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April 18April 18--19 2013, Prague19 2013, Prague

WG1 - E. Nigro

WG2 - G. Cefarelli

D. Sannino

A. Ferraro Di.St. – Department of Structures for

Engineering and Architecture

University of Naples Federico II

ITALY

ThermoThermo--mechanical analysis of steel columns mechanical analysis of steel columns

using different finite element types and using different finite element types and

constitutive laws constitutive laws

Benchmark study: Progetto C.A.S.E. per L’AquilaBenchmark study: Progetto C.A.S.E. per L’Aquila

The “C.A.S.E. Project for L’Aquila” was developed in L’Aquila (province of

Abruzzo, Italy) after the seismic event of 06/04/2009, in order to face up the

housing emergency. The project was characterized by the fabrication of several

seismic insulated buildings.

Isolationdevice

Hereafter the performance evaluation of the structure in lack of passive

protection systems is analyzed

steel column

Concrete slab

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AnalysisAnalysis and Benchmark and Benchmark goalsgoals

� Detailed analysis

Because the column is characterized by

graet values of local slenderness, detailed

analyses are developed in order to

evaluate accurately thermal field and

stress distribution in the capital of the

column, as well as eventual local buckling

phenomena in the stem of the column.

ABAQUS

Non linear analysis including large displacements effects

Brick49075 elements15185 nodes

� BenchmarkThe benchmark is developed in order to

evaluate the influence of the finite element

used in the analysis as well as the influence

of simplified constitutive law for steel at high

temperature

STRAND7 / STRAUS7

Model Type of finite element

Abaqus 10 nodes tetrahedral elements

Straus7 brick 4 nodes tetrahedral elements

Straus7 plate 4 nodes quadrilateral elements

Straus7 beam2 nodes monodimensional

elements

Plate6873 elements6641 nodes

Beam31

elements

T<=400°C

T=500°C

T=600°C

T=700°C

T=800°CT=900°C

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0.00 0.05 0.10 0.15 0.20

ε

ComparisonComparison betweenbetween thermothermo--mechanicalmechanical propertiespropertiesSteel thermal properties in accordance with EC3-1-2

0

2

4

6

8

10

12

14

16

18

20

0 200 400 600 800 1000 1200

(∆l/l)=14⋅10-6( θa-20)

(∆∆∆∆l/l)x103

Steel Temperature (°C)

0

200

400

600

800

1000

1200

0 200 400 600 800 1000 1200

[J/kgK]

ca=650 J/kgK

Steel Temperature (°C)

ca (J/kgK)

0

10

20

30

40

50

60

0 200 400 600 800 1000 1200

λa=27,3W/mK

Steel Temperature (°C)

λλλλa (W/mK)

STRAND7

Simplified (elastic-plastic) constitutive law for steel at high temperatures

Steel constitutive law in accordance with EC3-1-2

ABAQUS

Differences: no parabolic branch, no softening

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0

200

400

600

800

1000

1200

1400

1600

1800

2000

0 300 600 900 1200 1500 1800 2100 2400 2700 3000

Axi

al L

oad

[kN

]

Time [s]

Mechanical analysis

Mechanical analysis results are different in term of

behaviour, however they are quite similar in

terms of collapse time

0.0

200.0

400.0

600.0

800.0

1000.0

1200.0

1400.0

1600.0

0 750 1500 2250 3000 3750 4500 5250 6000

Tem

per

atu

re [

°K]

Time [s]

Different constitutive laws for steel at high temperature

positive

Fire Curve ISO834

Applied Axial Load

Thermal Analysis

Thermal analysis results are

obviously identical. This is fundamental

to permit the comparison based

on different constitutive law

ABAQUS ABAQUS –– STRAND7: STRAND7: differentdifferent constitutiveconstitutive lawslaws

0

50

100

150

200

250

300

350

400

450

500

0 300 600 900 1200 1500 1800 2100 2400 2700 3000

Stre

ss

[N/m

m2 ]

Time [s]

Von Mises StressYielding stressProportionality limit

0

50

100

150

200

250

300

350

400

450

500

0 300 600 900 1200 1500 1800 2100 2400 2700 3000

Str

ess

[N/m

m2 ]

Time [s]

Von Mises StressYielding stressProportionality limit

Different constitutive laws for steel at high temperature

positive

Fire curve ISO834

Applied Axial Load

The differences of results are due to different constitutive laws.The two models show different behaviour after the achievement of proportional limit

0.0

200.0

400.0

600.0

800.0

1000.0

1200.0

1400.0

1600.0

0 750 1500 2250 3000 3750 4500 5250 6000

Tem

per

atu

re [

°K]

Time [s]

0

200

400

600

800

1000

1200

1400

1600

1800

2000

0 300 600 900 1200 1500 1800 2100 2400 2700 3000

Axi

al L

oad

[kN

]

Time [s]

ABAQUS ABAQUS –– STRAUS7: different constitutive lawsSTRAUS7: different constitutive laws

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Different constitutive laws for steel at high temperature

positive

Localized Fire (Hasemi)

Applied Axial Load

The differences of results are due to different constitutive laws.The two models show different behaviour after the achievement of proportional limit

ABAQUS ABAQUS –– STRAND7: different constitutive lawsSTRAND7: different constitutive laws

Different plastic strain

InfluenceInfluence of of DifferentDifferent Finite Finite ElementElement : Strand7: Strand7

Brick Plate

Time [s]

The plate model shows greater deformation due to local stress concentration

Simplified constitutive law

for steel at high temperature

T<=400°C

T=500°C

T=600°C

T=700°C

T=800°CT=900°C

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0.00 0.05 0.10 0.15 0.20

ε

Fire curve Hasemi

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InfluenceInfluence of of DifferentDifferent Finite Finite ElementElement : Strand7: Strand7

Beam Brick

The greater displacement shown by the beam model can be justified considering that in this

model there aren’t local plastic strain.

Simplified constitutive law

for steel at high temperature

T<=400°C

T=500°C

T=600°C

T=700°C

T=800°CT=900°C

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0.00 0.05 0.10 0.15 0.20

ε

Time [s]

Fire curve Hasemi

• Influence of a simplified constitutive law for steel in case of fire

Good evaluation of structural collapseDifferent stress distribution in the memberDifferent evaluation of strain field and residual displacements

• Modeling using 1-dimensional (BEAM) elementIgnore local buckling phenomenon (column)Ignore local crisis phenomenonIgnore local stress concentration (capital)

Thermal analysis consistent with 3D modelExcessive stress concentrations

ConclusionsConclusions

• Modeling using 2-dimensional (PLATE) element

Correct thermal analysisEvaluation of stress concentrations and local buckling phenomenon

• Modeling using 3-dimensional (BRICK) element

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ThanksThanks forfor youryour attentionattention