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A course onFire Design of Steel Structures
Eurocode 1: Actions on StructuresPart 1-2 General actions Actions on
structures exposed to fire
Eurocode 3: Design of Steel StructuresPart 1-2 General rules Structural fire design
Professor Paulo Vila Real
Stockholm, 29 of April 2013
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Introduction
Thermal Actions
Mechanical Actions
Thermal Analysis
Mechanical Analysis
Case Study
Scope
In all these topics the software for fire design of steel structural
members, Elefir-EN, will be used
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Introduction
Used Eurocodes in this course
Ambient temperature design
EN 1990 Basis of structural design
EN 1991-1-1-3, 4, 5 Actions on structures - General actions - Densities,
self-weight, imposed loads for buildings, Snow loads,
Wind loads, Thermal actions
EN 1993-1-1 Design of steel structures
General rules and rules for buildings
EN 1993-1-4 Design of steel structures
Supplementary rules for stainless steels
EN 1993-1-5 Design of steel structuresPlated structural elements
Fire design
EN 1990 Basis of structural design
EN 1991-1-2 Actions on structures exposed to fire
EN 1993-1-2 Design of steel structures Structural fire design
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Each country has its own regulations for fire safety of buildings
where the requirements for fire resistance are given
Standards for checking the structural fire resistance of the
buildings - in Europe the structural EUROCODES
Introduction
Two type of regulations or standards
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Introduction - Fire Resistance
Criteria R, E and I Example: UK Approved document B
R
E
I
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Introduction
Fire Resistance
Classif ication criteria
RER Load REILoad Load
heat hea
t
flames
flames
hotgases
hotgases
- Load bearing only: mechanical resistance (criterion R)
- Load bearing and seprarting: criteria R, E and when requested, I
R Load bearing criterion; E Integrity criterion; I Insulation criterion
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Introduction
Standard Fire Resistance Criteria R, E and I
Standard fire curve
Fire resistance is the time since the begining of the standard fire curve ISO 834
until the moment that the element doesnt fulfi ll the functions for what it has been
designed (Load bearing and/or separating functions)
2018log345 10 tT
Curva ISO 834
0
200
400
600
800
1000
1200
0 20 40 60 80 100 120
min
C
ISO 834 curve
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Introduction
Regulations for f ire safety of buildings
Normally the risk factors are:
Height of the last occupied storey in the building (h) over the reference
plane
Number of storeys below the reference plane (n)
Total gross floor area
Number of occupants (effective)
h
n
Reference plane
R30, R60, R90, ...
or
REI30, REI60. REI90, ...
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Introduction.
Regulations for fire safety Example: UK Approved document B
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Introduction.
Regulations for fire safety Example: UK Approved document B
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Introduction
The software Elefir-EN supplied with the ECCS Book
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Introduction
The software Elefir-EN supplied with the ECCS Book
800 kN
800 kN
50 kNm
- 50 kNm
Nfi,Ed
M1fi,Ed
M2fi,Ed
Nfi,Ed
Member analysis and continuous beams
AB C
D
qfi,Ed
AB
qfi,Ed
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Mechanicalresponse
+
Thermal
response
Thermal
response
Introduction
The software Elefir-EN supplied with the ECCS Book
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- The load-bearing function is ensured when collapse is prevented duringthe complete duration of the fire including the decay phase or
alternatively during the required period of time under standard fire
exposure.
Introduction
Prescriptive or performance-based approach
or
t
Sandard fire ISO 834
Prescriptive approacht
Natural fire
Performance-based approach
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1. Definition of the thermal loading - EC1
2. Definition of the mechanical loading - EC0 +EC1
3. Calculation of temperature evolution within the structuralmembers - EC3
4. Calculation of the mechanical behaviour of the structure
exposed to fire - EC3
Fire Design of Steel Structures
Four steps
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16
S
G
Q
Fire
W
AC
TIONS
Actions for temperature analysisThermal Action
FIRE
Actions for structural analysis
Mechanical Action
Dead Load GImposed Load QSnow SWind W
Eurocode 1:
Actions on Structures
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17
S
G
Q
Fire
W
AC
TIONS
Actions for temperature analysisThermal Action
FIRE
Eurocode 1:
Actions on Structures
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Thermal actions
Heat transfer at surface of building elements
rnetcnetdnet hhh,,,
Total net heat flux
dneth
,
dneth
,
dneth
,
dneth
,
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Thermal actions
Heat transfer at surface of building elements
Temperature of the fire
compartment
])273()273[( 44, mrmfrneth
)(, mgccneth Convective heat flux
Radiative heat flux
rg
t
or
t
Nominalfire
Naturalfire
Total net heat fluxrnetcnetdnet hhh ,,,
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Prescriptive Rules
(Thermal Actions given
by Nominal Fire)
Performance-Based Code
(Physically based Thermal Actions)
Design Procedures
Actions on Structures Exposed to Fire
EN 1991-1-2 - Prescript ive rules or performance-based approach
t
t
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Actions on Structures Exposed to Fire
EN 1991-1-2 - Prescript ive rules or performance-based approach
Simplified fire models
Nominal fires
Standard fire ISO 834External fire
Hydrocarbon fire
Natural fires
Parametric fire
Localised fire
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Simplified fire models
Nominal Temperature-Time Curve
200
400
600
800
1000
1200
0 1200 2400 3600
Time (s)
Gas temperature (C)
External Fire
Standard Fire
Hydrocarbon Fire
EC3 and EC9 do not use
this external fire curve.
A special Annex B on
both Eurocodes gives
a method forevaluating the heat
transfer to external
steelwork
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Boundary properties
Ceiling height
Opening Area
Fire area
Rate of heat release
Fire load density
Geometry
Fire
List of Physical Parameters needed for
Natural Fire Model
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Fire resistant enclosuresdefining the fire compartment
according to the national regulations
Material properties of
enclosures: c
Definition of openings
Characteristics of the Fire Compartment
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OccupancyFire Growth
Rate
RHRf
[kW/m]
Fire Load qf,k80% fractile
[MJ/m]
Dwelling Medium 250 948
Hospital (room) Medium 250 280
Hotel (room) Medium 250 377
Library Fast 500 1824
Office Medium 250 511
School Medium 250 347
Shopping Centre Fast 250 730
Theatre (movie/cinema) Fast 500 365
Transport (public space) Slow 250 122
Characteristics of the Fire Load from EN 1991-1-2
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Design value of the fire load density
[MJ/m2
]nqqk,fd,f mqq 21
10921
10
1
nnnn
i
nin
m Combustion factor. Its value is between 0 and 1. For mainly cellulosic
materials a value of 0.8 may be taken. Conservatively a value of 1 can be
used
q1 factor taking into account the fire activation risk due to the size of thecompartment
q2 factor taking into account the fire activation risk due to the type ofoccupancy
n factor taking into account the different fire fighting measures
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Fire Load DensityFire Load Density
1,90
2,00
2,13
Danger ofFire Act ivation
Compartment
floor area Af [m]
1,50
1,1025
250
2500
5000
10000
q10,78
1,00
1,22
1,44
1,66
Danger ofFire Act ivationq2
Examples
ofOccupancies
Art gallery, museum,
swimming pool
Residence, hotel, office
Manufactory for machinery& engines
Chemical laboratory,
Painting workshopManufactory of f ireworks
or paints
Automatic
Water
Extinguishing
System
Independent
Water
Supplies
Automatic fi re
Detection
& Alarm
by
Heat
by
Smoke
Automatic
Alarm
Transmission
to
Fire Brigade
Function of Act ive Fire Safety Measuresni
0 1 2
Automatic Fire Suppression Automatic Fire Detect ion
n1 n2 n3 n4 n5
0,61 0,87 or 0,73 0,871,0 0,87 0,7
Work
Fire
Brigade
Off Site
Fire
Brigade
Safe
Access
Routes
Fire
Fighting
Devices
Smoke
Exhaust
System
n10
Manual Fire Suppression
n6
n7
n8
n9
0,61 or 0,780,9 or 1
1,5
1,0
1,5
1,0
1,5
Characteristics of the Fire Load from EN 1991-1-2
k,fni2q1qd,f q.m...q
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RHR [MW]
Time [min]0 tdecay
70% (qf,d Afi)Decay phase
Rate of Heat Release Curve from EN 1991-1-2
Characteristics of the Fire Load
2
tt)t(Q
Qmax = Afi x RHRf
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Demonstration of real fire tests in car parks and high buildings Contract no. 7215 PP 025, Projecto Europeu
Car of class 3
Rate of Heat Release of a class 3 car.
Experimental evaluation: Natural Fire Model
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An idealized Rate of Heat Release Curve for a car burning
Characteristics of the Fire Load
30
Curve of the rate of heat release of one car
from ECSC Project: Demonstration of real fire tests in car parks and
high buildings.
Note: This curve can be introduced in Elefir-EN as an user defined RHR curve
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Annex C of EN 1991-1-2:
Flame is not impacting the ceiling of a compartment (Lf< H) Fires in open air
The flame length Lfof a
localised fire is given by :
Flame axis
L
z D
f
H
(z) = 20 + 0,25 (0,8 Qc)2/3 (z-z0)-5/3 900C
Lf = -1,02 D + 0,0148 Q2/5
Localised Fire:
HESKESTAD Method
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Annex C of EN 1991-1-2: Flame is impacting the ceiling (Lf> H)
Localised Fire:
HASEMI Method
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Fire load density -
Opening factor -
Wall factor -
- area of vertical openings; - total area of enclosure
Limitations :
Afloor 500 m
No horizontal openings
H 4 m
Wall factor from 1000to 2200
Fire load density, qt,d from 50 to 1000 MJ/m
dfq ,
tv AhAO /
cb
tAvA
Parametric fire
Needed parameters
Temperature = (t)
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Annex A of EN 1991-1-2
Parametric fire curves function of - O
For a given qf,d, b, At and Af
0
200
400
600
800
1000
0 10 20 30 40 50 60 70 80 90 100 110
[min]
[ C]
2/102.0 mO
2/106.0 mO
2/11.0 mO
2/114.0 mO
2/120.0 mO
2/105.0 mO
2/107.0 mO
Ventilation controlled fires Fuel controlled fires
Fully Engulfed Compartment
Parametric Fire
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Office
Af = 45,0 m2
O = 0,08 m1/2
qf,k = 511 MJ/m2
m = 0,8
Fully Engulfed Compartment
Parametric Fire - Influence of the Actives Fire Safety Measures
Time [min]
No Fire Active Measures
Off Site Fire Brigade
Safe access routes
Automatic Fi re Detect ion & Alarm by Smoke
Fire fighting devices
Automat ic water ext inguishing system - Spr inklers
Automatic alarm transmission to fi re br igade
qf,d (MJ/m2) 1567 815 397 210
1567 = 511x0,8x1,14x1x
1x1x1x1x1x1x1x1,5x1,5x1,5
815 = 511x0,8x1,14x1x
1x1x1x1x1x1x0,78x1x1,5x1,5
397 = 511x0,8x1,14x1x
1x1x1x0,73x1x1x0,78x1x1x1,5
210 = 511x0,8x1,14x1x
0,61x1x1x0,73x0,87x1x0,78x1x1,5x1,5
Influncia das protec es activas
0
200
400
600
800
1000
1200
1400
0 10 20 30 40 50 60 70 80
Tempo (min)
Temperatura(C)
k,fi
niq1d,f qmq = q2
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Time-temperature curves
Worked examples with the software Elefir-EN
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Compartment fire
Nominal curves
- Standard temperature-time curve ISO 834
- Hydrocarbon temperature-time curve
Parametric fire curve
Localised fire
Hasemi method
Heskestad method
User defined curve
Time-temperature curves
Worked examples with the software Elefir-EN
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Nominal Time-temperature curves
Worked examples with the software Elefir-EN
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Gas temperature. Examples with the software Elefir-EN
Standard f ire curve ISO 834 and Hydrocarbon Fire
Standard fire ISO 834
Hydrocarbon fire
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Gas temperature. Examples with the software Elefir-EN
Parametric fire curve
Example 3.3 from the ECCS Book: calculate and plot the
parametric time temperature curve for a bedroom in a hotel. Theplan view is rectangular with dimensions of 3.2 m by 6.4 m. The
floor to ceiling distance is 2.60 m. The floor and the ceiling are
made of normal weight concrete while the walls are made of
normal weight concrete covered by a 12.6 mm thick layer ofgypsum. The only opening is a door of size 1.10 m by 2.20 m.
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Gas temperature. Examples with the software Elefir-EN
Parametric fire curve
Normal weight concreteUnit mass = 2300 Kg/m3
Conductivity = 1.6 W/mK
Specific heat = 1000 J/KgK
b = 1918 J/(m2s1/2K)
Gypsum
Unit mass = = 1150 Kg/m3Conductivity = = 0.485 W/mKSpecific heat = c = 1000 J/KgKb = 749 J/(m2s1/2K)
Material of boundaries:
cb
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Hotel room
q f,d = 377 MJ/m (no active fire fighting measures)
Medium (20 min.)
Af = 3.2 x 6.4 = 20.48 m
At = 90.88 m2
H = 2.6 m
h x b = 1.1 x 2.2 m2
heq = 1.1 m
Av = 2.42 mO = 0.0395 m1/2
b = 1290 J/m2s0.5K
Building type:
Fire load:
Fire growth rate:
Floor area:
Total area:Height:
One opening:
Average window height:
Area of vertical openings:Vertical opening factor:
Wall factor:
Gas temperature. Examples with the software Elefir-EN
Parametric fire curve - parameters
teqv A/hAO
AvhAhi
ivieq
iiiA/Abb
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t,d f,d f tq q A A
where
0,43 h < tlim
= 0,333 h fuel controlled
0,43 h > tlim = 0,333 h ventilation controlled
0,2 10-3 qt,d / O = 0,43 h
Gas temperature. Examples with the software Elefir-EN
Fuel or venti lation controlled?
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0.2 t* 1.7 t* 19 t*g 20 1325 1 0.324 e 0.204 e 0.472 e
t* t
2
2O b
0.04 1160
Calculation of the heating curve:
where:
Gas temperature. Examples with the software Elefir-EN
Heating curve
heating curve
tmax
max
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3
t,d
max
lim
0.2 10 q O
t t max t
The maximum temperature is needed for determining
the cooling curve:
Gas temperature. Examples with the software Elefir-EN
Maximum temperature
heating curve
tmax
max
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t* t
3max t,dt * 0.2 10 q O
g max max625 t * t * x
where
If fire is ventilation controlled: x = 1.0
If fire is fuel controlled: x = tlim / t*max
Calculation of the cooling curve:
Gas temperature. Examples with the software Elefir-EN
Cooling curve
cooling curve
tmax
max
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Gas temperature. Examples with the software Elefir-EN
Parametric fire curve
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Gas temperature. Examples with the software Elefir-EN
Parametric fire curve
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Gas temperature. Examples with the software Elefir-EN
Parametric fire curve
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Gas temperature. Examples with the software Elefir-EN
Parametric fire curve
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Gas temperature. Examples with the software Elefir-EN
Parametric fire curve
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Gas temperature. Examples with the software Elefir-EN
Parametric fire curve
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Determination of the gas temperatures at the level of the
ceiling exposed to a localized fire in a library. Natural firemodel for localised fires
EN 1991-1-2: Annex C
Localised fire
Task
Heskestad Method Hasemi Method
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Library
H = 3.0 m
Afi = 72 m2
m = 0.8
Building
Type:
Height:Fire area:
Combustion factor:
Localised fire
Parameters
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Localised fire
Example with the software Elefir-EN
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Localised fireExample with the software Elefir-EN
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Localised fireResults from Elefir-EN
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RHR
Flame legth
Temperature
Localised fireResults from Elefir-EN
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Development of the fire area
Development of the diameter
Localised fireResults from Elefir-EN
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Example B.1 from ECCS Book: calculate the evolution of the
rate of heat release and flame length of a localised fire in a
ticket counter that has an area of 36 m. It is assumed that theflame does not touch the ceiling.
Consider that :
- the ticket counter is considered as a library
- the fire load is is mainly cellulosic (m = 0.8)
- the height of the compartment is H = 6 m
Active fire fighting measures:
- automatic fire detection and alarm by smoke- off site fire brigade but no work fire brigade
- safe access routes
- normal fire fighting devices
- no staircases and, thus, no requirement of an air exhaust system
Localised fireExample with the software Elefir-EN
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Localised fireExample with the software Elefir-EN
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Localised fireExample with the software Elefir-EN
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Localised fireExample with the software Elefir-EN
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RHR
Flame legth
Temperature
Localised fireResults from Elefir-EN
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Development of the fire area
Development of the diameter
Localised fireResults from Elefir-EN
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Localised fireExample with the software Elefir-EN
Example B.2 from ECCS Book: modify the RHR curve of previous
example if the fire described in Example B.1 occurs in a compartment
with five windows of 2 meters wide and 1 meter high.
21025 mAv
21mAvhAh
i
ivieq
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Localised fireExample with the software Elefir-EN
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User defined curveExample with the software Elefir-EN
Suppose that a temperature-time curve was obtained from another software or
that the data have been obtained from a real fire. It is possible to use this
curve with the software Elefir-EN.In this example the temperature-time curve was obtained with the software OZone
V2.2 and it was copied to a text file to be read by Elefir-EN:
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User defined curveExample with the software Elefir-EN
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User defined curveResults from Elefir-EN
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1. Definition of the thermal loading - EC1
2. Definition of the mechanical loading - EC0 +EC1
3. Calculation of temperature evolution within the structuralmembers - EC3
4. Calculation of the mechanical behaviour of the structureexposed to fire - EC3
Fire Design of Steel StructuresFour steps
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72
S
G
Q
Fire
W
ACT
IONS
Actions for temperature analysisThermal Action
FIRE
Actions for structural analysisMechanical Action
Dead Load GImposed Load QSnow S
Wind W
Actions on Structures
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S
G
Q
Fire
W
ACT
IONS
Actions for temperature analysisThermal Action
FIRE
Actions for structural analysisMechanical Action
Dead Load GImposed Load QSnow S
Wind W
Actions on Structures
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74
At room temperature (20 C)
1. Fire is an accidental action.2. The simultaneous occurrence of other independent
accidental actions need not be considered
1,1 Qk,1 Frequent value of the representative value of the variable action Q12,1 Qk,1 Quasi-permanent value of the representative value of the variable act ion Q1A
d
Indirect thermal action due to fire induced by the restrained thermal expansion
may be neglected for member analysis
In fire situation
1
,,01,1,1,1
,,i
ikiQkQj
jkjG QQG
di
ikikj
k AQQG 1,,21,1,21,1
11, )ou(
Combination Rules for Mechanical ActionsEN 1990: Basis of Structural Design
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Action 1 2Imposed loads in buildings, category
(see EN 1991-1-1)0.5 0.3
Imposed loads in congregation
areas and shopping areas0.7 0.6
Imposed loads in storage areas 0.9 0.8
vehicle weight 30 kN 0.7 0.630 kN vehicle weight 160 kN 0.5 0.3Imposed loads in roofs 0.0 0.0
Snow (Norway, Sweden ) 0.2 0.0
Wind loads on bui ldings 0.2 0.0
The Norwegian Annex
recommends 1,Q1,only when the wind isthe dominant action and
the Swedish Annex
recommends 1,Q1 forall dominant variable
actions. In bothCountries wind is
always considered and
so horizontal actions are
always taken into
account
di
ikikj
k AQQG
1,,21,1,21,1
11,
)ou(
Combination Rules for Mechanical ActionsEN 1990: Basis of Structural Design
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0.2W1.0G + 0.3Q
1.0G + 0.3Q
1.0G + 0.3Q
1.0G + 0.3Q
1.0G + 0.3Q
1.0G + 0.3Q
1.0G + 0.3Q
1.0G + 0.3Q
0N0N
1.0G + 0.3Q
1.0G + 0.3Q
1.0G + 0.3Q
1.0G + 0.3Q
1.0G + 0.3Q
1.0G + 0.3Q
1.0G + 0.3Q
1.0G + 0.3Q
Fire situation
Combination Rules for Mechanical ActionsEN 1990: Basis of Structural Design
ii212,1dfi, QQGE
ii211,1dfi, QQGE
Efi,d = G + 0,2 W + 0,3 Q Efi,d = G + 0,0 W + 0,3 Q
Representative value of the variable action : wind
or
ii212,11,1dfi, Q)Qor(GE
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The effect of actions
can be obtained from:
dfidfi EE
,
whereLoad combination in fire situation
Load combination at 20 C
Design value of the
effect of actionsat normal temperature
1,1,
1,1,1
kQkG
kkGAfi
QGQG
di ikikj k
AQQG
1 ,,21,1,21,11 1,
)ou(
Instead of using:
as a simplification can be taken as 0.65
Member analysisSimplified rule
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78
5m
Characteristic loading (kN/m):
Permanent Gk = 11.82
Variablel Qk,1= 22.8
- At normal temperature
G Gk + Q.1 Q1 = 1.35x11.82 + 1.5x22.8 = 50.16 kN/mDesign value of the moment at 20 C:
MEd = 50.16x52/8
= 156.75 kNm
- In fire situation
Gk +1.1 Q1 = 11.82 + 0.5x22.8 = 23.22 kN/mDesign value of the moment in fi re situation:
Mfi,Ed = 23.22x52/8
= 72.6 kNmMfi.Ed = fi MEd
=0.463 x 156.75 = 72.6 kNm
fi =23.22 / 50.16 = 0.463
EC3fi =0.65
or
Actions on StructuresExample: Office building
On the
safe
side
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1. Definition of the thermal loading - EC1
2. Definition of the mechanical loading - EC0 +EC1
3. Calculation of temperature evolution within the structuralmembers - EC3
4. Calculation of the mechanical behaviour of the structureexposed to fire - EC3
Fire Design of Steel StructuresFour steps
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80
Heat conduction equation
tcQ
yyxx p
)( cc hq
)()())(()(2244
r ara
h
aaa hqr
convection
radiation
Boundary conditions
Thermal response
Note: this equation can be simplified for the case of current steel profiles
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Thermal properties of carbon steel and stainless steel
0
10
20
30
40
50
60
0 200 400 600 800 1000 1200
(C)
a (W/mK)Stainless steel
Carbon s teel
0
1000
2000
3000
4000
5000
0 200 400 600 800 1000 1200
(C)
Ca (J/kgK)
Carbon s teel
Stainless s teel
Thermal conductivity (W/mK) Specific Heat (J/kgK)
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Temperature increase in time step t:
448
27327310675
mrmfr,net x,h
Heat flux has 2 parts:
Radiation:
mgcc,net
h
Convection:
Steel
temperature
Steel
Fire
temperature
Temperature increase of unprotected steelSimplified equation of EC3
thc
VAk d,netaa
msht.a
d,neth
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83
perimeter
c/s area
exposed perimeter
c/s area
h
b
2(b+h)
c/s area
thc
VAk d,netaa
msht.a
Section factor Am/VUnprotected steel members
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c/s area
b
2(b+h)
h
c/s area
h
2h+b
b
bm V][ A - Section factor as the profile has a hollow encasement fire protection
For I-sections under nominal fire: ksh = 0.9 [Am/V]b/[Am/V]
In all other cases: ksh = [Am/V]b/[Am/V]
For cross-sections convex shape: ksh = 1
Correction factor for theShadow effect ksh
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85
Structural fire protection
Passive Protection
Insulating BoardGypsum, Mineral fibre, Vermiculite.
Easy to apply, aesthetically acceptable.
Difficulties with complex details.
Cementitious Sprays
Mineral fibre or vermiculite in cement binder.
Cheap to apply, but messy; clean-up may be expensive.
Poor aesthetics; normally used behind suspended ceilings.
Intumescent Paints
Decorative finish under normal conditions.
Expands on heating to produce insulating layer.
Can be done off-site.
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86
Structural fire protection
Columns:
Beams:
St t l fi t ti
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Structural fire protectionIntumescent paint
St t l fi t ti
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Structural fire protectionCementitious Sprays
St t l fi t ti
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89
Structural fire protectionInsulating Board
Temperature increase of protected steel
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90
Steeltemperature
Steel
Protection
Fire
temperature
dp
Some heat stored in
protection layer.
V
Ad
c
cpp
aa
pp
Heat stored in protection layer
relative to heat stored in steel
t.g/t.at.gp
aa
ppt.a et
/V
A
c
d/
1
31
1 10
Temperature rise of steel in t ime
increment t
Temperature increase of protected steelSimplified equation of EC3
Section factor Ap/V
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h
b
t.g/
t.at.g
p
aa
pp
t.aet
/V
A
c
d/
1
31
1 10
Section factor Ap/VProtected steel members
Steel perimeter
steel c/s area
2(b+h)
c/s area
inner perimeter
of board
steel c/s area
Moist fire protection materials
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92
Moist fire protection materialsEffect of the moisture content
ISO834
Temp (C)
0Time (min)
crit
30 60 90
Time delay tv in the rise of
steel temperature when itreaches 100 C.
p
pp
v
dpt
5
2
p = moisture content in %
With moisture content
tv
100 C
Temperature development in protected and unprotected steel
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93
Temperature development in protected and unprotected steelWorked examples with the software Elefir-EN
Temperature development in protected and unprotected steel
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94
Temperature development in protected and unprotected steelWorked examples
Example 4.1 from ECCS Book: What is the temperature of an
unprotected rectangular bar with a cross-section of 200 x 50 mm2after 30 minutes of standard fire exposure on four sides?
15005020
0502022
m..
)..(
tb
)tb(V/Am
1shk
1-m505001 .]/[ VAk msh
Answer:As rectangular solid sections are not in the data base of the
software Elefir-EN the section factor must be evaluated first:
Temperature development in protected and unprotected steel
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95
Temperature development in protected and unprotected steelWorked examples
Other
Temperature development in protected and unprotected steel
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96
Temperature development in protected and unprotected steelWorked examples
Temperature development in protected and unprotected steelW k d l
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97
Temperature development in protected and unprotected steelWorked examples
Other
Temperature development in protected and unprotected steelW k d l
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98
e pe a u e de e op e p o ec ed a d u p o ec ed s eeWorked examples
Temperature development in protected and unprotected steelW k d l
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99
p p p pWorked examples
Example 4.2 from ECCS Book: What is the temperature of an
unprotected circular hollow section with a diameter of d = 220 mmand a thickness of t = 5 mm after 60 minutes of standard fire curve
exposure?
d
t
Temperature development in protected and unprotected steelWorked examples
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100
p p p pWorked examples
Other
Temperature development in protected and unprotected steelWorked examples
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101
p p p pWorked examples
Temperature development in protected and unprotected steelWorked examples
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102
Worked examples
Temperature development in protected and unprotected steelWorked examples
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103
Worked examples
Example 4.3 from ECCS Book: What is the temperature of an
unprotected HE 200 A profile after 30 minutes of standard firecurve exposure on four sides?
Temperature development in protected and unprotected steelWorked examples
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104
Worked examples
Temperature development in protected and unprotected steelWorked examples
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105
Worked examples
Temperature development in protected and unprotected steelWorked examples
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106
Worked examples
Example 4.4 from ECCS Book: What would be the thickness of
fibre-cement board encasement for a IPE 300 heated on threesides to be classified as R90 if the critical temperature is 654 C?
Temperature development in protected and unprotected steelWorked examples
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107
p
Temperature development in protected and unprotected steelWorked examples
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108
p
Temperature development in protected and unprotected steelWorked examples
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109
Temperature development in protected and unprotected steelWorked examples
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110
Example 4.5 from ECCS Book: How much time is needed for a column
of HE220B protected with gypsum board encasement with 20 mm ofthickness to reach the temperature of 559 C when heated by the
standard fire curve on four sides?
Temperature development in protected and unprotected steelWorked examples
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111
Temperature development in protected and unprotected steelWorked examples
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112
Temperature development in protected and unprotected steelWorked examples
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113
Temperature development in protected and unprotected steelWorked examples
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114
Temperature development in protected and unprotected steelWorked examples
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115
Temperature development in protected and unprotected steelWorked examples
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116
Temperature development in protected and unprotected steelWorked examples
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117
Right -clicking on the chart the
temperature-time curves can be
copied to be used in another
program, for instance with theExcel
Temperature development in protected and unprotected steelWorked examples
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118
Data obtained with the program Elefir-EN and chart made with Excel
0
200
400
600
800
1000
1200
0 20 40 60 80 100 120
Time [min.]
Temperat
ure[C]
ISO 834
Without moisture
content
With moisture content
Critical temp. 559 C
Effect of the moisture content in the temperature of the HE 220 B
Temperature development in protected and unprotected steelWorked examples
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119
Example from section 4.11.1 from ECCS Book: What is the
temperature of the unprotected circular hollow section of Example 4.2after 60 minutes of standard fire curve exposure if it is made of
stainless steel?
Temperature development in protected and unprotected steelWorked examples
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120
Temperature development in protected and unprotected steelWorked examples
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121
Temperature development in protected and unprotected steelWorked examples
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122
Localised fireTask
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123
Determination of the gas temperatures at the level of the
ceiling exposed to fire by burning cars and the temperature
of an IPE 500 using natural fire model for localised fires
EN 1991-1-2: Annex C
Heskestad Method Hasemi Method
Localised fires in a car parkFive fire scenarios
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124
H = 2.7 mD = 2.0 m
IPE 500
Height:Diameter of flame:
Steel Beams:
Fire Scenario 1
Fire Scenario 2 Fire Scenario 4
20 x 2.40 m
16.00 m
START
Fire Scenario 3
START
START
Fire Scenario 5
START
Most severe scenario
Localised fire
Two fire scenarios. Horizontal distance
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125r = 0.0 m
Horizontal distance
from flame axis to beam: r1 = r2 = 5.63 m
r3 = 6.57 m
Horizontal distance
from flame axis to beam:
Scenario 1 Scenario 2
2
2
2
1 ddr
i
r1r2r3
XX16 m
5 m
3rd 1st2nd
d1
d2ir
Localised fire
Rate of heat release
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126
Curve of the rate of heat release of one car
from ECSC Project: Demonstration of real fire tests in car parks and
high buildings.
Localised fire
Rate of heat release of three cars
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127
Curve of the rate of heat release of each car
1st 2nd 3rd
from ECSC Project: Demostration of real fire tests in car parks and
high buildings.
Localised fire
Flame length
Heskestad Method
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128
if Lr H Hasemi method has to be used
if Lr< H Heskestad method has to be used
0
1
2
3
4
5
6
7
Height[m]
0 10 20 30 40 50 60 70
Time[min]
Flame Length
Ceiling (H)
Hasemi Method
Localised fire
Example with the software Elefir-EN
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129
Localised fire
Example with the software Elefir-EN
Scenario 1
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130
Localised fire
Example with the software Elefir-EN
Scenario 1
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131
Localised fire
Results from Elefir-EN
Scenario 1
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132
Localised fire
Example with the software Elefir-EN
Scenario 2
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133
Scenario 2
Localised fire
Example with the software Elefir-EN
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134
Scenario 2
Localised fire
Results from Elefir-EN
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135
Scenario 2
Localised fire
Results from Elefir-EN
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136
Scenario 2
Localised fire
Results from Elefir-EN
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137
Fire Design of Steel Structures
Four Steps
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1. Definition of the thermal loading - EC1
2. Definition of the mechanical loading - EC0 +EC1
3. Calculation of temperature evolution within the structural
members - EC3
4. Calculation of the mechanical behaviour of the structureexposed to fire - EC3
Degree of simplif ication of the structure
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139
Analysis of: a) Global structure; b) Parts of the structure; c) Members
a) b)
c)
a) b)
c)
Stress (N/mm2)
Mechanical properties of carbon steel
Stress-strain relationship at elevated temperatures
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140Strain (%)
0.5 1.0 1.5 2.00
300
250
200
150
100
50
20C
200C300C
400C
500C
600C
700C
800C
Steel softens progressively
from 100-200C up.
Only 23% of ambient-
temperature strength
remains at 700C.
At 800C strength reduced
to 11% and at 900C to
6%.
Melts at about 1500C.
Mechanical properties of carbon steel
Stress-strain relationship at elevated temperatures
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141
Strain
Stress
E = tan a,
y,p, u,
fy,
fp,
t,
= 2% = 15% = 20%
St th/ tiff d ti
Stress (N/mm2)
30020C
Mechanical properties of carbon steel
Stress-strain relationship at elevated temperatures
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142
Strength/stiffness reduction
factors for elastic modulusand yield strength (2% total
strain).
Strain (%)0.5 1.0 1.5 2.00
300
250
200
150
100
50
20C
200C300C
400C
500C
600C
700C
800C
Elastic modulus at 600Creduced by about 70%.
Yield strength at 600C
reduced by over 50%.
f f
% of the value at 20 C
Reduction factors for stress-strain relationship of carbon steel
at elevated temperatures
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143
yyy ffk /,,
Yield Strength
Reduction factor for
yield strength andYoung modulus of
carbon steel
0 300 600 900 1200
1
.8
.6
.4
.2
Temperature (C)
Young Modulus
aaE EEk /,,
Reduction factors for stress-strain relationship of carbon steel
at elevated temperatures
Reduction factors at temperature a relative to the value of fy or Ea
at 20C
Steel Reduction factor Reduction factor Reduction factor
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144
Temperature
a
(relative tofy)for effective yield
strength
ky, = fy,/fy
(relative tofy)for proportional limit
kp, = fp,/fy
(relative toEa)for the slope of thelinear elastic range
kE, = Ea,/Ea
20C 1,000 1,000 1,000
100C 1,000 1,000 1,000
200C 1,000 0,807 0,900
300C 1,000 0,613 0,800
400C 1,000 0,420 0,700
500C 0,780 0,360 0,600
600C 0,470 0,180 0,310
700C 0,230 0,075 0,130
800C 0,110 0,050 0,090
900C 0,060 0,0375 0,0675
1000C 0,040 0,0250 0,0450
1100C 0,020 0,0125 0,0225
1200C 0,000 0,0000 0,0000
*
* This opt ion is never used in the calculations with Elefir-EN. It wasincluded just as an aid for the users.
Annex C of EN 1993-1-2
Mechanical properties of stainless steel
Stress-strain relationship at elevated temperatures
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145
20 C
300
(MPa) Stainless steelCarbon steel
20 C
300
(MPa) Stainless steelCarbon steel
S235 vs. 1.4301 (or 304)
Mechanical properties of carbon and stainless steel
Stress-strain relationship at room and at elevated temperature
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146
0
50
100
150
200
250
0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02
235
210
(0.2%)
0
50
100
150
200
250
0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02
235
210
(0.2%)
600 C
0
20
40
60
80
100
120
140
160
0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02
(MPa) Stainless steelCarbon steel
146.6
110.5
(2.0%)
600 C
0
20
40
60
80
100
120
140
160
0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02
(MPa) Stainless steelCarbon steel
146.6
110.5
(2.0%)
( )
Reduction factors of yield strength
Reduction factors of carbon steel and stainless steel
at elevated temperatures
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147
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
0 200 400 600 800 1000 1200
(C)
ky,Grade 1.4301
Grade 1.4401/1.4404
Grade 1.4003Grade 1.4571
Grade 1.4462
Carbon Steel
0.0
0.2
0.4
0.6
0.8
1.0
0 200 400 600 800 1000 1200
(C)
kE,
Stainless steel
Carbon steel
Reduction factors of Young
modulus
Checking Fire Resistance:
Strategies
Procedure usually adopted
with advanced calculationEurocodes allow fire
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148
with advanced calculation
models but also used with
simple EC3 method. Find
design time (time for
collapse) and compare with
required time.
Find reduced resistance at
design temperature for the
required time and compare
with the effect of the actions.
Most usual simple EC3
method. Find critical
temperature for loading,
compare with design
temperature at required time.
resistance to be establishedin any of 3 domains :
Time: tfi,d > tfi,requ
Load resistance: Rfi,d,t > Efi,d,t
Temperature: cr,d >d
R E,
Checking Fire Resistance:
Strategies with nominal fires
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149
1. Time:
tfi,d > t fi,requ
2. Load resistance:
Rfi,d,t > Efi,d
3. Temperature:d cr,d
2
1
3
Rfi,dEfi,d
d
cr,d
tfi,requ tfi,dt
t
1
3
2
R E,1. Load resistance:
Rfi,d,t > Efi,d
Checking Fire Resistance:
Strategies with natural fires
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150
Rfi,d
Efi,d
d
cr,d
t
t
2
1
2. Temperature:
d cr,dcollapse is prevented during the
complete duration of the fire
including the decay phase or
during a required period of time.
collapse is prevented during the
complete duration of the fireincluding the decay phase or
during a required period of time.
Note: With the agreement of authorities,
verification in the time domain can be
performed. The required periodo of t ime
defining the fire resistance must be accepted
by the authorities.
The Load-bearing function is ensured if collapse is prevented during the
Checking Fire Resistance:
Strategies with natural fires
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151
complete duration of the fire including the decay phase, or during a required
period of time.
Rfi,d, t
Efi,d
t
Rfi,d, t
Efi,d
t
R E, R E,
t fi,requ t fi,d1 t fi,requ
2
Collapse is prevented during the
complete duration of the fire
including the decay phase.
Collapse is prevented during a
required period of t ime, t1fi,req.
Checking Fire Resistance using Elefir-EN:
Strategies
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152
Time: tfi,d > t fi,requ
Resistance: Rfi,d,t > Efi,d
Temperature: cr,d >d
Time: t fi,d > t fi,requ
Temperature: cr,d
>d
Checking Fire Resistance using Elefir-EN:
Strategies
Gives cr,d to be used inExample for elements submited to tension
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153
the temperature domain:
cr,d >d
Gives Rfi,d,t
to be used in
the resistance domain:
Rfi,d,t > Efi,d
Gives tfi,d to be used in
the time domain:
tfi,d > t fi,requ
These four options are available for all the load cases
Temperature
Unprotectedd
Checking Fire Resistance in the temperature domain:
Strategy for nominal fires.
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154
time
dcrit
ISO 834
Unprotected
section
Protected
section
crit
d
d
trequ
Temperature Natural
fire
Checking Fire Resistance in the temperature domain:
Strategy for natural f ires
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155mxcrit time
critmx
mx UnprotectedsectionProtected
section
*
* - or using active fire
fighting measures
Temperature
Unprotected
Natural
fire
Checking Fire Resistance in the time domain:
Strategy for natural fires if accepted by the authorit ies
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156trequ t fi,dtime
crit
Unprotected
section
Protected
section
*
* - or using active fire
fighting measures
trequtfi,d t fi,d
T b l t d d t (N t i EC3)
Design procedures
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Tabulated data (Not in EC3)
Simple calculation models
Advanced calculation models
Tabulated data (Not in EC3)
Design procedures
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Tabulated data (Not in EC3)
Simple calculation models
Advanced calculation models
Cross-sections are classified based on the parameter
Classification of the cross-sections - 1
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159
210000235 Efy
For the case of carbon steel at normal temperature the, Young modulus
takes the value 210 GPa:
- At normal temperature
- At elevated temperature
with fy and E in MPa
yf
235
850235850 .f
.y
210000
E
f
235
k
k
210000
Ek
fk
235
210000
E
f
235
yy
,E,E
yyy
Classification of the cross-sections - 2
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160
85.0f
23585.0
f
235
k
k
yy,y
,E
y,yy,y,y
0
0,2
0,4
0,6
0,8
11,2
0 200 400 600 800 1000 1200
[C]
,
,
y
E
k
k
0,85
yf.
235850
Classification of the cross-sections - 3For carbon steel:
and tables from EN 1993-1-1
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161
Element Class 1 Class 2 Class 3
Flange c / t =9 c / t=10 c / t=14
Web subjected
to
compression
d / t=33 d / t=38 d / t=42
Web subectedtobending
d / t=72 d / t=83 d / t=124
For stainless steel:
210000
235850
E
f.
y
and tables from EN 1993-1-4
Fire Resistance:
Safety factors
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162
1
.8
% of the value at 20 CFactor de
reduo
Fire Resistance:
Tension members - 1
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163
]/[NkN fi,MMRd,yRd,,fi 0
NRd = design resistance of the cross-section Npl,Rdfor normal temperature design
The design resistance of a tensionmember with uniform temperature ais:
0 300 600 900 1200
.8
.6
.4
.2
Temperature (C)
yyy ffk /,,
or
fi,My,yRd,,fi /AfkN
Fire Resistance:
Tension members - 2
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164
y,yfiRd,,fi,b fAkN
1 Design buckling resistance of a
compression member with uniform
temperature a is
Fire Resistance:
Compression members with Class 1, 2 or 3 cross-sections - 1
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165
fi,M
Bracing system
lfi=0,7L
lfi=0,5L
,, / Ey kk
Non.dimensional slenderness:
22
1
fi
2121
With
yf/23565.0 (Curves a, b, c, d, a0)
Fire Resistance:
Compression members with Class 1, 2 or 3 cross-sections - 2
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166
The design moment
Fire Resistance: Laterally restrained beams with Class 1, 2
or3 cross-sections with uniform temperature - 1
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167
g
resistance of a Class 1, 2 or
Class 3 cross-section with a
uniform temperature a is:
fi,M
M,yRdRd,,fi kMM
0
MRd = Mpl,Rd Class 1 or 2 cross-sections
MRd = Mel,Rd Class 3 cross-sections
Adaptation factors to take into account
the non-uniform temperature distribution
Fire Resistance: Laterally restrained beams with Class 1, 2
or 3 cross-sections with non-uniform temperature - 2
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168
Temp
Moment Resistance:
21
0 1
fi,M
M,yRdRd,,fi kMM
1=1,0 for a beam exposed on all four sides
1=0,7 for an unprotected beam exposed on three sides
1=0,85 for a protected beam exposed on three sides
1 is an adaptation factor for non-uniformtemperature across the cross-section
Adaptation factores to take into account
the non-uniform temperature distribution
Fire Resistance: Laterally restrained beams with Class 1, 2
or 3 cross-sections with non-uniform temperature - 3
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169
Temp TempTemp
21
0 1
fi,M
M,yRdRd,,fi kMM
2=0,85 at the supports of a statically indeterminate beam
2 is an adaptation factor for non-uniform temperature alongthe beam.
Moment Resistance:
2=1.0 in all other cases
Fire Resistance: Laterally restrained beams with Class 1, 2
or 3 cross-sections with non-uniform temperature - 4
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170
Fire Resistance: Laterally restrained beams with Class 1, 2
or 3 cross-sections with non-uniform temperature - 5
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171
Fire Resistance: Laterally unrestrained beams with Class 1, 2 or
3 cross-sections - 1Fixed
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172
Lateral-torsional buckling
Unloaded position
Applied load
Buckled position
lfiLTRdfib fkWM1
Design lateral torsional buckling
resistance moment of a laterally
unrestrained beam at the max.
y,elW (if Class 3)
Fire Resistance: Laterally unrestrained beams with Class 1, 2 or
3 cross-sections - 2
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173
fi.Mycom..yy.plfi.LTRd..fi.b fkWM temp. in the comp. flange a.com is
com..Ecom..yLTcom..LT k/k
LT.fi the reduction factor for lateral-
torsional buckling in the fire designsituation.
2
,,
2
,,,,
,
][][
1
comLTcomLTcomLT
fiLT
2,,,,,, )(12
1comLTcomLTcomLT
yf/23565.0
(Curves a, b, c, d)cr
yypl
LTM
fW ,
Fire Resistance: Laterally unrestrained beams with Class 1, 2 or
3 cross-sections - 3
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174
Fire Resistance: Laterally unrestrained beams with Class 1, 2 or
3 cross-sections - 4
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175
Fire Resistance: Laterally unrestrained beams with Class 1, 2 or
3 cross-sections - 5
gg
z
tz
z
w
w
z
z
zcr zC)zC(
EI
GI)Lk(
I
I
k
k
)Lk(
EICM 2
222
22
2
2
1
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176
Elefir-EN can behelpful to find the
elastic critical
moment to be used
also with EC31-1, if
needed.
Design shear resistance
MRdwebyRdtfi VkV 0
Fire Resistance: Shear Resistance
Beams with Class 1, 2 or 3 cross-sections - 1
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177
fi,M
,MRdweb,,yRd,t,fi VkV 0
VRd is the shear resistance of the gross cross-section
for normal temperature design, according to EN 1993-1-1.
web is the average temperature in the web of thesection.
ky,,web is the reduction factor for the yield strength of steelat the steel temperature web.
Fire Resistance: Shear Resistance
Beams with Class 1, 2 or 3 cross-sections - 2
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178
Fire Resistance: Shear Resistance
Beams with Class 1, 2 or 3 cross-sections - 3
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179
Fire Resistance: Shear and bending
Beams with Class 1, 2 or 3 cross-sections - 1
Rd,t,fiEd,fi V.V 50
The effect of the applied shear force on the moment resistance of the section
can be neglected when the shear force is less than half the plastic shear
resistance of the section
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180
Otherwise use a reduced yield strength on the shear area
y y
fy(1- ) fy(1- )
2
,,
,1
2
Rdtfi
Edfi
V
V
Class 1 or 2 Class 3
Fire Resistance: Shear and bending
Beams with Class 1, 2 or 3 cross-sections - 2
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181
MkMkN
Without lateral-torsional buckling
Class 1 and 2
Fire Resistance: Members with Class 1, 2 or 3 cross-sections,
subject to combined bending and axial compression - 1
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182
1
fi,M
y,yz,pl
Ed,fi,zz
fi,M
y,yy,pl
Ed,fi,yy
fi,M
y,yfimin,
Ed,fi
fkW
Mk
fkW
Mk
fkA
N
1
fi,M
y,yz,el
Ed,fi,zz
fi,M
y,yy,el
Ed,fi,yy
fi,M
y,yfimin,
Ed,fi
fkW
Mk
fkW
Mk
fkA
N
Class 3
Class 1 and 2
MkMkN
With lateral-torsional buckling
Fire Resistance: Members with Class 1, 2 or 3 cross-sections,
subject to combined bending and axial compression - 2
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183
Class 3
1
fi,M
y,yz,pl
Ed,fi,zz
fi,M
y,yy,plfi,LT
Ed,fi,yLT
fi,M
y,yfi,z
Ed,fi
fkW
Mk
fkW
Mk
fkA
N
1
fi,M
y,yz,el
Ed,fi,zz
fi,M
y,yy,elfi,LT
Ed,fi,yLT
fi,M
y,yfi,z
Ed,fi
fkW
Mk
fkW
Mk
fkA
N
Fire Resistance: Members with Class 1, 2 or 3 cross-sections,
subject to combined bending and axial compression - 3
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184
Fire Resistance: Members with Class 1, 2 or 3 cross-sections,
subject to combined bending and axial compression - 4
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185
Fire Resistance: Members with Class 1, 2 or 3 cross-sections,
subject to combined bending and axial compression - 5
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186
Fire Resistance: Members with Class 1, 2 or 3 cross-sections,
subject to combined bending and axial compression - 6
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187
Fire Resistance: Members with Class 1, 2 or 3 cross-sections,
subject to combined bending and axial compression - 7
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188
If there are moments about the
major axis, the program allows
for the possibility of considering
LTB
Fire Resistance: verifications of the fire resistance not covered
by EN 1993-1-2
Clause 1.1.2 (Scope of Part 1.2 of Eurocode 3) of EN 1993-1-2 states This
Part 1-2 of EN 1993 deals with the design of steel structures for the
accidental situation of fire exposure and is intended to be used in conjunctionwith EN 1993-1-1 and EN 1991-1-2. This part 1.2 only identifies differences
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189
p y
from or supplements to normal temperature design
This means that for the cases not covered by EN 1993-1-2, the formulae
from the part 1.1 of EC3 should be used but modified to take into account the
effect of the temperature.
Fire Resistance: Cross-sectional verification of a member
subjected to bending and axial force (compression or tension) - 1
For class 1 and class 2
01.MM
MM Ed,fi,zEd,fi,y
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190
MM Rd,fi,z,NRd,fi,y,N
where MN,y,fi,Rd and MN,z,fi,Rd are the the design plastic moment resistance
reduced due to the axial force.
For class 3
01.
M
M
M
M
N
N
Rd,fi,z
Ed,fi,z
Rd,fi,y
Ed,fi,y
Rd,fi
Ed,fi
Fire Resistance: Cross-sectional verification of a member
subjected to bending and axial force (compression or tension) - 2
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191
For class 1 and class 2
0.1MM Ed,fi,zEd,fi,y
Fire Resistance: Cross-sectional verification of a member
subjected to bi-axial bending - 1
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192
MM Rd,fi,zRd,fi,y
For class 3
0.1M
M
M
M
Rd,fi,z
Ed,fi,z
Rd,fi,y
Ed,fi,y Ed,fi,yM
Ed,fi,zM
Example: a purlin
Fire Resistance: Cross-sectional verification of a member
subjected to bi-axial bending - 2
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193
AB C D
EI = Const.
p kN/m
l
E
l l l
a) Structural scheme.
Fire Resistance:
Design of continuous beams - 1
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194
A B C D
l
E
l l l
l l l l
A B C D E
b) End span mechanism.
c) Intermediate span mechanism
Typical collapse mechanisms for a continuous beam
Fire Resistance:
Design of continuous beams - 2
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195
Fire Resistance:
Design of continuous beams - 3
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196
Two procedures:
1. In the absence of calculation a critical temperature of 350 Cshould be considered (conservative results).
Fire Resistance:
Members with Class 4 cross-sections
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197
2. Alternatively use Annex E, considering the effective area
and the effective section modulus determined inaccordance with EN 1993-1-3 and EN 1993-1-5, i.e. based on
the material properties at 20C. For the design under f ire
conditions the design strength of steel should be taken as
the 0,2 percent proof strength instead of the strength
corresponding to 2% total strain.
Professor Paulo Vila Real
Tenso
fy,
f
Cross-sectional Class 1, 2 and 3
Eurocode 3: Fire Resistance
Design yield strength to be used with simple calculation models
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198Extenso
E = tan a,
y,p, u,
fp,
t,0,2%
f0.2p,
Cross-sectionalClass 4
= 2%
Annex E ofEN 1993-1-2
Two procedures:
1. In the absence of calculation, a crit ical temperature of 350 Cshould be considered (conservative results).
Eurocode 3: Fire Resistance
Members with Class 4 cross-sections
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199
2. Alternatively use Annex E, considering the effective area
and the effective section modulus determined inaccordance with EN 1993-1-3 and EN 1993-1-5, i.e. based on
the material properties at 20C.
, 20p C (Slenderness of the plates)(See next slide)
Professor Paulo Vila Real
y
y
cr
y
p
f
Ek
tb
b
Etk
ff 1
)1(12)1(12 2
2
22
22
1tb
Eurocode 3: Fire Resistance
Members with Class 4 cross-sections
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210000
235
235
210000
)1(12 2
2 E
fk
y
k
tb
k
tb
E
f
k
tb
y
4.28
1
4.28
210000
235
1
4.28
210000
235 E
fy
with yf andEin MPa
Professor Paulo Vila Real
For Class 4 cross-sections and
high temperatures:
,
0.2,
235 2351.00
E
p y y
k
k f f
Eurocode 3: Fire Resistance
Members with Class 4 cross-sections
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0
0.2
0.4
0.6
0.8
1
1.2
1.4
0 200 400 600 800 1000 1200
1.00
20C
, 20p C
Tenso
fy,
f 0 2
Cross-sectional Class 1, 2 and 3
Fire Resistance:
Design yield strength to be used with simple calculation modelsNote: for the time being
Elefir-EN does not
allow for Class 4
elements
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202Extenso
E = tan a,
y,p, u,
fp,
t,0,2%
fp0.2,
Cross-sectional Class
4
= 2%
Annex E of
EN 1993-1-2
crit,1crit,2 2a,cr fi,d = 576.1C ko!
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223
Nfi,Rd = 177 kN < Nfi,Ed = 780 kN ko!
Verification in the resistance domain:
Fire Resistance
Worked examples with the software Elefir-EN
Example 5.2 from the ECCS Book: Laterally restrained beam. Consider
a simply supported restrained beam 4.0 long, constructed from an IPE
300 section, in steel grade S235, supporting a concrete slab. Assuming
the steel beam does not act compositely with the concrete slab and thatthe design load in the fire situation is qfi,Ed = 33.8 kN/m, verify if it is
necessary to protect the beam for a fire resistance period of R90. If fire
protection is needed, use fibre-cement boards.
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224
protection is needed, use fibre cement boards.
Design value of the moment in f ire situation at
the mid span:
Mfi,Ed = 33.8x42/8
= 67.6 kNm
Design value of the shear in fire situation at the
supports:
Vfi,Ed = 33.8x4/2
= 67.6 kN
Solution:
Fire Resistance
Worked examples with the software Elefir-EN
At mid span:
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225
Fire Resistance
Worked examples with the software Elefir-EN
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226
Fire Resistance
Worked examples with the software Elefir-EN
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227
tfi,d = 16.7 min < trequ = 90 min ko!
Passive fire protection is needed!
Fire Resistance
Worked examples with the software Elefir-EN
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228
Fire Resistance
Worked examples with the software Elefir-EN
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229
Fire Resistance
Worked examples with the software Elefir-EN
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230
Fire Resistance
Worked examples with the software Elefir-EN
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231
Fire Resistance
Worked examples with the software Elefir-EN
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232
Fire Resistance
Worked examples with the software Elefir-EN
Check the shear resistance at the supports
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233
Fire Resistance
Worked examples with the software Elefir-EN
As the critical temperature of
729.5 is bigger than the critical
Check the shear resistance at the supports
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234
729.5 is bigger than the critical
temperature obtained for the
bending moment (624 C),
shear is not l imitative.
Fire Resistance
Worked examples with the software Elefir-EN
Example 5.3 from the ECCS Book: Unprotected column under axial
compression
Consider a 3.5 m long HE 180 B column in S275 grade steel, located in
an intermediate storey of a braced frame and subject to a compressionload of Nfi,Ed = 495 kN in the fire situation. Assuming that the column
doesnt have any fire protection and that the required fire resistance is
R30, verify the fire resistance
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235
Buckling length:
lfi = 0.5x3.5 = 1.75 kNm
Solution:
Fire Resistance
Worked examples with the software Elefir-EN
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236
Fire Resistance
Worked examples with the software Elefir-EN
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237
Fire Resistance
Worked examples with the software Elefir-EN
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238
tfi,d = 17.47 min < t requ = 30 min ko!
Fire Resistance
Worked examples with the software Elefir-EN
Example 5.6 from the ECCS Book: Unrestrained beam.
Consider a simply supported IPE 300, S235 grade steel beam from an office building,
with fork supports. The member is 5.0 m long and is subjected to a transverse
uniform load at normal temperature qEd = 19.2 kN/m. The transverse loading is
assumed to act at the shear centre of the beam. Evaluate the critical temperatureconsidering that the beam is unrestrained. Lateral-torsional buckling is not prevent
and may therefore occur.
Solution:Design value of the uniform load in fire situation:
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239
Design value of the moment span in f ire
situation at the mid span:
Mfi,Ed = 12.48x52/8 = 39.0 kNm
Design value of the shear in fire situation at thesupports:
Vfi,Ed = 12.48x5/2 = 31.2 kN
Design value of the uniform load in fire situation:
qfi,Ed = fixqEd = 0.65x19.2 = 12.48 kN/m
Fire Resistance
Worked examples with the software Elefir-EN
Check the shear resistance at the supports
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240
cr = 845.7 C
Fire Resistance
Worked examples with the software Elefir-EN
Lateral-torsional buckling:
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241
Fire Resistance
Worked examples with the software Elefir-EN
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242
cr = 517 C cr = min(845.7 C, 517 C)= 517 C
Fire Resistance
Worked examples with the software Elefir-EN
Example 5.7 from the ECCS Book: Unrestrained beam-column.
A 6.0 m long, simply supported beam-column constructed from an IPE 450 section is
subjected to a uniform load in a fire situation of qfi,Ed = 15.89 kN/m and to an axial
compression load of Nfi,Ed = 136.5 kN . Assuming that the steel grade is S235 andthat the load is applied at the shear centre of the beam, evaluate the critical
temperature in the following conditions:
a) When the beam-column is lateral restrained.
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243
b) When the beam-column is unrestrained. Lateral-torsional buckling is notprevent and may therefore occur.
15,89 kN/m
136.5 kN 136.5 kN
Fire Resistance
Worked examples with the software Elefir-EN
a) The beam-column is lateral restrained.
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244
Fire Resistance
Worked examples with the software Elefir-EN
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245
Fire Resistance
Worked examples with the software Elefir-EN
b) The beam-column is laterally unrestrained.
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246
Fire Resistance
Worked examples with the software Elefir-EN
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247
Fire Resistance
Worked examples with the software Elefir-EN
Check the shear resistance at the supports
Design value of the shear in fire situation at the
supports:
Vfi,Ed = 15.89x6/2 = 47.67 kN
Solution:
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248
Fire Resistance
Worked examples with the software Elefir-EN
Check the shear resistance at the supports
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249
cr = min(515.4 C, 881.7 C)= 515.4 C
Fire Resistance
Worked examples with the software Elefir-EN
Example 5.8 from the ECCS Book: Beam-column with restrained lateral
displacements.
Consider a 3.0 m high, HE 200 B column in an intermediate storey of a braced frame,
subjected to a bi-triangular bending moment diagram with moments at the ends in
fire situation of My,fi,Ed = 50 kNm about major axis and to an axial compressionload in fire situation of Nfi,Ed = 800 kN. Assuming that the steel grade is S235, and
that lateral-torsional buckling is not allowed, evaluate the critical temperature of
the column.
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250
800 kN
800 kN
50 kNm
- 50 kNm
50 kNm
- 50 kNm
Fire Resistance
Worked examples with the software Elefir-EN
Design value of the shear in fire situation at the
supports:
Vfi,Ed = [50 - (-50)]/3 = 33.3 kN
Solution:
Buckling length in fire situation:
lyfi = 0.5x3.0 = 1.5 m
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251
Fire Resistance
Worked examples with the software Elefir-EN
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252
Fire Resistance
Worked examples with the software Elefir-EN
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253
Fire Resistance
Worked examples with the software Elefir-EN
Check the shear resistance at the supports
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254
cr = min(516.6 C, 822.5 C)= 516.6 C
Fire Resistance
Worked examples with the software Elefir-EN
Example 5.9 from the ECCS Book: Class 4 column subjected to axial
compression.
Consider a 3.2 m high HE 500 A column in steel grade S460 in an intermediate storey
of a braced frame, subjected to an axial compression load. Evaluate the critical
temperature of the column for the following axial loads in a fire situation:
a) Nfi,Ed = 5460 kN.
b) Nfi,Ed = 3520 kN.
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255
Solution:
Buckling length in fire situation:
lyfi = 0.5x3.2 = 1.6 m
Fire Resistance
Worked examples with the software Elefir-EN
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Note: For the time being the program Elefir-EN
does not evaluate the crit ical temperature of
profi les with Class 4 cross-sections.
Fire Resistance
Worked examples with the software Elefir-EN
Example 5.10 from the ECCS Book: Three-span continuous beam.
Consider a three-span continuous beam in an office building, with equal spans of 6.0
m, constructed from an IPE 300 section in S235 grade steel, as shown in the Fig..
The beam is subjected to a permanent uniform load of Gk = 20 kN/m (including the
weight of the profile) and a live load of Qk = 8 kN/m. Assuming that the out ofplane displacements are restrained and that the beam is unprotected and supports
a concrete slab, evaluate the critical temperature.
A D
qfi,Ed
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Solution:
Load combination:
q fi,Ed = Gk + 2Qk = 20 + 0.3x8 = 22.4 kN/m
A B C
6.0 m
D
6.0 m 6.0 m
Fire Resistance
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Fire Resistance
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No shear effect.
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Fire Resistance
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No shear effect.
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cr = min(665.8 C, 708.7 C)= 665.8 C
Fire Resistance
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Considering shear effect.
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Fire Resistance
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Considering shear effect.
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Fire Resistance
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Considering shear effect.
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cr = min(664.0 C, 699.3 C)= 664.0 C
Fire Resistance
Worked examples with the software Elefir-EN
Example 5.11 from the ECCS Book: Member subjected to combined
bending and tension.
Consider an HE 200 A section in S355 grade steel subjected to tension and major axis
end moments as shown in the figure.a) Evaluate the critical temperature.
b) Verify the fire resistance of the member after 30 minutes of standard fire exposure
on four sides.
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Mfi,Ed= 20kNm
Nfi,Ed= 100 kNNfi,Ed
Mfi,Ed= -10kNm
Fire Resistance
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a) Evaluate the critical temperature.
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Fire Resistance
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Fire Resistance
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b) Fire resistance after 30 min of ISO 834 curve on 4 sides.
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Fire Resistance
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Fire Resistance
Worked examples with the software Elefir-EN
Example 5.12 from the ECCS Book: Laterally restrained stainless steel
beam.
Suppose that a welded section equivalent to the IPE 300 is made of Grade 1.4301
stainless steel. What is the critical temperature if it is supporting a concrete slaband subjected to a bending moment of Mfi,Ed = 67.6 kNm and what is the time
needed to reach the critical temperature if the profile is unprotected and exposed
to the ISO 834 fire curve in three sides?
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Fire Resistance
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Fire Resistance
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Fire Resistance
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Case Study
2.0 m
1.85 m
8.15 m
Case study from Chapter 9 using simple calculation models
Single storey hall for indoor sport activities
IPE 500
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For more details seeChapter 9 from
ECCS book
5.5 x 12 = 66 m
Case Study
6 x 14 = 84 m
Single storey hall for
indoor sport activities
Steel grade S355
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2.75 x 24 = 66 m For more details seeChapter 9 from
ECCS book
2.0 m1.85 m
8.15 m
Case StudySection N M
1
M2
q lfi,y
lfi,z
- [kN] [kNm] [kNm] [kN/m]
Recommended