SHEAR DESIGN EQUATIONS FOR FRP RC BEAMS Dr. Maurizio Guadagnini Dr. Kypros Pilakoutas Professor Peter Waldron Centre for Dept. of Civil and Structural Engineering The University of Sheffield, UK
Outline Shear resistance Predictive approaches Experimental investigation New approach Validation Conclusions
Shear Transfer Mechanisms strut tie strut Strut and Tie Arch F t Truss
Shear Resistance V = V c + V s Concrete contribution + Contribution of shear r/ment Empirical equation concrete in compression aggregate interlock dowel action
Shear and FRP r/ment σ (MPa) 2000 CFRP AFRP Prestressing Steel 1000 Reinforcing Steel GFRP 0 1 2 3 ε % Neutral axis depth (mm) 300 250 200 150 Steel RC section FRP RC section 100 50 0 3000 6000 9000 12000 15000 microstrain
Predictive Approach ε FRP = ε S F FRP = F S F = ε E A = ε E A = F FRP FRP FRP FRP S S S S A e = A FRP E FRP E S
Predictive Approach Limiting Strain = 0.2% - 0.25% σ (MPa) 2000 CFRP AFRP Prestressing Steel 1000 Reinforcing Steel GFRP 0 1 2 3 ε %
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?
Experimental programme 1 st phase of testing V c Concrete shear resistance 2 nd phase of testing V s Shear link contribution
1 st Phase of testing 2300 GFRP RC Beams A FRP = 452 mm 2 1800 2300 1000 Steel RC Beams A S = 434 mm 2 1800 1000
1 st phase of testing
Experimental set-up
Typical Load-displacement response Load (kn) 100 80 60 SB 40 GB 43 40 20 0 a/d ~ 3 0 2 4 6 8 10 12 14 16 18 20 Displacement (mm)
Load (kn) Centre for Load-displacement response for GFRP RC beams 180 160 GB 45 140 a/d ~ 1 120 100 GB 44 80 60 a/d ~ 2 40 20 a/d ~ 3 GB 43 0 0 2 4 6 8 10 12 14 16 18 20 Displacement (mm) = shear diagonal failure
Strain distribution along the flexural reinforcement Microstrain 6000 5000 4000 3000 2000 1000 0 SB40 (90.59 kn) GB43 (54.16 kn) Strain approach 0 500 1000 1500 2000 2500 Location of straingage (mm) New strain level proposed
2 nd phase of testing GFRP links CFRP links
Experimental set-up
Experimental set-up
Strain in the flexural reinforcement Load (kn) 160 140 120 100 80 60 40 20 0 Strain approach New strain level proposed 0 2000 4000 6000 8000 Microstrain
Load (kn) Centre for Strain in the shear reinforcement 160 140 120 100 80 60 40 20 0 Strain approach New strain level proposed 0 2000 4000 6000 8000 Microstrain
Decomposition of shear carrying mechanisms Beam SB40R Shear force (kn) 70 60 50 40 estimated shear r/ment contribution 2500 μstrain (flex. r/ment) 2500 μstrain (flex. r/ment - 1 st phase) 30 20 10 SB 40 estimated concrete contribution 4500 μstrain (shear r/ment) 2500 μstrain (shear r/ment) 0 0 2 4 6 8 10 Displacement (mm)
Decomposition of shear carrying mechanisms Beam GB43R Shear force (kn) 70 60 50 40 30 20 10 2500 μstrain flex. r/ment (1 st phase) 4500 μstrain (shear r/ment - 1 st +2 nd cycles) 2500 μstrain (shear r/ment - 1 st +2 nd cycles) GB 43 4500 μstrain flex. r/ment (1st phase) estimated concrete contribution estimated shear r/ment contribution 4500 μstrain (shear r/ment 3 rd cycle) 0 0 5 10 15 20 25 30 35 Displacement (mm)
Types of Shear Failure SB 40 a/d ~ 3 SB 41 a/d ~ 2 @ 116 kn @ 180 kn GB 43 a/d ~ 3 GB 44 a/d ~ 2 @ 103 kn @ 160 kn
Shear Crack Width Growth Beam SB40/R Beam GB43/R Load (kn) 140 120 100 SA Load (kn) 140 120 100 SA - 1 st +2 nd cycles 80 80 SA - 3 rd cycle 60 40 20 0 w m w SL SL Shear crack - 1 st phase Shear crack - 2 nd phase 0.0 0.5 1.0 1.5 2.0 2.5 3.0 Crack width (mm) 60 40 20 0 w m w SL SL - 1 st +2 nd cycles SL - 3 rd cycle 1 st phase 2 nd phase - 1 st +2 nd cycle 2 nd phase - 3 rd cycle 0.0 0.5 1.0 1.5 2.0 Crack width (mm)
Predicted values (kn) Centre for Strain Approach & Sheffield Approach 160 140 120 BS-8110 - Sheffield approach ACI-318-99 - Sheffield approach EC2-2001 (1 st draft) - Sheffield approach 100 80 60 40 20 0 0 20 40 60 80 100 120 140 160 Experimental data (kn)
Shear reinforcement requirement Ratio of shear r-ment (Strain/Sheffield) 3.5 3.0 2.5 v d =2MPa v d =1.75MPa v d =1.5MPa v d =1MPa 2.0 1.5 1.0 0.0 0.2 0.4 0.6 0.8 1.0 1.2 Normalized flexural stiffness E/5GPa)
Conclusions 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