March12March12--15 2014, Lulea15 2014, Lulea

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

using different constitutive lawsusing different constitutive laws

Di.St. – Department of Structures for

Engineering and Architecture

using different constitutive lawsusing different constitutive laws

Department of Civil and Structural

Engineering

D. Sannino

WG3 - I. Burgess

WG1 - E. Nigro

M. Alexandreu

Engineering and Architecture

University of Naples “Federico II”

ITALY

Engineering

University of Sheffield

ENGLAND

SummarySummary� Application of advanced calculation models in fire analyses requires

special attention by the designer to the modeling details and the type of finite element adopted for the

structural model. The assumptions made in modeling of the thermo-made in modeling of the thermo-mechanical properties influence the analytical results.

� The use of a simplified constitutive law does not significantly affect the results in terms of time of collapse

when the structures or substructures analyzed are characterized by collapse due to the attainment of collapse due to the attainment of limiting tensile stress in the material.

� For analyses in which buckling phenomena cause the dominant

collapse mode, this simplified constitutive law can significantly affect the results, both in terms of time to collapse and displacement

behavior.

ComparisonComparison betweenbetween thermothermo--mechanicalmechanical propertiespropertiesSteel thermal properties in accordance with EN1993-1-2

6

8

10

12

14

16

18

20

(∆l/l)=14⋅10-6( θa-20)

(∆∆∆∆l/l)x103

400

600

800

1000

1200[J/kgK]

ca=650 J/kgK

ca (J/kgK)

20

30

40

50

60

λa=27,3W/mK

λλλλa (W/mK)

T<=400°C1.0

1.2

0

2

4

6

0 200 400 600 800 1000 1200

Steel Temperature (°C)

0

200

0 200 400 600 800 1000 1200

Steel Temperature (°C)

0

10

0 200 400 600 800 1000 1200

Steel Temperature (°C)

STRAND7

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

Steel constitutive law in accordance with EC3-1-2

SAFIR-VULCAN

T=500°C

T=600°C

T=700°C

T=800°CT=900°C

0.0

0.2

0.4

0.6

0.8

0.00 0.05 0.10 0.15 0.20

ε

ComparisonComparison betweenbetween software software varyingvarying Load Load RatioRatio

400

450

500

550

600

650

700

750

800

Cri

tica

l Te

mp

era

ture

θcr

Slenderness 20

Vulcan

Strand7

Safir

Theory 400

450

500

550

600

650

700

750

800

Cri

tica

l Te

mp

era

ture

θcr

Slenderness 40

Vulcan

Strand7

Safir

Theory 400

450

500

550

600

650

700

750

800

Cri

tica

l Te

mp

era

ture

θcr

Slenderness 60

Vulcan

Strand7

Safir

Theory

300

350

0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8

Load Ratio

Theory

300

350

0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8

Load Ratio

Theory

300

350

0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8

Load Ratio

Theory

300

350

400

450

500

550

600

650

700

750

800

Cri

tica

l Te

mp

era

ture

θcr

Slenderness 80

Vulcan

Strand7

Safir

Theory

300

350

400

450

500

550

600

650

700

750

800

Cri

tica

l T

em

pe

ratu

re θ

cr

Slenderness 100

Vulcan

Strand7

Safir

Theory

300

350

400

450

500

550

600

650

700

750

800

Cri

tica

l T

em

pe

ratu

re θ

cr

Slenderness 120

Vulcan

Strand7

Safir

Theory

300

0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8

Load Ratio

300

0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8

Load Ratio

300

0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8

Load Ratio

� SAFIR and VULCAN models are almost perfectly in agreement. � The STRAND7 results differ from the other because of the constitutive law simplification.

� Differences from SAFIR and VULCAN in respect to EN1993-1-2 are due to geometric imperfections, defined by a horizontal force applied in the SAFIR and VULCAN models, so a slightly smaller value of critical temperature can be expected than when using the

perfect theoretical formula, especially for higher slenderness values.

ComparisonComparison varyingvarying SlendernessSlenderness

400

450

500

550

600

650

700

750

800

Cri

tica

l T

em

pe

ratu

re θ

cr

Load ratio 0,2

Vulcan

Strand7

Safir

Theory 400

450

500

550

600

650

700

750

800

Crit

ica

l te

mp

era

tu

re

θc

r

Load ratio 0,3

Vulcan

Strand7

Safir

Theory 400

450

500

550

600

650

700

750

800

Crit

ica

l te

mp

era

tu

re

θc

r

Load ratio 0,4

Vulcan

Strand7

Safir

Theory

300

350

400

0 20 40 60 80 100 120 140

Slenderness

Theory

300

350

400

0 20 40 60 80 100 120 140

Crit

ica

l te

mp

era

tu

re

Slenderness

Theory

300

350

400

0 20 40 60 80 100 120 140

Crit

ica

l te

mp

era

tu

re

Slenderness

Theory

300

350

400

450

500

550

600

650

700

750

800

Crit

ica

l te

mp

era

ture

θcr

Load ratio 0,5

Vulcan

Strand7

Safir

Theory

300

350

400

450

500

550

600

650

700

750

800

Crit

ica

l T

em

pe

ratu

re

θcr

Load ratio 0,6

Vulcan

Strand7

Safir

Theory

350

400

450

500

550

600

650

700

750

800

Crit

ica

l te

mp

era

tu

re

θcr

Load ratio 0,7

Vulcan

Strand7

Safir

Theory

� The STRAND7’s differences increase with the load ratio.� The results obtained by varying the slenderness show that the theoretical curves cross

the analytical curves for values of slenderness in the region of 75. This is comparable to the value of transition slenderness evaluated as:

300

0 20 40 60 80 100 120 140

Slenderness

300

0 20 40 60 80 100 120 140

Slenderness

300

0 20 40 60 80 100 120 140

Slenderness

ComparisonComparison in in termsterms ofof displacementsdisplacements

10

15

20

Vertical displacement

Node 9_Strand7 Node 17_Strand7

The two nodes

considered are at the

top (Node 17) and at

Slenderness : 40

Load Ratio : 0.2

-10

0 0 100 200 300 400 500 600

Horizontal displacement

-5

0

5

0 100 200 300 400 500 600 700

Displa cement [mm]

Temperature [°C]

Node 17_Strand7 Node 9_Safir

Node 17_Safir

Node 9_Vulcan

Node 17_Vulcan

top (Node 17) and at

the middle (Node 9) of

the column

The curves from STRAND7 are

more rigid than the others.

-70

-60

-50

-40

-30

-20

-10

Displa cement [mm]

Temperature [°[°[°[°C]

Strand7

Safir Vulcan

more rigid than the others.

The point at which the former

curves diverge from the others

coincides with the point at

which the proportionality limit

is passed by the steel in the

column elements.

Slenderness : 120

Load Ratio : 0.7

ConclusionsConclusions

� The analyses carried out show that the use of a simplified constitutive law for

steel at high temperature, especially in analyses characterized by buckling

phenomena, can significantly influence the results.

� The analyses were carried out using three different software codes, SAFIR,� The analyses were carried out using three different software codes, SAFIR,

VULCAN and STRAND7. The first two of these use the constitutive law for steel at

high temperature according to EN1993-1-2, while STRAND7 only allows a

simplified constitutive law.

� SAFIR and VULCAN analyses are almost completely in agreement. The

differences between these two software and the analytical results can be

justified by the way in which geometric imperfections were defined.

� Considering the STRAND7 results the influence of the simplified constitutive law

on the results is clear, especially for high load ratios and for slenderness

between 40 and 100. The buckling phenomenon is controlled most sensitively

by the tangent modulus of the force-displacement curve and therefore

depends on the shape of the stress-strain curve. For this reason the results from

STRAND7 differ from those from the other software. The largest differences are

evident for the values of load ratio.

ThanksThanks forfor youryour attentionattention