effective width in shear of reinforced concrete solid slab bridges under wheel loads
DESCRIPTION
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.TRANSCRIPT
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
+31(0)152787449