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.

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. Overview
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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19. LoA 2: Peak shear stress distribution
Experiment S25T1 (2)
Effective width in shear of reinforced concrete solid slab bridges under wheel loads
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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
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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
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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
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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
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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
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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
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26. Case study
Introduction
• 4-span bridge
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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
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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
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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
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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
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