For the assessment of existing structures and the design of new structures, it is important to have a good understanding of the flow of forces, here applied to reinforced concrete solid slabs. Two analyti-cal methods are used: finite element models with 3D solid elements and a plasticity-based model that is suita-ble for hand calculations, the Modified Bond Model. The slabs that are modeled are half-scale models of rein-forced concrete solid slab bridges. As the Eurocode live load model prescribes more heavily loaded trucks in the first lane, the load model is asymmetric. For the finite element models, limited use is made of the redistri-bution capacity of the slab. For the Modified Bond Model, the influence of torsion and the edge effect need to be taken into account. The results of these studies improve the current state-of-the-art for analysis and design of reinforced concrete slabs.

1. Challenge the future
Delft
University of
Technology
Modeling of symmetrically and
asymmetrically loaded reinforced
concrete slabs
Eva Lantsoght, Ane de Boer, Cor van der Veen

2. 2
Overview
• Introduction, plastic design models
• Experiments
• Finite element model: results
• Extended strip model: results
• Conclusions
Slab shear experiments, TU Delft

3. 3
Introduction
Problem Statement
Bridges from 60s and 70s
The Hague in 1959
Increased live loads
heavy and long truck
(600 kN > perm. max = 50ton)
End of service life + larger loads

4. 4
Introduction
Highway network in the Netherlands
• NL: 60% of bridges built before
1976
• Assessment: shear critical in 600
slab bridges
Highways in the Netherlands

5. 5
Introduction
Modeling of concrete slabs
• Linear elastic solutions
• Classic plate theory
• Equivalent frame method
• Plastic methods
• Strip method (Hillerborg)
• Yield line method
Slab shear experiments, TU Delft

6. 6
Experiments
Size: 5m x 2.5m (variable) x 0.3m = scale 1:2
Continuous support, Line supports
Concentrated load: vary a/d and position along width

7. 7
Experiments reinforcement
5000
200
200
Bottom side
A-A B-B
A-A B-B
Top side
Support1
Support2
Support3
2500
5000
300
250
265
300
50
100
A-A B-B10/240 10/240
20/120 20/120
20/120 10/240
20/12010/240
10/240
10/240
20/12020/120
50
265
300
IPE 700
L=2100 mm
Specimen dimensions
5000x2500x300 mm
3 Dywidag 36
with load cells
2 IPE 700, L=3300mm
Jack (Pmax=2000 kN)
Load cell
2 HEM 300
Support 1 Support 2
Support 3Load plate
200x200 mm
HEB240
Load cell 100 Ton, F205
Hinge (Pmax=3300 kN)
300
Hooked end reinforcement

8. 8
Experimental Results
Bottom
Flexural cracking
Cracking around load towards support
Shear failure
Front face
Flexural crack at 700 kN
Crack width
Failure at 954 kN,
crack width 1.8 mm

9. 9
Numerical model (3 D solids)
Concrete:
20 node solids 120x160x60 mm
5 elements over thickness slab
Reinforcement:
Embedded truss elements
Perfect bond
Dywidag bars:
2 node truss elements
Support:
Interface elements
Material model:
Concrete: crush and crack
Reinforcement: yield
2969
2526
loading plate
slab
interface
20854
2969

10. 10
Numerical results
0
200
400
600
800
1000
0 2 4 6 8 10
Load(kN)
Deflection (mm)
NLFEA
yielding of BOTF10T at step 14 (P=564.06 kN)
crushing of concrete at step 20 (P=618.06 kN)
yielding of TOPF10T at step 37 (P=776.06 kN)
yielding of TOPF10L at step 40 (P=814.06 kN)
peak load at step 45 (P=852.06 kN)
experimental

11. 11
Numerical results
Crack strain at peak load
0
0.5
1
1.5
2
2.5
3
0 0.001 0.002 0.003
s(N/mm2)
e (-)
Tensile stress
strain

12. 12
Numerical results
Crack strain at peak load
Minimum principal strain at step 20
Start crushing of concrete
-35
-30
-25
-20
-15
-10
-5
0
-0.02 -0.015 -0.01 -0.005 0
s(N/mm2)
e (-)
compressive stress
strain
-800
-600
-400
-200
0
200
400
600
800
-0.1 -0.05 0 0.05 0.1
s(N/mm2)
e (-)Yielding bottom reinforcement
Starts at 563 kN

13. 13
Numerical results
0
200
400
600
800
1000
0 2 4 6 8 10
Load(kN)
Deflection (mm)
Mean measured values of material strength
Characteristic values of material strength
Mean GRF values of material strength
Design values of material strength
experimental

14. 14
Numerical results unsymmetric load
20
200
200 x 8 mm plywood
2 sheets 100 x 5 mm
1 sheet 200 X 5 mm
HEM 300
1 sheet 200 x 5 felt P50
Simplesupport
250100
1250
2500
5000
812438
300
300
600 2700 900
3200 100 750 200 400
Continuoussupport
20
200
200 x 8 mm plywood
2 sheets 100 x 5 mm
1 sheet 200 X 5 mm
HEM 300
3 sheets 100 x 5 felt N100

15. 15
Experimental and numerical results
Lateral front face
At 400 kN crack width 0.15 mm
At 800 kN first shear crack
At 990 kN second shear crack
Failure at 1154 kN
0
200
400
600
800
1000
1200
0 5 10 15 20
Load(kN)
Deflection (mm)
NLFEA
crushing of concrete at step 17 (P=601.05 kN)
peak load at steo 19 (P=622.05 kN)
Experimental
Results clearly affected by absence hooked end
reinforcement
Numerical failure load at 907 kN with hooked end

16. 16
Strip Model (1)
• Alexander and Simmonds,
1990
• For slabs with
concentrated load in
middle

17. 17
Strip Model (2)

18. 18
Extended Strip Model (1)
• Adapted for slabs with concentrated
load close to support
• Geometry is governing as in
experiments
• Maximum load: based on sum capacity
of 4 strips
• Effect of torsion: presentation of
Daniel Valdivieso

19. 19
Unequal loading of strips
• Static equilibrium
• v2,x reaches max before v1,x
'
1, 0.166x c
a
v f d
L a



20. 20
Loads close to free edge
Edge effect:
when length of strip is too small to develop loaded length lw

21. 21
Extended Strip Model: results
• S1T1:
• PESM = 663 kN
• Ptest/PESM = 1,44
• S4T1:
• PESM = 775 kN
• Ptest/PESM = 1,49
• Results similar for load in
middle and at edge

22. 22
Summary & Conclusions
• Live loads: asymmetric loading
• Finite element models (3D solids): 2
direction asymmetric gives stress
concentrations
• Strip Model for concentric punching
shear: plastic design method
• Extended Strip Model performs well for
asymmetric loading situations

23. 23
Contact:
Eva Lantsoght
E.O.L.Lantsoght@tudelft.nl // elantsoght@usfq.edu.ec
+31(0)152787449