section Strain Distribution Stress Distribution Step 5: Calculate factored moment resistance Check if internal steel yields to ensure adequate deformability If yes, OK es = ecu (d-c)/c > εy ? If no, reduce FRP amount & recalculate ISIS EC Module 4

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**Beam/One-Way Slab Strengthening**

FRP Repair with reinforcement Beam/One-Way Slab Strengthening Section: 4 Analysis Procedure b ec a1Φcf’c c a = b1c d Cc h As es fs Ts Tfrp efrpu ffrpu bfrp Equiv. Stress Distribution Cross Section Strain Distribution Stress Distribution Step 6: Assume different failure mode Assume failure occurs by tensile failure of FRP efrp = efrpu ec < ecu Thus: ISIS EC Module 4

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**Beam/One-Way Slab Strengthening**

FRP Repair with reinforcement Beam/One-Way Slab Strengthening Section: 4 Analysis Procedure b ec a1Φcf’c c a = b1c d Cc h As es fs Ts Tfrp efrpu ffrpu bfrp Equiv. Stress Distribution Cross Section Strain Distribution Stress Distribution Step 7: Determine depth of neutral axis Eq. 4-15 fca1f’cb1bc ffrpAfrpEfrpefrpu = fsAsfy + ISIS EC Module 4

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**Beam/One-Way Slab Strengthening**

FRP Repair with reinforcement Beam/One-Way Slab Strengthening Section: 4 Analysis Procedure b ec a1Φcf’c c a = b1c d Cc h As es fs Ts Tfrp efrpu ffrpu bfrp Equiv. Stress Distribution Cross Section Strain Distribution Stress Distribution Step 8: Check if assumed failure mode is correct ec < ecu efrpu c / (h-c) < ecu ISIS EC Module 4

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**Beam/One-Way Slab Strengthening**

FRP Repair with reinforcement Beam/One-Way Slab Strengthening Section: 4 Analysis Procedure b ec a1Φcf’c c a = b1c d Cc h As es fs Ts Tfrp efrpu ffrpu bfrp Equiv. Stress Distribution Cross Section Strain Distribution Stress Distribution Step 9: Calculate factored moment resistance Mr = fsAsfy d - a 2 Eq. 4-17 + h - ffrpAfrpEfrpefrpu ISIS EC Module 4

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**Beam/One-Way Slab Strengthening**

FRP Repair with reinforcement Beam/One-Way Slab Strengthening Section: 4 With Compression Steel b ecu a1Φcf’c e’s f’s Cs A’s c a = b1c d Cc h As es fs Ts efrp ffrp Tfrp bfrp Equiv. Stress Distribution Cross Section Strain Distribution Stress Distribution • Similar analysis procedure Add a compressive stress resultant ISIS EC Module 4

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**Beam/One-Way Slab Strengthening**

FRP Repair with reinforcement Beam/One-Way Slab Strengthening Section: 4 Tee Beams bf hf h bfrp Afrp c Mr Mrf Mrw = + • Similar analysis procedure Neutral axis in flange: treat as rectangular section Neutral axis in web: treat as tee section ISIS EC Module 4

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**Beam/One-Way Slab Strengthening**

FRP Repair with reinforcement Beam/One-Way Slab Strengthening Section: 4 Flexural Example Problem statement Calculate the moment resistance (Mr) for an FRP-strengthened rectangular concrete section Section information b = 105 mm h = 350 mm 3-10M bars d = 325 mm CFRP f’c = 45 MPa efrpu = 1.55 % Afrp = 60 mm2 fy = 400 MPa Es = 200 GPa Efrp = 155 GPa ISIS EC Module 4

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**Beam/One-Way Slab Strengthening**

FRP Repair with reinforcement Beam/One-Way Slab Strengthening Section: 4 Flexural Example Solution Step 1: Assumed failure mode Assume failure of beam due to crushing of concrete in compression after yielding of internal steel reinforcement ISIS EC Module 4

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**Beam/One-Way Slab Strengthening**

FRP Repair with reinforcement Beam/One-Way Slab Strengthening Section: 4 Flexural Example Solution Step 2: Calculate concrete stress block factors a1 = 0.85 – f’c > 0.67 a a1 = 0.85 – (45) = 0.78 b1 = 0.85 – f’c > 0.67 a b1 = 0.85 – (45) = 0.86 ISIS EC Module 4

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**Beam/One-Way Slab Strengthening**

FRP Repair with reinforcement Beam/One-Way Slab Strengthening Section: 4 Flexural Example Solution Step 3: Find depth of neutral axis, c Use Equation 4-10: fca1f’cb1bc = ffrpAfrpEfrpefrp fsAsfs + 0.6 (0.78) (45) (0.86) (105) c 0.85 (300) (400) 350 - c 0.75 (60) (155000) 0.0035 c c = 90.5 mm ISIS EC Module 4

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**Beam/One-Way Slab Strengthening**

FRP Repair with reinforcement Beam/One-Way Slab Strengthening Section: 4 Flexural Example Solution Step 4: Check failure mode efrp = ecu (h-c)/c efrpu = Eq. 4-11 vs. efrp = 90.5 efrp = 0.01 < efrpu = Therefore, FRP rupture does NOT occur and assumed failure mode is correct ISIS EC Module 4

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**Beam/One-Way Slab Strengthening**

FRP Repair with reinforcement Beam/One-Way Slab Strengthening Section: 4 Flexural Example Solution Step 4: Check failure mode To promote ductility, check that steel has yielded: es = ecu d - c c es = = 0.009 > = ey 90.5 If the steel had NOT yielded, the beam failure could be expected to be less ductile, and we would need to carefully check the deformability of the member ISIS EC Module 4

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**Beam/One-Way Slab Strengthening**

FRP Repair with reinforcement Beam/One-Way Slab Strengthening Section: 4 Flexural Example Solution Step 5: Calculate moment resistance Mr = fsAsfy d - a 2 Eq. 4-12 + h - ffrpAfrpEfrpefrp 0.85 (300) (400) 325 - 0.86 x 90.5 2 0.75 (60) (155000) (0.01) 350 - 0.86 x 90.5 2 Mr = 50.9 106 N· mm = 50.9 kN· m 65% increase over unstrengthened beam! ISIS EC Module 4

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**Beam/One-Way Slab Strengthening**

FRP Repair with reinforcement Beam/One-Way Slab Strengthening Section: 4 Shear Strengthening Assumptions FRP sheets can be applied to provide shear resistance Many different possible configurations May be aligned at any angle to the longitudinal axis May be applied in continuous sheets or in finite widths ISIS EC Module 4

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**Beam/One-Way Slab Strengthening**

FRP Repair with reinforcement Beam/One-Way Slab Strengthening Section: 4 Shear Strengthening Assumptions FRP sheets can be applied to provide shear resistance Many different possible configurations Section ne = 1 ne = 2 May be applied on sides only or as U-wraps *U-wraps also improve the anchorage of flexural FRP external reinforcement ISIS EC Module 4

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**Beam/One-Way Slab Strengthening**

FRP Repair with reinforcement Beam/One-Way Slab Strengthening Section: 4 Shear Strengthening Assumptions wfrp sfrp b To avoid stress concentrations, allow for a minimum radius of 15 mm Section ISIS EC Module 4

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**Beam/One-Way Slab Strengthening**

FRP Repair with reinforcement Beam/One-Way Slab Strengthening Section: 4 Shear Strengthening Design Principles External strengthening with FRPs: Flexural failure Generally fairly ductile Shear failure Sudden and brittle Undesirable failure mode Control shear deformation to avoid sudden failure ISIS EC Module 4

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**Beam/One-Way Slab Strengthening**

FRP Repair with reinforcement Beam/One-Way Slab Strengthening Section: 4 Shear Strengthening Design Principles Shear resistance of a beam: Vr = Vc Vs Vfrp + Eq. 4-18 ISIS EC Module 4

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**Beam/One-Way Slab Strengthening**

FRP Repair with reinforcement Beam/One-Way Slab Strengthening Section: 4 Shear Strengthening Design Principles Shear resistance of a beam: Vc = 0.2 fc√f’c bwd Eq. 4-19 Vs = fs fy Av d s Eq. 4-20 ISIS EC Module 4

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**Beam/One-Way Slab Strengthening**

FRP Repair with reinforcement Beam/One-Way Slab Strengthening Section: 4 Shear Strengthening Design Principles Shear resistance of a beam: Vfrp = ffrp Afrp Efrp efrpe dfrp (sinb + cosb) sfrp Eq. 4-21 Afrp = 2 tfrp wfrp a dfrp: distance from free end of FRP to bottom of internal steel stirrups a ISIS EC Module 4

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**Beam/One-Way Slab Strengthening**

FRP Repair with reinforcement Beam/One-Way Slab Strengthening Section: 4 Shear Strengthening Design Principles Effective strain in FRP, efrpe: a Eq. 4-23 efrpe = R efrpu ≤ 0.004 Prevents shear cracks from widening beyond acceptable limits Ensures aggregate interlock! Reduction factor, R: a Eq. 4-24 R = al1 f’c2/3 rfrp Efrp l2 Carbon: l1 = 1.35, l2 = 0.30 0.8 Glass: l1 = 1.23, l2 = 0.47 ISIS EC Module 4

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**Beam/One-Way Slab Strengthening**

FRP Repair with reinforcement Beam/One-Way Slab Strengthening Section: 4 Shear Strengthening Design Principles FRP shear reinforcement ratio, rfrp: a Eq. 4-25 rfrp = 2 tfrp bw wfrp sfrp ISIS EC Module 4

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**Beam/One-Way Slab Strengthening**

FRP Repair with reinforcement Beam/One-Way Slab Strengthening Section: 4 Shear Strengthening Design Principles Another limit on effective strain in FRP, efrpe: Eq. 4-26 efrpe ≤ ak1k2Le 9525 0.8 a Parameters, k1 and k2: Eq. 4-27 k1 = f’c 27.65 2/3 Eq. 4-28 k2 = dfrp- ne Le dfrp ISIS EC Module 4

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**Beam/One-Way Slab Strengthening**

FRP Repair with reinforcement Beam/One-Way Slab Strengthening Section: 4 Shear Strengthening Design Principles a Effective anchorage length, Le: Eq. 4-29 Le = 25350 tfrpEfrp 0.58 ISIS EC Module 4

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**Beam/One-Way Slab Strengthening**

FRP Repair with reinforcement Beam/One-Way Slab Strengthening Section: 4 Shear Strengthening Design Principles Limit on spacing of strips, sfrp: Eq. 4-30 sfrp ≤ wfrp + d 4 ISIS EC Module 4

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**Beam/One-Way Slab Strengthening**

FRP Repair with reinforcement Beam/One-Way Slab Strengthening Section: 4 Shear Strengthening Design Principles Limit on maximum allowable shear strengthening, Vfrp: Eq. 4-31 Vr ≤ Vc + 0.8λfc√f’c bwd Shear contribution due to steel stirrups and FRP strengthening must be less than this term ISIS EC Module 4

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**Beam/One-Way Slab Strengthening**

FRP Repair with reinforcement Beam/One-Way Slab Strengthening Section: 4 Shear Strengthening Example Problem statement Calculate the shear capacity (Vr) for an FRP-strengthened concrete section Section information Section b = 105 mm h = 350 mm 3-10M bars d = 325 mm 4.76 mm Ø GFRP wrap Elevation λ = 1.0 f’c = 45 MPa efrpu = 2.0 % fy = 400 MPa (rebar) Efrp = 22.7 GPa fy = 400 MPa (stirrup) ss = 225 mm c/c tfrp = 1.3 mm wfrp = 100 mm sfrp = 200 mm ISIS EC Module 4

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**Beam/One-Way Slab Strengthening**

FRP Repair with reinforcement Beam/One-Way Slab Strengthening Section: 4 Shear Strengthening Example Solution Step 1: Calculate concrete and steel contributions Concrete: Vc = 0.2 fc√f’c bwd Vc = 0.2 (0.6) √45 (105) (325) Vc = N = kN Vs = fs fy Av d s = 0.85 (400) (36) (325) 225 Vs = N = kN Steel: ISIS EC Module 4

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**Beam/One-Way Slab Strengthening**

FRP Repair with reinforcement Beam/One-Way Slab Strengthening Section: 4 Shear Strengthening Example Solution Step 2: Determine Afrp, rfrp, Le for effective strain calculation Afrp: Afrp = 2 tfrp wfrp = 2 (1.3) (100) Afrp = 260 mm2 rfrp = 2 tfrp bw wfrp sfrp = 2 (1.3) 105 100 200 rfrp = rfrp: ISIS EC Module 4

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**Beam/One-Way Slab Strengthening**

FRP Repair with reinforcement Beam/One-Way Slab Strengthening Section: 4 Shear Strengthening Example Solution Step 2: Determine Afrp, rfrp, Le for effective strain calculation Le = 25350 tfrpEfrp 0.58 = 1.3 x 22700 Le = 64.8 mm Le: ISIS EC Module 4

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**Beam/One-Way Slab Strengthening**

FRP Repair with reinforcement Beam/One-Way Slab Strengthening Section: 4 Shear Strengthening Example Solution Step 3: Determine k1, k2 and effective strain, efrpe [Limit 2] k1 = f’c 27.65 2/3 = 45 = 1.38 k1: Because of u-wrap k2 = dfrp- ne Le dfrp = 325 – 1 (64.8) 325 = 0.80 k2: ISIS EC Module 4

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**Beam/One-Way Slab Strengthening**

FRP Repair with reinforcement Beam/One-Way Slab Strengthening Section: 4 Shear Strengthening Example Solution Step 3: Determine k1, k2 and effective strain, efrpe [Limit 2] Note: This strain is one of three limits placed on the FRP efrpe = 0.8 (1.38) (0.80) (64.8) 9525 efrpe = efrpe ≤ ak1k2Le Eq. 4-26 efrpe: ISIS EC Module 4

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**Beam/One-Way Slab Strengthening**

FRP Repair with reinforcement Beam/One-Way Slab Strengthening Section: 4 Shear Strengthening Example Solution Step 4: Determine R and effective strain, efrpe [Limit 1] R = 0.229 R = al1 f’c2/3 rfrp Efrp l2 R = 0.8 (1.23) 45 2/3 (22700) 0.47 R: ISIS EC Module 4

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**Beam/One-Way Slab Strengthening**

FRP Repair with reinforcement Beam/One-Way Slab Strengthening Section: 4 Shear Strengthening Example Solution Step 4: Determine R and effective strain, efrpe [Limit 1] Note: This strain is one of three limits placed on the FRP efrpe: Eq. 4-23 efrpe = R efrpu ≤ 0.004 efrpe = (0.02) efrpe = ISIS EC Module 4

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**Beam/One-Way Slab Strengthening**

FRP Repair with reinforcement Beam/One-Way Slab Strengthening Section: 4 Shear Strengthening Example Solution Step 5: Determine governing effective strain, efrpe For design purposes, use the smallest limiting value of: efrpe = Eq. 4-23 efrpe = Eq. 4-23 efrpe = Eq. 4-26 ISIS EC Module 4

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**Beam/One-Way Slab Strengthening**

FRP Repair with reinforcement Beam/One-Way Slab Strengthening Section: 4 Shear Strengthening Example Solution Step 6: Calculate contribution of FRP to shear capacity Vfrp = ffrp Afrp Efrp efrpe dfrp (sinb + cosb) sfrp Eq. 4-21 0.5 (260) (22700) (0.004) (325) (sin90 + cos90) 200 Vfrp = N = 19.2 kN Vfrp: ISIS EC Module 4

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**Beam/One-Way Slab Strengthening**

FRP Repair with reinforcement Beam/One-Way Slab Strengthening Section: 4 Shear Strengthening Example Solution Step 7: Compute total shear resistance of beam Vr: Vr = Vc Vs Vfrp + Eq. 4-21 Vr = Vr = 64.4 kN ISIS EC Module 4

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**Beam/One-Way Slab Strengthening**

FRP Repair with reinforcement Beam/One-Way Slab Strengthening Section: 4 Shear Strengthening Example Solution Step 8: Check maximum shear strengthening limits Eq. 4-31 Vr ≤ Vc + 0.8λfcf’cbwd 64400 ≤ (1) (0.6) (45) (105) (325) 64400 ≤ a OK ISIS EC Module 4

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**Beam/One-Way Slab Strengthening**

FRP Repair with reinforcement Beam/One-Way Slab Strengthening Section: 4 Shear Strengthening Example Solution Step 9: Check maximum band spacing d Eq. 4-30 sfrp ≤ wfrp + 4 200 ≤ 100 + 325 200 ≤ 181 a Not true, therefore use 180 mm spacing ISIS EC Module 4

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**Beam/One-Way Slab Strengthening**

FRP Repair with reinforcement Beam/One-Way Slab Strengthening Section: 4 Add’l Considerations Additional factors to consider: FRP anchorage and development length Deflections Creep-rupture stress limits sometimes govern FRP-strengthened design External strengthening with FRPs may reduce flexural deformability Crack widths Vibrations 3-layers FRP Deflection Load 1-layer FRP Creep No FRP Fatigue Ductility ISIS EC Module 4

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

Repair with reinforcement Column Strengthening Section: 5 Overview 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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**Increased load capacity**

FRP Repair with reinforcement Column Strengthening Section: 5 Overview The result: Increased load capacity Increased deformation capability ISIS EC Module 4

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**Design equations are largely empirical (from tests) **

FRP Repair with reinforcement Column Strengthening Section: 5 Overview Design equations are largely empirical (from tests) ISIS equations are applicable for the following cases: Undamaged concrete column Short column subjected to concentric axial load Fibres oriented circumferentially ISIS EC Module 4

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FRP Repair with reinforcement Column Strengthening Section: 5 Circular Columns Slenderness Limits Strengthening equations only valid for non-slender columns. Thus, from CSA A23.3: lu Dg ≤ Eq. 5-1 6.25 Pf / f’cAg 0.5 Ag = gross cross-sectional area of column f’c = concrete strength Pf = factored axial load lu = unsupported length Dg = column diameter ISIS EC Module 4

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FRP Repair with reinforcement Column Strengthening Section: 5 Circular Columns Slenderness Limits Strengthening equations only valid for non-slender columns. Thus, from CSA A23.3: lu Dg ≤ Eq. 5-1 6.25 Pf / f’cAg 0.5 The axial load capacity is increased by the confining effect of the wrap Column may become slender! Ensure that column remains short ISIS EC Module 4

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FRP Repair with reinforcement Column Strengthening Section: 5 Circular Columns Confinement Based on equilibrium, the lateral confinement pressure exerted by the FRP, flfrp: flfrp = Eq. 5-2 2 Nb ffrp ffrpu tfrp Dg Nb = number of FRP layers ffrp = material resistance factor for FRP ffrpu = ultimate FRP strength tfrp = FRP thickness ISIS EC Module 4

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FRP Repair with reinforcement Column Strengthening Section: 5 Circular Columns Confinement The benefit of a confining pressure is to increase the confined compressive concrete strength, f’cc f’cc = f’c + k1 flfrp Eq. 5-3 f’c = ultimate strength of unconfined concrete k1 = empirical coefficient from tests ISIS EC Module 4

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**f’cc = f’c + k1 flfrp = f’c (1 + apcww)**

Repair with reinforcement Column Strengthening Section: 5 Circular Columns Confinement ISIS design guidelines suggest a modification to f’cc: f’cc = f’c + k1 flfrp = f’c (1 + apcww) Eq. 5-4 FRP type f’c apc = performance coefficient depending on: (currently taken as 1.0) member size ww = 2 flfrp fc f’c Eq. 5-5 = ISIS EC Module 4

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**Column Strengthening Minimum confinement pressure flfrp ≥ 4 MPa**

Repair with reinforcement Column Strengthening Section: 5 Circular Columns Confinement Limits To ensure adequate ductility of column Minimum confinement pressure Why? Limit flfrp ≥ 4 MPa To prevent excessive deformations of column Maximum confinement pressure Why? flfrp ≤ f’c 2 apc 1 ke - fc Limit = 0.85 (Strength reduction factor to account for unexpected eccentricities) ISIS EC Module 4

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**Prmax = ke [a1fcf’cc (Ag-As) + fs fy As]**

FRP Repair with reinforcement Column Strengthening Section: 5 Circular Columns Axial Load Resistance Factored axial load resistance for an FRP-confined reinforced concrete column, Prmax: Prmax = ke [a1fcf’cc (Ag-As) + fs fy As] Eq. 5-9 Same equation as for conventionally RC column, except includes confined concrete strength, f’cc ISIS EC Module 4

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**Confinement only in some areas**

FRP Repair with reinforcement Column Strengthening Section: 5 Rectangular Columns External FRP wrapping may be used with rectangular columns There is far less experimental data available for rectangular columns Strengthening is not nearly as effective Confinement only in some areas Confinement all around ISIS EC Module 4

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FRP Repair with reinforcement Column Strengthening Section: 5 Add’l Considerations Shear External FRP wrapping may be used with circular and rectangular RC columns to strengthen also for shear Particularly useful in seismic upgrade situations where increased lateral loads are a concern ISIS EC Module 4

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FRP Repair with reinforcement Column Strengthening Section: 5 Add’l Considerations Strengthening Limits The confining effects of FRP wraps are not activated until significant radial expansion of concrete occurs Therefore, ensure service loads kept low enough to prevent failure by creep and fatigue ISIS EC Module 4

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**Column Strengthening Problem statement Information**

FRP Repair with reinforcement Column Strengthening Section: 5 Example Problem statement Determine the FRP wrap details for an RC column as described below Information RC column factored axial resistance (pre-strengthening) = 3110 kN lu = 3000 mm Dg = 500 mm Ag = mm2 Ast = 2500 mm2 fy = 400 MPa f’c = 30 MPa ffrpu = 1200 MPa tfrp = 0.3 mm ffrp = 0.75 New axial live load requirement PL = 1550 kN New axial dead load requirement PD = 1200 kN New factored axial load, Pf = 4200 kN ISIS EC Module 4

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**Column Strengthening Solution lu Dg ≤ 6.25 Pf / f’cAg a OK 3000 500 ≤**

FRP Repair with reinforcement Column Strengthening Section: 5 Example Solution Step 1: Check if column remains short after strengthening Eq. 5-1 lu Dg ≤ 6.25 Pf / f’cAg 0.5 a OK 3000 500 ≤ 6.25 /(30 x ) 0.5 6 7.4 ISIS EC Module 4

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**Prmax = ke [a1fcf’cc (Ag-As) + fs fy As]**

FRP Repair with reinforcement Column Strengthening Section: 5 Example Solution Step 2: Compute required confined concrete strength, f’cc Take equation 5-9 and rearrange for f’cc: Prmax = ke [a1fcf’cc (Ag-As) + fs fy As] Eq. 5-9 f’cc = Pf ke - fs fy As a1fc (Ag-As) a ISIS EC Module 4

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**Column Strengthening Solution - 0.85 (400) (2500) f’cc =**

FRP Repair with reinforcement Column Strengthening Section: 5 Example Solution Step 2: Compute required confined concrete strength, f’cc a1: a1 = 0.85 – f’c = 0.85 – (30) = 0.81 f’cc = 0.85 (400) (2500) 0.81 (0.6) ( ) f’cc: f’cc = 43.4 MPa ISIS EC Module 4

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**f’cc = f’c + k1 flfrp = f’c (1 + apcww)**

Repair with reinforcement Column Strengthening Section: 5 Example Solution Step 3: Compute volumetric strength ratio, ww Take equation 5-4 and rearrange for ww: f’cc = f’c + k1 flfrp = f’c (1 + apcww) Eq. 5-4 ww = f’cc f’c - 1 apc = 43.4 30 1 ww: ww = ISIS EC Module 4

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**Column Strengthening Solution flfrp:**

Repair with reinforcement Column Strengthening Section: 5 Example Solution Step 4: Compute required confinement pressure, flfrp Take equation 5-5 and rearrange for flfrp: ww = rfrp ffrp ffrpu fc f’c = 2 flfrp Eq. 5-5 flfrp = 2 ww fc f’c = 0.447 (0.6) (30) flfrp: flfrp = 4.02 MPa ISIS EC Module 4

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**Column Strengthening Solution a Minimum: a Maximum: OK, limits met**

FRP Repair with reinforcement Column Strengthening Section: 5 Example Solution Step 4: Compute required confinement pressure, flfrp Check flfrp again confinement limits: flfrp = 4.02 > 4.0 a Minimum: flfrp = < a Maximum: f’c 2 apc 1 ke - fc 30 2 (1) 0.85 - 0.6 = 8.65 OK, limits met ISIS EC Module 4

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**Column Strengthening Solution Nb: a Use 4 layers**

FRP Repair with reinforcement Column Strengthening Section: 5 Example Solution Step 5: Compute required number of FRP layers Take Equation 5-2 and rearrange for Nb: flfrp = Eq. 5-2 2 Nb ffrp ffrpu tfrp Dg Nb = flfrp Dg 2 ffrp ffrpu tfrp 4.02 (500) 2 (0.75) (1200) (0.3) Nb: Nb = 3.72 a Use 4 layers ISIS EC Module 4

95
**Column Strengthening Solution**

FRP Repair with reinforcement Column Strengthening Section: 5 Example Solution Step 6: Compute factored axial strength of FRP-wrapped column Use Equations 5-2, 5-5, 5-4 and 5-9: flfrp = 2 Nb ffrp ffrpu tfrp Dg 4.32 MPa flfrp: ww = = 2 flfrp fc f’c 0.48 ww : ISIS EC Module 4

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**Column Strengthening Solution f’cc: f’cc = f’c (1 + apcww) = 44.4 MPa**

FRP Repair with reinforcement Column Strengthening Section: 5 Example Solution Step 6: Compute factored axial strength of FRP-wrapped column Use Equations 5-2, 5-5, 5-4 and 5-9: f’cc: f’cc = f’c (1 + apcww) = 44.4 MPa Prmax: Prmax = ke [a1fcf’cc (Ag-As) + fs fy As] Prmax = 4230 kN > Pf = 4200 kN Note: Additional checks should be performed for creep and fatigue ISIS EC Module 4

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**Specifications & Quality Control**

FRP Repair with reinforcement Specifications & Quality Control Section: 6 Strengthening of structures with FRP is a relatively simple technique However, it is essential to performance to install the FRP system properly Specifications Quality Control / Quality Assurance ISIS EC Module 4

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**Specifications & Quality Control**

FRP Repair with reinforcement Specifications & Quality Control Section: 6 Specifications Approval of FRP materials Handling and storage of FRP materials Staff and contractor qualifications Concrete surface preparation Installation of FRP systems Adequate conditions for FRP cure Protection and finishing for FRP system ISIS EC Module 4

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**Specifications & Quality Control Quality Control and Quality Assurance**

FRP Repair with reinforcement Specifications & Quality Control Section: 6 Quality Control and Quality Assurance Material qualification and acceptance Qualification of contractor personnel Inspection of concrete substrate FRP material inspection Testing to ensure as-built condition ISIS EC Module 4

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**Additional Applications**

FRP Repair with reinforcement Additional Applications Section: 7 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 in initial stages of development ISIS EC Module 4

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**Additional Applications**

FRP Repair with reinforcement Additional Applications Section: 7 NSM Techniques Newer class of FRP strengthening techniques: near surface mounting reinforcement (NSMR) Unstrengthened concrete T-beam Longitudinal grooves cut into soffit FRP strips placed in grooves Grooves filled with epoxy grout Research indicates NSMR is effective and efficient for strengthening ISIS EC Module 4

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**Field Applications Maryland Bridge FRP Winnipeg, Manitoba**

Repair with reinforcement Field Applications Section: 8 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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**Field Applications John Hart Bridge FRP Prince George, BC**

Repair with reinforcement Field Applications Section: 8 John Hart Bridge Prince George, BC 64 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**

FRP Repair with reinforcement Field Applications Section: 8 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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**Field Applications St. Émélie Bridge FRP**

Repair with reinforcement Field Applications Section: 8 St. Émélie Bridge Sainte-Émélie-de-l'Énergie, Quebec Single-span, simply supported tee-section bridge Strengthened for flexure and shear Site preparation: 3 weeks, FRP installation: 5 days ISIS EC Module 4

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**Canadian codes exist for the design of FRP-reinforced concrete members**

Repair with reinforcement Design Guidance Section: 9 Canadian codes exist for the design of FRP-reinforced concrete members CAN/CSA-S6-00: The Canadian Highway Bridge Design Code (CHBDC) CAN/CSA-S806-02: Design and Construction of Building Components with Fibre Reinforced Polymers ISIS EC Module 4

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**Additional Information**

FRP Repair with reinforcement Additional Information Section: 9 Available from ISIS Design Manual No. 3: Reinforcing Concrete Structures with Fiber Reinforced Polymers ISIS Design Manual No. 4: Strengthening Reinforced Concrete Structures with Externally-Bonded Fiber Reinforced Polymer ISIS EC Module 1: An Introduction to FRP Composites for Construction ISIS EC Module 3: An introduction to FRP-Reinforced Concrete Structures ISIS EC Module 4: An Introduction to FRP-Strengthening of Reinforced Concrete Structures ISIS EC Module 4

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COMPRESSION FIELD THEORY FOR SHEAR STRENGTH IN CONCRETE

COMPRESSION FIELD THEORY FOR SHEAR STRENGTH IN CONCRETE

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