Bridging the gap between one way and two-way shear in slabs
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The document presents a comprehensive overview of plastic design methods for analyzing one-way and two-way shear in concrete slabs, detailing various models and their applications. It specifically discusses the extended strip model, its adaptations for different loading conditions, and includes a case study of the Ruytenschildt Bridge, which underwent testing and analysis for capacity predictions. The conclusions highlight the effectiveness of the extended strip model in assessing slab capacity and the outcomes of the tests performed on the existing bridge structure.
Bridging the gap between one way and two-way shear in slabs
- 1. The Concrete Convention andExposition Bridging the gap between one-way and two- way shear in slabs Eva Lantsoght, Cor van der Veen, Ane de Boer, Scott Alexander
- 2. The Concrete Convention andExposition Overview • Introduction: plastic design methods • Strip model for concentric punching shear • Extended Strip Model • Application to Ruytenschildt Bridge • Summary & Conclusions Slab shear experiments, TU Delft
- 3. The Concrete Convention andExposition Plastic design methods • Solutions for – One-way shear – Two-way shear – Flexure • Lower bound methods – Strut-and-tie models – Hillerborg´s strip method • Upper bound methods – Yield line methods Strut-and-tie model of dapped-end beam Mattock, A. H. (2012). "Strut-and-tie Models for Dapped-End beams," Concrete international, 34(2), 35-40.
- 4. The Concrete Convention andExposition Design gap between one-way and two-way shear • One-way shear – beam shear – Over effective width – Beam tests • Two-way shear – punching shear – Over punching perimeter – Slab-column connection tests • Slab bridges under concentrated live loads? S6T4 cracking
- 5. The Concrete Convention andExposition Strip Model for concentric punching shear (1) • Alexander and Simmonds, 1990 • For slabs with concentrated load in middle
- 6. The Concrete Convention andExposition Strip Model for concentric punching shear(2)
- 7. The Concrete Convention andExposition Extended Strip Model(1) • Adapted for slabs with concentrated load close to support • Effect of geometry, continuity, and torsion • Maximum load: based on sum capacity of 4 strips
- 8. The Concrete Convention andExposition Extended Strip Model (2) • Unequal loading of strips in y-direction • Static equilibrium • v1 reaches max before v2 • Reduction for self-weight ' 2 0.166M c x M a v f d L a
- 9. The Concrete Convention andExposition Extended Strip Model (3) • Size effect added • Increase in capacity of strip between load and support • Effect of continuity on moment capacity hogging and sagging reinforcement
- 10. The Concrete Convention andExposition Extended Strip Model (4) • Edge effect: – when length of strip is too small to develop loaded length lw • Effect of torsion
- 11. The Concrete Convention andExposition Extended Strip Model (5) Comparison between Extended Strip Model and slab shear experiments
- 12. The Concrete Convention andExposition Ruytenschildt Bridge (1) • Existing reinforced concrete slab bridge (1962) • Test to failure in two spans • 4 concentrated load – one tandem • Cyclic loading protocol • Failure only achieved in span 2
- 13. The Concrete Convention andExposition Ruytenschildt Bridge (2) Existing bridge Partial demolition and building new bridge
- 14. The Concrete Convention andExposition Ruytenschildt Bridge (3)
- 15. The Concrete Convention andExposition Test results proofloading Span 2• Maximum load 3991 kN • Large flexural cracks • Flexural failure – yielding of reinforcement • Settlement of bridge pier with 1.5cm – Elastic recovery to 8mm • Prediction ESM: 3157 kN • Tested/Predicted = 1.26 • Safe lower bound
- 16. The Concrete Convention andExposition Summary & Conclusions • Extended Strip Model – Plasticity-based model – For analysis of capacity of slabs – One-way shear in strips – Two-way flexure in quadrants – Effect of torsion considered • Case study: Ruytenschildt Bridge – Existing slab bridge scheduled for replacement – Testing in 2 spans, failure in span 2 – Good, safe prediction of ESM
- 17. The Concrete Convention andExposition Contact: Eva Lantsoght E.O.L.Lantsoght@tudelft.nl // elantsoght@usfq.edu.ec +31(0)152787449