Ductility and Robustness of Concrete Structures

Ductility and Robustness of

Concrete Structures

Professor Ian GilbertProfessor Ian Gilbert

Centre for Infrastructure Engineering and SafetyCentre for Infrastructure Engineering and Safety

The University of New South WalesThe University of New South Wales

� Ductility is the ability of a structure or structural member to undergo

large plastic deformations without significant loss of load carrying

capacity.

Introduction

Curve A - Slab S8 (As /bd = 0.0038 Class N bars) - Ductile

25

20

App

lied

Loa

d, (

kN)

DUCTILE BEHAVIOUR

Curve B - Slab S2 (As /bd = 0.0029 Class L mesh) - Brittle

0 40 80 120 160 200

Mid-span Deflection (mm)

15

10

5

0

App

lied

Loa

d, (

kN)

NON-DUCTILE BEHAVIOUR

Why is Ductility Required in Structures ?

1) to give warning of impending collapse by the development of large

deformations prior to collapse;

2) to enable actions in indeterminate structures to redistribute themselves

near ultimate so that intentional and unintentional deviations from the

‘true’ distribution can be accommodated;

3) to ensure that many of the assumptions routinely made in the analysis

and design of concrete structures are reasonable and appropriate;and design of concrete structures are reasonable and appropriate;

4) in seismic regions, to enable major distortions to be

accommodated and energy to be absorbed without collapse during an

earthquake; and

5) to assist in providing ‘robustness’ (the ability to withstand

unforeseen local accidents without collapse).

Points 2), 3) and 4) have been extensively researched, while the

requirements for 1) and 5) are more difficult to quantify.

Ductility levels in Reinforced Concrete

� Ductility may be considered at three levels:

(1) Material ductility which depends on the properties and strength

of concrete and steel (i.e. the stress-strain laws)

- Concrete is generally regarded as non-ductile in both

tension and compression

100

120

- Steel reinforcement is generally regarded as ductile

(but this is not necessarily the case for wire mesh)

0 0.001 0.002 0.003 0.004 0.005 0.006Strain

0

20

40

60

80

100

Str

ess

(MP

a)

800

600

400

StressStress(MPa)(MPa)

Typical StressTypical Stress--Strain Curves for ReinforcementStrain Curves for Reinforcement

εεεεsu

Class L welded wire fabric – non-ductile

fsu

fsy

Hot rolled bar - ductile

0.00 0.05 0.10 0.15 0.20

400

200

0

εεsusu = 0.015 = 0.015 εεsusu = 0.05= 0.05(Minimum ultimate elongations in AS3600-2009

for Class L and Class N, respectively)

StrainStrain



(1) Material ductility which depends on the properties and strength


(2) Local ductility (or hinge ductility) which depends on the cross-

sectional properties, reinforcement quantities and position, and

the bond-slip relationship at the steel-concrete interface.

This refers to the ductility of the critical cross-section at the locationThis refers to the ductility of the critical cross-section at the location

of maximum moment and this depends on the magnitude of the

ultimate curvature and the length of the plastic hinge that can

develop as the peak moment is approached.

Local ductility is essential for the rotation at the peak moment

region necessary for moment redistribution, for finding

alternative load paths and for the development of the full

plastic capacity.

Moment

Increasing Ast

Moment vs curvature for slabs with ductile reinforcement

Ast

d

(Mu1, κu1)

(Mu2, κu2)

A more heavily reinforced section, Ast2 > Ast1

Curvature, κ

Hinge length, ℓh ≈ dMulti-crackhinges are typical

Rotation of hinge = ℓh x κu

A ductile under-reinforced section – Ast1

Ast

dMoment

Increasing Ast

Moment vs curvature for slabs with non-ductile reinforcement

Hinge length, ℓh ≈ 2db to 5db(Mu1, κu1)

(Mu2, κu2)

db

Ast2

Curvature, κ

Hinge length, ℓh ≈ 2db to 5dbSingle-crack hinges are typical in slabs containing WWF

Rotation of hinge = ℓh x κ

u1 κu1

Ast1

If the hinge ductility is sufficiently high (i.e. if the rotation at the plastic hinges is sufficient), a mechanism can develop and the fullplastic capacity of the system can be realized.

Ast1

A

Ast2

P

Ast3

Bending Moment Diagram

Mu.1

Mu.3

Mu.2

Rotation is required at left support for load to increase from P1 to P2

Rotation is required at both left and right supports for load to increase from P2 to P3

P = P1P = P2P = P3(collapse load)

As P increases, the first hingeforms at the left support when P = P1

Load

Load vs deflection for under-reinforced continuous slab with ductile reinforcement

PSecond hinge formation

P2

Formation of mechanism

P3

Moment redistribution

DeflectionFirst cracking

Further cracking at service loads

First hinge formation (at overload)P1

Second hinge formation

This deflection is often relatively small



1) Material ductility which depends on the properties and strength


2) Local ductility (or hinge ductility) which depends on the cross-

sectional properties, reinforcement quantities and position, and

the bond-slip relationship at the steel-concrete interface.

3) Structural or system ductility .3) Structural or system ductility .

Structural ductility is related to the plastic deformation of the

member or structure after the plastic mechanism has formed

(i.e. after all the plastic hinges have developed).

Structural ductility affects the robustness of the structural system

and its ability to absorb and dissipate inelastic energy without

substantial loss of load resistance and without jeopardising the

integrity or stability of the overall structural system.

Load

Load vs deflection for under-reinforced continuous slab with ductile reinforcement

P

P2

P3

The hinge rotation required to facilitate moment redistribution and produce a mechanism is usually small compared to the hinge rotation required to produce the plastic deformation associated with adequate structural ductility

Pmax

Deflection

P1

∆1 ∆2 ∆u

Structural ductility

Ductile slab after ultimate load test

Load Pmax, ∆u

Ductility and warning of overstress

� In order to provide warning of failure, it is necessary for a member to

have a strain-hardening response, not merely for it to be ductile.

� The visible damage or deformation that is going to provide warning of

failure must occur at loads slightly below the collapse load.

Deflection

Pmax, ∆uP3

i.e. Pmax must be greater than P3 and ∆u must be much greater than ∆2

∆2

Ductility and warning of overstress

� Codes of practice generally provide little design guidance (although it is

often argued that the limit on the neutral axis depth for beams and slabs

at the ultimate limit state provides an indirect means of providing

warning of failure).

� If warning of failure is required, it could be logically introduced into

codes by requiring that beams and slabs be able to sustain their design codes by requiring that beams and slabs be able to sustain their design

loads while deflecting to some specified amount – say span/50 – a highly

visible deflection.

A span/50 mid-span deflection corresponds to a support rotation of 0.04

rad or a rotation capacity of the mid-span section of 0.08 rad.

Ductility and Robustness

� Robustness is the requirement that structures should be able to

withstand damage without total collapse.

“A structure should be detailed so that it can withstand an event

without being damaged to an extent disproportionate to that event.”

� The requirement that surrounding members should not rupture and

collapse requires that the members and materials have adequate

ductility.

� In particular, reinforcement, which is assumed in the design to constitute

the ties in rc structures, must obviously be highly ductile.

Slabs containing low ductility reinforcement

� This rest of this presentation summarises a research project conducted

at the University of New South Wales on the strength and ductility of

reinforced concrete slabs containing low ductility reinforcement in the

form of Class L welded wire fabric (WWF).

� Over 50 slabs containing Class L reinforcement were tested.

� The project was funded by the Australian Research Council from 2003 to

2010.

Simply-supported one-way slabs

Continuous one-way slabs

Corner-supported two-way slabs

Edge-supported two-way slabs

Typical Behaviour of a Simply-Supported One-Way Slab

containing Class L Reinforcement

- this slab has the minimum reinforcement permitted by

AS3600-2009 (and L/D=22)

A typical Continuous One-Way Slab containing

Class L Reinforcement

Experimental Program – Two-way Slabs

Full range load tests on eleven two-way, corner-supported

reinforced concrete slab panels containing either Class L WWF

or Class N deformed bars were tested.

� The slabs were subjected to transverse loads applied by a deformation

controlled actuator in a stiff testing frame.

� The results of the tests are presented and evaluated, with particular

emphasis on the strength, ductility and failure mode of the slabs.

Experimental Program

Free edges

x

y

A ALy

Pinsupport

Rollersupport

d

D

dx

y

Section A-A

Ly = 2080 mmor 3280 mm

Rollersupport

Rollersupport

x

Free edges

Ly

L

PlanRoller support detail

Lx = 2080 mm

Reinforcement ratio Slab ID

Ly (mm)

Lx (mm)

D (mm)

Steel Class & Type b

Bar dia.

(mm) px

(%) py

(%)

εsu

(%)

S2S-1 2080 2080 103.1 L - SL62 6.0 0.18 0.17 2.47 S2S-2 2080 2080 101.4 L - SL82 7.6 0.30 0.27 2.11 S2S-3 2080 2080 100.1 L - SL102 9.5 0.47 0.41 3.73 S2S-4 2080 2080 100.0 N - N12 12.0 0.51

Experimental Program

S2S-4 2080 2080 100.0 N - N12 12.0 0.51 0.44 7.69 S2S-5 2080 2080 106.1 N - N10 10.0 0.52 0.46 9.65 S2S-6 2080 2080 100.0 N - N12 12.0 0.48 0.44 14.11 S2R-1 3280 2080 103.7 L - SL62 6.0 0.17 0.16 2.46 S2R-2 3280 2080 95.9 L - SL82 7.6 0.30 0.27 2.30 S2R-3 3280 2080 106.7 L - SL102 9.5 0.42 0.38 3.09 S2R-4 3280 2080 100.0 N - N12 12.0 0.51 0.44 7.69 S2R-5 3280 2080 101.6 N - N10 10.0 0.55 0.48 9.65

Load versus deflection

50

60

70

80

90

100

S2R-5

S2R-4

S2R-3

Tot

al L

oad

(kN

)

0 20 40 60 80 100 120 140 160 180 2000

10

20

30

40

50

S2R-2

Mid-panel deflection (mm)

Tot

al L

oad

(kN

)

S2R-1

80

100

120

140

S2S-6

S2S-5

S2S-4

Tot

al L

oad

(kN

)


0 20 40 60 80 100 120 140 160 180 2000

20

40

60

S2S-4

S2S-3S2S-2


Tot

al L

oad

(kN

)

S2S-1

40

50

60

70

80

Tot

al L

oad

(kN

)


S2S-2

S2R-2

0 10 20 30 40 50 60 70 80 90 100 110 120 130 1400

10

20

30


Tot

al L

oad

(kN

)

Slabs containing Class L meshpy = 0.30%

SQUARE SLAB S2S-2 CONTAINING CLASS L MESH

60

70

80

90

100

110

120T

otal

Loa

d (k

N)


S2S-4

S2R-4

punching shearfailure

0 10 20 30 40 50 60 70 80 90 100 110 120 130 1400

10

20

30

40

50

60


Tot

al L

oad

(kN

)

Slabs containing Class N barpy =0.44%


0.78

1.04

1.30

1.56

1.82

2.08

0.00 0.26 0.52 0.78 1.04 1.30 1.56 1.82 2.08

0.78

1.04

1.30

1.56

1.82

2.08

1.1

Cle

ar s

pan

alon

g y-

axis

(m

)

1.3

0.00 0.26 0.52 0.78 1.04 1.30 1.56 1.82 2.08

0.78

1.04

1.30

1.56

1.82

2.08

Cle

ar s

pan

alon

g y-

axis

(m

)

33

0.00 0.26 0.52 0.78 1.04 1.30 1.56 1.82 2.08

0.00

0.26

0.52

0.00

0.26

0.52

Cle

ar s

pan

alon

g y-

axis

(m

)

Clear span along x-axis (m)

0.2

0.8

.06

(a) At a load of 35 kN before cracking.

0.00 0.26 0.52 0.78 1.04 1.30 1.56 1.82 2.08

0.00

0.26

0.52

Cle

ar s

pan

alon

g y-

axis

(m

)

Clear span along x-axis (m)

9

17

25

(b) At a load of 64 kN in the post-peak stage

Deflection contours of slab S2S-2.

Ductility Ratio:

20

30

40S

pan

Load

, P (

kN)

W

Ductility ratio:

∆1 ∆2

0 10 20 30 400

10

Mid-span deflection (mm)

Spa

n Lo

ad, P

(kN

)

W0

W1 µw = (W1+W0)/W0

∆2

If µw < 2.0 – brittle (regarded as undesirable)

If µw > 5.0 – ductile (regarded as desirable)

Ductility

3

4

5

6

Duc

tility

Rat

io, (

W0+

W1)

/W0

Ductility ratio versus uniform elongation

0

1

2

0 2 4 6 8 10 12

Uniform Elongation, ε su (%)

Duc

tility

Rat

io, (

W

1.5%

Summary and Conclusions

1. The two-way corner supported slabs reinforced with Class L welded wire fabric fail in a brittle mode by fracture of the tensile reinforcement and, generally, not by crushing of the compressive concrete.

2. Two-way corner-supported slabs containing Class L welded wire fabric are unable to undergo significant welded wire fabric are unable to undergo significant plastic deformation without a significance reduction in the applied load. This is true for both square and rectangular slabs.

3. All slabs containing Class L welded wire fabric had ductility ratios (W1+W0)/W0 less than 2.0.

Summary and Conclusions

The existing procedures for the design and analysis of reinforced concrete slabs at the ultimate limit state have been developed based on the assumption that the reinforcing steel is elastic-plastic with unlimited strain capacity.

This is not the case when using Class L reinforcing steel.

The brittle nature of the failure of the slabs containing

4.

5.

6. The brittle nature of the failure of the slabs containing Class L reinforcement has resulted in the recent change to the Australian Standard, AS3600-2009, wherein the strength reduction factor for slabs is effectively and appropriately reduced from φ = 0.8 for Class N steel to φ = 0.64 for Class L reinforcement.

Such a reduction in φ is consistent with the code approachfor non-ductile members where the ductility ratio (W1+W0)/W0 is less than 2.0.

6.

7.

Edge-supported slabs

Plan

Edge-

supported

slabs

100

150

200

250

300

Tot

al A

pplie

d Lo

ad (

kN)

Peak load

Extensive yielding

First yield

Tot

al A

ppli

ed L

oad

(kN

)

W0 +W1

0

50

0 50 100 150 200Midspan Deflection (mm)

Mid-panel deflection (LVDT1) (mm)

First cracking Tot

al A

ppli

ed L

oad

(kN

)

Slab containing Class L Slab containing N barsS1R-1 S1R-2

W0

Ductility ratio:

µw = (W1 + W0)/W0 = 4.3

Ductility ratio:

5.7

Two clamped edges

Clamped area

Clam

ped area

=

143

0

3600

2400

Clampededges

A A

B

Rollersupport

Freeedges

Clam

ped area

L

= 1

430

L = 2630

2400

B

y

x 160

1395 1395

Origin

y

Plan

Large deformation without collapse

3

4

5

6

Du

ctili

ty R

atio

, (W

0+W

1)/W

0

Clamped on two sides

Supported on all four sides

0

1

2

0 2 4 6 8 10 12

Uniform Elongation, ε su (%)

Du

ctili

ty R

atio

, (W

Concluding Remarks

The corner supported slabs reinforced with Class L have the same ductility issues as one-way slabs, collapsing much like a one-way slab with the steel in one direction fracturing in a single failure crack across the mid-span region in one direction.

1.

The six edge-supported slabs containing Class L tested at UNSW were surprisingly deformable. It appears that slabs reinforced with Class L perform more satisfactorily, as they become more redundant and there are more possible load paths.

2.

Concluding Remarks

In the edge-supported slabs tested at UNSW, the failure load exceeded the yield-line load, as loads were carried by membrane action and torsion (as well as in bending).

There were many cracks at close centres in the peak moment regions, in contrast to the single crack hingesthat characterize one-way slabs.

3.

4.

that characterize one-way slabs.

The slabs deformed significantly and continued to carry load even after wires in particular areas fractured.

There was no sudden collapse in these very redundantedge-supported slabs and the ductility ratio is less dependent on the ductility of the reinforcement.

5.

6.

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Ductility and Robustness of Concrete Structures

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