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