Design Methodology and Calculations using Fiber-Reinforced

Mark Jarvinen, P.E. (MA)

Monday, July 12, 2021

Design Methodology and Calculations using Fiber-Reinforced Polymer Systems

Presented by Mark Jarvinen, P.E. Simpson Strong-Tie

SE University, July 2021 www.LearnWithSEU.com

Repair. Protect. Strengthen.

Learning Objectives

• Learn ACI 440.2R-17 / ACI 318 design philosophy

• Understand FRP strengthening limitations

• Design FRP flexural reinforcement for RC beams

• Design FRP shear reinforcement for RC beams

• Improve RC column strength with FRP confinement

2


General Design Considerations

• Based on traditional reinforced concrete design principles of ACI 318

• FRP strengthening systems……

• Designed to resist tension

• Maintain strain compatibility between the FRP and concrete substrate

• Presumed to have no compressive strength

• Should not be used on substrates when f ’c < 2500 psi

3


FRP Design Philosophy

• Designed in accordance with ACI 318 strength and serviceability provisions

• Using strength reduction (Φ) and load (1.2 DL, 1.6 LL, etc.) factors stated in ACI 318 (and ACI 562 – Strengthening Limits)

• Additional FRP-related strength reduction factors (Ψf) apply to strength contributed by FRP

• ΦVn = Φ(Vc + Vs) ………adding FRP………….. ΦVn w/FRP = Φ(Vc + Vs + Ψf Vf )

• Accounts for uncertainties inherent in FRP systems vs. reinforced concrete

• FRP-related strength reduction factors are calibrated to produce reliability indices above 3.5

4


FRP Design Philosophy – Bond Vs. Contact

• Design Principles for FRP reinforcement systems can be broken down into two categories:

• Bond Critical versus Contact Critical applications

• Bond Critical – Full bonding of the FRP composite surface to the base material is essential to support assumed behavior (ex. flexural or shear strengthening)

• Contact Critical – Relies solely on FRP contact with the base material, (bond is not critical) and an FRP-to-FRP bond, via lap splice, to serve the intended reinforcement function (ex. column confinement)

5


Fiber Reinforcement

• Carbon (high strength upgrades)

– High strength & modulus, low strain

– Excellent resistance to environments, creep, & fatigue

• E-glass (low strength upgrades & protection)

– High strength & strain, low modulus

– More sensitive to environments, creep, & fatigue 0

0.2

0.4

0.6

0.8

1

1.2

0.000 0.005 0.010 0.015 0.020

Str

ess (

ksi)

Strain (in/in)

MOE:

* 60ksi steel, Es = 29000ksi

* Carbon FRP, ECFRP = 14200ksi

* E-Glass FRP, EGFRP = 3300ksi

Es

1

ECFRP

1

1

EGFRP

Carbon Fiber Composite

GR60 Steel

Glass Fiber Composite

6


Strengthening Limits

• Damage and Material/Installation Defects

• Loss of resin bond or damage to FRP by physical abuse, accident, or vandalism could

result in failure or collapse of a strengthened member

• ACI 562-16 Eq. 5.5.2a: (ΦRn)existing ≥ (1.1D + 0.5L + 0.2S)new

• ACI 562-16 Eq. 5.5.2b: (ΦRn)existing ≥ (1.1D + 0.75L)new (ACI 440.2R-17 Eq. 9.2)

• ACI 562-16: Code Requirements for Evaluation, Repair, and Rehabilitation of Concrete Buildings

• Live load factor shall be 1.0 if there is high likelihood that live load will be sustained

• Φ-factors are those articulated in ACI 318 (ACI 318-14; Sec. 21.2.1)

7


Strengthening Limits

• Structural Fire Endurance

• Fire and FRP - resin may reach temperatures beyond the glass transition temperature (Tg)

• FRP reinforcement is assumed completely lost in a fire and concrete and steel rebar properties are diminished per ACI 216.1

• Existing member (w/o FRP contribution) must be checked for support of loads shown below w/ reduced concrete and rebar performance,

• ACI 562-16 Eq. 5.5.3: Φex R ≥ (0.9 or 1.2)D + 0.5L + 0.2S (ACI 440.2R-17 Eq. 9.2.1b)

• ACI 440.2R-17 Eq. 9.2.1a: Φex R ≥ 1.0D + 1.0L

• Φex = 1.0

• R is the nominal resistance of the structure, computed using probable material properties during the fire event

• Live load factor shall be 1.0 if there is high likelihood that live load will be sustained

• Fire endurance can also be established via testing such as per ASTM E119 8


Poll Question #1

Strengthening limits for FRP reinforcements articulated in Chapter 5 of ACI 562-16 include the following:

A. Provisions for reducing factored live load when live load is likely

to be sustained B. Criteria for preventing structural failure or collapse caused by

physical damage and installation defects C. Criteria for preventing structural failure or collapse caused by

fire exposure D. Both B and C

9


FRP Design Material Properties

• Typically, FRP manufacturers report the following FRP material properties:

• Ultimate Tensile Strength – ƒƒu* = 128,000 psi

• Ultimate Tensile Strain at Rupture (Elongation @ Break) – Ɛƒu* = 0.9% (0.009 in./ in.)

• Thickness per layer of FRP Composite – tƒ = 0.04 in.

• Tensile Modulus of Elasticity (MOE) – Eƒ = 14,200,000 psi

Note: Material property values shown are for SST’s Code-listed, 22 oz./sq. yd., unidirectional carbon fabric, reference T-R-CSSCUCF22, dated 05/23/16 (also ICC ES ESR-3403)

10


FRP Design Material Properties (Cont’d)

• FRP material properties, reported by manufacturers, shall be reduced based on anticipated, in-service, environmental exposure

• Equations below establish the max. FRP design tensile properties

11


Flexural Strengthening

• General comments regarding flexural strengthening with FRP

• 40% is typical maximum increase in flexural strength

• Positive and negative moment strengthening are possible

• Limited to reinforced concrete (RC) and bonded prestressed concrete (PC) members

• Helps to limit crack widths

• Guidance for use of FRP flexural reinforcement in plastic hinge zones of ductile frame elements resisting seismic loads is addressed in Ch. 13

12


Flexural Strengthening – Failure Modes

• The following flexural failure modes should be investigated

1. Concrete crushing prior to rebar yielding

2. Rebar yielding followed by FRP rupturing

3. Rebar yielding followed by concrete crushing

4. Shear/tension delamination of concrete cover

5. Debonding of FRP composite (resin layer) from the concrete base material

• Failure modes 2 and 3 are the preferred failure modes

• The governing failure mode dictates the flexural strength of the section

13


Poll Question #2

Which of the following is the most desirable failure mode at the limit state when designing FRP flexural strengthening?

A. Concrete crushing prior to rebar yielding

B. Rebar yielding followed by FRP rupturing

C. FRP debonding or concrete delamination

14


Illustrations Related to Debonding Failures

15


Flexural Strengthening – Debonding Strain

• Effective strain (Ɛƒe) in FRP composites shall be limited to the strain level at which debonding may occur (Ɛƒd) as defined by the following empirical equations:

• For near-surface-mount (NSM) FRP applications

Ɛƒd = 0.7 Ɛƒu

• For carbon and glass fabric and precured laminate FRP applications

16


Flexural Strengthening - Assumptions

• Calculations are based on actual member dimensions, reinforcement, and material properties of member being strengthened

• Plane sections remain plane after loading

• Max. compressive strain of concrete is Ɛcu = 0.003

• Neglect tensile strength of concrete

• FRP has linear-elastic stress/strain relationship to failure

• No slipping occurs between FRP and concrete

• Shear deformations within resin layer are neglected

17


Flexural Strengthening Calculations

• Suggested FRP flexural strengthening calculations procedure (Refer to “Flexural Strengthening Design Example” handout)

• Existing Condition Checks

• Beam loading

• Min. flexural reinforcement (rebar)

• Reinforcement ratio (rebar)

• Strengthening limits

• Physical damage

• Fire endurance

• Initial concrete strain at extreme tensile fiber

18



• Initial Concrete Strain at Extreme Tensile Fiber (Beam Soffit) (Refer to “Flexural Strengthening Design Example” handout)

• Gives strain in concrete due to service loads imposed prior to FRP application

• Initial concrete strain will be subtracted from total strain at extreme tensile fiber at ultimate limit state

• Cracked section moment of inertia (Icr)

• εbi = MDL y / Ec Icr

19



• Determine FRP Design Properties (Refer to “Flexural Strengthening Design Example” handout)

• Establish FRP properties

• Choose an FRP material for design

• Consider and apply appropriate FRP Environmental Reduction Factor to FRP’s ultimate tensile stress and strain

• Check design strain against debonding strain limits (debonding strain limits often govern)

20



• Determine Neutral Axis Depth (c) at Ultimate Limit State (Refer to “Flexural Strengthening Design Example” handout)

• Calculation Philosophy

• Satisfy strain compatibility and force equilibrium

• Max. concrete strain: εcu ≤ 0.003

• Max. effective FRP strain: εfe ≤ εfd ≤ 0.9 εfu

• Consider the governing mode of failure

• Modify compressive stress block appropriate for the concrete strain level

• Uses trial-and-error/iterative solution approach

21



• Determine Neutral Axis Depth (c) at Ultimate Limit State (Refer to “Flexural Strengthening Design Example” handout)

• Calculation Procedure

• Estimate “c” (good starting point is 0.2d - 0.25d)

• Determine failure mode (evaluate FRP strain)

• Calculate material strains

• Calculate material stresses and forces

• Custom conc. stress block

• Verify “c” via force equilibrium

• If “c” hasn’t converged, then revise, and start at the top

22



• Determine Flexural Design Strength w/ FRP (Refer to “Flexural Strengthening Design Example” handout)

• After “c” converges

• Calculate flexural design strength including FRP

• Check flexural design strength vs. max. factored bending moment

23



• Serviceability Criteria (Refer to “Flexural Strengthening Design Example” handout)

• Check ACI 318 serviceability requirements (deflections and crack widths) as impacted by increased loading and FRP strengthening

• Use service (not factored) loads and cracked, transformed section

• To avoid inelastic deformations: steel (rebar) stress ƒs,s ≤ 0.80 ƒy

• Concrete stress ƒc,s ≤ 0.6 ƒ’c

24



• Creep-Rupture and Fatigue Stress Limits (Refer to “Flexural Strengthening Design Example” handout)

• Check creep-rupture of FRP under sustained loads and risk of failure due to fatigue under cyclic loads

• Use service (not factored) loads and cracked, transformed section

• To avoid creep rupture/cyclic fatigue failure: FRP stress ƒf,s ≤ Table 10.2.9 limits

25


Shear Strengthening

• General comments regarding shear strengthening with FRP

• FRP has shown to increase shear strength of existing RC beams and columns by wrapping or partially wrapping the member

• FRP fiber are oriented transverse to the member’s longitudinal axis or perpendicular to shear cracks providing additional shear strength

• Subject to strengthening limits of ACI 562-16

• Fully wrapped members can provide strengthening for moment frames resisting seismic loads and plastic hinge regions

26


Shear Strengthening

• Repairing shear cracks

• Existing shear cracks should be repaired by epoxy injection prior to FRP application

• Repairing shear cracks with ASTM C881, Type IV (load bearing) resins restores aggregate interlock and confidence in concrete’s shear strength contribution

27


Shear Strengthening

• FRP Wrapping Schemes

• Three types of FRP wrapping schemes can be used to shear strengthen rectangular beams and columns

• Completely wrapped members are most efficient, followed U-wraps

• FRP can be wrapped continuously or in discrete strips. Discrete strips allow moisture migration

28


Shear Strengthening – Effective Shear Strain

• Effective strain (Ɛƒe) allowed in FRP composites used for shear strengthening is limited by the following criteria:

• Completely wrapped members

Ɛƒe = 0.004 ≤ 0.75 Ɛƒu

• Three-sided U-wraps and two-sided schemes

Ɛƒe = κv Ɛƒu ≤ 0.004

29


Poll Question #3

Which answer best describes the three types of FRP wrapping schemes most commonly used for FRP shear reinforcements?

A. Orthogonal wraps, longitudinal wraps, and perpendicular wraps

B. Transverse wrapping, discretely wrapped, and over wrapped

C. Completely wrapped, three-sided U-wraps, and two-sided

30


Shear Strengthening Calculations

• Suggested FRP shear strengthening calculations procedure (Refer to “Shear Strengthening Design Example” handout)

• Existing Condition Checks

• Beam loading

• Min. shear reinforcement (rebar)

• Max. stirrup spacing (rebar)

• Strengthening limits

• Physical damage

• Fire endurance

31



• Determine FRP Design Properties (Refer to “Shear Strengthening Design Example” handout)

• Establish FRP properties (similar to procedure used for flexure)

• Choose an FRP material for design

• Apply appropriate FRP Environmental Reduction Factor to FRP’s ultimate tensile stress and strain

• If using discrete U-wraps or two-sided shear reinforcing schemes, determine max. center-to-center spacing of wraps (measured from centerline-to-centerline)

32



• Determine Effective Shear Strain for Design (Refer to “Shear Strengthening Design Example” handout)

• Effective shear strain for bonded U-wraps

• Ɛƒe = κv Ɛƒu ≤ 0.004

• κv - a function of conc. strength, wrapping scheme, FRP stiffness, etc.

• Le - the length over which a majority of the bond stress is maintained

• k1 - accounts for conc. strength

• k2 - accounts wrapping scheme

• dfv - effective depth of FRP shear reinforcement

33



• Determine Shear Design Strength w/ FRP (Refer to “Shear Strengthening Design Example” handout)

• After calculating the effective shear strain “Ɛƒe”

• Calculate the effective stress in the FRP

fƒe = Ɛƒe Eƒ

• Calculate shear design strength including FRP φVn

w/FRP = φ (Vc + Vs + Ψf Vf); where

• Check shear design strength vs. max. factored shear force

34



• Check Shear Strengthening Limits (Refer to “Shear Strengthening Design Example” handout)

• Total shear strength provided by reinforcement (steel rebar plus FRP) shall be limited to the ACI 318 criteria for steel strength alone

26.4 k + 20.3 k = 46.7 k ≤ 170 k

35



• Determine Longitudinal Beam Length Requiring FRP (Refer to “Shear Strengthening Design Example” handout)

• Review factored shear force diagram to determine limits of FRP U-wraps

36


Axial Strengthening

• Column Confinement w/ FRP

• Shown to improve strength and ductility

• Increase in peak axial load is immediate benefit

• ƒ’c vs. ƒ’cc

• Ductility enhancements require more complex calculations

• Accomplished by completely wrapping column with fibers orienting transversely to longitudinal axis of member

37


Axial Strengthening

• Columns: Pure Axial Compression Confined w/ FRP

• The axial compressive strength of an FRP-confined, non-slender, non-prestressed compression section can be expressed as

φPn

Pu

38


Axial Strengthening

• Calculating Confined Compressive Strength, ƒ’cc

• Equation for max. confined concrete compressive strength

ƒ’cc = ƒ’c + Ψf 3.3 κa ƒl

Where……

Ψf - FRP-related adjustment factor (0.95) κa - efficiency factor based on column’s x-sec’l geometry

fl - max. confinement pressure

κε – FRP strain efficiency factor (0.55)

fl = 2 Eƒ n tƒ εfe / D; εfe = κε εfu; ƒl / ƒ’c ≥ 0.08

39


Axial Strengthening

• Calculating Confined Compressive Strength, ƒ’cc (cont’d)

• Geometric efficiency factors based on column’s x-section (κa and κb)

• For Circular x-sections:

κa = κb = 1.0

• For Noncircular x-sections:

κa = Ae /Ac (b/h)2 κb = Ae /Ac (h/b)0.5

D = (b2 + h2) 0.5

Ae - x-section of effectively-confined conc. section

Ac - x-section of conc. in compression member

40


Axial Strengthening

• Calculating Confined Compressive Strength, ƒ’cc (cont’d)

• Geometric efficiency factors based on noncircular column’s x-section

• Ae Consists of the area within four parabolas, outside of which the concrete is negligibly confined

• An equation for Ae /Ac is as follows:

Where…..

ρg - long. steel reinf. ratio; rc - corner radius; Ag - gross area

41


Axial Strengthening

• Serviceability Criteria

• FRP jackets contain concrete damage and maintain structural integrity of columns as loading approaches ultimate magnitudes

• Severe cracking (radial) should be prevented under service loads by limiting transverse strains

• Transverse strains are adequately limited by limiting concrete service stresses:

ƒc,s ≤ 0.65 ƒ’c

• Service stresses in longitudinal steel should be limited as well:

ƒs,s ≤ 0.60 ƒy

42


Combined Axial Compression and Bending

• Wrapping columns provides enhancements to members subjected to combined axial compression and bending

• For axial load eccentricities greater than 0.1h (0.1D), P-M Diagrams for the FRP-confined member are useful

• Max. effective strain limit: εfe = 0.004 ≤ κε εfu

• Strength enhancements are only valid when Pu & Mu fall above the balanced line – strength enhancements are only significant for compression-controlled members

43


Learning Objectives

• Learn ACI 440.2R-17 / ACI 318 design philosophy

• Understand FRP strengthening limitations

• Design FRP flexural reinforcement for RC beams

• Design FRP shear reinforcement for RC beams

• Improve RC column strength with FRP confinement

44

Mark Jarvinen, P.E. (MA)

Monday, July 12, 2021

Mark Jarvinen, P.E. (MA) Sr. Field Engineer Concrete Construction Products Simpson Strong-Tie [email protected]

mailto:[email protected]

Which General Design Consideration for FRP

Strengthening Systems is the answer to this session’s

challenge question?

•Designed to resist tension •Maintain strain compatibility between FRP and concrete •Presumed to have no compressive strength •Should not be used on substrates when f ’c < 2500 psi

CHALLENGE QUESTION:

Please circle the answer that is announced so that you can use the information to complete your quiz for PDH.

Documents

Design Methodology and Calculations using Fiber-Reinforced