0MC2010: The Critical Shear Crack Theory as a mechanical

model for punching shear design and itsapplication to code provisions

Prof. Dr Aurelio Muttoni

Dr Miguel Fernndez Ruiz

cole Polytechnique Fdrale de Lausanne, Switzerland

1Load test 1909

Claude A. P. Turner (1869 1955)

Load test 1908

Robert Maillart (1872-1940)

Introduction

2Introduction

3Geneva, Switzerland, 1976

Bluche, Switzerland, 1981

Wolverhampton, UK, 1997

Cagliari, Italy, 2004

Introduction

4Introduction

Design based on empirical formulas without taking into account size-effect

No shear reinforcement, no integrity reinforcement

Brittleness

Gretzenbach, Switzerland, 2004

5Introduction

Jonen, Switzerland, 2007

(Photo courtesy HALFEN AG, Switzerland)

Need for a mechanical model for slabs without and with shear reinforcement

0%

20%

40%

60%

80%

100%

120%

140%

160%

180%

200%

0% 100% 200% 300% 400%

Deformation capacityF

orc

e

Without punching shear reinforcement

With punching shear

reinforcement

0%

20%

40%

60%

80%

100%

120%

140%

160%

180%

200%

0% 100% 200% 300% 400%

Deformation capacityF

orc

e

Without punching shear reinforcement

With punching shear

reinforcement

6Introduction

1. Development of a mechanical model: the Critical Shear Crack Theory

2. Extensive validation by testing

7The CSCT: experimental verification in Lausanne

28

102

73 1

0

20

40

60

80

100

120

125 250 320 400 500

Thickness [mm]

Nu

mb

er o

f te

sts

8The CSCT: experimental verification in Lausanne

28

102

73 1

0

20

40

60

80

100

120

125 250 320 400 500

Thickness [mm]

Nu

mb

er o

f te

sts

9The CSCT: experimental verification in Lausanne

28

102

73 1

0

20

40

60

80

100

120

125 250 320 400 500

Thickness [mm]

Nu

mb

er o

f te

sts

10

The CSCT: experimental verification in Lausanne

28

102

73 1

0

20

40

60

80

100

120

125 250 320 400 500

Thickness [mm]

Nu

mb

er o

f te

sts

11

The CSCT: experimental verification in Lausanne

28

102

73 1

0

20

40

60

80

100

120

125 250 320 400 500

Thickness [mm]

Nu

mb

er o

f te

sts

Total #: 141 tests

12

Fundamentals of the CSCT

y

Walraven J.C. 1981, Fundamental Analysis of Aggregate Interlock, Journal of the Structural Division, Vol. 107, No. 11, pp. 2245 2270.

extreme parameters

13

Fundamentals of the CSCT

Muttoni A., 2008, Punching shear strength of reinforced concrete slabs without transverse reinforcement, ACI Structural Journal, V. 105, No 4, pp. 440-450

theoretical model based on aggregate interlock

simplified failure criterion

14

Fundamentals of the CSCT: punching shear design

Average

Characteristic

Muttoni A., 2008, Punching shear strength of reinforced concrete slabs without transverse reinforcement, ACI Structural Journal, V. 105, No 4, pp. 440-450

Load-rotation curve

Failure criterionyR

VR

15

Physical model: application to non-symmetrical cases (moment transfer)

Evaluation of w accounting for transfer moment (msd)

Shear field and shear forces along control perimeter

16

Physical model: application to non-symmetrical cases (moment transfer)

MC 2010 EC 2

17

Physical model: application to non-symmetrical cases (moment transfer)

Vocke, H, 2002, Zum Durchstanzen von Flachdecken im Bereich von Rand- und Ecksttzen, PhD. thesis, University of Stuttgart, 228 p.

18

Physical model: application to non-symmetrical cases (moment transfer)

Vocke, H, 2002, Zum Durchstanzen von Flachdecken im Bereich von Rand- und Ecksttzen, PhD. thesis, University of Stuttgart, 228 p.

19

Physical model: application to bridge deck slabs

Avg: 1.07; CoV: 13%

Vaz Rodrigues, R., Fernndez Ruiz, M., Muttoni, A., 2008, Punching shear strength of R/C bridge cantilever slabs, Engineering Structures, Elsevier, Vol. 30, No. 11, pp. 3024-3033

20

Physical model: application to shear-reinforced slabs

Fernndez Ruiz, M., Muttoni, A., 2009, Applications of the critical shear crack theory to punching of R/C slabs with transverse reinforcement, ACI Structural Journal, Vol. 106, No. 4, 2009, pp. 485-494

21

Physical model: application to shear-reinforced slabs (2nd failure mode)

22

Physical model: application to shear-reinforced slabs (2nd failure mode)

23

Physical model: application to shear-reinforced slabs

Fernndez Ruiz, M., Muttoni, A., Kunz, J., 2010, Strengthening of flat slabs against punching shear using post-installed shear reinforcement, ACI Structural Journal, Vol. 107, No. 4, pp. 434-442

24

Physical model: application to shear-reinforced slabs (3rd failure mode)

25

Physical model: application to shear-reinforced slabs

Fernndez Ruiz, M., Muttoni, A., 2009, Applications of the critical shear crack theory to punching of R/C slabs with transverse reinforcement, ACI Structural Journal, Vol. 106, No. 4, 2009, pp. 485-494

26

Physical model: retrofitting

27

Physical model: retrofitting

28

Physical model: retrofitting

29

Physical model: fibre-reinforced concrete

30

Physical model: fibre-reinforced concrete

Voo, J.Y.L. and Foster, S.J., 2004, Tensile Fracture of Fibre Reinforced Concrete: Variable Engagement Model, Sixth Rilem Symposium on Fibre Reinforced Concrete (FRC), Varenna, Italy, 20-22 September, pp. 875-884

31

Code provisions

MC-2010: 8 pages (with commentary)

32

Code provisions

MC-2010: 8 pages (with commentary)

EC-2: 10 pages

33

NMC-Calculation of Load-rotation curve: Levels-of-Approximation approach

Preliminary design

Typical design

Assessment of existing structures, design of special cases

Schertenleib P., Muttoni A., Schwartz J., 2003, Pices comprimes, Documentation SIA, D 0182 Introduction la norme SIA 262, Zrich, Switzerland, pp. 67-77

34

NMC: Levels-of-Approximation approach

Level I of approximation

http://ibeton.epfl.ch/MC2010Punching

35

NMC: Levels-of-Approximation approach

Level II of approximation

36

37

Conclusions

The CSCT is grounded on a consistent mechanical model and has been checked against extensive experimental data

The accuracy of the mechanical parameters can be progressively refined in various levels of approximation

The theory can be easily adapted to unusual cases, providing the designer with a clear understanding of the structural behaviour

The CSCT can be consistently used to investigate and to design shear-reinforced and fibre-reinforced slabs

The theory can be implemented efficiently into design codes

38

Coefficient ke

39

Influence of transfer moments

s

ididd

sdb

eVMVm

28

,

40

Fibre-reinforced concrete

41

CSCT vs. other codes (1/2)

42

CSCT vs. other codes (2/2)

43

Crushing strength (1/2)

44

Crushing strength (2/2)

45

Influence of column size

V

y

46

Slabs with punching shear reinforcement (crushing of concrete struts)

MC-90, EC-2