SHEAR DESIGN EQUATIONS FOR FRP RC BEAMSci.group.shef.ac.uk/CI_content/FRP/FRPRCS6_03_MG.pdf · Beam...

Centre for Cement and Concrete

��NFR

Dr. Maurizio GuadagniniDr. Kypros Pilakoutas

Professor Peter Waldron

Centre for Cement and ConcreteDept. of Civil and Structural Engineering

The University of Sheffield, UK

SHEAR DESIGN EQUATIONSFOR FRP RC BEAMS


��NFR

OutlineOutline

• Shear resistance

• Predictive approaches

• Experimental investigation

• New approach

• Validation

• Conclusions


��NFR

strutstrut

tie

Ft

Strut and Tie

Arch

Truss

Shear Transfer MechanismsShear Transfer Mechanisms


��NFR

Shear ResistanceShear Resistance

V = Vc + VsConcrete

contributionEmpirical equation

concrete in compressionaggregate interlockdowel action

Contribution of shear r/ment+


��NFR

1000

2000

%

σ

ε

(MPa)

0 1 2 3

Reinforcing Steel

Prestressing Steel

AFRP

GFRP

CFRP

Shear and FRP r/mentShear and FRP r/ment

microstrain0 3000 6000 9000 12000 15000

Neu

tral a

xis

dept

h(m

m)

50

100

150

200

250

300

Steel RC sectionFRP RC section


��NFR

FRP SF F=FRP Sε ε=

FRP FRP FRP FRP S S S SF E A E A Fε ε= ⋅ ⋅ = ⋅ ⋅ =

FRPe FRP

S

EA AE

= ⋅

Predictive ApproachPredictive Approach


��NFR

Limiting Strain = 0.2% - 0.25%Predictive ApproachPredictive Approach

1000

2000

%

σ

ε

(MPa)

0 1 2 3

Reinforcing Steel

Prestressing Steel

AFRP

GFRP

CFRP


��NFR

• Are the shear mechanisms for steel and FRP RC similar?

• Is it correct to simply add the separate shear contributions from the concrete and reinforcement?

• Is the limiting strain concept valid?


��NFR

Experimental programmeExperimental programme

1st phase of testing

2nd phase of testing

Concrete shear

resistance

Shear link contribution

Vc

Vs


��NFR

1st Phase of testing1st Phase of testing

Steel RC Beams

AS = 434 mm2

GFRP RC Beams

AFRP = 452 mm2

1000

2300

1800

1000

2300

1800


��NFR

1st phase of testing1st phase of testing


��NFR

Experimental set-upExperimental set-up


��NFR

Displacement (mm)0 2 4 6 8 10 12 14 16 18 20

Load

(kN

)

0

20

40

60

80

100SB 40

GB 43

a/d ~ 3

Typical Load-displacement responseTypical Load-displacement response


��NFR

Displacement (mm)0 2 4 6 8 10 12 14 16 18 20

Load

(kN

)

020406080

100120140160180

GB 45

GB 43

GB 44

Load-displacement response forGFRP RC beamsLoad-displacement response forGFRP RC beams

� = shear diagonal failure

a/d ~ 3

a/d ~ 2

a/d ~ 1


��NFR

Location of straingage (mm)0 500 1000 1500 2000 2500

0

1000

2000

3000

4000

5000

6000

SB40 (90.59 kN)GB43 (54.16 kN)

Strain distribution along the flexural reinforcementStrain distribution along the flexural reinforcement

Strain approach

New strain level proposedM

icro

stra

in


��NFR

2nd phase of testing2nd phase of testing

GFRP linksCFRP links


��NFR

Experimental set-upExperimental set-up


��NFR

0 2000 4000 6000 8000

Load

(kN

)

020406080

100120140160

Strain in the flexural reinforcementStrain in the flexural reinforcement

Strain approach

New strain level proposed

Microstrain


��NFR

0 2000 4000 6000 8000

Load

(kN

)

020406080

100120140160

Strain in the shear reinforcementStrain in the shear reinforcement

Strain approach

New strain level proposed

Microstrain


��NFR

Displacement (mm)0 2 4 6 8 10

Shea

r for

ce (k

N)

0

10

20

30

40

50

60

70

estimatedconcrete

contribution25

00 μ

stra

in(f

lex.

r/m

ent)

2500

μst

rain

(fle

x. r/

men

t - 1

st pha

se)

4500 μstrain (shear r/ment)

2500 μstrain (shear r/ment)SB 40

estimatedshear r/mentcontribution

Decomposition of shear carrying mechanismsDecomposition of shear carrying mechanisms

Beam SB40R


��NFR

Displacement (mm)0 5 10 15 20 25 30 35

Shea

r for

ce (k

N)

0

10

20

30

40

50

60

70

estimatedconcrete

contribution

2500 μstrain(shear r/ment - 1st+2nd cycles)

4500 μstrain(shear r/ment - 1st+2nd cycles)

2500

μst

rain

flex.

r/m

ent

(1st p

hase

)

4500

μst

rain

flex.

r/m

ent

(1st

pha

se)

GB 43

estimatedshear r/mentcontribution

4500 μstrain(shear r/ment 3rd cycle)

Beam GB43R

Decomposition of shear carrying mechanismsDecomposition of shear carrying mechanisms


��NFR

SB 40 a/d ~ 3 SB 41 a/d ~ 2

GB 43 a/d ~ 3 GB 44 a/d ~ 2

@ 116 kN

@ 103 kN @ 160 kN

@ 180 kN

Types of Shear FailureTypes of Shear Failure


��NFR

Shear Crack Width GrowthShear Crack Width Growth

Beam SB40/R Beam GB43/R

Crack width (mm)0.0 0.5 1.0 1.5 2.0 2.5 3.0

Load

(kN

)

0

20

40

60

80

100

120

140

Shear crack - 1st

phaseShear crack - 2nd phase

SL

SA

wSLwm

Crack width (mm)0.0 0.5 1.0 1.5 2.0

Load

(kN

)0

20

40

60

80

100

120

140

2nd phase - 1st+2nd cycle2nd phase - 3rd cycle

SL - 3rd cycle

SA - 1st+2nd cycles

SA - 3rd cycle

SL - 1st+2nd cycles

1st phase

wSLwm


��NFR

Strain Approach & Sheffield ApproachStrain Approach & Sheffield Approach

Experimental data (kN)0 20 40 60 80 100 120 140 160

Pre

dict

edva

lues

(kN

)

0

20

40

60

80

100

120

140

160BS-8110 - Sheffield approachACI-318-99 - Sheffield approach

EC2-2001 (1stdraft) - Sheffield approach


��NFR

Shear reinforcement requirementShear reinforcement requirement

Normalized flexural stiffness E/5GPa)0.0 0.2 0.4 0.6 0.8 1.0 1.2

Rat

ioof

shea

rr-m

ent(

Stra

in/S

heffi

eld)

1.0

1.5

2.0

2.5

3.0

3.5

vd = 1 MPa

vd = 1.5 MPa

vd = 1.75 MPa

vd = 2 MPa


��NFR

• The strain in both the flexural and shear FRP r/ment can reach values that are much higher than those currently adopted

• Shear resisting mechanisms are mobilised in a similar way in both GFRP and steel RC beams and failure modes are characterised by similar behaviour

• The principle of strain control is accepted, but a new limit of 4,500 με is proposed

ConclusionsConclusions

SHEAR DESIGN EQUATIONS FOR FRP RC BEAMSci.group.shef.ac.uk/CI_content/FRP/FRPRCS6_03_MG.pdf · Beam...

Documents

Transcript of SHEAR DESIGN EQUATIONS FOR FRP RC BEAMSci.group.shef.ac.uk/CI_content/FRP/FRPRCS6_03_MG.pdf · Beam...