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Challenge the future
DelftUniversity ofTechnology
Modeling of symmetrically and asymmetrically loaded reinforced
concrete slabsEva Lantsoght, Ane de Boer, Cor van der Veen
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Overview• Introduction, plastic design models• Experiments• Finite element model: results• Extended strip model: results• Conclusions
Slab shear experiments, TU Delft
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IntroductionProblem StatementBridges 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
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IntroductionHighway network in the Netherlands
• NL: 60% of bridges built before 1976
• Assessment: shear critical in 600 slab bridges
Highways in the Netherlands
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IntroductionModeling 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
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Experiments
Size: 5m x 2.5m (variable) x 0.3m = scale 1:2
Continuous support, Line supportsConcentrated load: vary a/d and position along width
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Experiments reinforcement
5000
200
200
Bottom sideA-A B-B
A-A B-BTop side
Support 1
Support 2
Support 3
2500
5000
300
250
265
30050
100
200
200
Bottom sideA-A B-B
A-A B-B10/240 10/240
20/120 20/120
20/120 10/240
20/12010/240
10/240
10/240
20/12020/120
A-A B-B
50
265
300
Top side
Supp
ort 1
Supp
ort 2
Supp
ort 3
2500
IPE 700L=2100 mm
Specimen dimensions 5000x2500x300 mm
3 Dywidag 36with load cells
2 IPE 700, L=3300mm
Jack (Pmax=2000 kN)Load cell
2 HEM 300
Support 1 Support 2
Support 3Load plate200x200 mm
HEB240Load cell 100 Ton, F205
Hinge (Pmax=3300 kN)
300
Hooked end reinforcement
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Experimental Results
BottomFlexural crackingCracking around load towards supportShear failure
Front face Flexural crack at 700 kNCrack width Failure at 954 kN, crack width 1.8 mm
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Numerical model (3 D solids)
Concrete:20 node solids 120x160x60 mm5 elements over thickness slabReinforcement:Embedded truss elementsPerfect bondDywidag bars: 2 node truss elementsSupport:Interface elements
Material model:Concrete: crush and crackReinforcement: yield
2969
2526
loading plate
sl ab
interf ace
20854
2969
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Numerical results
0
200
400
600
800
1000
0 2 4 6 8 10
Loa
d (k
N)
Deflection (mm)
NLFEAyielding 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
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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
/mm
2 )
e (-)
Tensile stress
strain
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Numerical results Crack strain at peak load
Minimum principal strain at step 20Start crushing of concrete
-35
-30
-25
-20
-15
-10
-5
0-0.02 -0.015 -0.01 -0.005 0
s(N
/mm
2 )
e (-)
compressive stress
strain
-800
-600
-400
-200
0
200
400
600
800
-0.1 -0.05 0 0.05 0.1s(N
/mm
2 )
e (-)Yielding bottom reinforcementStarts at 563 kN
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Numerical results
0
200
400
600
800
1000
0 2 4 6 8 10
Loa
d (k
N)
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
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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
Simple su
pport
250100
1250
2500
5000
812
438
300
300
600 2700 900
3200 100 750 200 400
Con
tinuo
us sup
port
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
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Experimental and numerical results
Lateral front faceAt 400 kN crack width 0.15 mmAt 800 kN first shear crackAt 990 kN second shear crackFailure at 1154 kN
0
200
400
600
800
1000
1200
0 5 10 15 20
Loa
d (k
N)
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 reinforcementNumerical failure load at 907 kN with hooked end
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Strip Model (1)
• Alexander and Simmonds, 1990
• For slabs with concentrated load in middle
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Strip Model (2)
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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
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Unequal loading of strips
• Static equilibrium• v2,x reaches max before
v1,x
'1, 0.166x c
av f dL a
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Loads close to free edge
Edge effect: when length of strip is too small to develop loaded length lw
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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
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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