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Eva Lantsoght

Presentation held at my PhD defense

Design Tecnologia Negócios

Challenge the future
Delft
University of
Technology
Shear in Reinforced Concrete Slabs
under Concentrated Loads close to Supports
Eva Lantsoght

2
Overview
• Background
• Slabs under concentrated loads
• Overview of experiments
• Beams vs. slabs
• Modified Bond Model
• Application to practice
• Conclusions

3
Background (1)
Bridges from 60s and 70s
The Hague in 1959
Increased live loads
common heavy and long truck (600 kN)
End of service life + larger loads

5
Background (3)
• First checks since mid-2000s
• 3715 structures to be studied
• 600 slab bridges
• But: checks according to design
rules
• => Residual capacity???
• Hidden reserves of the bearing
capacity
Highways in the Netherlands

6
Slabs under concentrated loads (1)
• Transverse load redistribution
• Additional dimension in slabs
• Expected higher capacity than
beams
• First experiments: Regan
(1982)

7
Slabs under concentrated loads (2)
• Shear stress over effective
width
• Fixed width, eg. 1 m
• Load spreading method

8
Goals
• Assess shear capacity of slabs
under concentrated loads
• Determine effective width in
shear

9
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

10
Experiments (2)
• 2nd series experimental work:
• Slabs under combined loading
• Line load
• Preloading
• 50% of strength from slab strips
• Concentrated load
• loading until failure
• Conclusions from 1st series valid
when combining loads?
• Total: 26 experiments, 8 slabs

12
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

13
Slabs vs. beams (2)
5000 1000 1500 2000 2500
b (mm)

14
Modified Bond Model (1)
• Based on Bond Model
(Alexander and
Simmonds, 1990)
• For slabs with
concentrated load in
middle

16
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

22
Modified Bond Model (9)
Experiments vs Eurocode shear Experiments vs Modified Bond Model

23
Application to practice (1)
• Evaluating existing solid slab bridges:
• 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

24
Application to practice (2)
Detail of load spreading

25
Application to practice (3)
• Checks at indicated sections
• 9 existing Dutch solid slab bridges + MBE example

26
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

27
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

28
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
• Application to practice: reduction in
loads

29
Contact:
Eva Lantsoght
E.O.L.Lantsoght@tudelft.nl
+31(0)152787449

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The shear capacity of slabs under concentrated loads is particularly of interest for bridge decks under concentrated live loads. Often, one-way shear will be analyzed by considering the slab as a wide beam (without taking advantage of the transverse load redistribution capacity of the slab) and two-way shear by considering the punching area around the load. Since experiments showed that the failure mode of slabs under concentrated loads is a combination of one-way and two-way shear as well as two-way flexure, a method was sought that bridges the gap between traditional one-way and two-way shear approaches. The proposed method is a plasticity-based method. This method is based on the Strip Model for concentric punching shear and takes the effects of the geometry into account for describing the ultimate capacity of a slab under a concentrated load. The model consists of “strips” that work with arching action (one-way shear) and slab “quadrants” that work in two-way shear. As such, the resulting Extended Strip Model is suitable for the design and assessment of elements that are in the transition zone between one-way and two-way shear.

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In August 2014, the Ruytenschildt Bridge, a reinforced concrete solid slab bridge, in Friesland, the Netherlands was tested until failure. One of the goals of the experiment is to analyze the failure mode of the slab bridge under a tandem of 4 wheel loads and to compare the capacity of the full bridge structure to the predicted results, to have an idea of the residual strength of existing bridges. The methods used are experi-mental (testing of the bridge to failure in two of its five spans) and analytical. The analytical work involved predicting the bending moment capacity, the shear capacity and the punching capacity of the bridge. In both spans, the bridge failed in flexure. The total capacity during the experiment was significantly higher than pre-dicted. The results indicate that the traditional rating procedures for shear are very conservative when applied to slab bridges that benefit from transverse load redistribution.

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For the assessment of existing structures and the design of new structures, it is important to have a good understanding of the flow of forces, here applied to reinforced concrete solid slabs. Two analyti-cal methods are used: finite element models with 3D solid elements and a plasticity-based model that is suita-ble for hand calculations, the Modified Bond Model. The slabs that are modeled are half-scale models of rein-forced concrete solid slab bridges. As the Eurocode live load model prescribes more heavily loaded trucks in the first lane, the load model is asymmetric. For the finite element models, limited use is made of the redistri-bution capacity of the slab. For the Modified Bond Model, the influence of torsion and the edge effect need to be taken into account. The results of these studies improve the current state-of-the-art for analysis and design of reinforced concrete slabs.

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Proof load testing can be a suitable method to show that a bridge can carry the required loads from the code without distress. This paper addresses the preparation, execution, and analysis of a proof load test on a four-span reinforced concrete solid slab bridge, viaduct de Beek. The bridge has one lane in each direction, but was restricted to a single lane, since an assessment showed that the capacity is not sufficient to allow both lanes. For this proof load test, the bridge was heavily equipped with sensors, so that early signs of distress can be seen. The difficulty in this test was that, for safety reasons, only the first span could be tested, but that the lowest ratings were found in the second span. A direct approval of the viaduct by proof loading was thus not possible, and an analysis was necessary after the field test. The result of this analysis is that only by allowing 6.7% of plastic redistribution in the second span, sufficient capacity can be demonstrated.

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Lekenpraatje

1. Challenge the future Delft University of Technology Shear in Reinforced Concrete Slabs under Concentrated Loads close to Supports Eva Lantsoght

2. 2 Overview • Background • Slabs under concentrated loads • Overview of experiments • Beams vs. slabs • Modified Bond Model • Application to practice • Conclusions

3. 3 Background (1) Bridges from 60s and 70s The Hague in 1959 Increased live loads common heavy and long truck (600 kN) End of service life + larger loads

4. 4 Background (2)

5. 5 Background (3) • First checks since mid-2000s • 3715 structures to be studied • 600 slab bridges • But: checks according to design rules • => Residual capacity??? • Hidden reserves of the bearing capacity Highways in the Netherlands

6. 6 Slabs under concentrated loads (1) • Transverse load redistribution • Additional dimension in slabs • Expected higher capacity than beams • First experiments: Regan (1982)

7. 7 Slabs under concentrated loads (2) • Shear stress over effective width • Fixed width, eg. 1 m • Load spreading method

8. 8 Goals • Assess shear capacity of slabs under concentrated loads • Determine effective width in shear

9. 9 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

10. 10 Experiments (2) • 2nd series experimental work: • Slabs under combined loading • Line load • Preloading • 50% of strength from slab strips • Concentrated load • loading until failure • Conclusions from 1st series valid when combining loads? • Total: 26 experiments, 8 slabs

11. 11 Experiments (3)

12. 12 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

13. 13 Slabs vs. beams (2) 5000 1000 1500 2000 2500 b (mm)

14. 14 Modified Bond Model (1) • Based on Bond Model (Alexander and Simmonds, 1990) • For slabs with concentrated load in middle

15. 15 Modified Bond Model (2)

16. 16 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

17. 17 Modified Bond Model (4)

18. 18 Modified Bond Model (5)

19. 19 Modified Bond Model (6)

20. 20 Modified Bond Model (7)

21. 21 Modified Bond Model (8)

22. 22 Modified Bond Model (9) Experiments vs Eurocode shear Experiments vs Modified Bond Model

23. 23 Application to practice (1) • Evaluating existing solid slab bridges: • 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

24. 24 Application to practice (2) Detail of load spreading

25. 25 Application to practice (3) • Checks at indicated sections • 9 existing Dutch solid slab bridges + MBE example

26. 26 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

27. 27 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

28. 28 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 • Application to practice: reduction in loads

29. 29 Contact: Eva Lantsoght E.O.L.Lantsoght@tudelft.nl +31(0)152787449

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