UNIVERSITY OF SPLIT

FACULTY OF CIVIL ENGINEERING, ARCHITECTURE AND GEODESY

CHAIR FOR STEEL AND TIMBER STRUCTURES

A NEW IMPLICIT SCHEME FOR

INCLUDING STEEL CREEP STRAIN

INTO STRUCTURAL FIRE ANALYSIS

Dr Neno Torić

LONDON, THE INSTITUTION OF STRUCTURAL

ENGINEERS

DATE: 24 SEPTEMBER 2013.

• Introduction

• Implicit/explicit modelling scheme

• Research concept

• Experimental verification

• Numerical modelling

• Discussion

OVERVIEW

3

INTRODUCTION

• Strain components in steel during fire exposure:

tot th cr( ) ( , ) ( , , )T T T t

Thermal strain Stress related strain Creep strain

• Stationary creep strain values usually derived from stationary heating of

steel coupons

• Stationary stress-strain curves

INTRODUCTION

t

=const=0

Failure

stress

T

t

Failure

temp.

=const

• Transient creep strain values usually derived from transient heating of

steel coupons

• Transient stress-strain curves

INTRODUCTION

6

• Implementation of creep strains into structural analysis:

• Explicit creep model

dx

h2

h2

d

M

M

ultM

tot th cr( ) ( , ) ( , , )T T T t

IMPLICIT / EXPLICIT MODELLING SCHEME

tg EI

res

IMPLICIT / EXPLICIT MODELLING SCHEME

• Implementation of creep strains into structural analysis:

• Explicit creep model

Conversion of creep strains directly into internal forces/deflections

M/Ncreep

8

• Implicit creep model

‘’Effective’’ material stress-strain law

Stationary stress-strain law

‘’Effective’’ stress-strain law

IMPLICIT / EXPLICIT MODELLING SCHEME

• Implementation of creep strains into structural analysis:

9

steady-state test EC3

transient-state test

Steel – steady state test vs. transient state test vs. EUROCODE 3 (T=800°C)

• Material stress-strain law

cr

RESEARCH CONCEPT

10

RESEARCH CONCEPT

• Stress-strain curves for steel: steady state vs. transient state

11

RESEARCH CONCEPT

New implicit creep concept

(a) Temperature field calculation;

(b) creep strain calculation;

(c) strain modified curve

12

RESEARCH CONCEPT

• Software for analysis of structures exposed to fire

Comprised of:

• 3D nonlinear heat transfer model,

• Structural analysis model

1

2 3

4

5

6 7

8

1

2

3

(0,0,0)

2 node

beam/column FE

(6 D.O.F.)

8 node FE

+

13

EXPERIMENTAL VERIFICATION

Furnace

Loading frame

Specimen

Horizontal force

Vertical force

• Fire tests on simply supported steel members

Furnace

V

625 1250 625

2500

V

V

Furnace

V

625 1250 625

2500

V

V

H

H

EXPERIMENTAL VERIFICATION

• Test setup

Testing method Transient

Load type Flexure Flexure + axial

force

Element (Steel S355)

Test 1 Test 2 Test 3

Test time (min) 115 190 100

Force (kN)

Axial (kN)

- 400 400

Vertical (kN)

200 200 250

EXPERIMENTAL VERIFICATION

• Stationary stress-strain curves

NUMERICAL MODELLING

• Creep model (Dorn/Harmathy, 1967.)

• Time hardening rule

Z

cr ,0cr,0 1

cr cosh 22ln

R

0

Ht

RTe dt

Z - Zener-Hollomon parameter [h-1]

- dimensionless creep parameter cr,0

- Temperature compensated time

H - creep activation energy [J/mol]

TR - temperature [K],

Creep strains start to develop at approximatelly TR 400-450°C for carbon steel

NUMERICAL MODELLING

• Results (Fire test 1)

Comparison of results between model and experiment –

temperatures of the lower flange

NUMERICAL MODELLING

• Results (Fire test 1)

NUMERICAL MODELLING

• Results (Fire test 1)

20 Test 1:Comparison of results between model and experiment – midspan deflection

• Results (Fire test 1)

NUMERICAL MODELLING

Furnace

V

625 1250 625

2500

V

V

Furnace

V

625 1250 625

2500

V

V

H

H

21 Test 2:Comparison of results between model and experiment – midspan deflection

NUMERICAL MODELLING

• Results (Fire test 2) Furnace

V

625 1250 625

2500

V

V

Furnace

V

625 1250 625

2500

V

V

H

H

Test 3:Comparison of results between model and experiment – midspan deflection

• Results (Fire test 3) Furnace

V

625 1250 625

2500

V

V

Furnace

V

625 1250 625

2500

V

V

H

H

NUMERICAL MODELLING

23

• Application of strain modifed curves/new implicit scheme in structural fire

analysis calculation was presented

• Verification of the proposed implicit scheme was tested on results of three

different experiments conducted on testing of simply supported steel beams

exposed to high temperature

• Numerical results of the three presented examples show good agreement

with the experiment by using strain modified curves in terms of predicting

the structural response

• Implicit stress-strain curves proposed by EC3 show unconservative results

when steel elements are heated for a longer time period above 400°C

• Further research is planned on testing the implicit scheme on restrained

steel members

DISCUSSION

• Application of the proposed implicit scheme is valid not only for modeling of

the response of axially unrestrained steel beams but also for steel beams

with low level of axial restraint

• Verification of the implicit scheme in the cooling phase

FURTHER CONSIDERATION

0

10

20

30

40

50

60

70

0 0.004 0.008 0.012 0.016 0.02 0.024

Strain

Str

es

s [

MP

a]

EN1992-1-2 - 20°C

EN1992-1-2] - 230°C

EN1992-1-2 - 400°C

EN1992-1-2 - 500°C

EN1992-1-2 - 600°C

EN1992-1-2 - 700°C

EN1992-1-2 - 800°C

STEADY S. TEST - 20°C

STEADY S. TEST - 230°C

STEADY S. TEST - 400°C

STEADY S. TEST - 500°C

STEADY S. TEST - 600°C

STEADY S. TEST - 700°C

STEADY S. TEST - 800°C

Concrete – steady state test vs. EC2