effective width in shear of reinforced concrete solid slab bridges under wheel loads

14-01-2014

Challenge the future

DelftUniversity ofTechnology

Effective width in shear Of reinforced concrete solid slab bridges

under wheel loads

Eva Lantsoght, Ane de Boer, Cor van der Veen, Joost Walraven

2Effective width in shear of reinforced concrete solid slab bridges under wheel loads

Overview

•Introduction•Principle of Levels of

Approximation•Experiments•LoA I: Load spreading•LoA II: Shear stress distribution•Case study•Summary

3Effective width in shear of reinforced concrete solid slab bridges under wheel loads

IntroductionProblem Statement

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

4Effective width in shear of reinforced concrete solid slab bridges under wheel loads

IntroductionHighway network in the Netherlands

•NL: 60% of bridges built before 1976

•Assessment: shear critical in 600 slab bridges

Highways in the Netherlands

5Effective width in shear of reinforced concrete solid slab bridges under wheel loads

Principle of Levels of ApproximationModel Code 2010

•Approach from fib Model Code 2010

•Solution strategy = different levels of approximation

•Eg: Shear capacity in Model Code 2010

6Effective width in shear of reinforced concrete solid slab bridges under wheel loads

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?

7Effective width in shear of reinforced concrete solid slab bridges under wheel loads

Experiments

Size: 5m x 2.5m (variable) x 0.3m = scale 1:2

16ft x 8ft (variable) x 1ft

Continuous support, Line supportsConcentrated load: vary a/d and position along width

8Effective width in shear of reinforced concrete solid slab bridges under wheel loads

LoA I: Load spreadingEffective width in shear

45° load spreading - Dutch practice

45° load spreading – French practice

Or: fixed value (eg. 1m = 3.3ft)

9Effective width in shear of reinforced concrete solid slab bridges under wheel loads

LoA 1: Load spreadingResults of experiments

BS = 0.5m = 1.6 ft wide BX = 2.0m = 6.6ft wide

10Effective width in shear of reinforced concrete solid slab bridges under wheel loads

LoA 1: Load spreadingResults of experiments

500

0 1000 1500 2000 2500b (mm)

11Effective width in shear of reinforced concrete solid slab bridges under wheel loads

LoA 1: Load spreadingStatistical 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%

12Effective width in shear of reinforced concrete solid slab bridges under wheel loads

LoA 1: Load spreadingFinite 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

13Effective width in shear of reinforced concrete solid slab bridges under wheel loads

LoA 1: Load spreadingFinite 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

14Effective width in shear of reinforced concrete solid slab bridges under wheel loads

LoA 1: Load spreadingFinite 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

15Effective width in shear of reinforced concrete solid slab bridges under wheel loads

LoA 1: Load spreadingFinite 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

16Effective width in shear of reinforced concrete solid slab bridges under wheel loads

LoA 1: Load spreadingApplication to slab bridges (1)

•Loading at edge

•Asymmetric effective width

17Effective width in shear of reinforced concrete solid slab bridges under wheel loads

LoA 1: Load spreadingApplication to slab bridges (2)

Effective width per axle instead of per wheel print

18Effective width in shear of reinforced concrete solid slab bridges under wheel loads

LoA 2: Peak shear stress distributionExperiment S25T1 (1)

Size: 5m x 2.5m x 0.3m = scale 1:2 Continuous support, line supports with load cells

Concentrated load

19Effective width in shear of reinforced concrete solid slab bridges under wheel loads

LoA 2: Peak shear stress distributionExperiment S25T1 (2)

20Effective width in shear of reinforced concrete solid slab bridges under wheel loads

LoA 2: Peak shear stress distributionExperiment S25T1 (3)

•Failure at Pu = 1461 kN•Study: 9 intervals up to 90% of ultimate capacity

21Effective width in shear of reinforced concrete solid slab bridges under wheel loads

LoA 2: Peak shear stress distributionFinite element model

•TNO Diana

•Slab: shell elements •Supports: solid elements •Felt: interface elements

•40% orthotropy assumed

•Phased activation of supports

22Effective width in shear of reinforced concrete solid slab bridges under wheel loads

LoA 2: Peak shear stress distributionFinite element model (2)

Reaction forces match sufficiently reaction forces of experiment

23Effective width in shear of reinforced concrete solid slab bridges under wheel loads

LoA 2: Peak shear stress distributionShear stress analysis: Experiment

•Assume force distributed constantly per load cell

•Example: P = 1314 kN

•Total force over 2dl

•Resulting shear stress

,2

86 mm3 2 4 580 kN

358 mmtot dF FS FS FS

,2

2 2 2

580 kN4.13 MPa

2 2 265 mm

tot dd

l

F

d

24Effective width in shear of reinforced concrete solid slab bridges under wheel loads

LoA 2: Peak shear stress distributionShear 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

25Effective width in shear of reinforced concrete solid slab bridges under wheel loads

LoA 2: Peak shear stress distributionRecommendations

Concentrated load 585 kN 1314 kN Shear stress τ2d

(MPa) τ4d (MPa)

τ2d (MPa)

τ4d (MPa)

Measurements 1.51 0.87 4.13 2.63 Model, integrating stresses

1.30 1.10 3.28 2.70

Model, reaction forces 1.39 1.27 3.25 2.60 Use distribution width of 4dl

Note: vRd,c = 0.68 MPa => UC = 1.62 at 40% of Pu

At 40% and 90% of Pu

26Effective width in shear of reinforced concrete solid slab bridges under wheel loads

Case studyIntroduction

•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

27Effective width in shear of reinforced concrete solid slab bridges under wheel loads

Case StudyResults

•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

28Effective width in shear of reinforced concrete solid slab bridges under wheel loads

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

29Effective width in shear of reinforced concrete solid slab bridges under wheel loads

Contact:

Eva Lantsoght

E.O.L.Lantsoght@tudelft.nl

+31(0)152787449