Modeling of symmetrically and asymmetrically loaded reinforced concrete slabs

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

5

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

6

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

7

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

8

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

9

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

10

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

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

/mm

2 )

e (-)

Tensile stress

strain

12

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

13

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

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

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

15

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

16

Strip Model (1)

• Alexander and Simmonds, 1990

• For slabs with concentrated load in middle

17

Strip Model (2)

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

Unequal loading of strips

• Static equilibrium• v2,x reaches max before

v1,x

'1, 0.166x c

av f dL a

20

Loads close to free edge

Edge effect: when length of strip is too small to develop loaded length lw

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

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

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