SHEAR DESIGN EQUATIONS FOR FRP RC BEAMS

Transcription

1 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

2 Outline Shear resistance Predictive approaches Experimental investigation New approach Validation Conclusions

3 Shear Transfer Mechanisms strut tie strut Strut and Tie Arch F t Truss

4 Shear Resistance V = V c + V s Concrete contribution + Contribution of shear r/ment Empirical equation concrete in compression aggregate interlock dowel action

5 Shear and FRP r/ment σ (MPa) 2000 CFRP AFRP Prestressing Steel 1000 Reinforcing Steel GFRP ε % Neutral axis depth (mm) Steel RC section FRP RC section microstrain

6 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

7 Predictive Approach Limiting Strain = 0.2% % σ (MPa) 2000 CFRP AFRP Prestressing Steel 1000 Reinforcing Steel GFRP ε %

8 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?

9 Experimental programme 1 st phase of testing V c Concrete shear resistance 2 nd phase of testing V s Shear link contribution

10 1 st Phase of testing 2300 GFRP RC Beams A FRP = 452 mm Steel RC Beams A S = 434 mm

11 1 st phase of testing

12 Experimental set-up

13 Typical Load-displacement response Load (kn) SB 40 GB a/d ~ Displacement (mm)

14 Load (kn) Centre for Load-displacement response for GFRP RC beams GB a/d ~ GB a/d ~ a/d ~ 3 GB Displacement (mm) = shear diagonal failure

15 Strain distribution along the flexural reinforcement Microstrain SB40 (90.59 kn) GB43 (54.16 kn) Strain approach Location of straingage (mm) New strain level proposed

16 2 nd phase of testing GFRP links CFRP links

17 Experimental set-up

18 Experimental set-up

19 Strain in the flexural reinforcement Load (kn) Strain approach New strain level proposed Microstrain

20 Load (kn) Centre for Strain in the shear reinforcement Strain approach New strain level proposed Microstrain

21 Decomposition of shear carrying mechanisms Beam SB40R Shear force (kn) estimated shear r/ment contribution 2500 μstrain (flex. r/ment) 2500 μstrain (flex. r/ment - 1 st phase) SB 40 estimated concrete contribution 4500 μstrain (shear r/ment) 2500 μstrain (shear r/ment) Displacement (mm)

22 Decomposition of shear carrying mechanisms Beam GB43R Shear force (kn) 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 μstrain flex. r/ment (1st phase) estimated concrete contribution estimated shear r/ment contribution 4500 μstrain (shear r/ment 3 rd cycle) Displacement (mm)

23 Types of Shear Failure SB 40 a/d ~ 3 SB 41 a/d ~ kn GB 43 a/d ~ 3 GB 44 a/d ~ kn

24 Shear Crack Width Growth Beam SB40/R Beam GB43/R Load (kn) SA Load (kn) SA - 1 st +2 nd cycles SA - 3 rd cycle w m w SL SL Shear crack - 1 st phase Shear crack - 2 nd phase Crack width (mm) 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 Crack width (mm)

25 Predicted values (kn) Centre for Strain Approach & Sheffield Approach BS Sheffield approach ACI Sheffield approach EC (1 st draft) - Sheffield approach Experimental data (kn)

26 Shear reinforcement requirement Ratio of shear r-ment (Strain/Sheffield) v d =2MPa v d =1.75MPa v d =1.5MPa v d =1MPa Normalized flexural stiffness E/5GPa)

27 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