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Lecture given on 10/09 at Vrije Universiteit Brussel

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- 1. Challenge the future Delft University of Technology Shear in Reinforced Concrete Slabs under Concentrated Loads close to Supports Eva Lantsoght
- 2. Shear in reinforced concrete slabs under concentrated loads close to supports 2 Overview • Introduction • Overview of experiments • Beams vs. slabs • Modified Bond Model • Code extension proposal • Application to practice • Conclusions
- 3. Shear in reinforced concrete slabs under concentrated loads close to supports 3 Motivation (1) Bridges from 60s and 70s The Hague in 1959 Increased live loads heavy and long truck (600 kN > perm. max = 50ton) End of service life + larger loads
- 4. Shear in reinforced concrete slabs under concentrated loads close to supports 4 Motivation (2)
- 5. Shear in reinforced concrete slabs under concentrated loads close to supports 5 Motivation (3) • First checks since mid-2000s • 3715 structures to be studied • 600 slab bridges shear-critical • But: checks according to design rules • => Residual capacity??? • Hidden reserves of the bearing capacity Highways in the Netherlands
- 6. Shear in reinforced concrete slabs under concentrated loads close to supports 6 Project description (1) • Capacity of existing bridges • TU Delft • Concrete Structures • Structural Mechanics • TNO • RWS • Concrete Structures • Long-term tensile strength • Beam shear – sustained loads • Continuous girders – shear • Prestressed slabs – punching • Slab bridges - shear/punching Concrete bridges
- 7. Shear in reinforced concrete slabs under concentrated loads close to supports 7 Live Loads in NEN-EN 1991-2:2003
- 8. Shear in reinforced concrete slabs under concentrated loads close to supports 8 Shear Failure (1) Shear failure of the de la Concorde bridge, Laval Shear failures of bridges: rare but brittle failures
- 9. Shear in reinforced concrete slabs under concentrated loads close to supports 9 Shear Failure (2) Beam shear vs. Punching shear Beam shear, one-way shear Punching shear, two-way shear • Punching shear over perimeter • Beam shear over (effective) width
- 10. Shear in reinforced concrete slabs under concentrated loads close to supports 10 Shear Failure (3) Beam shear • Since 1899 (Ritter) • 1955: collapse of warehouse • Most experiments: • Beams • Heavily reinforced • Small size • Slender (a/d ≥ 2,5) • Basis for design codes amount of shear experiments done
- 11. Shear in reinforced concrete slabs under concentrated loads close to supports 11 Shear Failure (3) Beam shear • Since 1899 (Ritter) • 1955: collapse of warehouse • Most experiments: • Beams • Heavily reinforced • Small size • Slender (a/d ≥ 2,5) • Basis for design codes Influence of shear span
- 12. Shear in reinforced concrete slabs under concentrated loads close to supports 12 Shear Failure (4) Punching shear Categories of methods for punching shear Shear stress Beam analogy Strut and tie Plate theory / FEM The nature of shear failure is still not fully understood!
- 13. Shear in reinforced concrete slabs under concentrated loads close to supports 13 Slabs under concentrated loads (1) • Transverse load redistribution • Additional dimension in slabs • Expected higher capacity than beams • First experiments: Regan (1982)
- 14. Shear in reinforced concrete slabs under concentrated loads close to supports 14 Slabs under concentrated loads (2) • Shear stress over effective width • Fixed width, eg. 1 m • Load spreading method
- 15. Shear in reinforced concrete slabs under concentrated loads close to supports 15 Slabs under concentrated loads (2) • Shear stress over effective width • Fixed width, eg. 1 m • Load spreading method
- 16. Shear in reinforced concrete slabs under concentrated loads close to supports 16 Goals • Assess shear capacity of slabs under concentrated loads • Determine effective width in shear
- 17. Shear in reinforced concrete slabs under concentrated loads close to supports 17 Experiments (1) Size: 5m x 2,5m (variable) x 0,3m = scale 1:2 Continuous support, Line supports Concentrated load: vary a/d and position along width
- 18. Shear in reinforced concrete slabs under concentrated loads close to supports 18 Experiments (2) • 2nd series experimental work: • Slabs under combined loading • Line load • Preloading • 50% of strength from slab strips • Concentrated load until failure • Conclusions from 1st series valid when combining loads? • 26 experiments, 8 slabs • Overall: 156 experiments, 38 slabs
- 19. Shear in reinforced concrete slabs under concentrated loads close to supports 19 Experiments (3)
- 20. Shear in reinforced concrete slabs under concentrated loads close to supports 20 Slabs vs. beams (1) • Transverse load redistribution • Geometry governing in slabs • Location of load • result of different load-carrying paths • Mid support vs end support • influence of transverse moment • Wheel size • more 3D action
- 21. Shear in reinforced concrete slabs under concentrated loads close to supports 21 Slabs vs. beams (2) 5000 1000 1500 2000 2500 b (mm)
- 22. Shear in reinforced concrete slabs under concentrated loads close to supports 22 Modified Bond Model (1) • Based on Bond Model (Alexander and Simmonds, 1990) • For slabs with concentrated load in middle
- 23. Shear in reinforced concrete slabs under concentrated loads close to supports 23 Modified Bond Model (2)
- 24. Shear in reinforced concrete slabs under concentrated loads close to supports 24 Modified Bond Model (3) • Adapted for slabs with concentrated load close to support • Geometry is governing as in experiments • Determine factor that reduces capacity of “radial” strip • Maximum load: based on sum capacity of 4 strips
- 25. Shear in reinforced concrete slabs under concentrated loads close to supports 25 Modified Bond Model (4)
- 26. Shear in reinforced concrete slabs under concentrated loads close to supports 26 Modified Bond Model (5)
- 27. Shear in reinforced concrete slabs under concentrated loads close to supports 27 Modified Bond Model (6)
- 28. Shear in reinforced concrete slabs under concentrated loads close to supports 28 Modified Bond Model (7)
- 29. Shear in reinforced concrete slabs under concentrated loads close to supports 29 Modified Bond Model (8)
- 30. Shear in reinforced concrete slabs under concentrated loads close to supports 30 Modified Bond Model (9) Experiments vs Eurocode shear Experiments vs Modified Bond Model
- 31. Shear in reinforced concrete slabs under concentrated loads close to supports 31 Code extension proposal Limit State function Experiment vs. Design value • Experiment • mean values • Test/Predicted ratio • Design value • characteristic values f d P P R R Reliability analysis based on load and resistance
- 32. Shear in reinforced concrete slabs under concentrated loads close to supports 32 Code extension proposal Random variables 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% 0 2 4 6 8 10 12 36 38 40 42 44 46 48 50 52 More Frequency fc,cube,mean (MPa) Frequency Cumulative % concrete compressive strengthTest/Predicted
- 33. Shear in reinforced concrete slabs under concentrated loads close to supports 33 Code extension proposal Slabs subjected to Wheel Loads • Enhancement factor depends on fck • Experiments: fck not as in shear formula • Effect of reduced support width • Proposal for av ≤ 2.5dl 1/3 , , , ,100 1.9 225 ck Rd c prop Rd c l ck eff red l f V C k f b d , 0.52 0.48 sup eff red eff l b b b
- 34. Shear in reinforced concrete slabs under concentrated loads close to supports 34 Application to practice (1) • Evaluating existing solid slab bridges: • NEN-EN 1992-1-1:2005 • 25% reduction of contribution concentrated load close to support • β =av/2d • Combined: βnew =av/2,5d • Effective width: French method and minimum 4d
- 35. Shear in reinforced concrete slabs under concentrated loads close to supports 35
- 36. Shear in reinforced concrete slabs under concentrated loads close to supports 36 Application to practice (3) • Checks at indicated sections • 9 existing Dutch solid slab bridges
- 37. Shear in reinforced concrete slabs under concentrated loads close to supports 37 Application to practice (4) • Shear stresses: influence of recommendations • QS-EC2: wheel loads at av = 2,5dl • QS-VBC: wheel loads at av = dl • QS-EC2 18% reduction in loads • Shear capacity: • QS-EC2: vRd,c ~ ρ, d • low reinforcement + deep section = small shear capacity • QS-VBC: τ1 ~ fck only • QS-EC2 improved selection ability
- 38. Shear in reinforced concrete slabs under concentrated loads close to supports 38 Economics • Repair cost • Demolition cost • Recycling cost • New construction Environment • Impact of repair • Impact of replacement • CO2 emissions • Materials • Transport Social • Visual impact • Traffic delays • Employment Sustainability
- 39. Shear in reinforced concrete slabs under concentrated loads close to supports 39 Impact on Sustainability Example replacement of 3-span slab bridge (deck only) • Economic cost: 500k – 640k € • Environmental cost: 136 ton CO2 • Blast furnace cement: 74 ton CO2 • Portland slag cement: 122 ton CO2 • Social cost: case-dependent • can be 9 times economic cost • Scope: 600 slab bridges
- 40. Shear in reinforced concrete slabs under concentrated loads close to supports 40 Summary & Conclusions • Slabs under concentrated loads behave differently in shear than beams • Beneficial effect of transverse load redistribution • Modified Bond Model improvement as compared to Eurocode • Code extension proposal for transverse load redistribution • Application to practice: reduction in loads
- 41. Shear in reinforced concrete slabs under concentrated loads close to supports 41 Contact: Eva Lantsoght E.O.L.Lantsoght@tudelft.nl +31(0)152787449

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