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Material Modelling of the Post-Peak Response of Reinforced Concrete at ElevatedTemperatures

Carstensen, Josephine Voigt; Pankaj, P.; Jomaas, Grunde

Publication date:2011

Document VersionPublisher's PDF, also known as Version of record

Link back to DTU Orbit

Citation (APA):Carstensen, J. V., Pankaj, P., & Jomaas, G. (2011). Material Modelling of the Post-Peak Response ofReinforced Concrete at Elevated Temperatures. Poster session presented at 10th International Symposium onFire Safety Science, Maryland, United States. http://www.iafss.org/html/Maryland/marylandhome.htm

MATERIAL MODELLING OF THE POST‐PEAK RESPONSE OF REINFORCED CONCRETE AT ELEVATED TEMPERATURES

J.V. Carstensen a, P. Pankaj b and G. Jomaas a

a Department of Civil Engineerig at the Technical University of Denmark (DTU)b BRE Centre for Fire Safety Engineering at the University of Edinburgh

BRE Centre for Fire Safety EngineeringUniversity of Edinburgh

TENSION STIFFENINGThe uncracked part of the concrete still contri-butes to the strength after cracking is initiated.

Concrete

SteelTension stiffening

cu

ts !ts fct,m=

"

#

"

#

"c "0 y

ts

"u"

Pservice

Concr

ete

does

not

crac

k

Concr

ete

is a

ssum

ed

to b

e fu

lly p

last

ic

P cr

Concr

ete

has

no

tensi

le s

tren

gth

aft

er

crac

kin

gTen

sile

sti

ffen

ing, δΔ

Pure

rei

nfo

rcem

ent

δ

P

This can be modelled based on the fracture energy by an interaction stress contribution as suggested by Cervenka et al. and Feenstra and de Borst.

Concrete

SteelTension stiffening

cu

ts !ts fct,m=

"

#

"

#

"c "0 y

ts

"u"

FRACTURE ENERGYThe fracture energy is a material invariant that coresponds to the area beneath the stress-plastic displacement (or cracking) diagram.

Element is too large

Compressive behaviour Tensile behaviour; combined concrete and interaction stress contribution

The reinforcement ratio is too small

Element is too smallElement is too large

Problems in the Ambient ConditionA validity range for the element size and a minimum reinforcment ratio is formulated.

MOTIVATIONFor FE-analysis of reinforced concrete at elevated temperatures the current material models yield convergence problems for different mesh sizes. For ambient conditions, it has been established that using a fracture energy based material model cir-cumvents this issue. It is therefore relevant to extend these models to the elevated temperature conditions.

200 400 600 800 10000

0.5

1

1.5

T [oC]

GcT/G

c

200 400 600 800 10000

500

1000

1500

T [oC]

hm

axT [

mm

]

Lie and Lin

Anderberg and Thelandersson

Li and Purkiss

Eurocode 2

Compressive Fracture EnergyTensile Fracture Energy

Based on the model by Terro, GfT follows the decay of tensile strength;

GcT is found for the models by;

200 400 600 800 10000

0.5

1

1.5

T [oC]

GcT/G

c

200 400 600 800 10000

500

1000

1500

T [oC]

hm

axT [

mm

]

Lie and Lin

Anderberg and Thelandersson

Li and Purkiss

Eurocode 2

200 400 600 800 10000

0.5

1

1.5

T [oC]

GcT/G

c

200 400 600 800 10000

500

1000

1500

T [oC]

hm

axT [

mm

]

Lie and Lin

Anderberg and Thelandersson

Li and Purkiss

Eurocode 2GfT = x(T) . Gf

EVOLUTION OF FRACTURE ENERGY WITH TEMPERATUREThe inherent fracture energies are found as function of temperature for the existing elevated tempe-rature behaviour models for concrete.

And the models including the effect of the load induced thermal strains (LITS) by;

EXAMPLEREINFORCED CONCRETE SLAB

= 8 mm!

= 6 mm

= 1 mW

= 4 mL

= 150 mms

= 150 mmD

c = 25 mm

c = 25 mm

L = 4 m

= 10.7 kN/mq

50 mm

p

!p

x

y

The validity range for the element size:

Tmax = 715 oC and the hence

72.5 mm < h < 129.6 mm

The level of reinforcement is found to be suifficient.

Concrete grade C30 and steel Grade 500 andGcT as is computed as inherent in Eurocode 2.

200 400 600 800 10000

500

1000

1500

T [oC]

h

[mm

]

h

maxTCompressive Parameters

hmaxT

Tensile Parameters

hminT

Admissiblevalues of h

CONCLUSION- GfT follows the decay of material strength.

- There is a significant spread in the existing compressive post-peak behaviours.

- The LITS does not appear to influence GcT.

- For the considered example, analysis above 800 oC will not converge.

REFERENCESCervenka et al., Computer Aided Analysis and Design of Concrete

Structures, Pineridge Press, 1-21 (1990)

Feenstra and de Borst, Journal of Engineering Mechanics 121:

587-595 (1995)

Anderberg and Thelandersson, Lund (1976)

Lie and Lin, Fire Safety: Science and Engineering 882: 176-205

(1985)

Li and Purkiss, Fire Safety Journal 40(7): 669-686 (2005)

Eurocode 2 - Part 1-2, CEN (2004)

Terro, ACI Structural Journal 95(2): 183-193 (1998)

0 0.01 0.020

0.2

0.4

0.6

0.8

1

κC

σ C /f

cm

h = 100 mmh = 500 mmh = 2000 mm

0 1 2x 10−3

0

0.2

0.4

0.6

0.8

1

εct

σ ct /f

ct,m

ρ

s,eff = 0.04

ρs,eff

= 0.035

ρs,eff

= 0.025

0 1 2x 10−3

0

0.2

0.4

0.6

0.8

1

εct

σ ct /f

ct,m

h = 50 mmh = 25 mm

0 1 2x 10−3

0

0.2

0.4

0.6

0.8

1

εct

σ ct /f

ct,m

h = 500 mmh = 1000 mm