modeling of symmetrically and asymmetrically loaded reinforced concrete slabs
TRANSCRIPT
Challenge the future
DelftUniversity ofTechnology
Modeling of symmetrically and asymmetrically loaded reinforced
concrete slabsEva Lantsoght, Ane de Boer, Cor van der Veen
2
Overview• Introduction, plastic design models• Experiments• Finite element model: results• Extended strip model: results• Conclusions
Slab shear experiments, TU Delft
3
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
4
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
