Bridging the gap between one way and two-way shear in slabs

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.

1. Bridging the gap between one-way and two-way shear in slabs Eva Lantsoght, Cor van der Veen, Ane de Boer, Scott Alexander

2. 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. 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. 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. Strip Model for concentric punching shear (1) Alexander and Simmonds, 1990 For slabs with concentrated load in middle

6. Strip Model for concentric punching shear(2)

7. 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. Extended Strip Model (2) Unequal loading of strips in y - direction Static equilibrium v 1 reaches max before v 2 Reduction for self-weight

9. 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. Extended Strip Model (4) Edge effect : when length of strip is too small to develop loaded length l w Effect of torsion

11. Extended Strip Model (5) Comparison between Extended Strip Model and slab shear experiments

12. 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. Ruytenschildt Bridge (2) Existing bridge Partial demolition and building new bridge

14. Ruytenschildt Bridge (3)

15. 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. 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. Contact: Eva Lantsoght [email protected] // [email protected] [phone]