Flexural and Punching Shear - Sheffieldci.group.shef.ac.uk/CI_content/FRP/FRPRCS5_AWE.pdf · Centre for Cement and Concrete Flexural and Punching Shear Design of FRP RC Flat Slabs

Centre forCement and Concrete

Flexural and Punching Shear Design of FRP RC Flat SlabsFlexural and Punching Shear Design of FRP RC Flat Slabs

Dr Abdel Wahab El-GhandourLecturer (Ain Shams Univ.)

Dr Kypros PilakoutasReader (Univ. of Sheffield)

Professor Peter WaldronProfessor (Univ. of Sheffield)

Centre forCement and Concrete OutlineOutline

Context of Work

Experimental Program

Finite Element Verification

Parametric Study

Flexural Design Guidelines

Punching Shear Design Guidelines

Conclusions

Centre forCement and Concrete Context Of WorkContext Of Work

• Eurocrete Project• Aim: Durable FRP Reinforcement• Partners: 9 Companies + University of Sheffield• Funds: 5.6 million ECU

• fib TG 9.3 + ConFibreCrete Research Network• Aim: Design Guidelines• Members: Over 40 International Experts• TMR: 11 Institutions from 9 EC Countries• Funds: 1.3 million Euro


Work Done Work Done @ @ SheffieldSheffield(on FRP Rebar)(on FRP Rebar)

RC Beams: Flexure, Shear, Bond & Ductility

RC Slabs: 2-D Flexure, Punching Shear, Bond

Sub-elements: Tensile strength, Bond

Development of Design Guides and Philosophy

Various Case Studies on Precast Concrete Elements

Design of New Structural Elements / Applications


Parametric StudyComparisons with Test Results

ANALYTICAL PROGRAM (ABAQUS)

Series (2)Ground anchor slab testing

Phase (1)Square slabs

Phase (2)Circular slabs

TGS-S1 to 3 TGS-G1 to 3 TGS-A to D TAS-1 to 6

Series (1)Flat slab testing

Phase (1)S = 200 mm

Phase (2)S = 100 mm

No shear Shear

SG1SC1

SGS1SCS1

No shear Shear

SG2 & 3SC2

SGS2

EXPERIMENTAL PROGRAM

Steel GFRP SpiralHoop

Work on FRP RC SlabsWork on FRP RC Slabs


Experimental ProgramSlab Details

Experimental ProgramExperimental ProgramSlab DetailsSlab Details

Without Shear Reinforcement

With Shear Reinforcement

Without Shear Reinforcement

With Shear Reinforcement

Typical CFRP ‘Shearband’

First Series Second Series


FEASensitivity Study

FEAFEASensitivity StudySensitivity Study

Element Type

Mesh Sensitivity

Integration Points

Support Conditions

Reinforcement Model

Concrete ModelUniaxial Compressive Stress-Strain CurveInitial Compressive Young’s ModulusRatio of Uniaxial Comp. to Tensile StrengthTension StiffeningShear Retention

Mesh (C): 20 × 20 elem.


FEA VerificationComparisons with Test Results

FEA VerificationFEA VerificationComparisons with Test ResultsComparisons with Test Results

0

50

100

150

200

250

300

0 5 10 15 20Displacement D850 (mm)

Loa

d (k

N)

testanalysis

Slab SG2


Parametric StudyReinforcement Ratio

Parametric StudyParametric StudyReinforcement RatioReinforcement Ratio

0

200

400

600

800

1000

1200

1400

1600

0 2 4 6 8 10 12 14 16Displacement D850 (mm)

Load

(kN

)

ρ = 3.6 %ρ = 3 %ρ = 1.8 %ρ = 0.9 %ρ = 0.45 %ρ = 0.225 %ρ = 3.6 %ρ = 3 %ρ = 1.8 %ρ = 0.9 %ρ = 0.45 %ρ = 0.225 %

Glass Carbon

Expected Failure Trajectory

fcu = 60 MPa L/t = 23


Parametric StudyConcrete Grade

Parametric StudyParametric StudyConcrete GradeConcrete Grade

0

100

200

300

400

500

600

700

800

0 2 4 6 8 10 12 14 16 18Displacement D850 (mm)

Load

(kN

) fcu = 60fcu = 50fcu = 35fcu = 25fcu = 60fcu = 50fcu = 35fcu = 25

Glass Carbon

ρ= 0.9 % L/t = 23

Expected Failure Trajectory for Carbon

Expected Failure Trajectory for Glass


Parametric StudySpan to Depth Ratio

Parametric StudyParametric StudySpan to Depth RatioSpan to Depth Ratio

0

500

1000

1500

2000

2500

0 5 10 15 20 25Displacement D850 (mm)

Load

(kN

)

L/t = 15L/t = 20L/t = 23L/t = 30L/t = 35L/t = 15L/t = 20L/t = 23L/t = 30L/t = 35

Glass Carbon

Expected Failure Trajectory for Carbon

Expected Failure Trajectory for Glass

ρ = 0.9 % fcu = 60 MPa

Centre forCement and Concrete Flexural Guidelines

Design EquationFlexural GuidelinesFlexural Guidelines

Design EquationDesign Equation

(L/t) = 24.2 (250/Δr)1.9 (Eρ/99000)0.1 (fcu/40)-0.44

Parametric Study CFRP RC Slabs

Ultimate Loads

Service Loads = Ultimate Loads / 1.6

Service Loads + FEA Load-Deflection curves → Service Deflections (δser)

δser = L / Δr


Derivation of Design EquationFlexural GuidelinesFlexural Guidelines

Derivation of Design EquationDerivation of Design Equation

0.85

0.9

0.95

1

1.05

0 1 2 3 4 5Ef ρ / 99000

Δr /

250

CFRP slabs parametric studyBest-fit curve

y = 0.928 x0.0546

R2 = 0.9814


Derivation of Design EquationFlexuralFlexural GuidelinesGuidelines


0.2

0.6

1

1.4

0.4 0.6 0.8 1 1.2 1.4 1.6fcu / 40

r

CFRP slabs parmetric studyBest-fit curve

y = 1.0406 x-0.2331

R2 = 0.9167


Derivation of Design EquationFlexural GuidelinesFlexural Guidelines


0.2

0.6

1

1.4

0.4 0.6 0.8 1 1.2 1.4 1.6(L/t) / 23

Δr /

250

CFRP slabs parametric studyBest-fit curve

y = 0.9506 x-0.5547

R2 = 0.9914

(Δr/250) = 0.918 (Eρ/99000)0.0546 (fcu/40)-0.2331 [(L/t)/23]-0.5547


Flexural GuidelinesDerivation of Design Equation

Flexural GuidelinesFlexural GuidelinesDerivation of Design EquationDerivation of Design Equation

0

10

20

30

40

50

0 10 20 30 40 50(L/t) FEA

(L/t)

cal

c.

L/t calc. = L/t FEACFRP slabs parametric studyBest-fit curve

y = 0.9995 x

R2 = 0.9585

(L/t) = C (250/Δr)c1 (Eρ/99000)c2 (fcu/40)c3

(L/t) = 24.2 (250/Δr)1.9 (Eρ/99000)0.1 (fcu/40)-0.44


Punching Shear GuidelinesFailure Patterns (2nd Series)

Punching Shear GuidelinesPunching Shear GuidelinesFailure Patterns (2Failure Patterns (2ndnd Series)Series)

Section through Slab SG3 at Failure

Section through Slab SGS2 at Failure

Section through Slab SC2 at Failure


Punching Shear GuidelinesConcrete Shear Resistance

Predictive Approaches

Punching Shear GuidelinesPunching Shear GuidelinesConcrete Shear ResistanceConcrete Shear Resistance

Predictive ApproachesPredictive Approaches

Strain Approachvc = (100 Ae / bv d)1/3 (400 / d)1/4 (0.27) (fcu)1/3 ,

Ae = AFRP (EFRP / Esteel)

Modified Approachvc = (100 Ae / bv d)1/3 (400 / d)1/4 (0.27) (fcu)1/3 ,

Ae = AFRP (EFRP / Esteel) (φ)ε = εFRP / εyield steel

when εFRP = 0.0045, φ = 1.8


Strain Approach

vc = (100 Ae / bv d)1/3 (400 / d)1/4 (0.27) (fcu)1/3 , where Ae = Ar (Er / 200)

Modified Approach

vc = (100 Ae / bv d)1/3 (400 / d)1/4 (0.27) (fcu)1/3 , where Ae = Ar (1.8Er/200)

100125150175200225

250275300325350

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Reinforcement Ratio (%)

Pult.

/ (fc

u/25

)0.33 Modified Glass

Clarke GlassModified CarbonClarke CarbonSG1 Exp.SG2 Exp.SG3 Exp.SC1 Exp.SC2 Exp.


Normalised Exp. & Pred. Capacities (BS 8110)


NormalisedNormalised ExpExp. & . & PredPred. Capacities (BS 8110). Capacities (BS 8110)



Verification of the Modified Approach (BS 8110)


Verification of the Modified Approach (BS 8110)Verification of the Modified Approach (BS 8110)

0

50

100

150

200

250

300

350

400

450

0 50 100 150 200 250 300 350 400 450

Pult. exp. (kN)

Pult.

pre

d. (k

N)

Pexp. = Ppred.Series CSeries CSSeries H

0

50

100

150

200

250

300

350

400

450

0 50 100 150 200 250 300 350 400 450

Pult. exp. (kN)Pu

lt. p

red.

(kN

)

Pexp. = Ppred.Series CSeries CSSeries H

STRAIN APPROACH(BS 8110)

MODIFIED APPROACH

(BS 8110)

Centre forCement and Concrete CONCLUSIONSCONCLUSIONSCONCLUSIONS• Flexural Design Guidelines

• FEA can predict flexural deformations(though convergence problems encountered)

• Main parameters influencing deflections (L/t, E, ρ, fcu)

• General Design Equation proposed [L/t = f(Δr, E, ρ, fcu)]

• Punching Shear Design Guidelines

• Strain App. is conservative• Modified App. offers good predictions (φ = 1.8)

Documents

Flexural and Punching Shear - Sheffieldci.group.shef.ac.uk/CI_content/FRP/FRPRCS5_AWE.pdf · Centre for Cement and Concrete Flexural and Punching Shear Design of FRP RC Flat Slabs