FRP Strengthening of RC Flexural Members - Ductility Issues

Transcription

1 FRP Strengthening of RC Flexural Members - Ductility Issues A presentation to ACIC April 22, Southampton Professor R. Delpak Division of Civil Engineering School of Technology University of Glamorgan

2 The need for structural strengthening 5 all motor vehicles cars and taxis other vehicles Billion vehicle kilometers Year ( ) Increase in UK traffic volume over the past 5 years

3 The Machine Bridge - near Pontypridd

4 Fibre Reinforced Plastic (FRP) Composites Light Weight: a quarter of that of steel. High Strength: up to 5,5 N/mm 2. Excellent resistance to corrosion. Other advantages compared with steel: superior toughness and thermal properties; excellent damping effect; reduced number of parts; and good fatigue resistance, and lower WLC. D B Tann/R Delpak 2

5 There are still many design related issues to be resolved in FRP strengthening of RC structures One of these issues is the apparent lack of ductility of FRP composites

6 But it is, of course, always desirable for a structure to fail mildly rather than in a brittle manner at the ultimate limit state!

7 And, FRP strengthened elements do not necessarily have to fail in a brittle manner even though the FRP materials are brittle An optimum design approach, which incorporates appropriate level of ductility is therefore essential.

8 What is ductility? How to determine it? A seemingly rather simple question, but admittedly this is an arguable one!

9 There is a need for us to, once and for all, define and AGREE (!) ductility, especially for FRP strengthened RC members.

10 Definition Ductility: Ability of material to sustain PLASTIC deformation before fracture. Deformability: Material ability to deform, elastically or irretrievably, before failure. Ductility is a special form of deformability. In the context of flexural elements strengthened by FRP, ductility may be interpreted as the members ability to sustain plastic deformation before the moment resistance is significantly reduced. D B Tann/R Delpak 2

11 General Expression of Deformability/Ductility ϕ = u y Ductility index, ϕ, is generally determined as the ratio of ultimate deformation, u, divided by the corresponding values of deformation at the material yield point, y. D B Tann/R Delpak 2

12 Such an approach is not applicable to FRP strengthened elements!! ? FRP strengthened RC beam Load P (kn Conventional RC beam Concrete cracking. 2. Internal steel yielding. 3. Just before ultimate failure Maximum Span Deflection, δ (mm)

13 Test Beam Set Up W/2 W/ D B Tann/R Delpak 1999

14 Load P (kn) Control Beam Beam A1 Beam A2 Beam A3 Beam A4 Beam A5 Serviceability Limit CFRP Beams Mid-Span Deflection (mm) Control Beam P 2 24 mm P 2

15 Depth (mm).5 kn 1 kn 2 kn 4 kn 6 kn 8 kn Depth (mm) 1 kn 12 kn 14 kn 16 kn 18 kn 2 kn 22 kn 26 kn 3 N 34 kn 38 kn 42 kn 48 kn 6 kn 64 kn 66 kn Strain Strain Beam A1

16 8 7 6 Beam A3 Control Beam Load (kn) Concrete Strain (Microstrain)

17 Moment C1 - Defl. based C1 - Strain based Curvature (x1-6 1/mm) ((a) Beam A1 Moment C2 - Defl. based C2 - Strain based Curvature (x1-6 1/mm) (b) Beam A Moment C3 - Defl. based C3 - Strain based Curvature (x1-6 1/mm) (c) Beam A3 Moment C4 - Defl. based C4 - Strain based Curvature (x1-6 1/mm) (d) Beam A4 3 3 Moment C5 - Defl. based C5 - Strain based Curvature (x1-6 1/mm) (e) Beam A5 Moment Control - Defl. based Control - Strain based Curvature (x1-6 1/mm) (f) Control Beam

18 3 Contrl Beam Beam A1 Beam A2 Beam A3 Beam A4 Beam A5 Moment (knm) CFRP Beams Control Beam Mid-Span Curvature (x1-6 1/mm)

19 D B Tann/R Delpak 1999

20 Comparison of Load vs. Deflection of Conventional RC Beams with CFRP Repaired RC Beams (Just before ULS) Serviceability Limit 7 Load W (kn) Control Beam 3 2 2,4 mm Maximum Span Deflection (mm) Contrl Beam - Steel Only Beam 33 - (R) Beam 33 - (O) Beam 31 - (R) Beam 35 - Steel and CFRP (O) Beam 39 - (R) Beam 39 - (O) FEM D B Tann/R Delpak 1999

21 The adhesive layer remained most intact at failure, although in a number of cases, the delamination of CFRP plate was apparent. D B Tann/R Delpak 1999

22 D B Tann/R Delpak 1999

23 D B Tann/R Delpak 2

24 D B Tann/R Delpak 1999

25 Failure Modes of FRP Strengthened RC Beams (a) FRP fabrics/plate rupture in tension (b) Concrete crushing in compression (c) Ripping off of concrete cover, with FRP still bonded to the concrete

26 Proposed Deformability Calculation δ φ 95 = δ r

27 b ε cu.8f cu /γ mc x A s d x.9x C s C c h d d-x z A s ε s T s A p Cross Section ε p Strain Distribution BS 811 Stress Block T p

28 Major Assumptions Plain sections remain plain during loading full composite action between concrete and FRP material. Linear strain compatibility between concrete, steel and FRP plate. BS 811 simplified rectangular stress block.

29 2 Beam Depth (mm) Strain (x 1 e-6)

30 Neutral Axis Depth for FRP Strengthened Balanced Section h x sb = f pu 1+ γ m.35 E γ p ep

31 FRP area limit for ductile strengthening A pmax =.8f cu bh.95f.67f pu y A s

32 For a given moment, M, where M < M max the required FRP area A pr = M.85 f.67 f pu y d A d s

33 Critical Ratio of Steel Reinforcement for Ductile Strengthening.4 x f ρ = sb cu s.95 f h y

34 Increase of Load ULS (%) Steel Reinforcement Ratio (%)

35 Ductility Calculation ϕ du 1 E = tot E el

36 7 6 B 5 Load (kn) 4 3 Loading Unloading 2 1 Elastic deformation A A' C Maximum Span Deflection (mm)

37 12 M3-Loading M3-Unloading 1 P u B Load (kn) P 1 P 2 S 1 S 2 A A' A Maximum Span Deflection (mm) S Equivalent Elastic Energy elastic stored energy E el C

38 Beam Ref. P u kn S 1 kn/m S 2 kn/m S kn/m δ y mm E tot knm m E el ϕ df knmm ϕ du ϕ du Control A A A A A A A A A A B B B B B B

39 Conclusions (1) FRP strengthening is most suited for solid RC slabs, flanged beams, and singly reinforced rectangular sections. The ductility of strengthened beams, if properly designed and detailed, is acceptable in accordance with the normally expected behaviour of RC structures.

40 Conclusions (2) Higher strength of FRP materials, say greater than 2 MPa, is only useful if the material s modulus of elasticity also reaches a higher level, say above 2 kn/mm 2. The FRP manufacturers should develop a confidence level and try their best to ensure a reasonably consistent value for the material factor of safety. This factor of safety should be limited, if possible, to a value of the order of 1.5. Excessively larger FOS for materials may result in over-strengthening and thus brittle failure.

41 Conclusions (3) As the modulus of elasticity for FRP composites normally decreases slightly with the age the material, a factor of safety for modulus of elasticity should be applied, independent from the factor of safety for material. This value should ideally, be controlled within 1.1. FRP strengthening is NOT suitable for doubly reinforced sections, if strengthening is carried out, it will only change the originally expected ductile failure mode to a brittle mode of failure without any substantial increase in the load carrying capacity.

42 Conclusions (4) FRP strengthening is particularly suitable for strengthening structures with high grade of concrete, in such cases the high strength of concrete could be more fully utilised. FRP strengthened RC beams can fail in ductile manner if designed as under strengthened sections

43 Thank you for your attention.