1
Academic year 2009-2010
1. Introduction
2
Fire in a building cause deaths and destruction
of goods (Department Store « Innovation »,
1967).
 Division of buildings in compartments


Three types of criteria should be fulfilled :
insulation, integrity and resistance.
1. Introduction
3


90’s : fire research focused on the single elements.
Then, global behaviour of steel structures without
focusing on the behaviour of connections because :
a) Exposure of joints to fire is lower than for
beams and columns.
b) More material is concentrated in the joint zone
Conclusion : A same level of fire protection for joints
and structural elements was considered as sufficient
1. Introduction
4

Cooling phase : key issue for the fire resistance
of steel structures (WTC, Cardington, Coimbra
tests,…)
1. Introduction
5
Development of tensile forces due to axial
restraints and plastic deformations
 Limited ductility of bolts and welds components
when joint resistance is not sufficient
 Bolts and welds strengths under fire decreases
faster than the carbon steel strength

1. Introduction
6
Behaviour of bolts and welds at elevated
temperatures (Riaux, Kirby, Latham)
 Behaviour of bolted joints (Wainman, Universities
of Manchester and Sheffield)
 Investigations about the influence of connections
behaviour on the performance of beams under
fire (University of Manchester)

1. Introduction
7
7th Cardington test
 Investigations on rigid and semi-rigid connections
under natural fire (University of Coimbra)

The objective of the present work is to focus on the
behaviour of simple steel connections (and of
connected beams) under natural fire.
Overview of the thesis
8
1.
2.
3.
4.
5.
6.
Introduction
Distribution of temperature in joints
Prediction of internal forces in steel joints under
natural fire
Experimental tests and models for the behaviour
of connection components under heating/cooling
Experimental tests and numerical investigations
for the mechanical behaviour of steel
connections under natural fire
General conclusions and perspectives
9
Academic year 2009-2010
2. Distribution of temperature
10
Time-temperature curve divided in four stages
 Analytical models, Zone models and Field models
to predict the distribution of temperature of the
compartment

2. Distribution of temperature
11
Lumped Capacitance Method for steel members
(EN 1993-1-2 and EN 1994-1-2) + joints (Annex
D of EN 1993-1-2)
 Temperature profile of joints covered by a
concrete slab (EN 1993-1-2)

2. Distribution of temperature
12
Uniform temperature in the zone considered
 Heat exchanges between the steel section and the
concrete slab are not taken into account
(adiabatic)
 Zone considered for joints not defined accurately

2. Distribution of temperature
13
1200
Temperature (°C)
1000
800
600
Flange
400
Flange + Slab
200
0
0
20
40
60
80
Time (min)
100
120
140
2. Distribution of temperature
14
1200
Temperature (°C)
1000
800
600
Flange
400
Flange + Slab
200
0
0
20
40
60
80
Time (min)
100
120
140
2. Distribution of temperature
15
Adapted to ISO curve
 Ratios independent of time
 Geometry of the joint not considered in detail

2. Distribution of temperature
16
Predict temperature at flanges levels accounting
for the presence of the concrete slab
 Profile of interpolation for temperature between
flanges

Adaptations to existing methods or new methods
 Validations against numerical simulations under
heating and cooling phases

2. Distribution of temperature
17
Diamond 2009.a.5 for SAFIR
FILE: IPE300mixte
NODES: 1042
Diamond 2009.a.4 for SAFIR
ELEMENTS: 894
FI LE: FEP_I PE300_ISO
SOLIDS PLOT
NODES: 7467
ELEMENTS: 4888
STEELEC3
SILCONCEC2
SOL IDS PLOT
STEELEC 3
STEELEC 3
STEELEC 3
SI LCONC EC2
STEELEC 3
STEELEC 3
STEELEC 3
STEELEC 3
STEELEC 3
IPE 180 to IPE 550 sections
STEELEC 3
STEELEC 3
STEELEC 3
STEELEC 3
STEELEC 3
STEELEC 3
STEELEC 3
Z
STEELEC 3
Z
STEELEC 3
STEELEC 3
Y
STEELEC 3
X
X

Y
ISO and parametric fires
X
STEELEC 3
Y
STEELEC 3
Z
STEELEC 3
STEELEC 3
Case n°
Beam
Column
Plate
1
IPE 300
HEA 300
200*380*10
2
IPE 550
HEM 300
410*625*25
2. Distribution of temperature
18

Lumped capacitance Method : (Am/V) of the flange
Diamond 2009.a.5 for SAFIR
FILE: IPE300mixte
NODES: 1042
Diamond 2009.a.5 for SAFIR
ELEMENTS: 894
CONTOUR PLOT
FILE: IPE300mixte
TEMPERATURE PLOT
NODES: 1042
TIME: 1800 sec
833.50
800.00
750.00
700.00
650.00
600.00
550.00
500.00
450.00
400.00
22.30
ELEMENTS: 894
SOLIDS PLOT
TEMPERATURE PLOT
Point of reference
Y
X
Z
TIME: 1800 sec
833.50
800.00
750.00
700.00
650.00
600.00
550.00
500.00
450.00
400.00
22.30
2. Distribution of temperature
19

Lumped Capacitance Method : (Am/V)joint = (Am/V)beam/2
IPE 300 configuration
1000
900
Temperature (°C)
800
700
600
500
Param. Fire Curve - 30 min
Param. Fire Curve - 60 min
SAFIR 3D - 30min
Lumped Capacitance - 30min
SAFIR 3D - 60min
Lumped Capacitance - 60min
400
300
200
100
Point of reference
0
0
20
40
60
80
Time (min)
100
120
140
2. Distribution of temperature
20

Lumped Capacitance Method : (Am/V) of the flange
(3 sides heated)
IPE 300 beam
Point of reference
Y
2. Distribution of temperature
21

Composite Section Method
bslab
hslab
hconc
bconc


t
 min  20  110   ; hslab  [mm]
 t0 


 10 
t0  60    min 
t 
 fb 
hconc
hconc
T°
hslab
20 mm
theating
tcooling
Time
theating
tcooling
Time
2. Distribution of temperature
22

Composite Section Method
Heating
Heating + Cooling
1200
1000
900
800
700
800
Temperature (°C)
Temperature (°C)
1000
600
SAFIR - Gamma = 2.0
Composite Section Method - Gamma = 2.0
400
SAFIR - ISO Curve
Composite Section Method - ISO Curve
200
600
500
400
Comp. Sect. Method 90min
300
SAFIR 90min
Comp. Sect. Method 60min
200
SAFIR - Gamma = 0.4
SAFIR 60min
Comp. Sect. Method 30min
100
Composite Section Method - Gamma = 0.4
SAFIR 30min
0
0
0
20
40
60
80
Time (min)
100
120
140
0
30
60
90
Time (min)
120
150
180
2. Distribution of temperature
23
Heat Exchange Method

Qtransferred  Qgas  Qtop bottom  Qconcrete  ca  a V  a ,t  Qheating
40
Qslab  bb  t
Flux flange-slab (kW/m²)
35
30
Lumped
Capacitance
Method
25
20
15
10
5
0
0
200
G = 0.4
G = 0.7
G = 1.0
G = 1.5
G = 2.0
Série1
Série2
Série4
Série5400
Série6
Qtop bottom
T  T1 t
 2
35
Flux flange-slab (kW/m²)
30
25
20
w
; T  150C
600
800
1000
325 
heating T   475  0.616*475  150   0.035*T  730 ; T  730C
T1, T2 : Temperatures of the top and bottom flanges


T

T       5 1  
 ;
x : Length of heat transfer (chosen equal to the root
 T fillet)

2
cooling
max
max
20C  T  Tmax,heating
max,heating
15
10
5
0
-5 0
t
T  20

Temperature (°C)
40
T   150
150  20
2
x
 475  T 
heating T   475  475  150  
 ; 150C  T  730C
heating
100
G = 0.4
G = 0.7
G = 1.0
G = 1.5
G = 2.0
Série1
Série2
Série4
200 Série5
300
Série6
400
500
-10
-15
Temperature (°C)
600
700
800
900
20
150
475
G = 0.4
G = 0.7
G=1
G = 1.5
G=2
Flux (kW/m²) Flux (kW/m²) Flux (kW/m²) Flux (kW/m²) Flux (kW/m²)
0
0
0
0
0
17
20
23
26
28
24
28
31
34
36
2. Distribution of temperature
24

Heat Exchange Method
Graph n°1 : IPE 300 beam – G = 1 – theating = 30 min
Graph n°2 : IPE 550 beam – G = 1 – theating = 30 min
900
900
1000
800
800
900
700
700
600
500
400
300
Parametric Fire Curve
200
SAFIR 2D-Model
600
500
400
Parametric Fire Curve
300
30
60
90
Time (min)
120
150
500
400
Parametric Fire Curve
SAFIR 2D-Model
Heat Exchange Method
200
Heat Exchange Method
100
0
0
0
600
300
100
0
700
SAFIR 2D-Model
200
Heat Exchange Method
100
800
Temperature (°C)
Temperature (°C)
Temperature (°C)
Graph n°3 : IPE 550 beam – G = 1 – theating = 60 min
0
30
60
90
Time (min)
120
150
0
30
60
90
120
Time (min)
150
180
210
2. Distribution of temperature
25

Lumped Capacitance Method : (Am/V)joint = (Am/V)beam/2

Composite Section Method
2. Distribution of temperature
26
Heat Exchange Method

Qtransferred  Qgas  Qtop bottom  Qconcrete  ca  a V  a ,t  Qheating
40
Flux flange-slab (kW/m²)
35
30
Lumped
Capacitance
Method
Atop bottom
25
20
15
10
5
0
0
200
G = 0.4
G = 0.7
G = 1.0
G = 1.5
G = 2.0
Série1
Série2
Série4
Série5400
Série6
Qtop bottom
600
800
Atransfer slab  lb bb  t p bp   min  hslab ; lc   *  hc  2bc 
 lQt transfer
 slab
t b Atransfer
 Aslab2 t
b
T  T 
  2 1
35
Flux flange-slab (kW/m²)
30
p
1000
c
T  20 ; T  150C
T   150

Atopbottom 150
t  20
2
x 
 475  T 
heating  T   475  475  150  

; 150C  T  730C
325 
heating T   475  0.616*475  150   0.035*T  730 ; T  730C

T1, T2 : Temperatures of the top and bottom flanges

cooling T   max  max  5 1  
T
T
 max,heating
25
20
15
10
5
0
-5 0
p
heating
Temperature (°C)
40
wb
100
G = 0.4
G = 0.7
G = 1.0
G = 1.5
G = 2.0
Série1
Série2
Série4
200 Série5
300
Série6
400
500
-10
-15
Temperature (°C)
600
700
800
900
20
150
475



2
; 20C  T  Tmax,heating
G = 0.4
G = 0.7
G=1
G = 1.5
G=2
Flux (kW/m²) Flux (kW/m²) Flux (kW/m²) Flux (kW/m²) Flux (kW/m²)
0
0
0
0
0
17
20
23
26
28
24
28
31
34
36
2. Distribution of temperature
27

Heat Exchange Method
Graph n°1 : Heating
Graph n°2 : Heating + Cooling
Beam section : IPE 300
Beam section : IPE 300
900
1200
800
700
Temperature (°C)
Temperature (°C)
1000
800
600
ISO Curve
Bott. Fl. SAFIR
400
200
600
500
Param. Fire Curve
400
Bottom Flange SAFIR
300
Bottom Flange Analytical
Bott. Fl. Analytical
200
Top Fl. SAFIR
100
Top Flange Composite SAFIR
Top Fl. Analytical
Top Flange Composite Analytical
0
0
0
0
20
40
60
Time (min)
80
100
120
20
40
60
Time (min)
80
100
120
2. Distribution of temperature
28
Temperature profile suggested (beam + joint)
A.
Beam––IPE
IPE300
300
B. Joint
Graph n°1 : ISO (Heating)
1000
1000
hb
900
900
800
800
(°C)
Temperature(°C)
Temperature
2 hb
3
700
700
600
600
500
500
ISO - 60 min - SAFIR
ISO - 60 min - SAFIR
ISO - 60 min - Analyt.
ISO - 60 min - Analyt.
ISO - 30 min - SAFIR
ISO - 30 min - SAFIR
ISO - 30 min - Analyt.
ISO - 30 min - Analyt.
ISO - 15 min - SAFIR
ISO - 15 min - SAFIR
ISO - 15 min - Analyt.
400
400
300
300
200
200
100
100
ISO - 15 min - Analyt.
00
00
0.05
0.05
0.10.1
0.150.15
0.2 0.2
Vertical
Abscissa
Vertical
Abscissa
(mm)(mm)
0.25
0.25 0.3
0.3
Graph n°2 : Param (Cooling)
700
700
Reference Lines
2-D
3-D
Temperature (°C)
600
600
500
500
N30
N30--60
60min
min--SAFIR
SAFIR
ISO - 60 min - Analyt.
N30 - 60 min - Analyt.
N30 - 90 min - SAFIR
N30 - 90 min - SAFIR
N30 - 90 min - Analyt.
400
400
300
300
N30--120
90 min
N30
min --Analyt.
SAFIR
N30
N30--120
120min
min--Analyt.
SAFIR
200
200
N30 - 120 min - Analyt.
100
100
00
00
0.05
0.05
0.1
0.1
0.15
0.15
0.2
0.2
0.25
0.25
0.3
0.3
Vertical Abscissa (mm)
0.35
0.35
2. Distribution of temperature
29




Lumped Capacitance Method
Lumped Capacitance Method
Composite Section Method
Heat Exchange Method
30
V
M
N
Academic year 2009-2010
3. Prediction of internal forces
31
No restraintsNo restraints
Finite restraints
Infinite restraints
Infinite restraints
KA
Lt   T L
T  T 
t   2 1
h
FT 
FT  EA T
M t  EI 
T2  T1 
h
 T L
 1
L 

K

EA
 A


 T L
 1
1 



K
K
A,beam 
 A
t L
Mt 
2
1
L

K R 2 EI
In real cases : superposition of axial forces and bending
moments due to non-uniform elevation of temperature.
3. Prediction of internal forces
32


Vertical deflections induce beam shortening or axial forces
The combination of axial forces and vertical deflections
influences the distribution of bending moments
Equilibrium must be stated in the deformed configuration
FT  m  t   MT  M R  M P  0
Yin (2005)
3. Prediction of internal forces
33
All terms are function of the mid-span deflection m,max
Deflection profile :
Pinned :
Rigid :
z x 0  0
xL
z x  L   m ,max
2
z x 0  0
xL
z x  L   m,max
2
dz
dx
16  m,max  x 4 2 x 3

z pinned 


x


5 L  L3
L2

16  m,max  x 4 2 x 3
2
zrigid 


x


L2  L2
L

0
x 0
xL
x 0
xL
0
1
1
L
1



K R'
K R ET I K R
Semi-rigid :
cf 
Axial force :
z  1  c f  z pinned  c f zrigid
'
R
K L
1
EI
12
  dz  2 
L   1     dx  L
0 
  dx  
Lt   th L
L
d 2z
dx 2
FT  K Lm  K  L  Lt 
'
A
'
A
where :
1
1
L
1



K A'
K A ET A K A
3. Prediction of internal forces
34
All terms are function of the mid-span deflection m,max
Mid-span bending moment :
M T  ET I  m
x
L
2
d 2 zm
 ET I
dx 2
x
L
2
Support bending moment :
M R  KR 
x0
 KR
dzm
dx
x0
Inelastic interaction :
M
M
Mpl
Mpl
Mel
Mel
Fel
Fpl
F
Fel
Fpl
F
3. Prediction of internal forces
35
All terms are function of the mid-span deflection m,max
Adaptations for non-uniform profiles of temperature :
Pinned :
Rigid :
z x 0  0 z x  L   t ,max
xL
Mt 
2
d 2z
 T
t  2  
dx
h
zt  
 T
2h
x
2
 L x
ET I y  T
Semi-rigid :
h
M T  (1  c f ) M T ,s  c f M T , f
9.6  m,max
L2
9.6  m,max
 T
 ET I y

E
I
T y
L2
h
32  m,max
 T
 ET I y
 ET I y
2
L
h
M T ,s  ET I y
M R  c f M R, f
where :
MT , f
MT , f
3. Prediction of internal forces
36
Consideration of the elliptic branch for evaluation of FT
F
 L
2 
Lm, propor  A f y k p , 


Fpl
 EA K A 
2 A f y k y ,
Fpropor
Lm, pl  0.02 L 
KA
K A'    L EA  2 K A 
(fp , fy , E)
1
(Fpropor , Fpl , K’A)
Lm,propor Lm,pl
Lm
3. Prediction of internal forces
37
:
Consideration of the elliptic branch for evaluation of MT and
MR based on the development of a method to predict the
(M, diagram of a beam section under axial force and a
non-uniform distribution of temperature.
3. Prediction of internal forces
38
:
Comparison with FE model (SAFIR) with fibre elements
60
Top flange
Web
Bott. flange
429.6 °C
679.8 °C
669.7 °C
Bending moment (kN.m)
40
20
0
-20
Numer. - Sagg. - FT = 80 kN
-40
Numer. - Hogg. - FT = 80 kN
Analyt. - Sagg. - FT = 80 kN
Analyt. - Hogg. - FT = 80 kN
Numer. - Sagg. - FT = 200 kN
-60
Analyt. - Sagg. - FT = 200 kN
Numer. - Hogg. - FT = 200 kN
-80
Analyt. - Hogg. - FT = 200 kN
-100
-0.4
-0.3
-0.2
-0.1
0
0.1
Curvature (rad/m)
0.2
0.3
0.4
3. Prediction of internal forces
39
:
Expression of the thermally-induced bending moment Mt
Equation of compatibility :
t 
t L
2
t L
 beam   spring 
Mt L Mt

2 EI K R
+ Limitation of the bending moment to Mpl,beam and Mpl,joint
Mt 
2
L
1

2 EI K R
3. Prediction of internal forces
40
:
Extensional stiffness of the beam (2nd order effects)
L

FT,1 = 1
FT,1 = 1
L
F .F
M .M1
d 
dx   T T ,1 dx
EI
EA
0
0
K A,beam 
L
F
1
 L
L
d  M .M 1
FT .FT ,1 
dx

dx 


EI
EA
0
0

Rigid connections
Pinned connections
Deflection
0 mm
50 mm
200 mm
500 mm
Extensional Stiffness
226.0 kN/mm
209.5 kN/mm
100.1 kN/mm
25.5 kN/mm
Relative Extensional Stiffness
1.000
0.927
0.443
0.113
Deflection
0 mm
50 mm
200 mm
500 mm
Extensional Stiffness
226.0 kN/mm
212.6 kN/mm
112.6 kN/mm
31.0 kN/mm
Relative Extensional Stiffness
1.000
0.941
0.498
0.137
3. Prediction of internal forces
41
:
Coefficient of interpolation between deflection profiles
with pinned and rigid connections evaluated by stating
the equilibrium between the bending moments at the
beam extremity and the joint.
Abscissa (m)
0
dzbeam
dzrigid
pinned
IPE
300
 x  
1

c

c
 f  dx
f
dx
w = 10dkN/m
2
z pinned
d 2 zrigid
  x   1  c f 
 cf
2
 KR = 10.000
kN.m/rad
dx
dx 2

1
1.5
2
2.5
3
0
  x  0   1  c f ,new 
-0.5
Vertical deflection (mm)
z 
x  L =
1  5m
c f  z pinned  c f zrigid
0.5
-1
  x-1.5 0   c f ,new
d zrigid
-2
-2.5
dx
2
dx 2
Numerical
cf,Wang = 0.416
cf,new = 0.125
Symmetry
 1  c f ,new 
dz pinned
x 0
 c f ,new 32  m ,max
x 0
K R   x -3 0  EI   x  0  c f ,new 
-3.5
Equilibrium
16  m ,max
5
KR
10 EI
 KR
L
3. Prediction of internal forces
42
« Rugby goal post » sub-structure



Flush End-plate
2 tests on simply-supported
beams
3 tests on sub-structures with
Web Cleats
web-cleats connections
10 tests on sub-structures
with flush end-plate
connections
3. Prediction of internal forces
43
Mechanical Analysis : Simply-supported beams
800
Design
Actual
Load
Load Ratio
Ratio
0.42
0.5
0.58
0.7
Actual
Critical
Critical
Temperature
Load Ratio Temperature
620°C
0.42
620°C
565°C
0.58
565°C
Tcritical if T is uniform
Bottom flange Temperature (°C)
Design
ad Ratio
0.5
0.7
700
600
500
400
Test - L.R.= 0.5
300
Test - L.R.= 0.7
SAFIR - L.R.= 0.5
200
SAFIR - L.R.= 0.7
100
0
0
50
100
150
200
250
Mid-span Deflection (mm)
300
350
400
3. Prediction of internal forces
44
Diamond
FILE: Structu
NODES: 47
BEAMS: 22
TRUSSES: 0
SHELLS: 0
SOILS: 0
BEAMS PLO
IMPOSED D
Mechanical Analysis : Sub-structures with flush end-plate connections
Identical horizontal
displacement
Axial
restraints
F0
Symmetry
conditions
F0
F0
F0
Rotational
restraints
F0
F0
F0
Identical rotation
F0
3. Prediction of internal forces
45
Mechanical Analysis : Sub-structures with flush end-plate connections
KA = 8 kN/mm
1000
100
Hogging Bending Moment :
700
600
500
400
300
200
60
40
20
0
0
-20
100
-40
0
0
-60
Hogging Bending Moment (kN.m)
Axial Force :
80
800
Beam Axial Thrust (kN)
Mid-span deflections :
Bottom flange Temperature (°C)
900
Test - L.R.= 0.2
40 Test - L.R.= 0.5
Test - L.R.= 0.7
35 Test - L.R.= 0.9
SAFIR - L.R.= 0.2
30 SAFIR - L.R.= 0.5
SAFIR - L.R.= 0.7
25 SAFIR - L.R.= 0.9
Test - L.R.= 0.2
Test - L.R.= 0.5
Test - L.R.= 0.7
20
Test - L.R.= 0.9Test - L.R.= 0.2
15
100
200
300
10
5
50
0
0
-5
100
100
SAFIR - L.R.= 0.2
Test - L.R.= 0.5
- L.R.= 0.5
Test
0.7
400 SAFIR
500
600 - L.R.=
700
Test - L.R.= 0.9
SAFIR - L.R.= 0.7
SAFIR - L.R.= 0.2
SAFIR - L.R.= 0.9
SAFIR - L.R.= 0.5
SAFIR - L.R.= 0.7
SAFIR - L.R.=200
0.9
150
800
Mid-span
Deflection
(mm)
200
300
400
500
Bottom flange Temperature (°C)
Bottom flange Temperature (°C)
900
1000
250
600
700
800
3. Prediction of internal forces
46
1. Simply-supported beam - Non-uniform distribution of T°
Deflections
Axial Force
100
600
50
Analytical - Modified Method
0
Axial Force (kN)
500
Numerical Model - SAFIR
400
300
200
0
100
200
300
400
500
600
-50
-100
-150
100
-200
Analytical - Modified Method
700
800
900
Sagging Bending Moment (kN.m)
100
700
Deflection (mm)
Bending Moments
80
60
40
Analytical - Modified Method
20
0
0
Numerical Model - SAFIR
0
0
100
200
300
400
500
600
Average Temperature (°C)
700
800
900
Numerical Model - SAFIR
100
200
300
400
500
600
-20
-250
Average Temperature (°C)
Average Temperature (°C)
700
800
900
3. Prediction of internal forces
47
2. Bilinear rotational restraints - Non-uniform distribution of T°
Bending Moments
Deflections
Axial Force
1400
300
1200
200
Analytical - Modified Model
100
Numerical - SAFIR
1000
120
100
80
Mid-span
60
Analytical - Modified Method
40
Numerical - SAFIR
20
0
0
100
200
300
400
500
600
700
800
900
1000
-20
Temperature (°C)
Analytical - Modified Method
800
Numerical - SAFIR
600
400
0
0
100
200
300
400
500
600
200
-400
0
100
200
300
400
500
600
Temperature (°C)
700
800
900
1000
800
900
1000
0
0
-200
-300
0
700
-100
-500
Temperature (°C)
Hogging Bending Moment (kN.m)
Axial Force (kN)
Deflection (mm)
Sagging Bending Moment (kN.m)
140
100
200
300
400
500
600
-5
-10
Analytical - Modified Model
Numerical - SAFIR
-15
Support
-20
-25
Average Temperature (°C)
700
800
900
1000
3. Prediction of internal forces
48
Modifications n°1 & 2 : Elliptic branch of the stress-strain
diagram of carbon steel for (F, Lm) and (M, m) diagrams
Hogging Bending
Moment
Deflection
(mm) (kN.m)
-10
0
100
200
300
400
500

700
800
900
1000
500
-20

-30
400
Analytical - Modified Method
-40
Analytical - Yin

Numerical - EN 1993-1-2
300
-50
200
Numerical - Elastoplastic
Analytical - Modified Method
-70
Analytical - Yin
-80
100
Numerical - EN 1993-1-2
-90
Numerical - Elastoplastic
-60



0
100
200
300
400
500
Analytical - Modified Method
Analytical - Yin
Distribution of T° : Ratios 0.8 – 1 – 1.2
Numerical - EN 1993-1-2
Numerical - Elastoplastic
500
KR = 3000 kN.m/rad (elastic)
w = 0.5 – K = 3%
0
-100
200
80
150
70
100
60
50
6 meter-long IPE 300 beam (S275)
600
Axial Force
(kN) (kN.m)
Sagging Bending
Moment
0
600
600
Temperature (°C)
Temperature (°C)
700
800
900
1000
-50
40
0
100
-100
30
-150
20
-200
10
-250
0
-300
0
200
300
400
500
600
700
400
500
600
Temperature (°C)
Temperature (°C)
700
800
900
1000
Analytical - Modified Method
Analytical - Yin
Numerical - EN 1993-1-2
Numerical - Elastoplastic
100
200
300
800
900
1000
Degree of accuracy enhanced
Better convergence at the transition « bending - catenary »
3. Prediction of internal forces
49
Analysis of the influence of the proposed modifications
Modification n°3 : Expression of the thermally-induced
bending moment Mt
Aimed at extending the field of application
of the Modified Method !
3. Prediction of internal forces
50
Analysis of the influence of the proposed modifications
Modification n°4 : Extensional stiffness KA of the beam
accounting for 2nd order effects
Results obtained from the Modified Method before and after
Modification n°4 are superposed


Deformability of the beam << Deformability of the spring
The extensional stiffness KA of the beam is modified for
large deflections where FT = FT,pl
3. Prediction of internal forces
51
Analysis of the influence of the proposed modifications
Modification n°5 : Coefficient of interpolation cf used for
deflection profile of the beam
600 0
100
200
300
400
-10

Deflection (mm)
Hogging Bending Moment (kN.m)
500
-20
Analytical - cf,new

400
-30
Analytical - cf,Yin
300-40
500
600
700
800
900
1000
Analytical - cf,new
-60
Analytical - cf,Yin
100

w = 0.5 – K = 3%
Numerical - Elastoplastic
0-80
0
100
200
300
Temperature
400
500 (°C)
600
Temperature (°C)


Numerical - EN 1993-1-2
Numerical - Elastoplastic
0
40
-50
100
700
800
900
1000
300
400
500
600
700
800
900
1000
400
500
600
Temperature (°C)
Temperature
(°C)
700
800
900
1000
Analytical - cf,Yin
-150
20
-200
10
-250
0
-300 0
200
Analytical - cf,new
-100
30
Numerical - EN 1993-1-2
-70
Analytical - cf,Yin
50
0
KR = 3000 kN.m/rad (elastic)
Numerical - Elastoplastic
-50
Analytical - cf,new
Distribution of T° : Ratios 0.8 – 1 – 1.2
Numerical - EN 1993-1-2

200
200
80
150
70
100
60
50
6 meter-long IPE 300 beam (S275)
Axial Force (kN)
Sagging Bending Moment (kN.m)
0
Numerical - EN 1993-1-2
Numerical - Elastoplastic
100
200
300
No influence on deflections and axial forces
Prediction of bending moments significantly improved (low T°)
3. Prediction of internal forces
52


Based on the 2 principles proposed for material law of carbon
steel when cooling (Franssen, 1990)
Validated only for the prediction of deflections and axial forces
Plastic strains constant
during the variation of T°
Length of the elastic branch
constant when unloading
3. Prediction of internal forces
53

The resolution of the General Equation is made at the end
Mid-span Bending Moment
of the heating phase (reference point)
M
Beam Temperature
The (FT, Lm) and (M, m) diagrams are
adapted for the
M
M
cooling
phase
Tref
M
(M ; 
)
M
The General Equation is solved at any instant of the cooling
phase
T

pl,t
pl,tref

propor,t
propor,tref
T,ref
pl,x=L/2
20°C
tref
t
Time
x=L/2,ref
x=L/2
3. Prediction of internal forces
54
1. Simply-supported beam - Non-uniform distribution of T°

6 meter-long IPE 300 beam (S275)

Tref : 600°C – 650°C – 700°C

w = 0.3 – K = 3%
Axial Force
Mid-span Bending Moment
200
90
400
150
80
350
100
300
50
250
200
Analytical - Modified Method
150
Numerical - SAFIR
0
0
100
200
300
400
-50
-100
100
-150
50
-200
0
-250
Analytical - Modified Method
Numerical - SAFIR
0
100
200
300
400
Average Temperature (°C)
500
600
700
Average Temperature (°C)
500
600
700
Sagging Bending Moment (kN.m)
450
Axial Force (kN)
Deflection (mm)
Deflections
70
60
50
40
30
20
Analytical - Modified Method
10
Numerical - SAFIR
0
-10
-20
0
100
200
300
400
500
Average Temperature (°C)
600
700
3. Prediction of internal forces
55
2. Bilinear rotational restraints - Uniform distribution of T°

Sagging Bending Moment (kN.m)
150
6 meter-long IPE 300 beam (S275)

Tref : 700°C – 700°C – 700°C

w = 0.5 – K = 10%
Mid-span
100
50
0
0
100
200
300
-50
400
500
600
700
Analyt. - Modified Method - Heating
Numer. - SAFIR - Heating
-100
Analyt. - Modified Method - Cooling
Numer. - SAFIR - Cooling
-150
Temperature (°C)
Deflections
Axial Force
25
Analyt. - Modified Method - Heating
Numer. - SAFIR - Heating
Analyt. - Modified Method - Cooling
Numer. - SAFIR - Cooling
450
600
400
350
400
Axial Force (kN)
Deflection (mm)
Bending Moments
800
300
250
Analyt. - Modified Method - Heating
200
Numer. - SAFIR - Heating
150
Analyt. - Modified Method - Cooling
100
Numer. - SAFIR - Heating
200
0
0
100
200
300
400
-200
50
500
600
20
Hogging Bending Moment (kN.m)
500
700
15
Analyt. - Modified Method - Heating
Numer. - SAFIR - Heating
Analyt. - Modified Method - Cooling
Numer. - SAFIR - Cooling
10
5
0
-5
-10
-15
0
100
200
300
400
Support
-400
-20
0
0
100
200
300
400
Temperature (°C)
500
600
700
-25
-600
Temperature (°C)
Temperature (°C)
500
600
700
3. Prediction of internal forces
56




Simplified method developed by Yin and Li has been
modified in order to improve the prediction of bending
moments in restrained beams (heating + cooling)
It has also been possible to limit the bending moment at the
beam extremities in order to account for joint resistance
A numerical model built in SAFIR software has been used as
reference for the validation of these modifications
For each modification, the enhancement of accuracy and the
extension of the field of application have been underlined
3. Prediction of internal forces
57



Good predictions of internal forces and deflections
Field of application remains limited to bilinear and constant
rotational restraints in spite of several modifications making
the algorithm more complex
Including the real behaviour of connections in this Method
seems difficult (contact between beam and column flanges,
M-N interaction) and the use of simple FE models is
recommended for the analysis of the behaviour of simple
steel connections
58
Academic year 2009-2010
4. Tests and models for bolts/welds
59




Riaux (1980) : Tensile and shear tests on Grade 8.8
bolts after heating
Kirby (1995) : Tensile and shear tests on Grade 8.8
bolts after heating
EN 1993-1-2
Gonzalez (2008) : Tensile tests on Grade 10.9 bolts
during heating and after cooling (residual)
Latham (1993) : Tests on fillet and butt welds after
heating
EN 1993-1-2
4. Tests and models for bolts/welds
60
Bolts



Heating phase : OK
Residual : Few data
Cooling phase : No data
Welds



Heating phase : OK
Residual : No data
Cooling phase : No data
4. Tests and models for bolts/welds
61
Temperature (T)
Temperature
(T)
Room temperature tests
 Steady-state tests at
elevated temperatures (a)
(a)(b)
perature
(T)
(T)  Steady-state tests
15 min 15 min
400°C200°C
- 900°C
performed
at- 800°C
various Tf
20°C - 600°C
after temperature
has
10-30 °C/mm
10-30 °C/mm T (b)
reached
u

t0t1
t1t2
tft2
Time Time
(t) (t)
Displ
1515
minmin
400°C
- 900°C
200°C
- 800°C
TTuu
xf
20°C - 600°C
Tf
10-30
°C/mm
10-30
°C/mm
0
t00
t1t1
t2 t2 tf
Time Time
(t) (t)
Displacement (mm)
Displacement
(mm)
Figure 1 : Steady state
(a) and Natural Fire (b) tests proc
failure
failure
xxff
0.010.01
mm/sec
mm/sec
00
tt00
t2tf
Time
Time
(t) (t)
Steady state (a) and Natural Fire (b) tests procedures for bolts experiment
4. Tests and models for bolts/welds
62
Heating
Tu = Tf [°C] n. tests
20
2
200
1
400
1
600
1
800
1
Tu [°C]
400
600
800
900
Cooling
Tf [°C]
200
100
20
400
300
200
100
20
600
400
300
200
100
20
20
n. tests
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
Heating
Tu = Tf [°C] n. tests
20
2
200
1
400
1
600
1
800
1
Tu [°C]
600
800
900
Cooling
Tf [°C]
400
300
200
100
20
600
400
300
200
100
20
20
n. tests
1
1
2
1
1
1
1
1
2
1
1
1
4. Tests and models for bolts/welds
63
Heating
Cooling
Tu = Tf [°C]
20
200
n. tests
1
1
400
600
1
1
800
1
Tu [°C]
400
600
800
900
Tf [°C]
200
100
n. tests
1
1
20
400
1
-
200
-
20
600
1
1
400
200
1
1
20
1
400
1
200
1
20
1
4. Tests and models for bolts/welds
64
1.2
1.2
1
1
kb (-)
0.6
Heating
TestsTests
Steady-state
Tu = 400°C Tests
Tu = 600°C Tests
Tu = 800°C Tests
0.8
kb (-)
Heating
Tests
Steady-state
Tests
Tu = 400°C Tests
Tu = 600°C Tests
Tu = 800°C Tests
0.8
0.6
0.4
0.4
0.2
0.2
0
0
0
100
200
300
400
500
Temperature
T (°C)(°C)
f
600
700
800
900
0
100
200
300
400
500
T tests
(°C)
Tf (°C)
600
700
800
900
4. Tests and models for bolts/welds
65
EN 1993-1-2
f ub T f , Tu   kb T f  . knr,b T f ; Tu  . f ub, 20C
knr ,b  1
0.4

Tu  max T f ; 500C 
knr,b T f ; Tu   min 1 ; 1 
300


for Tu  500C
for 500C  Tu  800C
Tf : Failure temperature
Tu : Upper temperature (at the end of heating phase)
4. Tests and models for bolts/welds
66
F
Tu (°C)
20
200
400
600
800
900
Fub,
Fpb,
Ftb,
kpb,
0.9
0.8
0.75
0.75
0.6
0.6
Sb,Tu ,T f  0.8 E As Lb
 EC 3
Fub,Tu ,T f  knr ,Tu ,T f kb,T f fub,20C As
Fpb,Tu ,T f  k pb,Tu . Fub,Tu ,T f

Ftb,Tu ,T f  min 500 MPa * As ; Fub,Tu ,T f
d pb,Tu ,T f  Fpb,Tu ,T f Sb,Tu ,T f
Sb,
dpb,
dyb,
dtb, dub,
d yb,Tu ,T f  1mm
d
Tu (°C)
Tu ≤ 600°C
600°C ≤ Tu ≤ 800°C
Tu ≥ 800°C
dtb,Tu ,T f  5 mm
dub, (mm)
7.5
lin. interpol.
12.5
dub,Tu ,T f  [7.5 ;12.5] mm

4. Tests and models for bolts/welds
67
70
90
Model - Tu = 20°C
Test - Tu = 20°C (1)
Test - Tu = 20°C (2)
Model - Tu = 200°C
Test - Tu = 200°C
Model - Tu = 400°C
Test - Tu = 400°C
Test - Tu = 400°C (2)
Force (kN)
70
60
50
40
Model - Tu = 400°C
60
Test - Tu = 400°C
Test - Tu = 400°C (2)
50
Force (kN)
80
30
Model - Tu = 600°C
Test - Tu = 600°C
40
Model - Tu = 800°C
Test - Tu = 800°C
30
20
20
10
10
0
0
0
2
4
6
Displacement (mm)
8
10
0
2
4
6
8
10
Displacement (mm)
12
14
16
Large displacements
4. Tests and models for bolts/welds
68
70
80
Model - Tu = 400°C
Test - Tu = 400°C
Model - Tu = 600°C
Test - Tu = 600°C
Model - Tu = 800°C
Test - Tu = 800°C
Model - Tu = 900°C
Test - Tu = 900°C
Force (kN)
60
50
40
Significant
loss of
strength
30
20
10
0
0
2
4
50
Large
displacements
6
8
Displacement (mm)
Analyt. Tu = 400°C
Experim. Tu = 400°C
Analyt. Tu = 600°C
Experim. Tu = 600°C
Analyt. Tu = 800°C
Experim. Tu = 800°C
60
Force (kN)
70
40
30
20
10
0
10
12
14
0
2
4
6
8
Displacement (mm)
10
12
14
4. Tests and models for bolts/welds
69
f
5
5
5
4
3
-
Tf (°C)
20
200
400
600
800
900
R
Rub,
Rb,
Sb,
db,
dub,
dfb,
Tf (°C)
20
200
400
600
800
900
 EC 3
Sb,Tu ,T f  8 d 2 f ub d M 16
Rb,Tu ,T f  knr ,Tu ,T f kb,T f Rb,20C
T ,T  Sb,T ,T Sst ,b,T ,T   f . u
f
1.2
1.2
1.2
1.4
1.75
-
Tf (°C)
20
200
400
600
800
900
Sst,
u
1
1
1
1
2
2
Tu (°C)
20
200
400
600
800
900
u
u
1
1
1
1
1.1
1.1
Tu (°C)
20
200
400
600
800
900
d
hf
4
5
6
6
6
-
Tu (°C)
20
200
400
600
800
900
f
u
f
u
f
T ,T  Ru,b,T ,T Rb,T ,T   f .  u
u
h
f
 b,T ,T
u
u
u
f
u
f
 h f hu
f
 u ,b,T ,T
 f ,b ,T
hu
1
1
1
1
1.25
1.25
u
f
Tu (°C)
20
200
400
600
800
900
f,b,Tu (mm)
6
6
7
11
15
-
4. Tests and models for bolts/welds
70
70
70
Test - Tu = 20°C
60
Test - Tu = 200°C
Model - Tu = 200°C
60
Model - Tu = 20°C
Test - Tu = 600°C
Test - Tu = 600°C
Test - Tu = 800°C
40
Model - Tu = 800°C
30
Significant
loss of
strength
20
10
0
0
1
2
3
Model - Tu = 600°C
50
Model - Tu = 600°C
Force (kN)
Force (kN)
50
Test - Tu = 800°C (1)
40
Test - Tu = 800°C (2)
Model - Tu = 800°C
30
20
10
0
4
5
Displacement (mm)
6
7
8
0
1
2
3
4
Displacement (mm)
5
6
7
4. Tests and models for bolts/welds
71
1.2
1.2
1.0
1.0
Tests - Heating
0.8
Tests - Tu = 800°C
Heating - Experimental
kw (-)
kw (-)
Tests - Tu = 600°C
Heating - EN 1993-1-2
0.8
Tests - Tu = 400°C
0.6
0.4
Tests - Tu = 900°C
0.6
0.4
0.2
0.2
0.0
0
200
400
600
800
1000
Temperature [°C]
0.0
0
100
200
300
400
Tf (°C)
500
600
700
800
900
4. Tests and models for bolts/welds
72
EN 1993-1-2
f uw T f , Tu   k w T f  . knr,w T f ; Tu  . f uw, 20C
knr ,w  1


knr ,w  1 
0.2
Tu  max T f ; 600C 
200
knr ,w  1 
0.2
800C  max T f ; 600C 
200

for Tu  600C
for 600C  Tu  800C

for 800C  Tu  900C
Tf : Failure temperature
Tu : Upper temperature (at the end of heating phase)
4. Tests and models for bolts/welds
73



The influence of heating-cooling cycles on bolts and
welds strength is significant (knr,b,min = 0.6 ; knr,w,min = 0.8)
Ductility of bolts is increased when submitted to a
heating-cooling cycle where Tu (at the end of the heating
phase) exceeds 500°C.
Material laws, including a descending branch, have been
proposed for bolts in tension and bolts in shear. They can
be applied to component-based models aimed at
predicting the behaviour of steel connections under
natural fire.
74
Pinned
Academic year 2009-2010
5. Tests and models of connections
75

Models for semi-rigid joints : curve fit models,
mechanical models, FE models and macro-elements
Curve-fit models
M
M 

 0.01  
A
 B
Ang (1984)
Mechanical models
Solid models
Macro-elements
n
Cerfontaine (2004)
Block (2006)
5. Tests and models of connections
76






Isothermal tests on isolated connections performed at the
University of Sheffield (Yu, 2009) + mechanical models
One of the natural fire tests performed at University of
Coimbra (Santiago, 2008)
Type of connection (FP, WC and HP)
Temperature (20°C – 450°C – 550°C
– 650°C)
Angle of the loading (35° – 55°)
Number, diameter and grade of bolts
5. Tests and models of connections
77
Test n°1 (Metz)







Heated gradually until failure
Test stopped at Tfurnace = 840°C
Flush end-plate
connections
(T
bottom flange = 800°C)
5.5 meter-long IPE 300 beam
Beam deflection > 220 mm
Thermally-protected HEA 220
No failure of bolts
column

K = 1%

L.R. = 0.3 (theoretically)
10mm-thick plate
IPE 300 beam
5. Tests and models of connections
78
Test n°2 (Metz)








Heated gradually until 700°C
Beam
= 58 mm
beforedeflection
natural cooling
(constant during cooling)
Flush end-plate connections
No failure of bolts
5.5 meter-long IPE 300 beam
Thermally-protected HEA 220
column
10mm-thick plate
K = 1%
L.R. = 0.3 (theoretically)
IPE 300 beam
5. Tests and models of connections
79
Test n°3 (Delft)








Heated gradually until d =
200 mm before natural
cooling
Temperature reached
650°C
in connections
the beam and
Fin
plate
600°C
near theIPE
joint
4.4
meter-long
300 beam
Failure of bolts after HEB
127300
Thermally-protected
minutes
column
K = 6.6%
L.R. = 0.3 (fy = 345 MPa)
5. Tests and models of connections
80
Test n°4 (Delft)








Heated gradually until d =
200 mm before natural
cooling
Temperature reached
670°Ccleats
in theconnections
beam and
Web
600°C
near theIPE
joint
4.4
meter-long
300 beam
No failure of bolts HEB 300
Thermally-protected
column
K = 6.6%
L.R. = 0.3 (fy = 345 MPa)
5. Tests and models of connections
81

The action of joints is represented by beam elements
including one fibre per bolt or compressive row
Cross-section of the
beam element
EI sec tion 
f y ,i 
FRd ,i
Ai
Ei 
Kini ,i L j
n fibres
E
i 1
i
Ai d
2
i
Ai
Lj
5. Tests and models of connections
82
Fin plate
Web cleats
Translated
BILIN_COMP
Translated
BILIN_COMP
Header Plate
Translated
BILIN_COMP
Flush end-plate
BILIN_COMP
BILIN_COMP
BILIN
BILIN_ASYM
BILIN_BOLTS
BILIN_TENS
5. Tests and models of connections
83
BILIN
s
BILIN_COMP
s1,1
fy
E
s
s
Ehard
s
pl ini
pl
E
Ehard
Translated
BILIN_COMP

fy
pl
fy
Ehard
BILIN_TENS

E0
Ehard
s
fy
Ehard
BILIN_ASYM
Ehard
s
fy,t
pl
Ehard,t
Et
Ec


pl
fy
Ehard
E0
E0

E0
fy
BILIN_BOLTS
s
fy
Symmetric to
BILIN_COMP !

E0
Ehard,c

fy,c
pl
5. Tests and models of connections
84
Failure criteria
1. Classes of ductility
Resistance
Plastic resistance of
weakest ductile component
Class A
Ultimate resistance of
Class C
weakest ductile component
Resistance of weakest brittle
component
Class B
Temperature
5. Tests and models of connections
85
Failure criteria
2. Criteria

Criterion n°1 : One fibre representing the
action of a class C bolt row is yielded
or

Resistance
Class C
Class A
Criterion n°2 : All the fibres representing
the action of bolt rows are yielded and at
least one bolt row is class B
Class B
Temperature
Plastic resistance of weakest
ductile component
Ultimate resistance of weakest
ductile component
Resistance of weakest brittle
component
5. Tests and models of connections
86
Test n°1 (Metz)
Diamond 2009.a.5 for SAFIR
Restraining system modelled by
one element (elastic spring)
fy = 355 MPa.
fub : 956 Mpa (tests at room T°)
FILE: Essai WP3 956 load 1%S355

250
F0
NODES: 123
50
BEAMS: 55
TRUSSES: 0
SHELLS: 0
SOILS: 0
Vertical Displacement (mm)
F0
40
IMPOSED DOF PLOT
F0
POINT LOADS PLOT
F0
F0
F0
F0
F0
F0
F0
F0
F0
F0
150
F0
F0
F0
F0
F0
F0
F0
SAFIR
0
20
30
40
50
60
70
10
0
SAFIR
0
10
20
30
40
50
60
70
80
-10
Y
10
Test Metz n°1
TIME: 7.168 sec

50
0
DISPLACEMENT PLOT ( x 1)
30
20
Test Metz n°1
100
Horizontal Displacement (mm)
F0
200
80
F0
Z
X
-50
F0
F0
F0
F0
1.0 E+00 m
Time (min)
-20
Time (min)
- Experimentally, failure after 70 min (Tfurnace = 797°C)
- Good correlation
5. Tests and models of connections
87
70
50
60
45
50
Test Metz n°2
40
SAFIR
Horizontal Displacement (mm)
Vertical Displacement (mm)
Test n°2 (Metz)
30
20
10
0
0
30
60
90
120
150
Time (min)
180
210
240
40
Test Metz n°2
35
SAFIR
30
25
20
15
10
5
0
-5 0
30
60
90
120
150
Time (min)
No failure
180
210
240
5. Tests and models of connections
88
Test n°3 (Delft) : Fin plate connections
300
Resistance of Component in Row 1 (kN)
300
Vertical displacement [mm] ===>
250
200
150
100
50
0
-50
Fin Plate in Bearing
Beam Web in Bearing (Pl)
Beam Web in Bearing (Ul)
Bolts in Shear
Fin Plate in Tens/Comp
250
200
150
Experimental
SAFIR
100
50
0
0
20
0
40
20
60
40
60
80
100
80
Time (min)
100
120
120
140
140
160
160
Time [min] ===>

Criterion n°2 reached after 119 min. – Experimentally : failure after 127 min.
5. Tests and models of connections
89
Test n°4 (Delft) : Web cleats connections
450
Component Resistance (kN) - Row 1
Vert. Displacment [mm] ===>
250
200
150
100
50
0
Cleat Bending
350
Web Bearing
300
Bolt Shear
250
T-Stub Mode 1
200
150
Experimental Results
T-Stub Mode 2
SAFIR Simulation
T-Stub Mode 3
100
50
0
-50
0

400
30
0
60
30
90
60
120
150
180
210
150
180
210
240
Time (min)
Time [min] ===>
120
90
The weakest components are ductile – No failure
240
5. Tests and models of connections
90
Parametric Analyses
Parameters investigated :




Type of connection : Fin plate, Web cleats, Header plate
Load ratio : 0.3, 0.5 and 0.7
Duration of the fire : Short (ISO) or Long (60 min)
Beam span : 6 m (IPE 300) or 12 m (IPE 550)
5. Tests and models of connections
91
Parametric Analyses : Fin plate connections
Bilinear Fibres Model
IPE 300 IPE 300
Hot
K = 3% Tmax,bolt
K = 10%
K = 15%
Case 1 Case 1
Fail. HOT
Fail.
C HOT
Short Fire
ShortFail.
FireHOT 625
w = 0.3 w = 0.3
Case 2 Case 2
NoFire
Failure 560
No Failure No
Short Fire
B Failure
Short
w = 0.5 w = 0.5
Case 3 Case 3
NoFire
Failure 530
No Failure No
Short Fire
A Failure
Short
w = 0.7 w = 0.7
Case 4 Case 4
Fail. HOT
Fail.
Long FireLongFail.
C HOT
FireHOT 655
w = 0.3 w = 0.3
Case 5 Case 5
No Failure No Failure
Long Fire No Failure 595
B
Long Fire
w = 0.5
w = 0.5
Case 6
Case 6
Long Fire No Failure No Failure No Failure
555
B
Long Fire
w = 0.7
w = 0.7
Cold
Tmax,bolt
K = 3%
Case 1
Fail.
A Fire
590 HOT
Short
w = 0.3
Case 2
Fail.
Short
A Fire
520 HOT
w = 0.5
Case 3
Failure
Short
A Fire No
460
w = 0.7
Case 4
Fail.
Long
A Fire
630 HOT
w = 0.3
Case 5
Fail. HOT
Long
A Fire
560
w = 0.5
Case 6
Long Fire No Failure
A
510
w = 0.7
Abaqus Model
IPE
550
IPE
550
Hot
K
= 10%
Cold
K
= 15%
Fail.
C HOT
Fail.
B HOT
Fail.
C HOT
Fail.
B HOT
NoBFailure
No B
Failure
Fail.
C HOT
Fail.
B HOT
Fail. HOT
C
Fail. HOT
B
No Failure
B
No Failure
B
K = 3%
Case 1
Short Fire
w = 0.3
Case 2
Short Fire
w = 0.5
Case 3
Short Fire
w = 0.7
Case 4
Long Fire
w = 0.3
Case 5
Long Fire
w = 0.5
Case 6
Long Fire
w = 0.7
IPE 300
K = 10%
K = 15%
No Failure
Fail. COOL Fail. COOL
No Failure
No Failure
No Failure
No Failure
No Failure
No Failure
No Failure
Fail. COOL
No Failure
No Failure
No Failure
No Failure
Case 1
Short Fire
w = 0.3
Case 2
Short Fire
w = 0.5
Case 3
Short Fire
w = 0.7
Case 4
Long Fire
w = 0.3
Case 5
Long Fire
w = 0.5
Case 6
Long Fire
w = 0.7
K = 3%
IPE 550
K = 10%
K = 15%
Fail. HOT
Fail. HOT
Fail. HOT
Fail. HOT
No Failure
Fail. HOT
No Failure
No Failure
No Failure
Fail. HOT
Fail. HOT
Fail. HOT
Fail. HOT
No Failure
No Failure
FEM model - Source : Corus Ltd
No Failure
No Failure
No Failure
No Failure
No Failure
No Failure
5. Tests and models of connections
92
Parametric Analyses : Web cleats connections
Time (min)
0
30
Bilinear Fibres 0Model
IPE 300
Case 1
Short Fire
Case 1
w = 0.3
Short Fire
Case
2
w = 0.3
Short
Fire
Case
2
w = 0.5
Short
Fire
w = 0.5
Case
3
Case
3
Short
Fire
Short Fire
w = 0.7
w = 0.7
Case
4
Case 4
Long
LongFire
Fire
ww==0.3
0.3
Case
Case55
LongFire
Fire
Long
0.5
ww==0.5
Case66
Case
Long Fire
Long Fire
w = 0.7
w = 0.7
K = 3%
B
No Failure
A
No Failure
A
No Failure
B
No Failure
-0.05
Hot
Cold
IPE 300
K = 10%
A
No Failure
-0.1B
No Failure
-0.15B
A
No Failure
A
No Failure
A
Fail. HOT
No Failure
-0.2
B
No Failure
-0.25
Fail. HOTB
-0.3
No Failure
A
No Failure
A
No FailureB
No Failure
No Failure
No Failure
A
A
-0.35
-0.4B
90
120
150
Cold
Case 1
Short Fire
w = 0.3
Case 2
Short Fire
w = 0.5
Case 3
Short Fire
w = 0.7
Case 4
Long Fire
w = 0.3
Case 5
Long Fire
w = 0.5
Case 6
Long Fire
w = 0.7
A K = 3%
No Failure
IPE 550
K = 10%
K = 15%
No Failure
No Failure
No Failure
No Failure
A
No Failure
A
No Failure
Fail. HOT
Fail. HOT
ANo Failure
Fail. HOT
Fail. HOT
ANo Failure
Fail. HOT
Fail. HOT
No Failure
Fail. HOT
Fail. HOT
A
Case 1
Short Fire
w = 0.3
Case 2
Short Fire
w = 0.5
Case 3
Short Fire
w = 0.7
Case 4
Long Fire
w = 0.3
Case 5
Long Fire
w = 0.5
Case 6
Long Fire
w = 0.7
-0.45
-0.5
ANSYS Model
180
IPE 550
K = 15%
Deflection (mm)
Hot
60
K = 3%
IPE 300
K = 10%
No Failure
No Failure
No Failure
No Failure
IPE300 - Curve 4 - 3%
K = 3%
IPE 550
K = 10%
K = 15%
No Failure
No Failure
No Failure
Case 2
IPE300
- Curve
5 - 3%
No Failure Short Fire No Failure
Fail. HOT
No Failure
Fail. HOT
Fail. HOT
Fail. HOT
Fail. HOT
Fail. HOT
Fail. HOT
Fail. HOT
Fail. HOT
K = 15%
IPE300 - Curve
4 1- 10%
Case
No Failure
Short Fire
IPE300 - Curve
4 - 15%
w = 0.3
w = 0.5
IPE300 - Curve
5 - 10%
Case 3
No Failure
No Failure
No Failure Short Fire
Fail. HOT
IPE300
- Curve 5 - 15%
w = 0.7
Case
IPE300 - Curve
6 4- 3%
No Failure Fail. COOL Fail. COOL Long Fire
Fail. HOT
w =6
0.3- 10%
IPE300 - Curve
Case 5
Fail. COOL No Failure IPE300
No Failure
Fail. HOT
Long6
Fire
- Curve
- 15%
w = 0.5
Case 6
No Failure
Fail. HOT
Fail. HOT
Fail. HOT
Long Fire
w = 0.7
FEM model - Source : CTICM
d >> L/20
5. Tests and models of connections
93
Parametric Analyses : Header plate connections
Bilinear Fibres Model
K = 3%
IPE 300
K = IPE
10%300 K = 15%
Hot
Cold
Case 1
Short Fire
CaseNo
1 Failure No Failure No Failure
w = 0.3
B
A
Short Fire
Case 2
w
=
0.3
Short Fire No Failure No Failure No Failure
w = 0.5Case 2
A
A
Fire
CaseShort
3
No Failure No Failure No Failure
Short Fire
w = 0.5
w = 0.7Case 3
Case 4
A
A
Short Fire
Long Fire No Failure Fail. COOL Fail. COOL
w = 0.3w = 0.7
Case 5Case 4
C Failure NoAFailure
Long Fire
Long No
FireFailure No
w = 0.5w = 0.3
Case 6
Case 5
Long Fire No Failure No Failure No Failure
B
A
Long Fire
w = 0.7
w = 0.5
Case 6
Long Fire
w = 0.7
A
A
Abaqus Model
IPE 550
K = 3%
Hot1
Cold
Case
Short Fire
w =C
0.3
Case 2
Short Fire
w = 0.5
C3
Case
Short Fire
w = 0.7
Case
B4
Long Fire
w = 0.3
Case 5
LongCFire
w = 0.5
Case 6
Long Fire
C
w = 0.7
C
Fail. HOT
IPE 550
K = 10%
K = 15%
Fail. COOL Fail. COOL
B
Fail. HOT
Fail. HOT
Fail. HOT
No Failure
No Failure
Fail. HOT
Fail. HOT
Fail. HOT
Fail. HOT
B
Fail. HOT
Fail. HOT
Fail. HOT
Fail. HOT
Fail. HOT
B
No Failure
A
B
B
K = 3%
Case 1
Short Fire
w = 0.3
Case 2
Short Fire
w = 0.5
Case 3
Short Fire
w = 0.7
Case 4
Long Fire
w = 0.3
Case 5
Long Fire
w = 0.5
Case 6
Long Fire
w = 0.7
IPE 300
K = 10%
K = 15%
Fail. COOL
No Failure
Fail. COOL
No Failure
Fail. COOL
No Failure
No Failure
Fail. COOL
No Failure
Fail. COOL
No Failure
Fail. COOL
No Failure
No Failure
No Failure
No Failure
No Failure
No Failure
Case 1
Short Fire
w = 0.3
Case 2
Short Fire
w = 0.5
Case 3
Short Fire
w = 0.7
Case 4
Long Fire
w = 0.3
Case 5
Long Fire
w = 0.5
Case 6
Long Fire
w = 0.7
K = 3%
IPE 550
K = 10%
K = 15%
Fail. HOT
Fail. HOT
No Failure
Fail. HOT
Fail. HOT
Fail. HOT
No Failure
Fail. HOT
No Failure
Fail. HOT
Fail. HOT
Fail. HOT
No Failure
Fail. HOT
Fail. HOT
Fail. HOT
No Failure
No Failure
FEM model - Source : Corus Ltd
5. Tests and models of connections
94
Parametric Analyses : Conclusions



Influence of ductility classes (design + Tmax) : ratio
« resistance of bolts in shear/resistance of beam web in
bearing » higher for web cleats than fin plates.
Bolts situated close to the top flange increase the fire
resistance but this effect is counter-balanced by failures
during cooling phase
Cases with large deflections (d > L/20) at the end of
the heating phase should be rejected
5. Tests and models of connections
95
Additional cases : Fin plate connections
K = 5%
K = 12%
5. Tests and models of connections
96
Proposed design procedure for simple connections
1. Heating phase




Evolution of temperature profiles (cfr. part 2)
Multiplication of w by 1.1 (restraints)
Evaluation of the time of fire resistance t1 (following EN)
Evaluation of cooling
Verification that cooling*t1 > theating
1.2
Value of

cooling (-)
1
0.8
0.6
0.4
0.2
0
0
10
20
30
40
Time of Fire resistance (min)
50
60
5. Tests and models of connections
97
Proposed design procedure for simple connections
2. Cooling phase
Recommendation n°2
n°1 :
TThe
resistance
thethe
brittle
end components
of heating phase
is higher than the
bottom
flange < Tof
lim at
or w > wresistance
plastic
of the weakest ductile component
lim
or
The resistance
the brittle
higherCthan
(accounting
for knrof
) multiplied
bycomponents
1.2  NOisCLASS
 Fin plate : wlim = 0.35
the
ultimate
resistance
theConnections
weakest ductile
Fin
Plate
Connections
Web of
Cleats
Headercomponent
Plate Connections
T [°C]
T [°C]
cleats
:w
= 0.25
K [%]
K [%]  Web
K [%]
lim
(accounting
for knr) multiplied
by
1.2
 NO
CLASS
BT [°C]
lim
2
5
10
15
710
640
580
540
lim
2
5
10
15

740
680
620
580
lim
2
5
10
15
780
740
660
600
Header plate : wlim = 0.45
5. Tests and models of connections
98
Proposed design procedure for simple connections
3. Summary
CLASS B
A
during cooling
cooling :: Inacceptable
C during
Acceptable
w
Inacceptable Heating
Inacceptable Heating
wlim
Inacceptable Cooling
Acceptable
t(Tlim)
theating
5. Tests and models of connections
99
Proposed design procedure for simple connections
Fin-plate connections
K = 3%
K = 10%
0.7
0.7
No Failure
Failure Cooling
Failure Beam
Failure Heating
Beam Criterion
Criterion 2a
Criterion 2b
No Failure
0.6
0.6
Failure Cooling
0.5
Beam Criterion
Load Factor w (-)
Load Factor w (-)
Failure Beam
Criterion 2a
Criterion 2b
0.4
0.3
0.2
0.1
0.5
0.4
0.3
0.2
0.1
0
0
8
10
12
14
16
t,heating (min)
18
20
22
24
8
10
12
14
16
t,heating (min)
18
20
22
24
5. Tests and models of connections
100
Column web in tension
Header plate in bending
F
F
d
d
Bolts in tension
Column flange in bending
F
F
d
General Material Law
s
d
fy,t
Global
Et
Ec
F
fy,c
e
d
On the contrary of Bilinear F.M., the Nonlinear F.M. allows
an automatic detection of connection failures !
5. Tests and models of connections
101
n°
Temp. (°C)

Grade
Diam. (mm)
nbol t(s )/row
1
2
3
20 450 550
55 55 55
8.8 8.8 8.8
20 20 20
1
1
1
4
650
55
8.8
20
1
5
6
7
20 450 550
35 35 35
8.8 8.8 8.8
20 20 20
1
1
1
8
650
35
8.8
20
1
9
550
35
8.8
20
2
10
550
55
8.8
20
2
11
20
35
10.9
20
1
12
550
35
10.9
20
1
13
20
35
8.8
24
1
5. Tests and models of connections
102
Cooling Phase
180
180
160
160
140
140
120
120
Force (kN)
Force (kN)
Heating Phase
100
80
Global - T = 20°C
Global - T = 450°C
Global - T = 550°C
Global - T = 650°C
60
40
100
80
Global - Tf = Tu = 20°C
60
Global - Tf = 20°C - Tu = 600°C
40
20
Global - Tf = 20°C - Tu = 800°C
20
0
0
0
3
6
9
12
15
18
Displacement (mm)
21
24
27
30
0
3
6
9
12
15
18
Displacement (mm)
21
24
27
30
5. Tests and models of connections
103
160
Test - T = 20°C
SAFIR - T = 20°C
Test - T = 450°C
SAFIR - T = 450°C
Test - T = 550°C
SAFIR - T = 550°C
Test - T = 650°C
SAFIR - T = 650°C
140
Force (kN)
120
100
80
60
40
20
0
0
2
4
6
8
10
Rotation (deg)
12
14
16
5. Tests and models of connections
104
200
Test - T = 20°C
SAFIR - T = 20°C
Test - T = 450°C
SAFIR - T = 450°C
Test - T = 550°C
SAFIR - Test = 550°C
Test - T = 650°C
SAFIR - T = 650°C
180
160
Force (kN)
140
120
100
80
60
40
20
0
0
2
4
6
Rotation (deg)
8
10
5. Tests and models of connections
105
300
Bolt Failure (Test)
Vertical displacement [mm] ===>
250
200
150
Bolt Failure (SAFIR)
100
Experimental
50
SAFIR - Bilinear Fibre Model
0
SAFIR - Nonlinear Fibre Model
-50
0
20
40
60
80
Time [min] ===>
100
120
140
160
5. Tests and models of connections
106
Finite restraints
Finite restraints
Finite restraints
Finite
K
K
K
Finite
K restraints
restraints
Finite
K restraints
No Failure
K
Failure Cooling
Failure Heating
18 m
15 m
0.00
0.10
0.20
0.30
0.40
0.50
0.60
Load Ratio (-)
F0
Joint represented
by Nonlinear
Fibres Model
F0
F0
F0
F0
F0
F0
F0
F0
F0
F0
F0
F0
F0
F0
F0
F0
F0
F0
F0
F0
F0
F0
F0
F0
5. Tests and models of connections
107



Component-based models and material laws defined for
the modelling of simple connections under natural fire
Bilinear Fibres Models and Nonlinear Fibres Models
validated against experimental tests and other numerical
simulations (solid models). Differences by the degree of
difficulty, the field of application and the ability to
predict connection failures
Predominent influence of ductility on the occurrence of
connection failures  design procedure proposed.
108
Academic year 2009-2010
6. General Conclusions
109




Proposal of new simple methods for the prediction of temperature in 2Dbeam sections and 3D-joint zones covered by a concrete slab and
calibration on numerical results
Validation against experimental tests performed at the University of
Manchester of a model built in SAFIR for the prediction of internal forces
in axially- and rotationally-restrained beams under fire conditions
Adaptations to the simplified method developed by Yin and Li for
predicting bending moments profiles in axially- and rotationallyrestrained beams during heating and cooling phases of a fire and
extension to joints with a bilinear moment-rotation diagram
Treatment of results of tests performed on bolts and welds under fire.
6. General Conclusions
110




Development of analytical models for bolts (tension or shear) and welds
during the heating and cooling phases of a fire
Definition of two models and material laws for modelling the action of
simple steel connections under natural fire conditions
Definition of failure criteria for connections modelled by Bilinear Fibres
Models and validations against experimental tests and numerical results
obtained with more complex models
Realisation of parametric analyses using the Bilinear Fibres Models for
fin plate, double web cleats and header plate connections and definition
of design procedures to avoid connection failures
6. General Conclusions
111


Development of Nonlinear Fibres Models for fin plate connections and
validation against experimental results of isothermal tests performed on
isolated joints (Sheffield) and a fire test performed on a sub-structure
(Delft)
Application of the Nonlinear Fibres Models to a large-scale steel
structure with fin plate connections
6. General conclusions
112



By use of quite simple methods that does not require FE
models, possibility to predict distribution of temperature in
beams and joints covered by a concrete slab
The use of simplified methods for predicting internal forces
in joints under natural fire is limited to cases where the
behaviour of joints is bilinear and constant
The influence of heating-cooling cycles on the resistance and
the ductility of bolts and welds should be considered (knr,b,min
= 0.6 ; knr,w,min = 0.8)  force-displacement models for bolts
6. General conclusions
113


The action of simple connections in steel structures under
natural fire may be represented by fibre models, able to
predict failures
The ductility of connections has a major influence on the
occurrence of connection failures  classes of ductility
6. General Conclusions
114





Validation of the Heat Exchange Method against experimental results
(beam-slab contact) + protected members
Analysis of the reversibility of deformations in carbon steel elements
subjected to a heating-cooling cycle
Integration of group effects and instability phenomena into numerical
models for connections
Definition of an adimensional fibre element for representing the action
of joints following the Component Method
Extension of this work to composite joints (tests available, models
adapted). Attention should be paid to the concept of collaborating
width)
115
Thank you for your attention !