Material properties for serviceability analysis

Sarah Kaethner

1

Serviceability

• Compression stiffness of concrete• Tension stiffness of concrete• Creep & long term loads

Creep E=Eo/(1+)

2

Compression Stress/Strain relationships

Linear elastic compression

05

10152025303540

0 500 1000 1500

strain x1e6

stre

ss N

/mm

2

Linear elasticcompression

•Linear- elastic

Useful for hand calcs…

Also …

•Peaked curve (‘Fig 3.2’ EC2)

•Parabola rectangle

•Bi-linear

•Rectangular…

•User defined (‘Explicit’)

fcm

0,4 fcm

c1

c

cu1

c

tan = Ecm

“Schematic”

3

Peaked curve eg EC2 and BS8110 Pt2

1>1.4εc1.E/fcuεc1

4

Peaked curve: AdSec

0

5

10

15

20

25

30

0 0.001 0.002 0.003 0.004

Linear(Max 12Segments)

Actual

Parabola (Max6 Segments)

5

Crept peaked curve

0

5

10

15

20

25

0 0.001 0.002 0.003 0.004

Linear(Max 12Segments)

Actual

Parabola (Max6 Segments)

E=Eo /(1+)

c1=c1 (1+)

6

EC2 Confined Concrete

c2,c

cu2,c

c

c

fck,c

fcd,c

0

A 2 3 ( = 2)

1 = fck,c

fck

cu

Curve A is modified to produce the confined stress strain relationship.

The confined maximum stress fck,c and the strains c2,c cu2,c are a function of the confining stress 2

Explicit curves can also be input.

7

Plane sections remain plane – but the stiffness of the tension zone reduces

FLEXURE

Strain Diagram

Neutral Axis

•Low strain - tension=compression•Cracking starts - stiffness reduces•All cracks formed - cracks open up•Fully cracked - no tension stiffness

CRACKING

Tension stiffness

8

Tension Stiffness in Codes

• BS8110 – envelope of tension stiffening gives ‘effective tensile Young’s modulus’

• BS5400 allows above BUT assumes analysis with no tension

• ACI, AS & EC2 - interpolating between fully elastic and fully cracked condition

9

Tension Stiffness in AdSecEC2 Example

For British codes AdSec also offers: 10

BS8110 Part 2 Fig. 3.1

Non-linear elastic

1 MPa (0.55 MPa long term)

Linear elastic

1 MPaCrackingmoment

0

0.2

0.4

0.6

0.8

1

1.2

0 100 200 300

strain x1e6

stre

ss N

/mm

2

Uncracked CURVE

CrackedENVELOPE

Initial slope =E/(1+)

0.55MPa

Section Stress

‘Stress-Strain Envelope’ 0.55MPa

PD6687 for UK EC2 is similar11

Section Stress Diagrams

Neutral Axis

fct

Strain

Cracking

Tension Stiffening of Concrete

‘ICE Note 372’

No TensionNon-linear elastic

1 MPa (0.55 MPa long term)

Linear elastic

1 MPaCrackingmoment

Ref: Concrete Society Technical Report 59

Stress-Strain Envelope

Stre

ss

Section Stress

12

Stress-strain curves & envelopes

Peaked compression curve +

ICE Note 372 tension envelope

Provides a fairly realistic model of the behaviour

Other curves are available for ‘letter of the code’ calcs & when this approach doesn’t work.

13

An alternative to stress-strain envelopesA whole-section approach

Interpolated methods EC2, AS & ACI

14

Calculated assumingconcrete has no tensile strength

Deflection

LoadCalculated assumingno cracking

Actual behaviour

Interpolated methods EC2, AS & ACI

15

S

(1 - )SS S

Idealised steel stress

EC2 interpolated model

Steel stresss2

s1

16

Zeta, , defines partially cracked behaviour.

When =1.0 Fully cracked behaviourWhen =0.0 Un-cracked behaviour

NOTE: For ACI and AS is called the ‘interpolation factor’

EC2 interpolated model

17

= 1 - ( first crack result / un-cracked analysis result)2

= 1 for short term, 0.5 for long term loading

Partially cracked behaviour = (cracked behaviour) + (1 - )(uncracked behaviour)

Deflection

Load

no cracking

ActualcrackedMcr

MEd

EC2 interpolated model

18

Deflection

Load

no cracking

ActualcrackedMcr

MEd

EC2 interpolated model

> min if the section cracked in previous load-states

Partially cracked behaviour = (cracked behaviour) + (1 - )(uncracked behaviour)

= 1 - ( first crack result / un-cracked analysis result)2

19

Comparison of tension stiffness

0.00E+00

5.00E-04

1.00E-03

1.50E-03

2.00E-03

2.50E-03

0 10 20 30 40 50 60 70 80 90

Stra

in a

t Ste

el

Moment (kNm)

BS8110

PD6687

TN372

EC2 EXP 7.18

EC2 EXP 7.9

no tension

Uncracked

Cracked

20