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. 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