Fire Resistance of Steel Structures

Aniket Gohil
MSC STRUCTURAL ENGINEERING | 1431523 | SUPERVISOR: DR. ZHAOHUI HUANG
FIRE RESISTANCE OF STEEL STRUCTURES
Detailed research in acknowledging the purpose and use of Eurocode in regards to fire resistance
design with aid of designing of a steel and truss frame and testing it under elevated temperatures
and fire load respectively.

CE5516 Fire Resistance of Steel Structures 1431523
Page 1
PROJECT SUMMARY
Materials and construction assemblies that include the use of fire resisting materials, measured in
terms of fire endurance time are known as fire resistance-rated-construction. These control the spread
of fire, preventing the loss of structural stability within the prescribed period, with use of fire
resistance. This is also based on occupancy of the building and fire safe objectives available.
In this project, use of finite elements software such as Vulcan and spreadsheet used to design and test
of steel and truss frames under fire and how they react under those circumstances. Spreadsheet is an
advance finite element computer programme used to develop and analyse structures and structural
elements. It is divided into different modules, each module representing an aspect of modelling, e.g.
geometry defining, adding material properties, loading, generating mesh, etc. With aid of these
modules, precise models and results are developed. Vulcan is a three-dimensional computer
programme developed at University of Sheffield. It is used for modelling steel, steel-framed
composites and reinforced concrete buildings in fire. The development of the model extends its
capability to model the dynamic and static behaviour of steel structural elements under fire. It is a
powerful tool to investigate the mechanism of the progressive collapse of an element due to local
failure.
For this particular dissertation, two programs will be used in order to understand and design for the
fire resistance of steel structures: spreadsheet and Vulcan. Various parametric analyses will be carried
out on the program Vulcan on steel members at elevated temperatures at different location within the
frame. Examining these members on Vulcan would mean that the members are analysed in holistic
manner. The tests will be carried out on both protected and unprotected steel members via both
Vulcan and the spreadsheet method. The parameters for the tests are based on fire regime and
characteristics of beam to column connectivity.
The dissertation is based on analysing 2D steel frame via Vulcan and spreadsheet. The building takes
a shape of a 2 storey non sway steel frame comprising of 5 bays, each at a distance of 9m. In the
transverse direction, there are 4 bays with a distance of 6m with a floor height of 4m. The sections for
the different elements used in the structure will be uniform. A number of five scenarios are designed
which include different fire regimes. As this analysis is not based on isolated members, different
characteristics of beam to column connectivity will be analysed including rigid and pinned
connections. For testing of isolated members, spreadsheet method will be used and cross examined on
Vulcan. The results achieved for the steel frame building for the scenarios will then be discussed in
relation to each other.

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ACKNOWLEDGMENTS
I would like to express my deepest gratitude and thankfulness to all those who helped me in all stages
to complete this dissertation. I appreciate their support and this would not have been possible without
them. I’d like to personally thank my supervisor Zhaohui Huang and for his help, motivation and
guidance. I would also like to thank my parents Rajesh Gohil and Jignasha Gohil, my sister Jagruti
Gohil and my friends Varad Gokhale, Manas Adhvaryu and Sulheman Khan for their unlimited
support.
I would also like express my deepest gratitude to my various course leaders whose knowledge in
various fields helped me to undertake a project which was not limited to a certain topic. To all my
relatives, friends and others who in a way or another shared their support, morally, financially and
physically.
Above all, thanking to the Great Almighty, the author of knowledge and wisdom, for his countless
love.
THANK YOU

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STATEMENT OF ORIGINALITY
Author’s declaration
I declare that the work in this dissertation was carried out in accordance with the requirements of the
University’s Regulations and Code of Practice for Taught Programmes and that it has not been
submitted for any other academic award. Except where indicated by specific reference in the text, this
work is my own work. Work done in collaboration with, or with the assistance of others, is indicated
as such. I have identified all material in this dissertation which is not my own work through
appropriate referencing and acknowledgement. Where I have quoted or otherwise incorporated
material which is the work of others, I have included the source in the references. Any views
expressed in the dissertation, other than referenced material, are those of the author.
SIGNED: ……………………………………………………………. DATE: ……………..
(Signature of student)

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TABLE OF CONTENTS
PROJECT SUMMARY..........................................................................................................................1
ACKNOWLEDGMENTS ......................................................................................................................2
STATEMENT OF ORIGINALITY........................................................................................................3
LIST OF FIGURES ................................................................................................................................7
LIST OF TABLES..................................................................................................................................8
INTRODUCTION ..................................................................................................................................9
1.1. Background.............................................................................................................................9
1.2. Aims and Objectives.............................................................................................................10
LITERATURE REVIEW .....................................................................................................................11
2.1. Fire and Testing ....................................................................................................................11
2.1.1. Building Fires................................................................................................................11
2.1.2. Compartment Fires........................................................................................................12
2.1.3. Building Regulations.....................................................................................................13
2.1.4. Standard Fire Curves and Furnace Testing ...................................................................15
2.1.5. Parametric Fire Curves..................................................................................................16
2.1.6. Cardington Fire Test .....................................................................................................18
2.1.7. Broadgate Fire...............................................................................................................22
MATERIAL PROPERTIES .................................................................................................................24
3.1. Thermal Properties of Steel at Elevated Temperature ..........................................................24
3.1.1. Thermal Expansion .......................................................................................................24
3.1.2. Volumetric Specific Heat..............................................................................................25
3.1.3. Thermal Conductivity ...................................................................................................26
3.2. Mechanical Properties of Steel at Elevated Temperature .....................................................27
3.2.1. Stress-Strain Relationship.............................................................................................28
HEAT TRANSFER ..............................................................................................................................29
4.1. Heat Transfer for Unprotected Steel Member.......................................................................29

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4.2. Heat Transfer for Protected Steel Members..........................................................................31
4.3. Section Factor .......................................................................................................................32
4.4. Protection Mechanisms.........................................................................................................33
FIRE RESISTANCE ASSESSMENT ..................................................................................................35
5.1. According to Eurocode 3 ......................................................................................................35
5.1.1. Calculations for Design Data ........................................................................................35
5.2. According to British Standard’s............................................................................................37
5.2.1. Load Ratio Method .......................................................................................................37
5.2.2. Moment Capacity Method ............................................................................................37
BEHAVIOUR OF STRUCTURAL ELEMENTS................................................................................38
6.1. Beam Analysis ......................................................................................................................38
6.2. Column Analysis...................................................................................................................39
METHODOLOGY ...............................................................................................................................40
7.1. Spreadsheet Method..............................................................................................................40
7.2. Vulcan...................................................................................................................................41
7.2.1. Computer Modelling.....................................................................................................41
7.2.2. Capabilities and Limitations .........................................................................................41
PROCEDURE.......................................................................................................................................43
8.1. Proposed Plan........................................................................................................................43
DESIGN OF STEEL FRAMED BUILDING.......................................................................................45
9.1. Primary Beam .......................................................................................................................46
9.2. Column..................................................................................................................................48
ANALYSIS OF 2D FRAME................................................................................................................49
10.1. Scenario 1: FIRST FLOOR – Bay 1 – ISO Fire with Rigid and Pinned Connections......50
10.2. Scenario 2: FIRST FLOOR – Bay 1 – Parametric Fire with Rigid and Pinned
Connections.......................................................................................................................................53
10.3. Scenario 3: FIRST FLOOR – Bay 3 – ISO Fire with Rigid and Pinned Connections......55

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10.4. Scenario 4: FIRST FLOOR – Bay 3 – Parametric Fire with Rigid and Pinned
Connections.......................................................................................................................................58
10.5. Scenario 5: FIRST FLOOR – Bay 1 – 3 – Simultaneous ISO Fire and Parametric Fire
with Rigid Connections.....................................................................................................................60
CONCLUSION.....................................................................................................................................62
FUTURE RECOMMENDATIONS .....................................................................................................64
REFERENCES .....................................................................................................................................65
APPENDIX I: Spreadsheet FiRE.xls for Determining Critical Temperature.......................................68
APPENDIX II: Scenario 1 of 6 (1 of 4 input models) ..........................................................................70

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LIST OF FIGURES
Figure 1: Schematic of Compartment Fire Growth...............................................................................13
Figure 2: Building regulations approved document B (Volume 1 and 2).............................................14
Figure 3: Time Temperature Curves according to Eurocode................................................................15
Figure 4: ISO 834 Standard Fire Curve ................................................................................................16
Figure 5: Floor layout of Cardington test building ...............................................................................19
Figure 6: Loading of Cardington steel framed building........................................................................19
Figure 7: Office layout for Cardington Fire Test..................................................................................21
Figure 8: Broadgate fire damages.........................................................................................................23
Figure 9: Thermal elongation of steel at elevated temperatures (European Committee for
Standardisation, 2005) ..........................................................................................................................24
Figure 10: Specific heat of steel as a function of the temperature........................................................26
Figure 11: Thermal conductivity of steel as a function of the temperature (European Committee for
Figure 12: Reduction factor for stress-strain steel at elevated temperatures.........................................27
Figure 13: Stress-strain relationship for steel at elevated temperatures (European Committee for
Figure 14: Stress-strain curve for strain illustrating yield and proof strength ......................................28
Figure 15: Heat transfer in an unprotected steel member .....................................................................29
Figure 16: Deformation (left) thermal stresses due to fire (right).........................................................29
Figure 17: Heat transfer in protected steel............................................................................................31
Figure 18: Section factor for protected and unprotected steel members (Haller & Cajot, 2006) .........32
Figure 19: Critical temperature for simple steel members based on standard fire test .........................36
Figure 20: Failure mechanism for simply supported beam (left) and continuous beam (right)............38
Figure 21: Plan view of the building.....................................................................................................45
Figure 22: Side view of the building....................................................................................................46
Figure 23: Standard fire curves for protected and unprotected primary steel beams............................47
Figure 24: Parametric fire curve for both protected and unprotected beam..........................................47
Figure 25: Simply supported beam model ............................................................................................49
Figure 26: Bay 1 exposed to ISO fire conditions..................................................................................50
Figure 27: Temperature deflection graph of bay 1 (node 82) with isolated member subjected to ISO
fire.........................................................................................................................................................50
Figure 28: Time deflection graph of bay 1 with isolated member subjected to ISO fire at node 82 ....51
Figure 29: Temperature - axial force graph for beam to column connections at bay 1 ........................51
Figure 30: Time - axial force graph for beam to column connections at bay 1 ....................................52

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Figure 31: Temperature deflection relationship of bay 1 and an isolated member subjected to
parametric at node 82............................................................................................................................53
Figure 32: Time deflection graph of bay 1 with isolated member subjected to parametric fire at node
82 ..........................................................................................................................................................53
Figure 33: Temperature - axial force graph for beam to column connections at bay 1 subjected to
parametric fire.......................................................................................................................................54
Figure 34: Time - axial force graph for beam to column connections at bay 1 subjected to parametric
fire.........................................................................................................................................................54
Figure 35: Bay 3 exposed to ISO fire ...................................................................................................55
Figure 36: Temperature deflection relationship of bay 3 and an isolated member subjected to ISO fire
at node 132............................................................................................................................................55
Figure 37: Time deflection graph of bay 3 with isolated member subjected to ISO fire at node 132 ..56
Figure 38: Temperature deflection graph of bay 3 with isolated member subjected to ISO fire at node
132 ........................................................................................................................................................56
Figure 39: Time deflection graph on bay 3 with isolated member subjected to ISO 834 fire..............56
132 ........................................................................................................................................................58
Figure 41: Temperature deflection graph of bay 3 with isolated member subjected to parametric fire
at node 132...........................................................................................................................................58
132 ........................................................................................................................................................59
Figure 43: Bays 1-3 exposed to ISO fire...............................................................................................60
Figure 44: Temperature deflection graph of bay 1 0 3 and isolated member subjected to
ISO/parametric fire conditions .............................................................................................................60
Figure 45: Time deflection graph of bays 1 - 3 subjected to ISO and parametric fire..........................61
Figure 46: Temperature axial force graph of beam to column connection at bay 1-3 subjected to
ISO/parametric fire ...............................................................................................................................61
LIST OF TABLES
Table 1: Fires by location and type, Great Britain, 2000/01 - 2013/14 [1]...........................................11
Table 2: Floor Loading Details.............................................................................................................19
Table 3: Thermal properties of common fire protection materials (ECCS Technical Committee 3,
1995).....................................................................................................................................................33
Table 4: Load reduction factor based on partial safety factor according to EC3..................................36
Table 5: Critical temperature values for primary beam members.........................................................46
Table 6: Fire resistance and protection steel column............................................................................48

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1INTRODUCTION
1.1. Background
Construction of a structure consists of many stages and layers, one of which is fire protection. Fire
protection is a key element in all structures. Current fire protection strategy integrates a combination
of active and passive fire protection measures. Active fire measures considers the use of fire alarms,
sprinklers, fire extinguishers, etc. that require either human involvement or automatic activation,
which helps control the fire and its effects during fire. Passive fire measures are built into the
structural system by the use of materials in construction of a building, dimensions of building
components and fire compartmentation.
Materials and construction assemblies that include the use of fire resisting materials, measured in
terms of fire endurance time are known as fire resistance-rated-construction (Clayton, 2012). These
control the spread of fire, preventing the loss of structural stability within the prescribed period, with
use of fire resistance. This is also based on occupancy of the building and fire safe objectives
available.
It is now commonly known that to design fire resistance of a beam it is the period of time that it can
maintain a deflection less than span/20 under standard ISO 834 fire condition. If tested without
protection, a usual beam would result in a fire protection of 15 to 20 minutes with its deflection
reached when the temperature is around 550° to 700° C depending on the load.
When designing a building, design practice codes and standards such as Eurocodes and ISO standards
are considered. Recommendations and guidelines are also provided by the local government and
Secretary State of Committee, called “Building regulations”. This consists of regulation determination
for: internal and external fire spread (B3 and B4 respectively of building regulations) and, access and
facilities for the fire service (B5 of building regulation) (BBC, 2014). Eurocode is a structural design
code covering – basis of design, actions on structures, design of elements in structures (concrete, steel,
composite concrete and steel, timber, masonry and aluminium) along with seismic and geotechnical
design.

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In this project, use of finite elements software such as Vulcan and Spreadsheet/CAE are used to
design and test of steel and truss frames under fire and how they react under those circumstances.
Spreadsheet/CAE is an advance finite element computer programme used to develop and analyse
structures and structural elements. It is divided into different modules, each module representing an
aspect of modelling, e.g. geometry defining, adding material properties, loading, generating mesh, etc.
With aid of these modules, precise models and results are developed. Vulcan is a three-dimensional
computer programme developed at University of Sheffield. It is used for modelling steel, steel-framed
composites and reinforced concrete buildings in fire. The development of the model extends its
capability to model the dynamic and static behaviour of steel structural elements under fire. It is a
powerful tool to investigate the mechanism of the progressive collapse of an element due to local
failure.
Fire resistance is an important part in building and structure design. With following Eurocodes and
building regulations, user safety is considered utmost. Along with that, structural life and fire spread
hazards are also considered (Collette, 2007). In case of fire, the ability of loaded structural material to
retain its strength can provide extra time for users in evacuation. It is a challenging task for fire
engineers in delivering structural element that is able to withstand high fire loads for a longer period.
1.2. Aims and Objectives
Aims: The main aim of this individual research project is to acknowledge the purpose and use of
Eurocode in regards to fire resistance design with aid of designing of a steel frame and testing it under
elevated temperatures and fire load respectively.
Objectives: In order to achieve the set aims to this individual research project and project, the
following objectives must be accomplished:
 Clearly understand the use of Eurocode 3 and Eurocode 1 in relation to building fire design,
putting it in practice to design a steel and truss frame.
 Calculating protected and unprotected steel under fire.
 Involving the use of Vulcan programme to understand the behaviour of steel frame at elevated
temperatures and truss frames under fire, failure point for one and progressive column and
analysis of two dimensional steel frame structure in fire.
 Comparing and analysing the achieved results to design fires, such as: Eurocode and ISO 834.
 Presenting how to minimise the risk of fire and fire spread with use of passive fire protection
measures.

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2LITERATURE REVIEW
In increase of extreme fire disasters, growth of safety from fire and of life and the developments in
current design standards, the field of fire safety is expanding day by day. Codes and standards provide
guidelines, regulations and techniques to improve fire resistance. With a combination from technical
advances, increased research, and the necessity to predict behaviour of structures, analysation of both
thermal and structural behaviour under fire conditions must be evaluated.
2.1. Fire and Testing
2.1.1. Building Fires
Fire has always been a risk to human life. There have been many scenarios where human life has been
left in danger due to building fires. The aim of fire safety design is to lessen the chances of fire
occurring in buildings. According to data collected by the government, fire scenarios have been
recorded each year.
Table 1: Fires by location and type, Great Britain, 2000/01 - 2013/14 [1]
107.3
85.5 59.0
39.1
2.7
17.2
102.2 66.9
29.5
221.8
251.3
116.3
13.6 7.6 7.70
50
100
150
200
250
300
350
400
Numberoffires(thousands)
Total Buildings Dwellings Other residential Non-residential
Outdoors Secondary fires Chimney fires

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As seen above in Table 1, the total number of primary fires recorded in 2000/01 was 209,400. At
present the total number of primary fires was decreased by 42% and resulted in 88,500. Similarly,
following the trend, total secondary and chimney fires in 2000/01 was 221,800 and 13,600
respectively which was decreased by 52% and 57%, resulting in 116,300 and 7,700 fires respectively.
As seen throughout the chart, there is a strong decreasing trend in all three sectors: primary, secondary
and chimney fires.
2.1.2. Compartment Fires
Compartment fires relate to the essence of fire growth. In this situation, a “compartment” is any
confined space that has the ability to control the ultimate air supply and thermal environment of fire.
These factors control the spread and growth of fire, its duration and its burning rate (Quintiere, 2006).
During a compartment fire, a Flashover stage is introduced where a rapidly occurring transitional
event leads in the development of compartment fire. Building Research Establishment (BRE) (2005)
states that a factors affecting compartment fires are method of storage, size of the compartment and
ventilation for air supply in the compartment. A flashover is when there is a rapid increase of heat in a
compartment leading to drastic spread of developed fire. Compartment fires are divided into two
stages; pre and post flashover. A pre flashover phase has a bigger influence on human life safety
where the rapid growth of fire and the upper layer of gas is recorded. On the other hand post flashover
fires have influence on structural integrity where a high turbulent flow of gasses and high
temperatures are recorded.
Additionally, post flashover fires are also considered as fuel controlled fires. This scenario is similar
to that of fuel burning in open air with enhancement and from radiant feedback from hot upper layer
of gas. In a fuel controlled burning, all of the heat is released inside a room, avoiding the flames to
extend out the windows like ventilation controlled fire. Figure 1 describes the schematic of
compartment fire growth, defining the flashover stages and ignition, heating and cooling phases. For a
structural design, it is vital to consider both the growth and decay phase of fire.
According to Eurocode, the fire resistance determination in this work is related to ventilation
controlled fire. Ventilation controlled fire depend largely on the shape and the size of the ventilation
opening (International Standard Organization, 1999). According to Corbett (2009), the ventilation
controlled fire in compartment fires is limited by the volume of cool air that can enter and volume of
hot gases that can leave the room. While there is insufficient air flow inside the room, all the gases
tend to not burn out. However these gases extend outwards through the window mixing with outside
air and additional combustion takes place.

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Using the data and the figure displayed above a computer model can be designed in order to provide
aid to fire analyst. This computer model will reveal information like the time of flashover, heat release
rate, fuel available for flashover, ventilation required to prevent flashover and temperature profiles of
the compartment. However it is also vital to understand that this is a computed result from fire
modelling and can be used as ‘reliable estimates’. Every fire is different in some way providing
different outcomes to one another.
2.1.3. Building Regulations
Building regulations are compulsory standards of design and construction that every building has to
achieve. In order to progress onto constructing a designed structure, one has to get an approval from
the Parliament. Laws and regulations which apply to design and construction are set out in Building
Act 1984[2]
.
Currently there are 14 sections to the building regulations, where each one is guided by an approved
document. The approved document provides guidance in meeting the legislations, not a set of rules to
follow. In an approved document, the legislation applied is described in detail followed by a number
of means which must be fulfilled to satisfy the regulations. It is important to comply with the Building
Regulations and there are many ways to do so. In order to comply with the legislation, “Deemed to
satisfy” provision (attached in the approval document) must be achieved.
Building Regulations Approved Document B (fire safety) complies with this particular dissertation.
Part B of the building regulations consists of five aspects of fire safety (HM Government, 2006):
Figure 1: Schematic of Compartment Fire Growth

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 B1 Means of warning and escape
Section B1 of the regulations ensures that in the event of fire in a building, it is easy for a person
inside the building to be notified with means of fire alarm and have a satisfactory standard of
means of escape.
 B2 Internal fire spread (linings)
Section B2 ensures that the internal linings inside the building do not
support the rapid spread of fire.
 B3 Internal fire spread (structure)
Section B3 ensures that in the event of fire, the spread of fire must be
slow and in cavities and voids with the provision of fire resisting
building materials and must include partitions where necessary. The
building must also ensure that no premature collapse should occur.
 B4 External fire spread
Section B4 ensures that in the event of external fire, the spacing between buildings must
discourage the spread of fire. This can be controlled by the number and size of the opening on
boundaries.
 B5 Access and facilities for the fire service
Section B5 ensures that the building should be designed in such a way that during the event of
fire, fire brigade can easily access the facility to control the fire and rescue anyone caught on fire.
For this particular project, Section B3 is highly related; stating that in the event of fire, the structure
should not easily lose its stability. In order to comply with the standard, load bearing must be added to
the structure so it maintains its ability for a reasonable amount of time.
According to British Standard 6336, there are three ways in which a structure can resist failing in the
event of fire:
 Insulation – resisting heat transmission
 Integrity – resisting plumes of flames and smoke
 Stability – resisting structural failure
Stability is crucial for structural members while integrity and insulation are both important for walls,
flooring and ceiling/roof.
Figure 2: Building
regulations approved
document B (Volume 1 and
2)

Page 15
2.1.4. Standard Fire Curves and Furnace Testing
ASTM E119 was one of the first tests to be published about establishing a fire resistance rating
system for steel members through prescribed method. It was called “Standard Test Methods for Fire
Tests of Building Construction and Materials”. Eurocode had since been developed from the basis of
ASTM E119 to develop fire resistance rating tests.
2.1.4.1. Eurocodes
Eurocode 1 Part 2 provides detailed information for design fire of both standard and parametric fire
used in calculations with Eurocode methods. Formulas are provided for three different types of fire
curves: standard, external and hydrocarbon.
Figure 3 shows the time temperature curve according to Eurocode. Using three of the formulas
(formula 01, 02 and 03) for fire curve where, “Θg” represents the gas temperature in degree Celsius
and “t” represents time in minutes.
It can be seen from figure 3 that data for hydrocarbon and external fire are similar in shape.
Hydrocarbon fire temperatures tend to be 75% higher than external fire. The standard fire curve is
similar in shape and values when compared to other standard curves like ISO.
Θg = 20 + 345 log10 (8t + 1) [°C] 01
The external curve is intended for the outside of the separating external walls. When this wall is
exposed to the external cloud of fire coming either from the inside or adjacent to the respective
external wall (Franssen, et al., 2006). Formula 2 defines about the external fire curve.
Figure 3: Time Temperature Curves according to Eurocode

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Θg = 660 (1 – 0.687e-0.32t
– 0.313e-3.8t
) + 20 [°C] 02
In terms of hydrocarbon fire, the following formula is used for to understand the effects of
hydrocarbon fire.
Θg = 1080 (1 – 0.325e-0.167t
– 0.675e-2.5t
) +20 [°C] 03
2.1.4.2. ISO 834
The standard fire curve presented by the International Standard Organisation, ISO 834 is achieved by
using formula 04 producing chart showed in figure 4.
Tg = To + 345 log10 (1 + 8t) 04
2.1.5. Parametric Fire Curves
Along with the use of standard fire curves, many codes and standards are now making use of
parametric fire curves. Parametric fire method is used as a method to approximate post flashover
compartment fires. Parametric fire curve is similar to that of compartment fire with almost same
requirements; the size of compartment, fuel load, ventilation condition and thermal properties of
compartment wall and ceiling (University of Manchester, 2007). When compared to standard fire
curve, parametric fire curves provide a more realistic estimate of the temperature within a
compartment which is more advantageous in structural fire design of steel members. The analysed
results assume that the temperature in the fire compartment is uniform. According to BS EN 1991 – 1
Figure 4: ISO 834 Standard Fire Curve

Page 17
– 2 (2002), the method in achieving natural fire model is divided into two categories: simplified fire
models and advanced fire models.
For simplified fire models, Annex A in BS EN 1991 – 1 – 2 contains guidelines in achieving
parametric fire curve in compartment fires. The equation used by the standard is given by Formula 05.
Θg = 20 + 1325 (1 – 0.324e-0.2t*
– 0.24e-1.7t*
– 0.472e-1.9t*
) [°C] 05
Where,
t* = t × Γ Γ = [O/b]2
/ (0.04/1160)2
t = time b = thermal absorptivity for total enclosure
O = opening factor of fire compartment.
Under Annex A of EN 1991 – 1 – 2, there are two restrictions given by;
1. The time-temperature curves are valid for compartment up to 500m2
without any roof openings and
a maximum floor size of up to 4m. It is also assumed that the fire load of the compartment is
completely burned out.
2. If the fire load densities are specified without any specific consideration to combustion behaviour
(see annex E), this approach will then only be applied to fire compartments with mainly cellulosic
type fire loads.
From the equation for parametric fir curve shown in formula 5, the most influential factor is its
opening factor, “O”. It is included in almost all parametric fire curve equations and is used to govern
the behaviour of fire. The opening factor represents the amount of ventilation depending on the
opening area in the compartment walls, on height of the openings and on the total area of enclosure
surface. The value of “b” is introduced in the parametric fire equation to account for the multiple
layers present in the enclosure surface. If however there are not multiple layers then the value of b can
be taken as 1. To calculate the value for b;
b = √(ρcλ)
With many variables and multiple equations needed to create the heating and the cooling phase of the
fire, parametric fire, as described by EN 1991, is said to be a challenging curve for use in design and
practice.
In case of advance fire models (BS EN 1993 – 1 – 2, 2005), the following of the three models should
be used:
1. One-zone models – a uniform time dependent temperature distribution in the compartment.

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2. Two-zone models – upper layer with time dependent thickness and time dependent uniform
temperature and lower layer with time dependent uniform and lower temperature.
3. Computational Fluid Dynamics – CFD models give the temperature evolution in the compartment
in a time and space dependent manner.
2.1.6. Cardington Fire Test
It is vital to understand the behaviour of fire to steel structures, in order to attain information for its
behaviour; a full-scale fire test was carried out in a research facility in the UK. Between 1995 and
1997 a full-scale fire test was conducted on a constructed steel structure at BRE test facility at
Cardington, UK. The test was directed by British Steel Swinden Technology Centre. The aim of the
test was to understand and develop numerical calculation procedures that guide in predicting the
structural behaviour of steel framed building under fire.
The large scale test comprised of four fire tests which were carried out on different parts of the
building in order to understand various facets of structural behaviour. The building was designed as
per the use of an office building and was tested in an open plan.
2.1.6.1. Facility
Four tests were conducted on an eight storey composite frame building within the BRE facility at
Cardington, UK. The frame constructed was of composite steel and concrete to meet the national code
“British Standards”, BS 5950. The steel frame building was also checked for compliance with
provision of EC3 ENV 1993 – 1 – 1 (pre standard for Eurocode 3 during the test phase). One of the
most important things that needs to be considered is that the building was tested under normal
commercial pressure, which would mean that the data produced are realistic and can be applied/
compared to a real structure in order to understand the behaviour of steel in actual fire conditions.
Cardington fire test structure constructed is a braced frame including three core; one central elevator
shaft and two stair wells at either end of the building. Figure 5 defines the layout of the structure,
showing that it consists of five 9m bays along the elevation and 6m-9m-6m bays across the gables
(British Steel plc, Swinden Technology Centre, 1999). The total area of the layout is 45m x 21m.

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For simplicity in design and the aim to reduce costs, only 4 types of beams were used (British Steel
plc, Swinden Technology Centre, 1999): 9m secondary beam of grade S275 with 305x165x40 UB,
9m primary beam of grade S275 with 610x229x101 UB, 6m primary beam of grade S355 with
356x171x51 UB and 9m perimeter beam with grade S355 with 356x171x51 UB.
Due to moderation in design load specification, only 1/3rd
of the definite imposed load was applied
during the tests. The imposed load was implemented using sandbags. On all floors except roof, a total
of 2.4 kN/m2
was used with use of 12 sandbags (demonstrated in Figure 6) around the area of 9mx6m,
each weighing around 1.1 ton. Full details of floor loading are described in Table 2.
Load Case Value (kN/m2
)
Composite Slab 2.06
Steel Sections 0.25
Raised Floor 0.4
Services 0.25
Ceilings 0.15
Partitions 1.0
Imposed 0.83 (1/3rd
of design load)
Table 2: Floor Loading Details
2.1.6.2. Tests Conducted
During the time frame of 1993 – 1995, four full scale fire tests were conducted on Cardington test
steel frame building. Each fire test was designed to understand structural behaviour in different ways.
Figure 5: Floor layout of Cardington test building
Figure 6: Loading of Cardington steel framed building

Page 20
Tests conducted with details about its objective, description, fire description and the measurement
needed are all defined below. The main focus of the test conducted was, after completion of the
project, the temperature data obtained will be used in understanding and designing of numerical
calculation procedures (British Steel plc, Swinden Technology Centre, 1999).
1D – Restrained Beam
The aim of this test was to understand the structural deformation when a beam is heated and restrained
by a composite slab spanning in two directions, with surrounding steel at ambient temperature.
The restrained beam test was carried out on the 7th
floor of the building using a 305x165x40 UB
spanning 9m. In order to achieve a uniform temperature result, a gas fired furnace of 8mx3m was
incorporated in the design and built up to the underside of the composite floor. In order to minimise
heat losses, ceramic fibre collars were fitted at the ends of the beam as they passed through the
furnace wall.
Measurements which were conducted from the test are: temperature, strain gauge measurement,
vertical deflection and rotational measurements.
2D – Plane Frame
The aim of this test was to understand the behaviour of series of beams and columns supported by the
fourth floor by taking a 2D slice across the building. Fire protection also played a necessary role at the
connections.
Understanding the importance of fire protection, all columns of fourth floor were lightly protected up
to a height of 200mm below the connection. However the beams (beam to beam and beam to column)
remained totally exposed to fire. To heat up the structure, at fourth floor a gas fired furnace of
21mx4m was constructed to form a 2.5m corridor across the building.
vertical deflection, column displacements and rotational measurements.
3D – Corner
The aim of this test was to understand the behaviour of the complete composite floor system,
particularly the importance of membrane action under fire.
This test was conducted on first floor of the building; a compartment of 80m2
area was built in one
corner of the structure. To ensure no load bearing function was provided from gable end walls and
wind posts, all of the restrained ties were removed. In addition, the slots in wall construction were
also provided below the beams to ensure that no additional support to the floor slab was given. This
would prove that the walls of the first floor or the entire structure were nothing more than a non-

Page 21
loadbearing for containing the fire. Ventilation with a 7m wide opening was also provided and
partially covered by insulated screen. Although the ventilation conditions were pre calculated,
opening factor of 0.031m1/2
, the screen allowed fractional support to the burning rate temperature
within the compartment. To test the structure with extreme temperature of around 1000°C, the fire
load was increased to 45kg with an increase in the opening factor of 0.034m1/2
.
Based on the structural behaviour to fire in 2D – plane frame test, 25mm of ceramic fibre blanket was
used on all columns and beam to column connections. However, fin plate connections and both
primary and secondary beams remained exposed to fire.
vertical deflection, column displacements and rotational measurements.
Office Fire (demonstration)
The aim of this test was to conclude the research from previous studies in a more realistic fire
scenario and at the same time assessing other structural behaviour not addressed previously.
A compartment of 18mx10m was constructed in the form of a realistic office. The compartment was
fitted with modern furniture that would be found in a real office along with placing (figure 7),
computers and filing system while making use of the same proportion of wood and plastic (this
information was achieved from a survey carried out in modern office accommodation). The fire
loading of 45.6kg was applied from the total of wood/m2
of floor area. Similarly to previous tests,
columns and beam to column connections were protected with 25mm of ceramic fibre and the beams
(primary and secondary) were left unexposed to fire.
Measurements which were conducted from the test are: temperature, strain gauge measurement and
vertical deflection.
Figure 7: Office layout for Cardington Fire Test

Page 22
2.1.6.3. Effect on Fire Protection
The tests conducted on the steel framed building at Cardington, UK described above play a critical
step in structural fire protection of steel members in various ways. These ways were described by
Wang (2002):
1. It is important to examine the use of fire protection on steel members. It is imprtant to know that if
chosen to add fire protection to steel members, in a real construction, this would add labour costa and
extend the time in construction.
2. Research attained from Cardington fire test can be used as knowledge and can also be used as
comparison data to newley designed building for the performance of unprotected steel members.
The results attained from Cardington Fire tests display how structural steel members react under fire
conditions. This can aid engineers in using the data in creating design fires and conditions in
accurately depicting fire occurring in multi storey offices.
All of the data that was recorded at Cardington is now available online by British Steel. With easier
access, engineers can now progress in analysing and understanding of individual steel members along
with the entire steel structure under fire conditions.
2.1.7. Broadgate Fire
A fire was developed during the construction of a fourteen storey building called Broadgate Building
in 1990. During the fire, smoke detectors were not operational and sprinkler systems were not in
operation. It was till such extent that, protection of beams and connections were yet to be applied as
well as fire protective cladding had not been applied to the columns. The entire structure was covered
in plumes of fire causing over £25 million worth of damage, of which only £2 million worth of
damage was caused to the structural steel frame (Wang, et al., 2013).
2.1.7.1. Fire
The Broadgate Fire happened during the construction of a fourteen storey steel framed building. The
structure inhered of steel columns with composite beams, supporting a composite long-span lattice
truss. According to the design, fire protection of the building was to provide for standard fire of 90
minutes, however, with on-going construction, the protection to the structural elements was yet to be
applied. With lack of active measures, the developed fire spread quickly at very high temperatures
causing severe damages.

Page 23
According to the reports published and articles provided by Wang, et al., the fire started on the first
floor. The temperatures recorded were over 1000°C in some parts of the floor and the maximum steel
temperature achieved was just below 600°C.
2.1.7.2. Implications
Observing the damages caused by fire at Broadgate building, two theories can be removed (Wang, et
al., 2013).
Theory 1: During the fire scenario, it is known that the fire load was very less as there was no
imposed load acting on the building; the temperatures experienced by the steelwork would have been
fairly lower than the critical temperature of steel which would mean that there would not have been
any structural element failure. However, in this case there was a massive structural element failure;
distortion and local buckling (bottom flanges and webs near the support) was suffered by steel beams.
Failures and damages were also suffered by structural columns (Figure 8a). Due to column failure, the
load bearing capacity was reduced, causing vertical deformation (Figure 8b).
Theory 2: Even after such damages caused on the first floor of the building, the structure was stable
and all the floors retained their durability, preventing the spread of fire to other floors of the building.
This could be because the structure redistributed its loads from the failed elements to other parts of the
structure.
(a) Buckled column and beam deformation (b) Floor deformation
Figure 8: Broadgate fire damages

Page 24
3MATERIAL PROPERTIES
Properties of steel results from both its me chemical composition and its thermal condition, this could
relate to how the steel has been manufactured, including fabrication process. The standards for the
product define the limits for quality, composition and performance and these limits are used by
structural engineers in designing structures. This chapter evaluates the chemical and thermal
properties of structural steel relating to high temperature.
3.1. Thermal Properties of Steel at Elevated Temperature
3.1.1. Thermal Expansion
Thermal properties of steel define that steel expands at high temperature. High temperature in steel
can be experienced when there’s fire. With high temperature, steel loses its strength (load beating
capacity). Although steel temperatures vary according to the density, thermal conductivity and
specific heat, these differences still do not hold any effect on the strength of steel. Figure 9 define the
steel temperature vs thermal elongation, of how strength of steel is decreased with an increase in
temperature (EN 1993 – 1 – 2: 2005).
Figure 9: Thermal elongation of steel at elevated temperatures (European
Committee for Standardisation, 2005)

Page 25
The coefficient of thermal expansion can be used in order to work out the expansion, using Formula
06:
Δl/l = α(T) ΔT 06
Where,
Δl = change in length α(T) = coefficient of thermal expansion
l = initial length ΔT = change in temperature
3.1.2. Volumetric Specific Heat
Specific heat relates to a materials capability to absorb heat. Specific heat for steel is a function of
temperature and is independent of the composition of steel (Farmahini, 2013). The specific heat, “cs”,
in terms of Eurocode (European Committee for Standardisation, 2005) can be achieved using the
Formula 07 given below.
cs = 425 + 7.73 (10-1
)T – 1.69 (10-3
)T2
+ 2.22 (10-6
)T3
[J/kg°C] for 20 ºC ≤ T ≤ 600 ºC 07a
cs = 666 + 13002 / (738 – T) [J/kg°C] for 600 ºC < T ≤ 735 ºC 07b
cs = 545 + 17820 / (T-731) [J/kg°C] for 735 ºC < T ≤ 900 ºC 07c
cs = 650 [J/kg°C] for 900 ºC < T ≤ 1200 ºC 07d
Where,
T = temperature of steel, °C
For simplicity in calculations, specific heat could be considered to be independent of temperature,
giving an average value for cs as 600 J/kg°C.
The variation of specific heat from the formula above when compared to the temperature of steel
provides with graph shown in Figure 10. As seen from the graph shown in Figure 10, it can be seen
that there is a sharp peak at 730°C. According to Eurocode 3, this is because of metallurgical change
in the steel crystal structure.

Page 26
3.1.3. Thermal Conductivity
Thermal conductivity relates to the rate at which a material conducts heat. In terms of steel, it all
depends on the temperature and the composition. In comparison to other properties described above
(thermal expansion and volumetric specific heat), thermal conductivity is affected by the
microstructure of steel. According to Eurocode 3, structural steel’s thermal conductivity can be
approximated using the graph shown in Figure 11.
The accurate thermal conductivity of steel can be attained using Formula 8. However, for simpler
calculations, thermal conductivity, λa can be taken as 45 W/mK.
Figure 10: Specific heat of steel as a function of the temperature
Figure 11: Thermal conductivity of steel as a function of the temperature
(European Committee for Standardisation, 2005)

Page 27
λa = 54 – 3.33 x10-2 θa [W/mK] for 20 ºC < θa ≤ 800 ºC 08a
λa = 27.3 [W/mK] for 800 ºC < θa ≤ 1200 ºC 08b
Where,
θa = steel temperature [°C]
As noted from Figure 11, there is linear decrease in thermal conductivity as the temperature increase
from 0°C to 800°C and remains constant afterwards.
Thermal conductivity of steel is higher to that of concrete. It is recorded that at room temperature,
thermal conductivity of steel is about 50 W/mK whereas for concrete it is 2 W/mK. Conductivity of
steel is uniform in normal sized sections, however, temperature differences can occur in large sections
or sections which are able to lose heat, e.g. top flange in contact with concrete slab.
3.2. Mechanical Properties of Steel at Elevated Temperature
Creep is the biggest concern in the mechanical properties of steel. If the steel temperature reaches
over 450°C, increase in both the stress and the temperature influences steel to deform. Mechanical
properties of steel change when strength and the stiffness is reduced in steel due to an increase in
temperature. Eurocode 3 defines the temperature dependence in detail using the chart shown in Figure
12. The reduction factor, kθ, is used to determine the resistance of steel to tension, compression,
moment and shear force.
Figure 12: Reduction factor for stress-strain steel at elevated temperatures

Page 28
3.2.1. Stress-Strain Relationship
According to Eurocode 3, the stress-strain relationship chart shown in Figure 13 can be used to
determine the strength and the deformation properties of steel at elevated temperatures. This applies
when the steel heating rates are between 2 K/min and 50 K/min.
From the figure shown above, the elements which are unknown:
fy,θ = effective yield strength εy,θ = yield strain
fp,θ = proportional limit εt,θ = limiting strain for yield strength
Ea,θ = slope of the linear elastic range εu,θ = ultimate strain
εp,θ = strain at proportional limit
According to Kodur & Franssen (2010), proof strength can be used in place of yield strength of steel
at elevatd temperatures. The proof strength of steel can be taken as the point from the stress-strain
curve with a line intersecting at 1% strain. Thi is well defined in the chart shown in Figure 14.
Figure 13: Stress-strain relationship for steel at elevated temperatures (European
Committee for Standardisation, 2005)
Figure 14: Stress-strain curve for strain illustrating yield and proof strength

Page 29
4HEAT TRANSFER
4.1. Heat Transfer for Unprotected Steel Member
If a structure was to go under a transient temperature increase with unprotected members, it could
result in a structural member reducing strength. At this high temperature, steel tends to expand and
lose strength causing it to buckle or fail in some cases.
If steel were to have high diffusivity, uniform temperatures exist through the member, whereas steel
with low diffusivity can expect a gradient temperature. Thermal gradient in a structural member will
cause the member to expand unevenly with compression stresses in the hotter section and tension
stresses in the other parts of the section.
The uneven expansion of the member will cause deformation, making the material swell towards the
source of the heat. In scenarios where deformation is restrained or be able to move, the member will
generate additional stresses (as seen in Figure 16) and add those to the external loads (as seen in
Figure 17).
Figure 15: Heat transfer in an unprotected steel member
Figure 16: Deformation (left) thermal stresses due to fire (right)

Page 30
During fire, the rise in temperature for steel members depend on the duration of heating,
thermophysical properties of fire and steel members. For this project, Vulcan and design spreadsheet
will be used to design for fire resistance of steel structures; in this program, three forms of heat
transfer are used to evaluate the steel temperature. For design spreadsheet, heat transfer can be
accounted with use of equations.
Formula 9 provides a method to work out the temperature increase in unprotected steel in time step t
(≤ 5 seconds):
a.t = (ksh/caa) × (Am/V) × hnet.d × t 09
Where,
ksh is the shadow effect caused by the local shielding of radiative heat transfer, due to shape of the
steel profile (“⌶” profiles have shadow effects and “◻” profiles don’t). ksh can be calculated using
Formula 10:
ksh = 0.9 × (Am/V)box / (Am/V) 10
According to Eurocode 1 (2002), thermal actions are achieved by net heat flux to surface member.
The net heat flux can be determined by heat transfer through convection and radiation and can be
achieved with Formula 11.
ḣnet = ḣnet,c + ḣnet,r [W/m2
] 11
Convection, in terms of fire situation, relates to plume from fire moving past transferring heat to a
cool solid object. Convection is a complex problem to study in terms of fire spread and one can only
assume the flame spread parameters. The net convection can be predicted by using Formula 12:
ḣnet,c = αc × (g – m) [W/m2
] 12
Radiation, in terms of fire situation, relates to transfer of heat energy via electromagnetic waves.
These waves can be absorbed by any object that is in the right sight of the heat source. The net
radiation per unit surface area can be predicted by using Formula 13:
ḣnet,r = 5.67 x10-8
× Φεres [(g + 273)4
– (m + 273)4
] [W/m2
] 13

Page 31
4.2. Heat Transfer for Protected Steel Members
In order to calculate the heat stored in protective layer for the member, φ, Formula 14 should be used:
φ = [(cpp) / (caa)] × dp × (Ap/V) 14
According to Eurocode 3, the temperature rise in steel in time step t (≤ 30 seconds) can be calculated
using Formula 15:
a.t = (λp / dp)/(caa) × (Ap/V) × (1/(1 + φ/3)) × (g.t – a.t) t – (eφ/10
– 1) g.t 15
The relationship between heat stored in protective layer and the temperature rise in steel relies on
hypothesis that there is no thermal capacity in the insulation. This would mean that transfer of heat to
the member would take longer time. Protective layer generally used contains moisture which causes a
level of increase in heat rate at around 100°C.
In heat transfer for protected steel members, temperature dependent property consists of thermal
conductivity, specific heat and density of insulating materials; of these specific heat and the density
do not change significantly. Thermal conductivity, however, does increase when the temperature goes
from 100°C to 1000°C. The process is very complex and in order to achieve the final thermal
conductivity, calculations need to be run through computer program. For simpler calculations, average
value for conductivity can be used based on the mean temperature of insulation when steel member
reaches maximum safe temperature, or, safety factor can be introduced with maximum acceptable
temperature of around 600°C.
Figure 17: Heat transfer in protected steel

Page 32
4.3. Section Factor
Section factor introduced in calculations for both protected and unprotected steel members, Am/V,
refers to the rise in temperature of steel section. The formula “Am/V” is where Am is the surface area
of a member through which heat is flowing to the steel section and V is mass of steel. During fire
scenarios, increase in Am would mean that there is rapid increase in temperature for the member,
inversely; increase in V would mean that there is slow increase in temperature. So, the lower the
section factor of a member, the lower the rate of increase in temperature.
In most cases, section factor for most members is somewhere between 10 and 300. If in cases where
the section factor is more than 300, then the temperature of the member is same as the furnace gases
and if lower than 10 then temperature is varied in the member. Figure 18a shown below displays the
section factors for selected types of unprotected members and Figure 18b displays the section factors
for selected type of protected members.
(a)
(b)
Figure 18: Section factor for protected and unprotected steel members (Haller & Cajot, 2006)

Page 33
4.4. Protection Mechanisms
Fire protection mechanisms are used in structures to delay rise in temperature in members when
exposed to fire. In order to achieve the best protective mechanism, a designer must be aware of the
rating of the used factor, such as the properties of the protective materials and the temperature it can
withhold. This usually can be achieved via testing of the structural mechanism, thus validating if it
meets the set criteria by the client and the designer.
The protection mechanisms commonly used in structures are listed below:
 Insulating – These are materials with low conductivity adding minimal weight to the
structural member. Usually consisting of SFRM (Sprayed Fire Resistive Material), mineral
fibreboard and ceramic wool.
 Absorbing – These are materials that release water of crystallisation in order to reduce the
pace at which the material heats up. Usually gypsum or concrete based products.
 Intumescent – These are materials that are applied in the form of coating. Different to
insulating materials, these protective materials tend to expand when exposed to high
temperatures and act as an insulation layer. Materials like this are expensive however provide
great results, such as reduced weight, durability and aesthetics.
The thermal properties of protective mechanisms described in Table 3 below:
Material Unit mass
[kg/m3
]
Moisture
content
[%]
Thermal
conductivity
[W/mk]
Specific heat
[J/kgK]
Spray-on
- mineral fibre
- vermiculite cement
- perlite
300
350
350
1
15
15
0.12
0.12
0.12
1200
1200
1200
High density sprays
- vermiculite (or perlite) and cement
- vermiculite (or perlite) and gypsum
550
650
15
15
0.12
0.12
1100
1100
Boards
- vermiculite (or perlite) and cement
- fibre silicate or fibre calcium silicate
- fibre cement
- gypsum boards
800
600
800
800
15
3
5
20
0.20
0.15
0.15
0.20
1200
1200
1200
1700
Compressed fibre boards
- fibre silicate, mineral wool, stone wool 150 2 0.20 1200
Concrete
- lightweight concrete
- concrete bricks
- bricks with holes
- solid bricks
2300
1600
2200
1000
2000
4
5
8
-
-
1.60
0.80
1.00
0.40
1.20
1000
840
1200
1200
1200
Table 3: Thermal properties of common fire protection materials (ECCS Technical Committee 3, 1995)

Page 34
Most SFRM protective layers make use of cementious or fibre materials to protect steel from heating.
Mineral fibre and vermiculite cement are most commonly used materials on steel columns, beams and
joists. Materials like these are commercially sold and have proprietary formulations; therefore, it is
crucial that designers must follow manufacture’s recommendations for application.
Protective mechanism like intumescent coatings is largely advantageous. Coatings used have an
appearance of thick film or paint and when these materials are exposed to fire, it chars, foams and
expands to form an insulating layer for the steel member. In order to retain this formed layer,
reinforcing is essential at sharp corners, e.g. flange tips.
Gypsum boards are largely used in protection of members too. These consist of non-combustible
cores and paper to form sheets which are available in range of sizes depending on the member or
recommendation. There are various types of gypsum boards available, special fire resistant types are
best for fire protection.
Mineral fibre products are generally more expensive than other SFRM products but are easy to install
and takes minimal maintenance. Unlike absorbing materials, these products do not consist of wet
process and are therefore easy to maintain too. Materials like these are generally used in projects
where speed and dry process is of important. These materials are supplied with outer sheathing of
either aluminium foil or similar products. Mineral fibre products are fixed to steel members in variety
of methods, such as wire ties, screws, bonding agent, etc.
Concrete protection is largely used in hollow steel members. The biggest advantage in using this
system is that no advance fire protection material is necessary and the load bearing for the member
will be increased (Steel Construction Institute, 2012), however, the member gets bulky and adds more
weight to the structure.

Page 35
5FIRE RESISTANCE ASSESSMENT
5.1. According to Eurocode 3
In order to meet the fire requirements, designers have to follow the given guidelines in Eurocode 3.
This is measured in terms of time. The value of time given via calculation mean that the fire resistance
will protect the structural member from standard fire until that time after which the member will fail.
The time requirements depend on the number of floors in the building, type of occupancy, the fire
load and the amount of active measures in the building.
Fire resistance assessment in terms of Eurocode 3 is based on either standard fire tests in a furnace or
calculations. For this particular dissertation, a graphical rendition of a member resistance is designed
as regards to the temperature; critical load temperature can then be worked out for the given load for
non-composite beams with lateral restraint and tension members.
5.1.1. Calculations for Design Data
The mechanical properties of steel and the protection mechanism change according to the
temperature. In fire scenarios, the effect of temperature on a structural member is constant. As
member temperature increases, the resistance will lose and on resistance failure, the member will fail.
This is called critical temperature, θa,cr. Critical temperature relies upon the member’s ability to
withstand high temperatures in fire conditions. It is independent to the size of the member or the rate
at which member heats up.
In order to achieve the critical temperature, utilisation factors of the member is involved and it is
calculated with measured yield stress. Utilisation factor is the ratio of design loading in fire to design
loading at ambient temperature. It can be calculated with Formula 16:
µ0 = Efi,d / Rfi,d,0 16
Where,
Efi,d = effects of action for fire design, Rfi,d,0 = resistance of isolated member for ambient temperature

Page 36
For simpler calculation, to achieve µ0, Formula 17 can be used:
µ0 = ηfi × (γM,fi / γM,1) 17
Where,
ηfi = (γGA Gk + ψ1,1 Qk,1) / (γGA Gk + γQ,1 Qk,1)
The simpler formula (Formula 17) is said to be traditional formula, as ηfi is calculated as the amount
of design loading at ambient temperature. The partial safety factor for steel is 1,0.
At ambient temperature, permanent loads and combination factor or variable loads are: 1.35 and 1.5,
respectively. Whereas in fire design, permanent loads and combination factor or variable loads are 1.0
and 0.5, respectively. Table 4 shows the load reduction factor based on partial safety factor according
to EC3.
Qk,1 / Gk 1 2 3 4
ηfi 0.53 0.46 0.43 0.41
Table 4: Load reduction factor based on partial safety factor according to EC3
Shown below in Figure 19 is a graph of critical temperature vs degree of utilisation, µ0, for simple
steel members based on standard fire test.
The curve achieved in the graph is based off formula from EC3 (Eq 4.22), where the critical
temperature is expressed as a function of the degree of utilisation μ0, for class 1, 2 and 3 steel
sections:
Θa,cr = 39.19 × ln × [(1/(0.9674 (µ0)3.833
) – 1] + 482 18
The formula used can only be applied to non-composite members with section classification of class
1, 2 or 3 sections subjected to tension or bending that are restrained to prevent instability effects.
Figure 19: Critical temperature for simple steel members based on
standard fire test

Page 37
5.2. According to British Standard’s
According to British Standards, in order to determine the fire resistance of a member, BS5950-8 shall
be used and worked out using the load ratio method. Load ratio method is independent in comparison
to other fire resistance methods as it only requires the temperature in the critical section of the
member with the strength reduction of the member in fire scenarios. The fire temperature in the
compartment or in the member is achieved from the fire test data or thermal model. Moment capacity
method is also provided by BS5950-8 but however is sophisticated than the load ratio method and is
generally used on complex structures where temperature data is available.
5.2.1. Load Ratio Method
The load ratio method describes all the combined effects acting on the structural member in fire
conditions. Load ratio for members in bending would be the applied moment on the member at fire
limit state divided by the moment capacity of the member. It is assumed that the member is not
subjected to second order effects resulting from deflection.
Load ratio provides the designer with stress in the member at the fire limit state relative to the design
strength of the member. The higher the load ratio, the higher the retention of strength in member
during fire. Therefore, the temperature of the critical element to resist the applied load will be lower.
5.2.2. Moment Capacity Method
Carrying out small scale fire test on a structural member of a complex structure to obtain thermal
profile has proven to be inexpensive. Using the data obtained from the test, its fire resistance can be
evaluated by considering its strength properties in the section at elevated temperatures. This is known
as the Moment Capacity method and can be applied to composite beams, shelf angles and slim floors.
It is the foundation of the method in determining the resistance of composite floors in fire.

6BEHAVIOUR OF STRUCTURAL ELEMENTS
A fire in a compartment can affect the entire structure, its members and its mechanical, physical,
chemical and thermal properties. A steel framed structure subjected to fire relies on a number of
properties: degradation of materials at high temperatures and restraint stiffness of the structure around
fire. Elevating temperatures in a structure are the reason for deflections and failures. Failure of a
member links to failure of a structure. Failure of the member relies upon the size and shape of the
member, the location of the member, the location of fire and the type of protective mechanism
applied.
6.1. Beam Analysis
The occurrence of beams with lateral buckling at elevated temperature is very rare as most beams are
braced by floor system (Bennetts & Thomas, 2002). Bennetts and Thomas’ research findings were
based off the data produced by Cardington Fire Test Building of eight storey steel framed building
subjected to full scale fire test. It was recorded by the group that, unprotected steel beams designed to
be composite linked with composite floor slab in fire perform better than an isolated beam subjected
to fire. With this research, it can be noted that protection for some structural members can be avoided
as they provide a better result overall, also saving time and cost of the project.
Lewinger, et al. (1999) designed and tested a three storey steel framed building under fire conditions
and reviewed the difference between design moment strength and ultimate moment strength and that
the moment capacity of the structure need to be evaluated as the reserve moment capacity. The results
for reverse moment strength were analysed and later discussed that after two hour of fire resistance,
the reverse moment strength with a yield stress of 250 MPa or 345 MPa is less than the temperature
moment strength. This measn that the higher the steel performance, the better its durability under fire
and ambient temperatures. Therefore the overall fire resistance of the structure can be improved with
the use of high performance steel. Shown below in figure is the failure mechanism of simply
supported beam and continuous beams.
Figure 20: Failure mechanism for simply supported beam (left) and continuous beam (right)

Page 39
6.2. Column Analysis
According to Bailey (1999), the internal and external columns at Cardington Fire Test facility are
subjected to high moments which are caused by the expansion of connecting beams during fire test. It
was also sated in the report by Bailey that if the moments were included withihn the member in the
design process, then calcaulations would prove that the member was subjected to failure due to local
plasticity. The research further stated that the instability in column was affected by the heating rates in
beam to column, cross seciton and span of the beams, end rigidity of heated column and axial load at
the column. It was also proven that, cross section of column, connection rigidity of beam to column
and the horizontal restraint to the heated beams had shown to have nominal effect on behaviour of
column during fire.
Going back to Bennetts and Thomas (2002) research on Cardington Fire Test data, the reduction in
the failure temperature for steel column varies with its slenderness, for example the failure
temperature of a bulky column with slenderness ratio of 40 will be reduced by 100°C. Both Bennetts
and Thomas’ and Bailey’ research prove similar point of where columns are affected with expansion
of connecting beams in fire. The research further studies that due to the expansion of the beams
linking to expansion of floors, significant bending moments were established withi the columns. Other
factors to consider when analysing the failure of column is the end connection, size of column to
beam connection and the temperature of the column. It should also be noted that the presence of
thermal gradient in column reduces the failure temperature even more, while uniform distribution
proves beneficial.

Page 40
7METHODOLOGY
For this particular dissertation, two programs will be used in order to understand and design for the
fire resistance of steel structures: spreadsheet and Vulcan. This chapter will provide with brief
information about the test methods, its capabilities and limitations.
7.1. Spreadsheet Method
The results achieved form the finite element program, Vulcan will be used in comparison to Eurocode
3 calculation method. This will be done with aid of excel spreadsheet filed called FiRE.XLS which is
generally used to predict the temperature of a steel member using heat transfer theory to understand
and estimate the heat energy transferred to the member. The methods to achieve heat transfer to
protected and unprotected members are generally the same, with use of different formulas presented
in Chapter 4 to allow for the effect of protection on the rate of heating for steel member.
With use of the spreadsheet, the temperature of the beam can be calculated between intervals, by
considering the energy transferred to the beam during the previous time step. The duration of the time
step does not affect the calculated temperature however only defines the temperature of steel member
at a particular time.
The spreadsheet assumes that the structural steel member is of constant thickness and does not have
thermal gradient. This is governed by the section factor of the member. This is called a lumped mass
approach where no regard for the actual geometry of the cross section is given. Constant value for the
thermal properties of steel, such as specific heat and density are used in the spreadsheet to simplify
the method and number of variables.
Thermal properties and geometry of the steel member are averaged values and will not exactly be the
same when constructed in place. This would prove that accuracy is a must, if however, errors occur,
then other factors such as the temperature of the fire and the member interaction with fire may not
exactly be the same. This however is very rare to occur in a real design and construction of structure.
It is known that the spreadsheet data provides higher temperatures than other finite element programs,
such as Spreadsheet, the results achieved are acceptable to be used in design of a compartment or
when it is a four sided exposure and when analysing the temperature elevation of a simply supported
members.

Page 41
7.2. Vulcan
7.2.1. Computer Modelling
It is highly expensive to perform structural fire test, in order for designers to understand and design
for fire, computer simulations are now highly used. The data achieved from the tests performed in
these programs are used in understanding and designing for structural members in elevated
temperatures. This type of method is becoming readily available over the recent years and engineers
are now using these programs to design structural members. For this project, Vulcan finite element
program will be used to design a for fire resistance.
Vulcan is a non-user friendly program which works from a textual input file. It precisely describes the
structure / compartment to be modelled as a series of node connected by beam to column, shell or
spring elements, each by its specific geometry and material property. A heating regime and
temperature increments are prescribed in the program. The file is then reformulated to make it more
user friendly and improve its flexibility for future enhancements.
Vulcan takes an input file, processes its nonlinear finite element analysis and creates an output file of
results. The input filed can be analysed in series of batch file, allowing parametric studies to be
performed easily. This output file can then be interrogates in spreadsheet program.
7.2.2. Capabilities and Limitations
With advantages in use of finite element programs to understand its capabilities, there are a few
limitations too. The beam to column elements in Vulcan are presented as two node line elements with
each note consisting of eight degrees of freedom. The degree of freedom for this element represents
the strain and displacement in each of the three dimensions together with three selected derivatives of
these degrees of freedom (which signifies either direct-strains or shear-strains) with twisting and
warping. The eight degrees of freedom are transformed into eleven global co-ordinates. In order for a
model to be solved it is therefore necessary that three degrees of freedom are constrained at each
node. This can be done either manually by applying external boundary conditions or via being
constrained by other elements.
Limitations in Vulcan are that, only I shaped section can be defined in the elements. The only way
other shaped elements can be approximated is by defining I section with similar cross section
properties similar to the ones of desired shape. Tapered elements can also be approximated by
dividing long element along its length into sub elements, which is in smaller cross sectional area.
Spring elements have the same degrees of freedom as beam-column elements (Huang, 2011),
however, spring elements ae normally used to represent semi rigid connections so their rotational

Page 42
stiffness properties are modified in an analysis to simulate behaviour of moment connection with
temperature dependent stiffness and capacity. The author can then reformulate the input file to specify
each spring element as one of a choice of pre-defined types. Based off the results from Cardington
Test Fire, pinned, rigid and semi rigid elastic characteristics have been also been defined along with
two temperature dependent characteristics representing full and partial depth end plate connections.

Page 43
8
PROCEDURE
In this dissertation various parametric analyses will be carried out on the program Vulcan on steel
members at elevated temperatures at different location within the frame. Examining these members on
Vulcan would mean that the members are analysed in holistic manner. The tests will be carried out on
both protected and unprotected steel members via both Vulcan and the spreadsheet method. The
parameters for the tests are based on fire regime and characteristics of beam to column connectivity.
The dissertation is based on analysing 2D steel frame via Vulcan and spreadsheet. The building takes
a shape of a 2 storey non sway steel frame comprising of 5 bays, each at a distance of 9m. In the
transverse direction, there are 4 bays with a distance of 6m with a floor height of 4m. The sections for
the different elements used in the structure will be uniform.
8.1. Proposed Plan
In order to design for fire resistance, the proposed plans are that before the testing begins, the section
size of the members will be selected prior to designing, the members will be analysed according to
Eurocode 3 via the spreadsheet. The fire resistance time for the elements will be evaluated and the
hand calculations will be proposed for both protected and unprotected steel members. Both types of
members will be tested against standard and parametric fires to observe how these members react to
various fire conditions.
Simply supported beams will then be tested in Vulcan at elevated temperatures. The analysis will only
be carried out on unprotected beams exposed to ISO and parametric fire. The entire frame will then be
tested on Vulcan; the frame will be divided into segments to allow variation of temperatures, stress
and strain.
A number of five scenarios are designed which include different fire regimes. As this analysis is not
based on isolated members, different characteristics of beam to column connectivity will be analysed
including rigid and pinned connections. For testing of isolated members, spreadsheet method will be
used and cross examined on Vulcan. The results achieved for the steel frame building for the
scenarios will then be discussed in relation to each other. The scenarios are mentioned on the next
page.

Page 44
List of 5 scenarios for the proposed steel frame building:
Scenario 1: FIRST FLOOR – Bay 1 will be exposed to ISO 834 time-temperature fire regime with use
of rigid and pinned beam to column connection.
Scenario 2: FIRST FLOOR – Bay 1 will be exposed to parametric time-temperature fire regime with
use of rigid and pinned beam to column connection.
Scenario 3: FIRST FLOOR – Bay 3 will be exposed to ISO 834 time-temperature fire regime with use
of rigid and pinned beam to column connection.
Scenario 4: FIRST FLOOR – Bay 3 will be exposed to parametric time-temperature fire regime with
use of rigid and pinned beam to column connection.
Scenario 5: FIRST FLOOR – Bays 1-3 will simultaneously be exposed to ISO 834 time-temperature
fire regime with use of rigid beam to column connection.

Page 45
9DESIGN OF STEEL FRAMED BUILDING
In this chapter, steel frame building will be designed also evaluating elements and section sizes.
Spreadsheet program will be used to determine critical temperature of the elements according to
Eurocode 3. As mentioned in previous chapter, this is a non-sway building with 5 bays, each at 9m
and in the transverse direction, 4 bays, each with 6m and a floor height of 4m. Figure 21 shows the
side view of the building. As seen from the figure, line of symmetry has been added in the side view
of the building at half way point, this allows for a repetitive frame of the structure to be analysed in
Vulcan more manageably.
Secondary beams are attached to the building along the longitudinal axes, with them being placed
halfway between each transverse bay. With attachment of secondary beams, it is assumed that
primary beams are laterally restrained and in torsion at the mid span. The plan view of the building is
shown in Figure 22.
Figure 21: Plan view of the building

Page 46
9.1. Primary Beam
A primary beam with a section size 610x305x179 UB has been selected and verified for the
calculation analysis. The member has been categorised as Class 1 section; cross-section that can form
a plastic hinge with rotational capacity from plastic analysis without reduction of the resistance. In
finite element analysis, this beam will be exposed to three sided heating to simulate the condition of a
concrete slab on top of the member. Fire resistance and protection of primary beam is shown in Table
5.
Fire resistance and protection of primary beam
(Class 1 Cross-Section)
fy = 355N/mm2
Design Bending Moment, Msd = 1548.2 kNm
Permanent action, Gk = 12.2 kN/m2
Resistance bending moment, MRd = 1630.9 kNm
Variable action, Qk = 23 kN/m2
Shear capacity, Vpl, Rd = 1613.7 kN
Combination factor, Ψ1.1 = 0.5 Design moment in fire, Mfi,sd = 719.9 kNm
Qk,1/Gk = 1.9 Adaptation factor, k1 = 0.85
Reduction factor, ηfi = 0.465 Adaptation factor, k2 = 1
Critical temperature, θcr = 629.7°C
Table 5: Critical temperature values for primary beam members
The critical temperature achieved for an unprotected beam exposed to ISO fire is calculated to be
658.659°C at a time of 9.33 minutes.
Standard fire curves calculated for protected and unprotected beams are shown in graph displayed in
Figure 23.
Figure 22: Side view of the building

Page 47
In order to protect the structure from fire, fire resistance shall be applied to extend the time until
structural failure. This also saves lives of people inside the building. For primary beam to achieve 60
minutes of fire protection and as per Eurocode 3, sprayed mineral protection of 10mm was used. After
the application, the temperature of primary bean reduced to 628.06°C.
Comparing the temperature data achieved from both protected and unprotected beams, it is not an
improvement in terms of failure time for the beam. This could be due to the time temperature curve
provided by the spreadsheet. The failure of the beam at relatively low time is due to the design fire
quickly reaching high temperatures as shown in Figure 24.
0
200
400
600
800
1000
1200
1400
0 600 1200 1800 2400 3000 3600 4200 4800 5400 6000 6600 7200
Temperature(oC)
Time (sec)
Starndard Fire
Gas Temp Protected Unprotected
0
200
400
600
800
1000
1200
1400
0 600 1200 1800 2400 3000 3600 4200 4800 5400 6000 6600 7200
Temperature(oC)
Time (sec)
Parametric Fire
Gas Temp Protected Unprotected
Figure 24: Parametric fire curve for both protected and unprotected beam
Figure 23: Standard fire curves for protected and unprotected primary steel beams

Page 48
For parametric fire, primary beam’s temperature is nowhere close to the critical temperature and is
found to be at 133.3°C at the 60 minute mark. In fact, the highest temperature achieved by the
protected beam in parametric fire is 234.8°C at 32.25 minutes. Therefore it is vital to make use of
unprotected primary beams in Vulcan analysis and to keep columns protected in order to extend the
column failure time.
It is interesting to note the characteristics of fire interacting with protected and unprotected beams. At
45 minute mark the fire temperature of protected beam is higher (190.3°C) than that of unprotected
beam (114.1°C). This is because the application of protection layer to the beam increases its overall
heat capacity of the member and gradually dissipates the heat.
9.2. Column
A column with a section size of 203x203x71 UC has been selected and verified for calculation
analysis. According to Eurocode 3 the member is classes as Class 1 section; cross-section that can
form a plastic hinge with rotational capacity from plastic analysis without reduction of the resistance.
Throughout the testing the column will be exposed to a four sided fire exposure with one hour
duration during the Vulcan analysis process. Fire resistance and protection of the column is shown in
Table 6.
Fire resistance and protection of column
(Class 1 Cross-Section)
fy = 355N/mm2 Total design axial compression, Nsd = 1696.2 kN
Combination factor, Ψ1.1 = 0.8 Effective length factor = 0.7
Qk,1/Gk = 1.9 slenderness, λ = 52.9
Reduction factor, ηfi = 0.600 Normalised slenderness, λ/λ1 = 0.692
Buckling resistance, Nb,Rd = 1754.87 kN Normalised slenderness at θa, λθ = 0.785
Design loading in fire, Nfi,sd = 1018.3 kN
Buckling resistance at time t with
uniform θa, Nb,fi,t,Rd
= 1932.8 kN
Table 6: Fire resistance and protection steel column
As mentioned above in primary steel analysis, all columns will be protected and as per column
analysis, it usually buckles at around 406°C. Temperature achieved from steel column at 60 minute
mark is 607.2°C for ISO fire and for parametric fire, the temperature achieved in steel column at 60
minute mark is 215°C. As seen from the temperatures, the column is sufficient to remain stable. Even
though the temperature achieved for column from ISO fire exceeds the limit, it would mean that the
beam would face higher temperature and is predicted that the beam will fail much earlier than the
column.

Page 49
10ANALYSIS OF 2D FRAME
When designing for fire, it is essential that critical members of the structure are evaluated for fire
resistance and these members should be tested for ISO 834 fire time temperature curve. It is not
economical to perform fire test for each member of the structure but with help from finite analysis
software, Vulcan, structural analysis simulation can be run under more realistic boundaries, providing
results faster and more accurate. This type of analysis also demonstrates the non-uniform temperature
distribution within the member section.
From the primary beam analysis, the section size chosen is a 610x305x179 UB with a span of 9m.
The beam is simply supported from both ends with one end of the beam free to move in longitudinal
direction. The beam will only be exposed to three sided heating and will be subjected to both standard
and parametric fire conditions.
For Vulcan, the beam is modelled as a 13 nodes, each spaced at a distance of 750mm. Three node
beam elements will be used for this analysis which means that the beam will result in six elements as
shown in Figure 25. The analysis will be followed for both protected and unprotected beams. The
permanent and variable actions for primary beams are 12.2 kN/m2
and 23 kN/m2
respectively.
In order to understand the analysis thoroughly, deflections attained by the beams within a structure
will be compared to the deflection of the isolated beams for both ISO and parametric fire test. As
mentioned priorly, all beams will be unprotected and column protected. Beams will be exposed to
three sided heating whereas; columns will be to four sided heating. The fire duration during testing is
designed to for 60 minutes.
1 2 3 4 5 6
1 2 3 4 5 6 7 8 9 10 11 12 13
Figure 25: Simply supported beam model

Page 50
10.1. Scenario 1: FIRST FLOOR – Bay 1 – ISO Fire with Rigid and Pinned
Connections
The first scenario is based on ISO 834 fire with rigid and pinned beam to column connection for bay
1. This scenario focuses on achieving ISO 834 time temperature for two cases. Pinned beam to
column connections are only considered for scenario 2, 3, and 4 where individual compartments are
tested.
Critical temperature achieved for the beam in this structure is reached at the mid span of 450mm as
per the ‘span/20’ rule set by BS5950 – 8. Beams with same connection types have closely the same
temperature deflection curve whose results and data are relatively related. So, whether the beam is
exposed to ISO fire or parametric fire, the deflection temperature achieved will be the same; the only
difference will be between time temperature relationship. The deflection temperature for simply
supported beam is also plotted for comparison.
According to the results achieved, the pinned connection and simply supported beams reach their
critical temperature at 485°C whereas rigid connections reach their critical temperature at 660°and
628°C for ISO and parametric fire respectively. The simply supported beam reaches highest
deflection of 1065mm before failing. Simply supported and pinned connection starts to lose their
strength at 220°C after which the point increases dramatically. The transition for rigid connection is
not as gradual; the connection starts to lose its strength at 510°C onwards.
Figure 26: Bay 1 exposed to ISO fire conditions
0 100 200 300 400 500 600 700
0
-200
-400
-600
-800
-1000
-1200
Temperature Deflection Relationship
Deflection(mm)
Temperature (°C)
Span/20
Rigid
Pinned
Simply Supported Beam (ISO)
Figure 27: Temperature deflection graph of bay 1 (node 82) with isolated member subjected to ISO fire

Page 51
It should be noted that there can never be a perfect rigid or pinned connection. The data presented is
just a comparison between the two rather than predicting what will happen to the connection itself. It
should also be noted that rigid connections’ deformation process occurs in such a manner that the
stress occurring is distributed along the span of the beam and the cooler areas of the structure provides
restraint so that the beam does not fail before reaching its critical temperature.
It is evident that with use of ISO fire, structural elements heat much quicker than that of parametric
fire. There are various ways possible to model for parametric fire, so, reaching the temperature peak
could take much longer than that of ISO fire. It must be noted that data generated by ISO fire are not
realistic and therefore, a designer must pay enough research time in producing more realistic
parametric fire. Eurocode 3 mentions that with ISO fire, an unprotected beam can take between 6.52
minutes – 9.25 minutes to reach its critical temperature. According to the results achieved from the FE
analyses, an unprotected beam can take between 7 minutes – 11.9 minutes to reach its critical
temperature.
From Figure 29, it can be noted that the axial force gradually increases and then restores its force by
declining. The axial force for rigid connection is noted to be at 68 kN at 498°C. The beam then fails in
tension mode.
0 200 400 600 800 1000 1200
0
-200
-400
-600
-800
-1000
-1200
Time Deflection Relationship
Deflection(mm)
Time (sec)
Span/20
Rigid
Pinned
Simply Supported Beam (ISO)
Figure 28: Time deflection graph of bay 1 with isolated member subjected to ISO fire at node 82
0 100 200 300 400 500 600 700
80
20
0
-80
40
60
-20
-40
-60
Temperature – Axial Force Relationship
AxialForce(kN)
Temperature (°C)
Rigid (ISO)
Pinned (ISO)
Figure 29: Temperature - axial force graph for beam to column connections at bay 1

Page 52
There are various ways in modelling for beam to column connections. This is compared by Huang
(2011) where he has compared his achieved results with Block, et al.’s (2007). The results have been
compared for a compresive component based models where in Block et al.’s model, the connection
used is represented as assembly of springs which represents individaul components of the connection,
such as tension bolt rows, shear bolt rows and compression parts of beam and column’ web and
flange. In comparison form Huang and Block et al.’s work, for this analyses two noded spring
element is used in which the stiffness and the strength is determined based on each component of the
connection. Therefore, the results achieved for this connection is predicted to be better when
comparted to prediction by Block et al.’s model.
80
20
0
-80
40
60
-20
-40
-60
0 200 400 600 800 1000 1200
Time – Axial Force Relationship
AxialForce(kN)
Time (sec)
Rigid (ISO)
Pinned (ISO)
Figure 30: Time - axial force graph for beam to column connections at bay 1

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