Effective Width in Shear of Reinforced Concrete Solid Slab Bridges under Wheel Loads

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For the assessment of reinforced concrete slab bridges in the Netherlands, the shear stress resulting from the dead loads and live loads is determined in a spreadsheet or from a finite element model. In a spreadsheet-based approach, an assumption for the distribution of the loads from the wheel prints is necessary. When finite element methods are used, it is necessary to determine over which length (a multiple of the effective depth) the peak shear stress can be distributed for comparison to the design shear capacity.
To recommend a load-spreading method, experiments were executed on slab strips of increasing widths. The shear capacity did not increase with the increasing width upon passing a threshold. This threshold is compared to different load spreading methods, indicating that a distribution from the far side of the wheel print is to be preferred. This recommendation is also supported by the results of a statistical analysis and the stress distribution in nonlinear finite element models.
To find the distribution width in a finite element method, a numerical model is compared to an experiment on a slab subjected to a concentrated load in which the support consists of a line of 7 bearings equipped with load cells measuring the reaction forces. These measurements were compared to the stress profile at the support from the model, showing that the peak can be distributed over 4 times the effective depth.
These recommendations for the effective width and distribution width are research-based tools that replace the previously used rules of thumb resulting from engineering judgement.

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Effective Width in Shear of Reinforced Concrete Solid Slab Bridges under Wheel Loads

  1. 1. Effective width in shear Of reinforced concrete solid slab bridges under wheel loads 14-01-2014 Eva Lantsoght, Ane de Boer, Cor van der Veen, Joost Walraven Delft University of Technology Challenge the future
  2. 2. Overview • • • • • • • Introduction Principle of Levels of Approximation Experiments LoA I: Load spreading LoA II: Shear stress distribution Case study Summary Effective width in shear of reinforced concrete solid slab bridges under wheel loads 2
  3. 3. Introduction Problem Statement Bridges from 60s and 70s Increased live loads heavy and long truck (600 kN > perm. max = 50ton) The Hague in 1959 End of service life + larger loads Effective width in shear of reinforced concrete solid slab bridges under wheel loads 3
  4. 4. Introduction Highway network in the Netherlands • NL: 60% of bridges built before 1976 • Assessment: shear critical in 600 slab bridges Highways in the Netherlands Effective width in shear of reinforced concrete solid slab bridges under wheel loads 4
  5. 5. Principle of Levels of Approximation Model Code 2010 • Approach from fib Model Code 2010 • Solution strategy = different levels of approximation • Eg: Shear capacity in Model Code 2010 Effective width in shear of reinforced concrete solid slab bridges under wheel loads 5
  6. 6. Principle of Levels of Approximation Shear assessment • Level I: Quick Scan sheet • Fast, simple and conservative spreadsheet • Unity check: loads/capacity • Level II: Finite Element Analysis • Shear stress distribution over support • Peak shear stress: distribute over which width? Effective width in shear of reinforced concrete solid slab bridges under wheel loads 6
  7. 7. Experiments Size: 5m x 2.5m (variable) x 0.3m = scale 1:2 16ft x 8ft (variable) x 1ft Continuous support, Line supports Concentrated load: vary a/d and position along width Effective width in shear of reinforced concrete solid slab bridges under wheel loads 7
  8. 8. LoA I: Load spreading Effective width in shear 45° load spreading - Dutch practice 45° load spreading – French practice Or: fixed value (eg. 1m = 3.3ft) Effective width in shear of reinforced concrete solid slab bridges under wheel loads 8
  9. 9. LoA 1: Load spreading Results of experiments BS = 0.5m = 1.6 ft wide BX = 2.0m = 6.6ft wide Effective width in shear of reinforced concrete solid slab bridges under wheel loads 9
  10. 10. LoA 1: Load spreading Results of experiments 0 500 1000 1500 b (mm) 2000 2500 Effective width in shear of reinforced concrete solid slab bridges under wheel loads 10
  11. 11. LoA 1: Load spreading Statistical analysis • Calculated from series vs. 45° load spreading • Comparison between database (literature) + experiments and methods • French load spreading method underestimates less • Lower COV for French load spreading method • Database: 63% vs 42% • Delft experiments: 26% vs 22% Effective width in shear of reinforced concrete solid slab bridges under wheel loads 11
  12. 12. LoA 1: Load spreading Finite element results (1) Models of 1.5m = 4.9ft wide a = center-to-center distance between load and support Effective width from shear stress distribution over support Effective width in shear of reinforced concrete solid slab bridges under wheel loads 12
  13. 13. LoA 1: Load spreading Finite element results (2) Models of 2.5m = 8.2ft wide a = center-to-center distance between load and support Effective width from shear stress distribution over support Effective width in shear of reinforced concrete solid slab bridges under wheel loads 13
  14. 14. LoA 1: Load spreading Finite element results (3) Models of 3.5m = 11.5ft wide a = center-to-center distance between load and support Effective width from shear stress distribution over support Effective width in shear of reinforced concrete solid slab bridges under wheel loads 14
  15. 15. LoA 1: Load spreading Finite element results (4) • French load spreading method gives safe estimate of beff • NLFEA: beff depends slightly on slab width • NLFEA: influence of a/d less than in French method • French method sufficient for LoA 1 Effective width in shear of reinforced concrete solid slab bridges under wheel loads 15
  16. 16. LoA 1: Load spreading Application to slab bridges (1) • Loading at edge • Asymmetric effective width Effective width in shear of reinforced concrete solid slab bridges under wheel loads 16
  17. 17. LoA 1: Load spreading Application to slab bridges (2) Effective width per axle instead of per wheel print Effective width in shear of reinforced concrete solid slab bridges under wheel loads 17
  18. 18. LoA 2: Peak shear stress distribution Experiment S25T1 (1) Size: 5m x 2.5m x 0.3m = scale 1:2 Continuous support, line supports with load cells Concentrated load Effective width in shear of reinforced concrete solid slab bridges under wheel loads 18
  19. 19. LoA 2: Peak shear stress distribution Experiment S25T1 (2) Effective width in shear of reinforced concrete solid slab bridges under wheel loads 19
  20. 20. LoA 2: Peak shear stress distribution Experiment S25T1 (3) • Failure at Pu = 1461 kN • Study: 9 intervals up to 90% of ultimate capacity Effective width in shear of reinforced concrete solid slab bridges under wheel loads 20
  21. 21. LoA 2: Peak shear stress distribution Finite element model • TNO Diana • Slab: shell elements • Supports: solid elements • Felt: interface elements • 40% orthotropy assumed • Phased activation of supports Effective width in shear of reinforced concrete solid slab bridges under wheel loads 21
  22. 22. LoA 2: Peak shear stress distribution Finite element model (2) Reaction forces match sufficiently reaction forces of experiment Effective width in shear of reinforced concrete solid slab bridges under wheel loads 22
  23. 23. LoA 2: Peak shear stress distribution Shear stress analysis: Experiment • Assume force distributed constantly per load cell • Example: P = 1314 kN • Total force over 2dl 86 mm Ftot ,2 d = FS 3 + ( FS 2 + FS 4 ) = 580 kN 358 mm • Resulting shear stress τ 2d = Ftot ,2 d 2d l 2 = 580 kN 2 ( 265 mm ) 2 = 4.13 MPa Effective width in shear of reinforced concrete solid slab bridges under wheel loads 23
  24. 24. LoA 2: Peak shear stress distribution Shear stress analysis: Model 1. Integrating shear stresses over distribution width around peak 2. Based on reaction forces in load cells, similar to approach for experiments Effective width in shear of reinforced concrete solid slab bridges under wheel loads 24
  25. 25. LoA 2: Peak shear stress distribution Recommendations At 40% and 90% of Pu Concentrated load Shear stress 585 kN τ2d τ4d (MPa) (MPa) 1.51 0.87 1.30 1.10 Measurements Model, integrating stresses Model, reaction forces 1.39 ⇒ Use distribution width of 4 d l 1.27 1314 kN τ2d τ4d (MPa) (MPa) 4.13 2.63 3.28 2.70 3.25 2.60 Note: vRd,c = 0.68 MPa => UC = 1.62 at 40% of Pu Effective width in shear of reinforced concrete solid slab bridges under wheel loads 25
  26. 26. Case study Introduction • 4-span bridge • • • • 1959 End spans = 10.1m (33.1ft) Mid spans = 14.4m (47.2ft) Width = 10m (32.8ft), 6m (19.7ft) carries traffic • QR24 reinforcement • fy = 240MPa = 35ksi • plain reinforcement • fck = 35MPa = 5000psi Effective width in shear of reinforced concrete solid slab bridges under wheel loads 26
  27. 27. Case Study Results • LoA 1 • vEd = 0.68MPa (99psi) • vRd,c = 0.91MPa (132psi) ⇒UC = 0.74 • LoA 2: • VEd = 278kN/m (19kip/ft) • VRd,c = 438kN/m (30kip/ft) ⇒UC = 0.63 • LoA 1 more conservative than LoA 2 Effective width in shear of reinforced concrete solid slab bridges under wheel loads 27
  28. 28. Summary & Conclusions 1. Level I of Assessment: Quick Scan method: French load spreading method 2. Level II of Assessment: Finite Element Model: Distribute peak shear stress over 4dl 3. Case study: LoA 1 more conservative than LoA 2 Effective width in shear of reinforced concrete solid slab bridges under wheel loads 28
  29. 29. Contact: Eva Lantsoght E.O.L.Lantsoght@tudelft.nl +31(0)152787449 Effective width in shear of reinforced concrete solid slab bridges under wheel loads 29

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