The Concrete Convention

and Exposition

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

Eva Lantsoght, Cor van der Veen, Ane de Boer, Scott Alexander

The Concrete Convention

and Exposition

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

The Concrete Convention

and Exposition

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.

The Concrete Convention

and Exposition

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

The Concrete Convention

and Exposition

Strip Model for concentric punching shear (1)

• Alexander and Simmonds, 1990

• For slabs with concentrated load in middle

The Concrete Convention

and Exposition

Strip Model for concentric punching shear(2)

The Concrete Convention

and Exposition

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

The Concrete Convention

and Exposition

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 xM

av f dL a

The Concrete Convention

and Exposition

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

The Concrete Convention

and Exposition

Extended Strip Model (4)

• Edge effect: – when length of strip is too small to

develop loaded length lw

• Effect of torsion

The Concrete Convention

and Exposition

Extended Strip Model (5)

Comparison between Extended Strip Model and slab shear experiments

The Concrete Convention

and Exposition

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

The Concrete Convention

and Exposition

Ruytenschildt Bridge (2)

Existing bridge Partial demolition and building new bridge

The Concrete Convention

and Exposition

Ruytenschildt Bridge (3)

The Concrete Convention

and Exposition

Test results proofloadingSpan 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

The Concrete Convention

and Exposition

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

The Concrete Convention

and Exposition

Contact:Eva LantsoghtE.O.L.Lantsoght@tudelft.nl // elantsoght@usfq.edu.ec+31(0)152787449