avan sin o stru tural st lwork: an intro u tion to stru ... · ii course: advanced structural steel...

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Course: Advanced Structural Steel Design

Section: Structural Fire Design

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Revision: 0.3 – April 2015

By: RS Walls

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UNIVERSITY OF STELLENBOSCH

ADVANCED DESIGN OF STRUCTURAL STEELWORK:

AN INTRODUCTION TO STRUCTURAL FIRE ENGINEERING

POST-GRADUATE DESIGN COURSE

COURSE NOTES BY: RICHARD WALLS

COURSE COORDINATOR: DR. HENNIE DE CLERCQ

APRIL 2015


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ADVANCED DESIGN OF STRUCTURAL STEELWORK:

STRUCTURAL STEEL FIRE DESIGN COURSE NOTES

Introduction to the Course

Welcome to what is one of the first university courses in structural fire engineering in South Africa.

As a component of the Stellenbosch University Advanced Steel Design course it aims to provide an

introduction to fire engineering and how to apply this to building design.

The content of this course can only be considered a brief introduction to a highly complicated field.

However, fire engineering is rapidly gaining momentum around the world. In South Africa engineers

are signing off buildings on a daily basis saying that they comply with building code regulations but

they may either be: (a) totally under-designed in terms of fire resistance and become a large liability

and safety hazard, or (b) totally over-designed which wastes large amounts of money.

Historically in this country fire engineering has been generally ignored at design time and then dealt

with by the architects or fire engineers afterwards, rather than having structural engineers getting

involved on the building side. However, building behaviour during a fire is most certainly a topic

which structural engineers should be addressing, as it forms part of our scope and training (when

supplemented by fire engineering guidelines).

Code Basis for the Course

The main code documents that form the basis for this course are:

- Performance-based member design and heat transfer equations: SANS 10162-1 Annex G

which is based on the Canadian steel design code CSA S16, along with its fire design Annex

(Annex K).

- Prescriptive design: British and European design guides. In the UK very good guidelines

have been published by the producers of fire protection materials as well as the steel

producers. The ECCS in Europe has also produced a number of guides.

- Fire loads, parametric curves and material behaviour: Eurocode (EN) documents. The

Eurocodes are the most technically advanced suite of design documents in the world,

covering numerous aspects in relation to fire engineering. However, they are also complicated

to apply and the design guidelines have a slightly different philosophy to our steel code.

NOTE: The different codes use different nomenclature and symbols for various items. Be careful of

this.

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Course Contents

This course is structured as follows:

1. An introduction to fire engineering

2. Discussions regarding structural fire design and approaches

3. Fire curves and heat transfer equations

4. Characterising the behaviour of steelwork at elevated temperatures

5. Member design at elevated temperatures

6. An overview of advanced design focussed mainly on composite floor behaviour and design in

fires.

Tutorials are included with the design sections of this course.

Additional Reading and Resources

The following books are useful books for further information and advanced fire design details:

Design Guides and Books

Buchanan, A., 2001. Structural Design for Safety. New York: Wiley. (Covers a very wide scope)

CISC, 2010. CISC Commentary on CSA S16-09 Annex K Structural Design for Fire Conditions,

Ontario: Canadian Institute of Steel Construction.

ECCS, 2001. Model Code on Fire Engineering. First ed. Berne: European Convention for

Constructional Steelwork. (Very useful for performance based design, fire curves, etc.)

Franssen, J.-M. & Vila Real, P., 2010. Fire Design of Steel Structures. First ed. Berlin: European

Convention for Constructional Steelwork. (Very good for steel topics, composite not covered)

Lamont, S., 2001. PhD Thesis: The Behaviour of Multi-Storey Composite Steel Framed Structures in

Response to Compartment Fires. Edinburgh: University of Edinburgh. (Thorough explanations on

various topics are provided in the introductory chapters and it is freely available online)

Lennon, T., 2011. Structural Fire Engineering. First ed. London: ICE Publishing. (Basic introduction

to fire engineering)

SCI, 1990. Fire Resistant Design of Steel Structures - A Handbook to BS 5950: Part 8. 1 Berkshire:

The Steel Construction Institute. (Free)

Wang, Y., Burgess, I., Wald, F., and Gillie, M., 2012. Performance Based Fire Engineering of

Structures. CRC Press.

Prescriptive Design

ASFP, 2014. Fire protection for structural steel in buildings "The Yellow Book". 5th ed. Hampshire:

Association for Specialist Fire Protection. (Very comprehensive for prescriptive design)

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Tata Steel & BCSA, 2013. Steel Construction: Fire Protection, Tata Steel & British Constructional

Steel Association (BCSA). (Basic pamphlet with design guidelines)

Software Tools

- Stellenbosch University is in the progress of developing software tools to assist structural

engineers with fire design.

- Arcelor Mittal - Fire Calculations Download Centre, http://amsections.arcelormittal.com.

- Elefir-EN – Useful software for design of steel members considering standard or parametric

fire curves. It has been developed by the University of Liege and can be purchased.

- Slab Panel Method software. Produced by the University of Auckland and HERA, New

Zealand. Stellenbosch University is currently developing this for potential use in South

Africa. Other similar software includes MACS+, TSLAB, etc.

- VULCAN is a commercially available software package for the design of structures in fire. It

has been produced by Sheffield University over many years through numerous research

projects.

Lecturer Contact Details:

Richard Walls (Pr. Eng.) – Stellenbosch University, Office S320H – [email protected]

http://amsections.arcelormittal.com/

mailto:[email protected]

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Table of Contents Introduction to the Course .................................................................................................................. ii

Code Basis for the Course ................................................................................................................... ii

Course Contents ................................................................................................................................. iii

Additional Reading and Resources .................................................................................................... iii

Design Guides and Books .............................................................................................................. iii

Prescriptive Design ........................................................................................................................ iii

Software Tools ............................................................................................................................... iv

Lecturer Contact Details: ................................................................................................................... iv

1 Introduction to Structural Fire Engineering ................................................................................. 1-1

1.1 What is Structural Fire Engineering ..................................................................................... 1-2

1.2 What is a Fire and when does it Influence a Building? ........................................................ 1-3

1.3 The Effects of Fires on Society ............................................................................................ 1-3

1.4 The Role of the Structural Engineer .................................................................................... 1-4

1.5 How to Protect Steelwork .................................................................................................... 1-5

1.5.1 Passive Protection ........................................................................................................ 1-5

1.5.2 Active Protection (sprinklers etc.)................................................................................ 1-6

1.5.3 Compartmentation ........................................................................................................ 1-8

2 Structural Fire Design Approaches and Requirements ................................................................ 2-1

1.6 Prescriptive and Performance Based Design ....................................................................... 2-1

2.1.1 Historical Development of Design Methods ................................................................ 2-1

2.1.2 Prescriptive Design ...................................................................................................... 2-1

2.1.3 The “Yellow Book” and the “Euro-nomogram” .......................................................... 2-1

2.1.4 Performance Based Design .......................................................................................... 2-1

2.1.1 Prescriptive vs. Performance-based Design ................................................................. 2-2

2.1.2 What is Failure? ........................................................................................................... 2-2

1.7 Building Requirements in a Fire .......................................................................................... 2-4

1.8 Loading at the Fire Limit State (FLS) .................................................................................. 2-6

3 Fire Curves and Heat Transfer Equations .................................................................................... 3-1

1.9 Standard Fire Curves ............................................................................................................ 3-1

The Standard Fire ......................................................................................................... 3-1 1.9.1

The Hydrocarbon Fire .................................................................................................. 3-1 1.9.2

The External Fire ......................................................................................................... 3-1 1.9.3

Discussion regarding the Standard Fires ...................................................................... 3-2 1.9.4

1.10 Parametric or Real Fires ....................................................................................................... 3-3

Real Fire Curves........................................................................................................... 3-3 1.10.1

Eurocode Parametric Curve Equations ........................................................................ 3-3 1.10.2

Thermal Inertia of Compartments ................................................................................ 3-7 1.10.3

Opening Factors ........................................................................................................... 3-8 1.10.4

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Comments on Fire Loading Conditions ....................................................................... 3-8 1.10.5

Time Equivalence of Parametric Curves...................................................................... 3-9 1.10.6

4 The Behaviour of Steel at Elevated Temperatures ....................................................................... 4-1

1.11 The Thermal Response of Steelwork – Material Properties ................................................ 4-1

Elongation of structural and reinforcing steels ............................................................ 4-1 1.11.1

Specific Heat of Steelwork .......................................................................................... 4-2 1.11.2

Thermal Conductivity .................................................................................................. 4-2 1.11.3

1.12 The Thermal Response of Steelwork – Structural Properties .............................................. 4-3

1.13 Bolt and Connection Behaviour ........................................................................................... 4-5

1.14 Heat Transfer Equations....................................................................................................... 4-6

The Ap/V Concept ........................................................................................................ 4-6 1.14.1

Unprotected Steelwork ................................................................................................. 4-7 1.14.2

Protected Steelwork ..................................................................................................... 4-8 1.14.3

5 Member Design for Fires ............................................................................................................. 5-1

1.15 Prescriptive Design .............................................................................................................. 5-1

1.16 The “Yellow Book” ............................................................................................................. 5-1

1.17 Euro-Nomogram .................................................................................................................. 5-2

1.18 Design to SANS 10162-1: Fire Design Annex .................................................................... 5-4

Tensile Resistance ........................................................................................................ 5-4 1.18.1

Compressive Resistance ............................................................................................... 5-4 1.18.2

Bending Resistance ...................................................................................................... 5-5 1.18.3

Combined Axial Force and Flexure ............................................................................. 5-6 1.18.4

6 Introduction to Advanced Design Methods ................................................................................. 6-1

1.19 Overview of Advanced Design / Performance-based methods ............................................ 6-1

1.20 Global structural behaviour considerations .......................................................................... 6-1

1.21 Background to Composite Floor Design Methods ............................................................... 6-3

1.22 Composite floor design methods .......................................................................................... 6-5

Outline of Technical Details ........................................................................................ 6-6 1.22.1

Calculation Procedure .................................................................................................. 6-7 1.22.2

1.23 Detailing Requirements Necessary for the SPM .................................................................. 6-8

1.24 Software for advanced design ............................................................................................ 6-14

7 References .................................................................................................................................... 7-1

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1 Introduction to Structural Fire Engineering

COURSE DESIGN EXAMPLE

To explain structural fire engineering we will be following a design example through this course to

explain the various topics covered. Imagine that you were designing the multi-storey building shown

below, and you were asked to sign it off as sufficient according to National Building fire regulations.

Figure 1.1: Layout of the design example building to be used in this course

At this point in time you might have no clue of what to do, but by the end of the course you will be

able to do the basics of structural fire design, namely:

1. Classify a building and determine the required fire rating of elements.

2. Do a quick design using prescriptive methods, or

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3. Generate a parametric time-temperature fire curve according to the building properties.

4. Calculate the heat transfer and maximum temperature of the steelwork.

5. Determine the steel mechanical properties at the elevated temperature.

6. Design the members using simple calculations according to the new South African steel code

design annex in SANS 10162.

7. Learn about the philosophy of designing the floor using catenary action, which limits the

amount of passive protection that is required on beams.

1.1 What is Structural Fire Engineering

According to the Institute of Fire Engineering in the UK the definition of structural fire engineering

is:

"The application of scientific and engineering principles, rules (codes), and expert

judgement, based on an understanding of the phenomena and effects of fire and of the

reaction and behaviour of people to fire, to protect people, property and the

environment from the destructive effects of fire." (IFE, 2014)

Thus, at the end of the day the main aim of structural fire engineering is to primarily ensure the safety

of building occupants, with the protection of property and good as a secondary objective. However,

with the increasing influence of insurance companies in building development the protection of assets

is becoming more and more important.

Events such as the collapse of the World Trade Centre have increased the interest and rate of research

and interest in structural fire engineering worldwide in recent years. A report from the Federal

Emergency Management Agency (FEMA, 2002) which followed the World Trade Centre disaster

stated that: “The behaviour of the structural system under fire conditions should be considered as an

integral part of structural design” (bold added). Thus, it can be seen that the structural engineering

industry is slowly moving from prescriptive based methods towards rational structural fire

engineering solutions, whereby fire considerations are starting to become core issues rather than

problems addressed as an addendum. However, to consider all aspects of fire design is a complex and

multi-disciplinary task, typically left for specialists. It requires the consideration of “active and

passive measures, movement of smoke and fire, detection systems, fire safety management, structural

response and risk analysis” (Bailey, 2004b).

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1.2 What is a Fire and when does it Influence a Building?

A fire can be described as the “process in which substances combine chemically with oxygen from the

air and typically give out bright light, heat, and smoke” (Oxford, 2014). This definition captures some

of the most important aspects that need to be addressed during a fire, namely: oxygen is used up

which can endanger the lives of people, smoke is produced which limits visibility and can cause

asphyxiation, and the heat generated can structurally affect buildings and reduce strength.

Many small, controlled fires occur within buildings each year such as those from candles, cigarettes or

braais (barbecues). These are typically of no concern to fire engineers unless they develop into fires

which can endanger personnel or damage property. As fires grow personnel life safety is typically at

risk long before structural stability is reduced, generally because of smoke generation and the

consumption of oxygen. Only once temperatures reach a few hundred degrees Celsius do they become

structurally significant (except when load bearing elements are combustible), and at this stage people

would have either been evacuated or be dead.

Fire Engineers (who historically have mainly been mechanical engineers in South Africa) generally

play a more important role in the early stages of fire development. They are required to design

ventilation systems, assess emergency exits, try to ensure compartmentation, design sprinkler and

other active fire prevention systems, and much more. In the case of larger and more expensive

buildings CFD (computational fluid dynamics) models of smoke flow may be created to try predict

smoke spread and design systems more efficiently.

1.3 The Effects of Fires on Society

In South Africa there were 410 deaths due to fires in 2011, which is significantly up from 192 deaths

in 2000 and 226 in 2001 (FPASA, 2013). A total of 37,721 recorded fires in the country caused an

estimated damage of R2.1bn during 2011, which does not even include indirect costs such as lost

production. In 2008 the UK experienced losses due to fire worth £1.3bn, which was up 16% from the

previous year (ASFP, 2010). In America the NFPA reports that there were 1.5 million fires in 2008,

with 35.5% being structural fires (SSN, 2010), meaning that approximately 0.5 million building fires

occurred in one year alone. Hence, in can be seen that across the world fires are a great concern.

The following interesting facts regarding fires that have occurred in Europe are present by Twilt

(1994): (a) The likelihood of a person being killed in a car accident is 30 times higher than being

killed in a building fire. (b) In a survey of 5 European countries between 74% (Netherlands) and 85%

(France) of fatal fires occurred in domestic buildings. Hence, deaths in commercial and industrial

structures are fairly rare. (c) The cause of deaths in buildings due to heat and smoke is generally

between 74% (Germany) and 99% (Switzerland). Thus, very few deaths are caused by collapse or by

people being burnt alive. (d) A survey showed that the monetary loss due to fires is in the order of

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about 0.2-0.29% as a portion of Gross National Product. (e) Of the cost of damages to buildings and

businesses due to fires only between 21-32% is structural damage whereas the rest is due to stock and

indirect losses (productivity etc.).

Large fires generally gain high media attention and can become well known. Pictures of some well-

known building fires are shown below based on details from Engelhardt (2013).

Figure 1.2: Famous large building fires

1.4 The Role of the Structural Engineer

The Commission of the European Communities outlines the general requirements of construction

works subjected to fire conditions as:

“the load bearing capacity of the construction can be assumed for a specific period of time,

the generation of and spread of fire and smoke within the works are limited,

the spread of fire to neighbouring construction work is limited,

occupants can leave the works or be rescued by other means,

the safety of rescue teams is taken into consideration.” (CEC, 1988)

Thus, it can be seen that a structural fire engineer should:

1. ensure structural stability and safety for a required length of time in a given fire,

2. design for compartmentation to limit fire spread,

3. consider evacuation routes and ensure that they are safe, and

Interstate Bank Building,

Los Angeles (1988)

This building burnt for 4

hours causing $50million

damage. Four floors were

destroyed.

Parque Central East Tower,

Caracas (2004)

Fire burned for 24 hours

across 17 stories. Up to 100

firefighters inside the

building. Firefighting

stopped after 12 hours due

to concerns regarding

structural collapse.

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4. allow for fire suppression by methods such as sprinklers or external fire brigades.

One major issue with fires is that their behaviour can be greatly affected by human interactions, which

makes the accurate prediction of fire spread and temperature more complicated. For instance,

Bontempi and Petrini (2010) highlight that if a warehouse has an internal fire and the building has all

its doors closed it will have a lower ultimate temperature than if the doors are left open, or if the doors

are opened after 5 minutes when a fire-fighting team arrives. Thus, in true rational design many fire

scenarios may need to be considered in a similar way to which various load cases should be

considered (dead + live, dead + wind etc.),

1.5 How to Protect Steelwork

1.5.1 Passive Protection

Figure 1.3: Market share in the UK of various fire protection systems (Tata Steel & BCSA, 2013)

Since this course revolves around structural steelwork it is important to know what options there are

for protecting structural steelwork. The main ways used are:

Protective boards: these are usually gypsum-type boards which can be fastened around steel

sections. They are often cheaper than other products but can take time to install and cannot be

easily profiled to suit more complicated shapes.

Spray-on products: numerous spray-on products have been developed to form a barrier to heat

transfer. They are normally applied more thickly than intumescent paints, but can be cheaper.

Often they are not aesthetically pleasing.

Intumescent paints: these paints expand and char when heated to form a thick layer which

insulates the steelwork. They are very commonly used and can follow any shape, so are

aesthetically pleasing. However, they can be expensive.

Concrete encasement, fire screens and other such systems can also be utilised.

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The market share of various protection systems in the UK is shown in Figure 1.3. To illustrate the

importance and impact that fire protection coatings can have on a project refer to Tables 1.1 and 1.2,

which provide prices for a local intumescent paint and spray-on vermiculite. Prices are for the supply

and installation of the protective coatings. For a UC 203x203x46 to obtain a 2hr fire rating it can be

seen that the price of the intumescent paint is almost 1.6 times the price of the steelwork! For a UC

305x305x137 the increase in cost to obtain a 1hr fire rating is about 12%. If an engineer could reduce

those thicknesses using performance-based design methods millions of Rands could be saved on

larger projects (and this can be done as seen in these notes!).

Fire Protection Costing

60min Fire Rating Costing

120min Fire Rating Costing

Section Mass

(kg/m): Ap/V (m

-1):

Steel Cost (R/m):

Intumescent Paint – Nullifire S707-60

Vermiculite Spray

Intumescent Paint – Nullifire

S707-120

Vermiculite Spray

(approx. prices)

UC 152x152x23 23.3 304 R 652.40 R772.79 R418.30 Not possible R760.81

UC 203x203x46 46.2 205 R 1,293.60 R503.48 R559.30 R2,075.90 R1,018.51

UC 305x305x137 137 106 R 3,836.00 R472.92 R855.41 R1,779.01 R1,557.74 Table 1.1: Cost of fire protection coating to provide various fire resistance ratings for different sized columns

Fire Protection Product Thickness

60min Fire Rating DFT (mm):

120min Fire Rating DFT (mm):

Section Mass

(kg/m): Ap/V (m

-1):

Intum. Paint – Nullifire S707-60

Vermic. Spray

Intum. Paint – Nullifire

S707-120

Vermic. Spray

UC 152x152x23 23.3 304 1.313 25 Not possible 35

UC 203x203x46 46.2 205 0.593 23 4.519 42

UC 305x305x137 137 106 0.329 19 2.486 45 Table 1.2: Thickness of coatings to obtain various fire ratings.

1.5.2 Active Protection (sprinklers etc.)

In the ‘Model Code on Fire Engineering’ produced by the ECCS (2001) it is stated that fire safety

may be achieved using the following means: (a) fire prevention, (b) active or operational measures,

and (c) passive or structural measures. Active measures involve suppressing or preventing the growth

of the fire by an intervention with the likes of automatic sprinklers, a fire brigade, or suppression

systems.

The use of sprinklers in buildings has become standard practice in South Africa and around the world.

This is especially enforced by insurance companies who specify sprinkler requirements which go

beyond the protection of personnel to the protection of infrastructure, property and stock. International

insurance companies such as FMGlobal have very strict policies which dictate exactly how fire

protection is to be approached in various situations, which can also lead to very expensive firefighting

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installations. However, the use of sprinklers does significantly reduce the chance of a structurally

significant fire. In New Zealand no fully developed fire has ever occurred in a sprinklered, multi-

storey building under normal operating conditions (Feeney & Buchanan, 2000).

The effect of sprinklers on fire loads has been debated. In Eurocode 1 it is noted that the fuel load of a

building can be reduced by up to 60% when an automatic sprinkler system is installed. However, for

this to be applied factors such as a reliable water supply, supervision of control valves, regular

maintenance etc. need to be present. The American AISC 2005 Specification, Appendix 4, allows for

the same 60% reduction in fire loads due to sprinklers (Iqbal & Harichandran, 2010). In the UK fire

design is governed by Approved Document B of the Building Regulations (2007), which allows for a

reduction of 30 minutes in the fire resistance of members if sprinklers are installed.

The chance of a fire when active firefighting methods are in place is highlighted in Table 2.3 below.

From this it can be seen that the likelihood of a fully developed fire decreases from 10% to 2% when

a sprinkler system is installed.

Protection Method Probability of fire

being out of control

Public fire brigade

Sprinkler

High standard fire brigade, combined with alarm system

Both sprinkler and high standard residential fire brigade

10-1

2 x 10-2

≤ 10-2

to 10-3

≤ 10-4

Table 2.3: The effect on the probability of fires due to active protection measures (Twilt, 1994)

In the 1960s in Fresno, California, fire regulations were changed which encouraged trade-offs

between active and passive fire protection methods, as discussed by Favre et al (1994). The change

permitted reductions of 50%, or 30 minutes, in fire resistances when an automatic sprinkler system

was installed. In many instances a sprinkler system could be installed in lieu of a 1-hour rated

building. Thus, in the major commercial and industrial areas the number of sprinkler protected

buildings went from 15-20% to 93% and 96% respectively during this period. Extensive research was

conducted 15 years before and after the change in regulations, with the results shown in Table 2.4

below. It can be seen that there was a 93.8% reduction in annual fire losses due to the extensive

introduction of sprinkler systems. This resulted in two of the three fire stations in the area being

relocated to elsewhere in the city and the city’s fire rating was improved, leading to insurance

benefits.

Years Total loss adjusted Loss per year to 1976 US dollars No. of fires

1954-69

1970-84

1,351,209

82,573

90,080

5,504

62

67

Table 2.4: Losses in Fresno, California, 15 years before and after a change in regulations which encouraged a change

to automatic sprinkler protection (Favre et al., 1994)

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Comments from the Fire Fighting Industry regarding modifying Fire Ratings

In some international codes the fire rating on buildings can be reduced if measures such as sprinklers

are installed. However, Bevan Wolff, technical expert at the FPASA (Fire Protection Association of

SA), makes the following comment regarding active and passive structural protection systems in this

country:

Passive protection measures are designed for the life of the building. Hence, if passive

measures rely on active protection measures then the active protection measures must

also be guaranteed for the life of the building.

If the fire rating given to a building is reduced because of the presence of active protection measures

(sprinklers, inerting systems etc.) it must be ensured that these are maintained, tested and considered

for the life of the structure.

1.5.3 Compartmentation

A vital aspect that must be specifically considered during fire engineering design is that of

compartmentation. Compartmentation involves the division of fire zones to limit the spread of fire.

This is explicitly considered in building codes such as SANS 10400 by limiting the maximum

division area allowed in various occupancy categories. Dividing walls must be fire rated and retain

their integrity during a fire. Firewalls, fire doors and other methods are commonly used for this. For

multi-storey buildings BS 9999 makes the following recommendation:

“In tall multi-storey buildings, it can be advisable for each storey to be a separate

compartment capable of resisting burn-out. This can protect occupants who might

have to exit past the fire storey when a fire is well developed, and can also protect fire

fighters who might have to work on storeys immediately above or below a fire when it

is well developed.” (BSI, 2008)

Advanced design guides have started proposing details for maintaining compartmentation even when

floors deflect substantially through the use of systems such as deformable ceramic blankets (Clifton,

2006). If compartmentation is lost fires can spread throughout buildings causing large-scale damage,

as shown in the figure below. This 32-storey building burnt for 24 hours and had to be demolished

after the fire. The Great Fire of London, which devastated a large part of that city, helped identify the

fact that to prevent fire spread there needs to be sufficient separation between adjacent buildings

(Corus, 2004). This now forms part of international building codes and guidelines.

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Figure 1.4: Fire in the Windsor Building in Madrid, Spain, shown during and after the blaze (Engelhardt, 2013). It

can be seen that compartmentation divides did not work or not enough were provided.

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2 Structural Fire Design Approaches and Requirements

1.6 Prescriptive and Performance Based Design

Before approaching the topic how structural design can be done it is important to discuss the different

approaches that engineers can take when doing designs. The two broad categories in which design can

be done are (a) prescriptive design, or (b) performance based or rational design. Often approaches

may fall somewhere between the two depending on how they are carried out.

2.1.1 Historical Development of Design Methods

Historically design has been done by considering members in isolation. Large furnaces were built to

test single beams and columns under load. It was found what temperature members failed at and

design methods were based upon this. Heating of members occurred according to the standard fire

(discussed below). In the past few decades significant advances have been made by considering entire

structural systems and realistic fires.

2.1.2 Prescriptive Design

Prescriptive design is basically the application of deemed-to-satisfy rules from codes to determine

what level of fire protection must be provided to structural elements. It does not consider structural

behaviour, considers little about loading conditions, fire temperatures and other such factors. The

guidelines presented in SANS 10400 building code are all prescriptive. The advantage of prescriptive

design is that it is quick to apply and check, and is generally conservative. However, the inherent

conservatism may lead to significant increases in the cost of fire protection systems.

2.1.3 The “Yellow Book” and the “Euro-nomogram”

In the UK a very good design guide for determining the thickness of protective materials when

designing steel members is the “Yellow Book” published by the Association for Specialist Fire

Protection (ASFP, 2014). It can be freely downloaded from www.asfp.org.uk. The European

Convention for Constructional Steelwork (ECCS) has published a number of publications on

steelwork in fires. In this course the Euro-Nomogram which has been produced to quickly determine

the thickness of protective coatings will be presented. Both this and the Yellow Book are semi-

prescriptive.

2.1.4 Performance Based Design

Performance based design involves the consideration of the actual behaviour of structural systems, the

development of heat in a fire, heat transfer, member fixities and other such factors. It can range from

being relatively simple to be highly advanced. For more expensive or critical structures the additional

time required to carry out detailed, advanced analyses may be justified.

http://www.asfp.org.uk/

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Figure 2.1 depicts the level of calculation and design required depending on what type of fire curves

and analysis models are utilised, according to Lennon et al (2007). Simple methods can be used for

single members and standard fires, whereas advanced design methods are required for global

structural behaviour and parametric curves. As computer power and design software capabilities

continue to increase it means that advanced analyses can now be more commonly used in practice,

and need not only be reserved for critical structures or research.

2.1.1 Prescriptive vs. Performance-based Design

In a comparison of prescriptive and performance-based approaches in structural fire design Budny

and Giuliani (2010) note that the characteristics of prescriptive approaches are: (a) individual

members are checked rather than systems as a whole, (b) methods are typically simplified, (c)

conventional fire curves are used rather than real or natural fire curves, (d) no specialised engineering

skills are required, (e) it is easy to identify who is responsible, and (f) methods are typically not open

to technical innovation. Conversely, performance-based, or rational, design methods are characterised

by: (a) the stability of entire systems is addressed, (b) often well-defined design procedures are not

provided, (c) there is a greater computational effort and level of skills required, (d) designs can

potentially be more safe and economical, (e) a variety of fire situations can be considered, and (f)

modelling methods affect results.

2.1.2 What is Failure?

A challenge with structural fire engineering is being able to define failure. Since it would be

acceptable for a structure to suffer some damage in a large fire it makes it very difficult to know what

fire limit state to design a building to. In some structures beams and columns have buckled during real

fires but floors remained in position such that people could get out and the structures didn’t collapse –

so would those be failures or not?

Various parameters for failure have been identified such as those given in BS 5950 Part 8 for:

- Beams: maximum deflection limited to span/20, or for deflections greater than span/30 the

rate of deflection must not exceed span2/(9000 x member depth) [mm/min].

- Columns: Failure to support the applied load or a lateral deflection of 120mm.

- Insulating materials or floors: objects on the unexposed face must not combust. Temperature

on the unexposed side must be limited to 140°C (average) or 180°C (maximum).

- Integrity: boundaries required for compartmentation must not allow the passage of smoke or

flames from one compartment to another.

Tests are done relative to the standard fire.

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Figure 2.1: Fire and response models for different fire curves and analysis models (Lennon et al., 2007)

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1.7 Building Requirements in a Fire

The fire resistance rating (FRR) required for various buildings according to SANS 10400 is given in

the Table 2.1 below. From this it can be determined what level of fire rating is required.

Fire resistance requirements are usually measured according to the length of time a structure can

withstand a standard fire. This is typically defined as short, medium or long resistances corresponding

to times of 30, 60 and 120 minutes respectively. Tests have shown that often steel members can attain

15 minutes or more fire resistance without any protection (ASFP, 2010). It has been shown that some

structures such as open carparks generally don’t need passive protection and inherently satisfy fire

requirements.

It is very important to note that tests are referenced relative to the standard fire, as will be explained

in detail below. Both structural and non-structural elements need to be fire rated to ensure that they

are suitable for their application. Elements tested according to the various standards (SANS, BS, EN)

are required to satisfy load-bearing, integrity and insulation tests to obtain a specific fire rating. South

African fire resistance requirements will be discussed in detail below. Construction materials in this

country are tested according to the guidelines of SANS 10177-2.

These aforementioned time measures are meant to ensure that sufficient time is provided to allow for

the safe evacuation of a building. However, fire ratings in excess of these requirements may often be

stipulated by a company’s insurance provider to limit property and stock damage.

In theory a structure should be able to survive the full burnout of all combustible materials in it or in a

specified part of it (ECCS, 2001). The inherent levels of safety and structural stability in the event of a

fire are often not well defined, and in the case of a standard fire have little physical significance.

NOTE: As a structural engineer be very careful in terms of how buildings are classified, especially in

terms of warehouses. Developers will often try classify all their warehouses as occupancy type J3 to

bring down the cost of fire protection systems. However, many warehouses should actually be

classified as J2 or J1 depending on what is stored there.

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Type of occupancy Class of

occupancy

Stability (min)

Single-

storey

building

Double-

storey

building

3 to 10

storey

building

11 storeys

and more

Basement

in any

building

Entertainment and public assembly A1 30 60 120 120 120

Theatrical and indoor sport A2 30 60 120 120 120

Place of instruction A3 30 30 90 120 120

Worship A4 30 60 90 120 120

Outdoor sport A5 30 30 60 90 120

High risk commercial services B1 60 60 120 180 120

Moderate risk commercial services B2 30 60 120 120 120

Low risk commercial services B3 30 30 90 120 120

Exhibition hall C1 90 90 120 120 120

Museum C2 60 60 90 120 120

High risk industrial D1 60 90 120 180 240

Moderate risk industrial D2 30 60 90 120 180

Low risk industrial D3 30 30 60 120 120

Plant room D4 30 30 60 90 120

Place of detention E1 60 60 90 120 120

Hospital E2 60 90 120 180 120

Other institutional (residential) E3 60 60 120 180 120

Medical facilities E4 30 30 Not

applicable

Not

applicable 120

Large shop F1 60 90 120 180 120

Small shop F2 30 60 120 180 120

Wholesalers' store F3 60 90 120 120 120

Office G1 30 30 60 120 120

Hotel H1 30 60 90 120 120

Dormitory H2 30 30 60 120 120

Domestic residence H3 30 30 60 120 120

Detached dwelling house H4 30 30 60 Not

applicable 120

Hospitality H5 30 30 Not

applicable

Not

applicable 120

High risk storage J1 60 90 120 180 240

Moderate risk storage J2 30 60 90 120 180

Low risk storage J3 30 30 90 90 120

Parking garage J4 30 30 30 90 120

NOTE 1 Unprotected steel may be used in the structural system of all single-storey and certain double-storey

buildings in spite of the fact that in many cases such structural members would not comply with the requirements of

this table. The practice is regarded as safe for all practical cases that are likely to occur in single-storey construction,

but the possible consequences of early distortion or collapse should be considered in the design of double-storey

buildings in order to be certain that escape routes will be able to serve their purpose for the required period.

Particular care should be exercised where thin sections are used or in "space-frame" type structures.

NOTE 2 A further problem arises in the application of the requirement of 4.2. Distortion or collapse of any structural

member should not cause loss of integrity or stability in any external wall facing a site boundary or another building

as this might lead to non-compliance with the safety distance requirement. Where such a situation occurs, it would

be necessary either to protect the steel to the extent required to attain the stability given in this table or to regard such

wall as being of type N for the purposes of 4.2.

Table 2.1: Fire resistance requirements for structural elements and components according to SANS 10400-T Table 6

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TUTORIAL: FIRE RESISTANCE RATING

Q: Based on SANS 10400 requirements what FRR should be provided for the building shown in

Example 1?

A: From Table 2.1 the following can be derived:

- The building will be used for offices so is Class G1

- The building is between 3 and 10 storeys.

- Therefore, a 60 minute fire rating is required for the structure.

EXAMPLE: FIRE RATINGS

What occupancy class (A1, D3, etc.) and fire rating (30min, 60min) would you provide for the

following:

1. A single-storey Ster-Kinekor cinema complex.

2. A double-storey art gallery.

3. The basement of a hospital.

4. 12-storey building storing flammable products (though hopefully nobody would be foolish

enough to build such a structure).

If any of the above require interpretation of the table state what you have considered when providing

the fire rating. Note that ultimately it will be the fire engineers and fire chiefs who agree on these

requirements.

5. Go to YouTube and search for the video “Fire at Seven Dials” by BREVideoUK. Watch the

video and take note of how the steelwork has failed and also note general details regarding

fighting a fire. Submit a few sentences regarding what the main problem was that caused the

fire to spread throughout the building?

1.8 Loading at the Fire Limit State (FLS)

In the same way that live and wind loads can be reduced in certain load cases so can they also be

reduced when designing structures for fires. According to the Canadian fire design annex the load

combination to be adopted at the fire limit state is:

𝐺𝑘 + 𝑄𝑇,𝑘 + 𝛾𝑄𝑘 (2.1)

where:

Gk characteristic permanent load

QT,k thermal effects due to expansion, contraction or deflection caused by temperature

changes due to the design fire. It can be taken as zero for statically determinate

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structures or for structures that have sufficient ductility to allow for redistribution of

temperature forces before collapse. [Even though these guidelines have generally

been sufficient they must be carefully considered in some structures as forces caused

in members restrained from expanding can be significant].

𝛾 1.0 for storage areas, equipment areas, and service rooms, 0.5 for other occupancies.

The Eurocode reduction factors are similar, but vary for some structures.

Qk characteristic imposed load

Notional translational loads shall be applied in combination with this gravity load combination.

Fire loading is currently outside the scope of the South African loading code, SANS 10160, along

with other actions such as those on containment structures, bridges, towers and masts (Dunaiski,

Retief, & Goliger, 2007). Thus, the inherent requirements of structures in South Africa cannot be

identified relative to existing codes. However, SANS 10160 does provide a philosophy for dealing

with accidental loading in Annex B of Part 1. Accidental loads are those which, according to SANS

10160 are “not expected during the design life”, but when they do occur then structures should

“not be damaged to an extent disproportionate to the original cause of the abnormal event”

(Retief & Dunaiski, 2009). According to the aforementioned design philosophy structures should be

categorised depending on the consequence of their failure and then a design strategy can be picked

accordingly

EXAMPLE: FIRE LOADING

Q: What load should be designed for at the ambient Ultimate Limit State (ULS) and at the Fire Limit

State (FLS) for the second floor column on Gridline B3 of the building in Figure 1.1? Assume that the

roof may be loaded in the future so the column may carry two full floors above it.

A: The loading can be determined as:

Permanent / Dead load: 𝐺 = 𝑁𝑜. 𝑜𝑓 𝑓𝑙𝑜𝑜𝑟𝑠 × 𝑇𝑟𝑖𝑏𝑢𝑡𝑎𝑟𝑦 𝑙𝑜𝑎𝑑 𝑎𝑟𝑒𝑎 𝑝𝑒𝑟 𝑓𝑙𝑜𝑜𝑟 × 𝐿𝑜𝑎𝑑

= 2 × 7.5𝑚 × 7.5𝑚 × 3.2𝑘𝑃𝑎 = 360𝑘𝑁

Imposed / Live load: 𝑄 = 2 × 7.5𝑚 × 7.5𝑚 × 3.4𝑘𝑃𝑎 = 382.5𝑘𝑁

ULS Loading = 1.2𝐺 + 1.6 𝑄 = 1044𝑘𝑁

FLS Loading = 𝐺 + 𝛼𝑄 = 360 + 0.5 × 382.5 = 551.3𝑘𝑁

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3 Fire Curves and Heat Transfer Equations

Before any structural element can be designed or fire rated it is necessary to have fire temperatures to

design against. This section discusses the historical development of time-temperature curves and their

current application.

1.9 Standard Fire Curves

The standard fire was proposed in 1918 and was not developed based on the response of elements to a

real fire, but rather what the authors considered a worst case time-temperature relationship between a

fire and a structure. It has now been adopted by numerous countries around the world with only minor

variation. Lennon (2011) considers it to be “enshrined in national, European and international

standards”. The main standards which govern the standard fire test are ASTM E119, ISO 834 and

NFPA 251. It is often referred to as the ISO 834 curve.

The standard fire does not consider a variety of factors which are known to affect fire behaviour such

as: fire source and load, ventilation characteristics and building properties. These curves can be

suitable for short duration fires, but typically for medium to long duration fires become inaccurate.

They have a steadily increasing temperature and do not consider a cooling phase or descending

branch.

The Standard Fire 1.9.1

For the standard ISO 834 fire the gas temperature in the firecell, θg, at a time t, in minutes, is given

by:

𝜃𝑔 = 20 + 345 log10(8𝑡 + 1) [°C] (3.1)

The Hydrocarbon Fire 1.9.2

For fires with a higher fuel energy content than considered for the standard fire, as might be found in

the petrochemical and associated industries, the hydrocarbon fire can be utilised:

𝜃𝑔 = 1080(1 − 0.325𝑒−0.167𝑡 − 0.675𝑒−2.5𝑡) + 20 [°C] (3.2)

The External Fire 1.9.3

For structures that might be subjected to the flames emerging from a building the less intense external

fire curve can be used, as given by:

𝜃𝑔 = 660(1 − 0.687𝑒−0.32𝑡 − 0.313𝑒−3.8𝑡) + 20 [°C] (3.3)

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A comparison of the above equations is given below.

Figure 3.1: Graphical representation of commonly used fire curves

Discussion regarding the Standard Fires 1.9.4

Franssen and Vila Real have the following comment to make regarding the use of the standard fire

curve and analysing members in isolation:

“If the fire and mechanical model (an isolated element) are arbitrary and do not

represent the real situation, why should there be an attempt to create a more accurate

model by introducing the indirect effects of actions. As mentioned by Professor A.

Buchanan from Canterbury University in his talks, there must be a consistent level of

crudeness.” (Franssen & Vila Real, 2010)

They go on further to highlight the important fact that “The resistance of a structure to a nominal

fire should not be compared to the duration required for evacuation or intervention”. Simply

put, a one hour fire rating does not mean that a building will fall down after a fire burns in it for one

hour, and neither does it mean that people have an hour to evacuate. It simply means that the structure

can survive one hour of an arbitrary fire curve which has little resemblance to a real fire. Furthermore,

a real fire curve at one hour cannot be compared to one hour of a standard fire curve. Great care must

be taken when comparing fire resistance ratings between real and standard fires.

0

200

400

600

800

1000

1200

0 20 40 60 80 100 120

Gas

Te

mp

era

ture

(ºC

)

Time (mins)

Standard

External

Hydrocarbon

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1.10 Parametric or Real Fires

Real Fire Curves 1.10.1

The development of temperature in a real fire is very different to that shown by the standard fire time-

temperature curve, as shown by the figure below. After ignition there is a slow period of growth until

flashover occurs. During the development of a fire a two-zone model is normally used which accounts

for the build-up of the heated upper zone and the cooler lower zone. The flashover point for a

compartment occurs when the gas temperature in the upper zone of the compartment reaches around

500-600ºC (Feasey, 1999), and it envelopes the cool bottom layer leading to a single zone situation.

At this point all combustible material in a compartment is burning, and is characterised by a rapid

temperature increase. Different models need to be applied for pre- and post-flashover behaviour.

Structural design is affected by the latter, but sprinkler activation, smoke movement models and

compartment tenability are governed by pre-flashover fires. As the fire progresses the fuel in the

compartment is consumed until the maximum temperature is reached, after which the fire starts to

cool down.

Figure 3.2: Typical development of gas temperature in a fire (Engelhardt, 2013)

It may seem counter-intuitive but the cooling phase can be as structurally dangerous as the heating

phase. When the structure heats up the beams expand, buckle and sag. When the structure cools down

tensile forces are induced in the members which have sagged, and this can lead to the failure of joints.

Eurocode Parametric Curve Equations 1.10.2

In Eurocode 1-1-2 (BSI, 2002) parametric fire curves which take into account a more realistic fire

behaviour are provided. These allow for the heating and cooling phases whilst considering the most

important factors affecting fire temperatures. They were developed based on the work in Europe by

Wickström (1985), and have now undergone 40 years of testing and validation relative to actual

building fires. They are typically valid for: (a) firecells up to 500m2, and (b) for a maximum

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compartment height of 4m. Going beyond these limits may require CFD modelling. The most

important parameters considered by any parametric curve are: (1) the fire load in the compartment, (2)

openings and ventilation conditions, and (3) the nature of the boundary walls and floors since they

either transmit heat from it or trap heat in the compartment.

(1) The basic temperature-time curve in the heating phase is given by:

𝜃𝑔 = 1325(1 − 0.324𝑒−0.2𝑡∗ − 0.204𝑒−1.7𝑡∗ − 0.472𝑒−19𝑡∗) + 20 [°C] (3.4)

where:

θg = gas temperature in the fire compartment [ºC]

t* = t.Γ [hours] (This can be considered as the time period modified by Γ to match the original

opening factor of 0.04/1160 utilised in calibration experiments) (3.5)

t = time [h]

Γ = (O/b)2/(0.04/1160)

2

𝑏 = √𝜌𝑐𝜆 with 400 ≤ 𝑏 ≤ 2200 [J/m2s

1/2K] – Thermal inertia of the firecell.

O = opening factor (𝐴𝑣√ℎ/𝐴𝑡) [m1/2

]

Av = area of ventilation openings [m2]

h = height of ventilation openings [m]

At = total area of enclosure, including openings [m2]

ρ = density of boundary enclosure [kg/m3]

c = specific heat of boundary enclosure [J/kgK]

λ = thermal conductivity of the enclosure boundary [W/mK]

(2) The maximum temperature, θmax, that will be experienced in the heating phase will occur at

time tmax (which becomes t*

max when modified by Γ). If tmax occurs before the limiting time,

tlim, then the limiting time is used instead. This is used to determine whether the fire is

governed by the fuel load or ventilation conditions. Note that at the change between the two

conditions an infinitely small change in parameters can cause a jump in theoretical results.

𝑡𝑚𝑎𝑥 = max[(0.2 × 10−3 × 𝑞𝑡,𝑑/𝑂𝑙𝑖𝑚); 𝑡𝑙𝑖𝑚] [h] (3.6)

t𝑚𝑎𝑥∗ = 𝑡𝑚𝑎𝑥. Γ [h] (3.7)

where:

qt,d = qf,d . Af / At (MJ/m2) – This is the design fuel energy density of the whole compartment

relative to the total boundary area including floor, walls and roof. 50 ≤ qt,d ≤ 1000 [MJ/m2]

tlim = 25min for slow growth fires, 20min for medium growth fires, and 15min for fast growth.

Values must be used in hours in calculations.

(3) If the limiting time is used for tmax then Γ must be modified. Hence, when tmax = tlim:

𝑡∗ = 𝑡. Γ𝑙𝑖𝑚 [h] (3.8)

with Γ𝑙𝑖𝑚 = (𝑂𝑙𝑖𝑚/𝑏)2/(0.04/1160)2

where 𝑂𝑙𝑖𝑚 = 0.1 × 10−3. 𝑞𝑡,𝑑/𝑡𝑙𝑖𝑚

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NOTE: The original value of Γ must always be used for the cooling phase, but Γ is modified to Γlim

for only the heating phase. The limiting opening factor is applied for firecells with large openings

when all the air entering through the openings may not be used for combustion, and this slows down

the temperature increase rate.

(4) Under certain conditions Γlim needs to be multiplied by the factor k to account for mass

transfers which also limit the elevation of the temperature in the firecell:

When O > 0.04, and qt,d < 75, and b < 1160, then Γlim is modified by:

𝑘 = 1 + (

𝑂 − 0.04

0.04) (

𝑞𝑡,𝑑 − 75

75) (

1160 − 𝑏

1160) (3.9)

(5) Once the maximum temperature has occurred the cooling phase is described by:

𝜃𝑔 = 𝜃𝑚𝑎𝑥 − 625(𝑡∗ − 𝑡𝑚𝑎𝑥∗ . 𝑥) if 𝑡𝑚𝑎𝑥

∗ ≤ 0.5 [h] (3.10)

𝜃𝑔 = 𝜃𝑚𝑎𝑥 − 250(3 − 𝑡𝑚𝑎𝑥∗ )(𝑡∗ − 𝑡𝑚𝑎𝑥

∗ . 𝑥) if 0.5 < 𝑡𝑚𝑎𝑥∗ < 2.0 [h] (3.11)

𝜃𝑔 = 𝜃𝑚𝑎𝑥 − 250(𝑡∗ − 𝑡𝑚𝑎𝑥∗ . 𝑥) if 𝑡𝑚𝑎𝑥

∗ ≥ 2.0 [h] (3.12)

where

t* = t.Γ [h] (3.13)

𝑡𝑚𝑎𝑥∗ = (0.2 × 10−3 × 𝑞𝑡,𝑑/𝑂). Γ [h] (3.14)

𝑥 = 1.0 if 𝑡𝑚𝑎𝑥 > 𝑡lim , or 𝑥 = 𝑡𝑙𝑖𝑚. Γ/tmax∗ , if 𝑡𝑚𝑎𝑥 = 𝑡lim (3.15)

(6) Fire Load Densities and Rate of Heart Release (RHR)

The design fire load qf,d can be calculated as follows:

𝑞𝑓,𝑑 = 𝑞𝑓,𝑘 .𝑚. 𝛾𝑞1. 𝛾𝑞2. 𝛾𝑛 [MJ/m2] (3.16)

where

m is the combustion factor. For mainly cellulosic materials m = 0.8.

𝛾𝑞1 is the partial factor accounting for the risk based on the size of the compartment

𝛾𝑞2 is the partial factor accounting for the risk based on the type of occupancy

𝛾𝑛 = ∏ 𝛾𝑛𝑖10𝑖=1 is the differentiation factor taking into account the different active fire-

fighting measures available. (It is currently unclear whether this can be

applied in South Africa.)

qf,k is the characteristic fire load density per unit floor area [MJ/m2]

Standard fire load densities are provided below for general occupancy requirements. An

extensive list of fire load densities accounting for numerous occupancy types have been

published by Buchanan (2001). Note that the 80% fractile value is typically used for design.

The fire load densities typically display a Gumbell probability distribution.

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Occupancy:

Fire load densities qf,k [MJ/m2] Rate of Heat Release

Stand. Deviation:

Average: 80%

Fractile: Gumbell Alpha:

Fire growth rate:

tlim [min]:

tα [sec]:

RHRf [kW/m2]:

Dwelling 234 780 948 0.0054782 Medium 20 300 250

Hospital (room) 69 230 280 0.018578 Medium 20 300 250

Hotel (room) 93 310 377 0.013784 Medium 20 300 250

Library 450 1500 1824 0.002849 Fast 15 150 500

Office 126 420 511 0.010174 Medium 20 300 250

School classroom 85.5 285 347 0.014993 Medium 20 300 250

Shopping centre 180 600 730 0.007122 Fast 15 150 250

Storage buildings * * * * * * * *

Theatre (cinema) 90 300 365 0.014243 Fast 15 150 500

Transport (public square) 30 100 122 0.04273 Slow 25 600 250

(*Depends highly on products stored so must be determined for each case.)

Table 3.1: Fire load densities and rate of heat release values for different occupancies

The fire load density is the measure of all fuel available for burning per unit floor area of the firecell.

The table below summaries the most common qf,k values for various occupancies. Make sure that you

distinguish between the fire load density of the floor area, and the design fire load density relative to

the boundary area of a firecell: qt,d = qf,d . Af / At [MJ/m2].

(7) 𝛾𝑞1 and 𝛾𝑞2 can be taken from the table below to account for the danger of fire activiation.

Compartment floor

area Af [m2]

Danger of fire

activation, 𝛾𝑞1

Danger of fire

activation, 𝛾𝑞2 Example of occupancies

25 1.10 0.78 Art gallery, museum, swimming pool

250 1.50 1.00 Offices, residence, hotel, paper industry

2500 1.90 1.22 Manufacturer of machinery and engines

5000 2.00 1.44 Chemical laboratory, painting workshop

10000 2.13 1.66 Manufacturer of fireworks or paints

Table 3.2: Partial factors to account for the danger of fire activation depending on compartment floor area or

occupancy. Use linear interpolation between values.

(8) The fire load can be reduced when active firefighting measures are present. However, it must

be guaranteed that these measures are operational and well maintained. Typically in South

Africa trade-offs between active and passive fire protection measures are not allowed. Hence,

for this course use 𝛾𝑛 = 1.0. The table below has been included for completeness and

potential future use. Reductions in fire load of up to 75% can be realised using this table.

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Table 3.3: Differentiation factor accounting for various active fire protection systems, as proposed in various

European documents. The bottom row contains the proposed values in the European Research on the Natural Fire

Safety Concept document (NFSC). (ECCS, 2001)

Thermal Inertia of Compartments 1.10.3

The thermal inertia of a firecell plays an important role with regards to the amount of energy lost

whilst a fire is burning. The following table provides guidance for b values for various construction

materials:

Material: λ – Thermal Conductivity

[W/m.K]:

ρ – Density [kg/m

3]:

cp – Specific Heat

[J/kg.k]:

b – Thermal inertia

[J/m2s

0.5K]:

Brickwork 1.00 2000 1114 1521

CaSi-board 0.069 450 748 151.9

Cerablanket 0.035 128 800 59.9

Gypsum board 0.5 1150 1000 749

Light wt. conc. 1.0 1500 840 1122

Middle wt. conc. 1.0 2000 840 1296

Normal wt. conc. 2.0 2300 900 2034

Structural steel 54.0 7850 425 13422

Wood 0.10 450 1113 223

Table 3.4: Material properties at ambient temperature for various construction materials

For monolithic construction the value of b can be taken as:

𝑏 = √𝑐𝜌𝜆 [J/m2s

0.5K] (3.17)

When different construction materials are used for the walls, floor and roof of a compartment then a

global thermal inertia is calculated for the firecell in respect to the area of each material (openings not

included):

𝑏 =∑𝑏𝑖𝐴𝑖

∑𝐴𝑖 [J/m

2s

0.5K] (3.18)

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Opening Factors 1.10.4

The opening factor, O, accounts for the openings in the vertical walls of a compartment. It ranges

between 0.02 and 0.2, with higher values meaning more ventilation. It has been derived from

integrating the Bernoulli equation for pressure differences between the outside and inside, and is

calculated as:

𝑂 = 𝐴𝑣√ℎ/𝐴𝑡 [m0.5

] (3.19)

where

Av = area of ventilation openings [m2]

h = height of ventilation openings [m]

At = total area of enclosure, including openings [m2]

When there are several openings present an averaged, equivalent opening height, heq, is used:

𝑂 = 𝐴𝑣√ℎ𝑒𝑞/𝐴𝑡 [m0.5

] (3.20)

ℎ𝑒𝑞 = ∑ 𝐴𝑣𝑖ℎ𝑖𝑖 /𝐴𝑣 [m] (3.21)

The estimated gas temperatures using the above equations are presented below for various opening

factor values ranging from 0.02 to 0.20. From this graph it can be seen that as the ventilation factor

increases the fires reach higher peak temperatures more quickly, but then has a much more rapid drop-

off. Such behaviour needs to be considered in structural design, especially for members with higher

thermal capacities.

Figure 3.3: Parametric fire curves according to EN1-1-3 for opening factors from 0.02 to 0.2. For this graph Af =

30m2, At = 200m2, b = 945 J/m2s1/2K, tlim = 20min and qf,d = 800 MJ/m2

Comments on Fire Loading Conditions 1.10.5

It should also be understood that in the same way that structures can have a variety of static load

combinations (dead + live, dead + wind, etc.) there could be a number of fire scenarios which

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influence the loading. Petrini (2010) highlights that according to ISO/TS 16733 the following items

have to be specified to define an entire fire scenario: (a) fire source, (b) physical characteristics of the

combustible material, and (c) the growth rate of the fire and the peak fire temperature. For EN 1-1-2

curves a variety of fires may be obtained depending on whether windows are open or closed in a

building, if partition walls are removed or if the fire load density changes.

Time Equivalence of Parametric Curves 1.10.6

Research and experience have shown that the standard fire typically does not reflect real fires, as

discussed extensively above. However, since the majority of tests and ratings are done using the

standard fire it is necessary to provide ways to equate real fires to an equivalent standard fire. The

most popular methods are the CIB formula and the Eurocode formula (Nyman, 2002).

1.10.6.1 Eurocode Formula

The Eurocode time equivalent, te, to an ISO 834 standard fire is given by:

𝑡𝑒 = 𝑘𝑏𝑤𝑓𝑒𝑓 [mins] (3.22)

where the ventilation factor, wf, is given by:

𝑤𝑓 = (

6.0

𝐻𝑟)0.3

[0.62 +90(0.4 − 𝛼𝑣)

4

1 + 𝑏𝑣𝛼ℎ] > 0.5 (3.23)

with

Hr is the compartment height [m]

ef is the design fire energy density, noted as qf.d above [MJ/m2]

Vertical ventilation ratio:

𝛼𝑣 =𝐴𝑣

𝐴𝑓⁄ 0.05 ≤ 𝛼𝑣 ≤ 0.25 (3.24)

Horizontal ventilation ratio:

𝛼ℎ =𝐴ℎ

𝐴𝑓⁄ 𝛼ℎ ≤ 0.20 (3.25)

The vertical opening factor is:

𝑏𝑣 = 12.5(1 + 10𝛼𝑣 − 𝛼𝑣2) (3.26)

1.10.6.2 CIB Formula

The CIB formula gives the equivalent fire time as:

𝑡𝑒 = 𝑘𝑐𝑤𝑓𝑒𝑓 [mins] (3.27)

Ventilation factor:

𝑤𝑓 =

𝐴𝑓

(𝐴𝑣𝐴𝑡𝐻𝑣0.5)

0.5 (3.28)

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Hv is the ventilation opening height, which we shall take as heq for multiple openings.

The CIB formula is more commonly used, but is only valid for compartments with vertical openings,

and cannot consider roof openings.

The kb and kc factors are obtained from the table below. Linear interpolation can be used between

values.

Formula: Term

b – Thermal inertia (J/m2.s.K)

General High

(> 2500)

Medium

(720-2500)

Low

(<720)

Eurocode kb 0.04 0.055 0.07 0.07

CIB kc 0.05 0.07 0.09 0.10

Table 3.5: Values of kc and kb for the CIB and Eurocode formulae (Nyman, 2002)

EXAMPLE: FIRE CURVES

QUESTION: For fire compartment of the building shown in Figure 1.1 do the following:

1. Generate a time-temperature fire curve according to EN 1-1-2.

2. Plot this curve against the standard fire curve.

3. Determine the equivalent fire rating of the curve generated.

The openings of the compartment are shown below. (Results have been calculated using a spreadsheet

with no rounding off until the final solution).

ANSWER 1.:

Compartment floor area: 𝐴𝑓 = 10𝑚 × 15𝑚 = 150𝑚2

Ventilation area, assuming all doors open and windows broken:

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𝐴𝑣 = 𝐷𝑜𝑜𝑟 𝑎𝑟𝑒𝑎 + 𝑊𝑖𝑛𝑑𝑜𝑤 𝑎𝑟𝑒𝑎 = 2 × 1 × 2 + 12 × 1.5 × 1.5 = 31𝑚2

Total boundary enclosure area:

𝐴𝑡 = 𝑊𝑎𝑙𝑙 + 𝐹𝑙𝑜𝑜𝑟 + 𝑅𝑜𝑜𝑓 𝑎𝑟𝑒𝑎 = 2 × (10 + 15) × 4 + 2 × 10 × 15 = 500𝑚2

Wall area excl. openings: 𝐴𝑤𝑎𝑙𝑙 = 2 × (10 + 15) × 4 − 31 = 169𝑚2

A. Design fire load:

The compartment is used for offices, so according to the 80% fractile value of Table 3.1:

𝑞𝑓,𝑘 = 511𝑀𝐽/𝑚2, and 𝑡𝑙𝑖𝑚 = 20𝑚𝑖𝑛

The fire is cellulosic: 𝑚 = 0.8.

By interpolating for 𝛾𝑞1 in Table 3.2 based on the floor area: 𝛾𝑞1 = 1.32

For office use: 𝛾𝑞2 = 1.00

We will conservatively not account for active suppression systems: 𝛾𝑛 = 1.00

𝑞𝑓,𝑑 = 𝑞𝑓,𝑘 .𝑚. 𝛾𝑞1. 𝛾𝑞2. 𝛾𝑛 = 511 × 0.8 × 1.0 × 1.32 × 1.0 = 540.5 𝑀𝐽/𝑚2

𝒒𝒕,𝒅 = 𝒒𝒇,𝒅 × 𝑨𝒇/𝑨𝒕 = 𝟓𝟒𝟎. 𝟓 × 𝟏𝟓𝟎/𝟓𝟎𝟎 = 𝟏𝟔𝟐. 𝟐𝑴𝑱/𝒎𝟐

B. Thermal inertia of the fire compartment:

According to Table 3.4: 𝑏𝑏𝑤𝑘 = 1521 𝐽/𝑚2𝑠0.5𝐾, and 𝑏𝑁𝑊𝐶 = 2034 𝐽/𝑚2𝑠0.5𝐾

𝒃 =∑𝒃𝒊𝑨𝒊

∑𝑨𝒊=

𝟐𝟎𝟑𝟒×𝟏𝟓𝟎+𝟐𝟎𝟑𝟒×𝟏𝟓𝟎+𝟏𝟓𝟐𝟏×𝟏𝟔𝟗

𝟏𝟓𝟎+𝟏𝟓𝟎+𝟏𝟔𝟗= 𝟏𝟖𝟒𝟗. 𝟏 𝑱/𝒎𝟐𝒔𝟎.𝟓𝑲

C. Ventilation factor:

Since there are multiple openings, determine the equivalent opening height:

ℎ𝑒𝑞 =∑ 𝐴𝑣𝑖ℎ𝑖𝑖

𝐴𝑣=

2 × (2 × 1) × 2 + 12 × (1.5 × 1.5) × 1.5

2 × (2 × 1) + 12 × (1.5 × 1.5)= 1.565𝑚

𝑶 = 𝑨𝒗√𝒉𝒆𝒒/𝑨𝒕 = 𝟑𝟏 × √𝟏. 𝟓𝟔𝟓 / 𝟓𝟎𝟎 = 𝟎. 𝟎𝟕𝟕𝟔 𝒎𝟎.𝟓

D. Heating Phase:

The maximum temperature will occur at time tmax:

𝑡𝑚𝑎𝑥 = max(0.2 × 10−3 ×𝑞𝑡,𝑑

𝑂; 𝑡𝑙𝑖𝑚) = max(0.418; 0.333) = 0.418hrs = 25.1min

Γ = (𝑂

𝑏)2

/ (0.04

1160)2

= (0.0776

1849.1)2

/ (0.04

1160)2

= 1.479

Since: 𝑡𝑚𝑎𝑥 ≠ 𝑡𝑙𝑖𝑚

𝑡𝑚𝑎𝑥∗ = 𝑡𝑚𝑎𝑥 × Γ = 0.418 × 1.479 = 0.619 , Γ𝑙𝑖𝑚 not required.

The maximum temperature experienced will be:

𝜃𝑚𝑎𝑥 = 1325(1 − 0.324𝑒−0.2𝑡∗ − 0.204𝑒−1.7𝑡∗ − 0.472𝑒−19𝑡∗) + 20

= 1325(1 − 0.324𝑒−0.2×0.619 − 0.204𝑒−1.7×0.619 − 0.472𝑒−19×0.619) + 20

= 𝟖𝟕𝟏. 𝟐°𝐂

Calculate other time increments to provide ordinates on the graph.

E. Cooling Phase

𝑡𝑚𝑎𝑥∗ = 0.2 × 10−3 × 𝑞𝑡,𝑑/𝑂 = 0.619ℎ𝑟𝑠

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Since: 𝑡𝑚𝑎𝑥 > 𝑡𝑙𝑖𝑚, 𝑥 = 1.0

0.5 < 𝑡𝑚𝑎𝑥∗ ≤ 2.0. Therefore: 𝜃𝑔 = 𝜃𝑚𝑎𝑥 − 250(3 − tmax

∗ ) (𝑡∗ − 𝑡𝑚𝑎𝑥∗ . 𝑥)

Temperature will return to ambient (20°C) at:

t∗ = 2.048ℎ𝑟𝑠, or 𝑡 = 1.39ℎ𝑟 = 83𝑚𝑖𝑛 (from substituting 𝜃𝑔 = 20°𝐶 and 𝜃𝑚𝑎𝑥 in the

equation above)

ANSWER 2:

From the above equations the following time-temperature curve has been produced.

Figure 3.4: Time-temperature curve for the firecell of Example 1, along with the standard fire curve

ANSWER 3:

a) For the Eurocode equation:

𝑘𝑏 = 0.051, by interpolating in Table 3.5 using 𝑏 = 1849𝐽/𝑚2𝑠0.5𝐾

Vertical ventilation: 𝛼𝑣 =𝐴𝑣

𝐴𝑓⁄ = 31

150⁄ = 0.207

Horizontal ventilation: 𝛼ℎ =𝐴ℎ

𝐴𝑓⁄ = 0

150⁄ = 0

Vertical opening factor: 𝑏𝑣 = 12.5(1 + 10𝛼𝑣 − 𝛼𝑣2) = 37.8

Ventilation factor: 𝑤𝑓 = (6.0

𝐻𝑟)0.3

[0.62 +90(0.4−𝛼𝑣)

4

1+𝑏𝑣𝛼ℎ] > 0.5

= (6.0

4.0)0.3

[0.62 +90(0.4−0.207)4

1+37.8×0] = 0.842𝑚0.25

Fire load: 𝑒𝑓 = 𝑞𝑓,𝑑 = 540.5𝑀𝐽/𝑚2

Thus, the equivalent standard fire time is: 𝒕𝒆 = 𝒌𝒃𝒘𝒇𝒆𝒇 = 𝟐𝟑. 𝟐𝒎𝒊𝒏

b) For the CIB equations:

𝑘𝑐 = 0.065, by interpolating in Table 3.5 using 𝑏 = 1849𝐽/𝑚2𝑠0.5𝐾

0

200

400

600

800

1000

1200

0 20 40 60 80 100 120

Tem

pe

ratu

re (

°C)

Time (min)

θg (degC): Std Fire

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𝑤𝑓 =𝐴𝑓

(𝐴𝑣𝐴𝑡𝐻𝑣0.5)

0.5 =150

(31 × 500 × 1.5650.5)0.5= 1.077𝑚0.25

𝒕𝒆 = 𝒌𝒄𝒘𝒇𝒆𝒇 = 𝟎.𝟎𝟔𝟓 × 𝟏. 𝟎𝟕𝟕 × 𝟓𝟒𝟎. 𝟓 = 𝟑𝟕. 𝟖𝒎𝒊𝒏

From these results it can be seen that the Eurocode and CIB equations calculate fairly different values.

However, it should be noted that both are significantly lower than the 60 minute fire rating required

by SANS 10400.

TUTORIAL: FIRE CURVES

i) Generate a time-temperature fire curve according to EN 1-1-2 for the following firecell:

A 10m x 5m library with a 3m inter-floor height.

The walls and ceiling are gypsum board, and the floor is light weight concrete.

1 Door: 1m x 2m high. 3 Windows: 2m x 2m.

ii) Determine the equivalent standard fire time using the EN and CIB equations.

*Note: This example has been put together to demonstrate a very hot fire. Most fires are

substantially cooler.

HINT: Use a 5 second time step when generating your curve so you can use the same

spreadsheet for the next tutorial.

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4 The Behaviour of Steel at Elevated Temperatures

Now that we know what type of fire can be used for design and what temperatures are experienced

with time it needs to be determined how steelwork will respond to these fire. In general the properties

of steel degrade with increasing temperature. By the time steelwork reaches 1200°C it behaves more

like spaghetti than a construction material.

1.11 The Thermal Response of Steelwork – Material Properties

The equations from this section are provided in Part 1-2 of Eurocode 3.

Elongation of structural and reinforcing steels 1.11.1

The thermal elongation (Δl/l) which structural and reinforcing steels experience when at elevated

temperatures can be determined by:

∆𝑙/𝑙 = −2.416 × 10−4 + 1.2 × 10−5𝜃𝑎 + 0.4 × 10−8𝜃𝑎2 for 20°C ≤ θa ≤ 750°C (4.1)

∆𝑙/𝑙 = 11 × 10−3 for 750°C < θa ≤ 860°C (4.2)

∆𝑙/𝑙 = −6.2 × 10−3 + 2 × 10−5𝜃𝑎 for 860°C < θa ≤ 1200°C (4.3)

where

θa is the length at 20°C of the steel member

∆𝑙/𝑙 is the elongation of the member induced by the temperature change

θa is the steel temperature

In simple calculation models the elongation can simply be taken as: ∆𝒍/𝒍 = 𝟏𝟒 × 𝟏𝟎−𝟔𝜽𝒂. The value

of 14 × 10−6 can be viewed as the elevated temperature coefficient of thermal expansion.

This behaviour is illustrated below. If steelwork is restrained from expanding it can introduce very

high forces within members which need to be considered (but are generally not).

Figure 4.1: Steel thermal elongation as a function of temperature

02468

101214161820

0 200 400 600 800 1000 1200Δl/

l -

Ste

el

Elo

ng

ati

on

(x1

0-3

)

θa - Steel temperature (°C)

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Specific Heat of Steelwork 1.11.2

The specific heat of a steel, ca, is the amount of energy required to heat 1kg of the material by 1

degree Kelvin or Celsius. It is important because it greatly influences the rate at which steelwork heats

up. The equations for determining the specific heat are:

𝑐𝑎 = 425 + 7.73 × 10−1𝜃𝑎 − 1.69 × 10−3𝜃𝑎2 + 2.22 × 10−6𝜃𝑎

3 [J/kgK]

for 20°C ≤ θa ≤ 600°C (4.4)

𝑐𝑎 = 666 + (13002

738−𝜃𝑎) [J/kgK] for 600°C ≤ θa ≤ 735°C (4.5)

𝑐𝑎 = 545 + (17820

𝜃𝑎−731) [J/kgK] for 735°C < θa ≤ 900°C (4.6)

𝑐𝑎 = 650 [J/kgK] for 900°C < θa ≤ 1200°C (4.7)

In simple models the value can be taken as: ca = 600 J/kgK.

The graph of specific heat is shown below. The spike in the middle is due to a phase change in the

steelwork whereby additional energy is absorbed without an increase in the temperature of the

steelwork. This causes the non-linear graphs often observed in relation to steelwork.

Figure 4.2: Specific heat of steel as a function of temperature

Thermal Conductivity 1.11.3

The thermal conductivity of steelwork, λa, is the rate at which it transmits heat. This property also

influences the rate at which steelwork heats up during a fire. It is given by:

𝜆𝑎 = 54 − 3.33 × 10−2𝜃𝑎 [W/mK] for 20°C ≤ θa ≤ 800°C (4.8)

𝜆𝑎 = 27.3 [W/mK] for 800°C ≤ θa ≤ 1200°C (4.9)

In simple calculation models a constant value of 𝝀𝒂 = 𝟒𝟓 W/mK can be used.

The graph of thermal conductivity against temperature is shown below. After the phase change the

thermal conductivity remains constant.

0

500

1000

1500

2000

2500

3000

0 200 400 600 800 1000 1200

ca -

Sp

ecif

ic H

eat

(J/k

gK

)


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Figure 4.3: Thermal conductivity as a function of temperature

1.12 The Thermal Response of Steelwork – Structural Properties

Now it must be determined how the structural properties of steelwork vary with increasing

temperature. For this purpose the Eurocode guidelines will be used, since even the Canadian code

references the elevated temperature properties from the Eurocodes. The Eurocodes use the concept of

a reduction factor, k, which is multiplied by the original material property. The reduction factors given

below for steelwork at temperature θa are:

ku,θ – Ultimate steel strength relative to yield strength.

ky,θ – Reduction factor for the steel yield strength. A curve has been fitted to this data as

shown below.

kE,θ – Reduction factor for the Young’s modulus. It is interesting to see that it reduces faster

than the yield strength.

kp,θ – This applies to the end of the proportional limit stage of the stress-strain graph, i.e.

when the graph starts becoming non-linear. This is not commonly used in general design.

k0.2p,θ – Reduction factor for the strength of hot-rolled and welded thin walled sections (Class

4 Sections). This accounts for local buckling. Generally Class 4 section behaviour at elevated

temperature is very complex.

From the table and graph below the strength and stiffness of steelwork at elevated temperatures can

quickly be determined. To assist with the use of spreadsheets various curves have been fitted to the

yield strength equation. The one below has been provided by Franssen and Vila Real (2010):

𝑘𝑦,𝜃 = {0.9674(𝑒

𝜃𝑎−48239.19 + 1)}

−13.833⁄

≤ 1 (4.10)

0

10

20

30

40

50

60

0 200 400 600 800 1000 1200

λa -

Th

erm

al c

on

du

ctiv

ity

(W/m

K)


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Figure 4.4: Reduction factors for various steel properties at elevated temperatures

Steel temp. θa

Reduction factors at temperature θa relative to the value of fy or Ea at 20°C

ky,θ – Yield Strength

kE,θ – Young’s Modulus

kp,θ – Prop. limit

ku,θ – Ultimate Strength

k0.2p,θ – Class 4 Sections

20 °C 1.000 1.000 1.000 1.250 1.000

100 °C 1.000 1.000 1.000 1.250 1.000

200 °C 1.000 0.900 0.807 1.250 0.890

300 °C 1.000 0.800 0.613 1.250 0.780

400 °C 1.000 0.700 0.420 1.000 0.650

500 °C 0.780 0.600 0.360 0.780 0.530

600 °C 0.470 0.310 0.180 0.470 0.300

700 °C 0.230 0.130 0.075 0.230 0.130

800 °C 0.110 0.090 0.050 0.110 0.070

900 °C 0.060 0.068 0.038 0.060 0.050

1000 °C 0.040 0.045 0.025 0.040 0.030

1100 °C 0.020 0.023 0.013 0.020 0.020

1200 °C 0.000 0.000 0.000 0.000 0.000

NOTE: For intermediate values of the steel temperature linear interpolation may be used

Table 4.1: Reduction factors for steelwork at temperature θa according to EN 3-1-2

Sections should be classified in the same way as that done at ambient temperature according to SANS

10162-1. Only those which are considered to experience local buckling before reaching yield stress

are to have the Class 4 curve applied to them.

0.000

0.200

0.400

0.600

0.800

1.000

1.200

1.400

0 200 400 600 800 1000 1200

Re

du

ctio

n F

acto

r

Temperature (°C)

ku,θ = fu,θ / fy

ky,θ = fy,θ / fy

kE,θ = Ea,θ / Ea

kp,θ = fp,θ / fy

k0.2p,θ = f0.2p,θ / fy

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1.13 Bolt and Connection Behaviour

Connections exhibit extremely complicated behaviour during a fire. This is a current topic of research

and beyond the scope of this course. However, the degradation of bolts and welds with increasing

temperature is shown below. It can be seen that the strength of connectors reduce faster than normal

structural steel. But, joints are often shielded by surrounding beams and have a much higher

concentration of mass so do not heat up as fast, and normally reach lower maximum temperatures.

Figure 4.5: Reduction factors for bolts (kb,θ) and welds (kw, θ) at elevated temperatures (EN 3-1-1)

Steel temperature θa

Reduction Factor

Bolts - kb,θ Welds - kw,θ

20 °C 1.000 1.000

100 °C 0.968 1.000

200 °C 0.935 1.000

300 °C 0.903 1.000

400 °C 0.775 0.876

500 °C 0.550 0.627

600 °C 0.220 0.378

700 °C 0.100 0.130

800 °C 0.067 0.074

900 °C 0.033 0.018

1000 °C 0.000 0.000

1100 °C 0.000 0.000

1200 °C 0.000 0.000 Table 4.2: Reduction factors for bolts and welds at elevated temperatures (EN 3-1-1)

0.000

0.200

0.400

0.600

0.800

1.000

1.200

0 200 400 600 800 1000 1200

Re

du

ctio

n F

acto

r

Temperature (°C)

kw,θ

kb,θ

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1.14 Heat Transfer Equations

The Ap/V Concept 1.14.1

An important concept to understand when using both prescriptive design methods and performance-

based design methods is that of the section factor, Am/V. When a steel member is encased this is

referred to as Ap/V. In older publications it used to be noted as Hp/A (heat perimeter per unit area). It

is calculated by:

𝑈𝑛𝑝𝑟𝑜𝑡𝑒𝑐𝑡𝑒𝑑 𝑆𝑒𝑐𝑡𝑖𝑜𝑛 𝐹𝑎𝑐𝑡𝑜𝑟:

𝐴𝑚

𝑉=

𝐸𝑥𝑝𝑜𝑠𝑒𝑑 𝑠𝑢𝑟𝑓𝑎𝑐𝑒 𝑎𝑟𝑒𝑎 𝑝𝑒𝑟 𝑢𝑛𝑖𝑡 𝑙𝑒𝑛𝑔𝑡ℎ

𝑉𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑚𝑒𝑚𝑏𝑒𝑟 𝑝𝑒𝑟 𝑢𝑛𝑖𝑡 𝑙𝑒𝑛𝑔𝑡ℎ

𝑃𝑟𝑜𝑡𝑒𝑐𝑡𝑒𝑑 𝑆𝑒𝑐𝑡𝑖𝑜𝑛 𝐹𝑎𝑐𝑡𝑜𝑟: 𝐴𝑝

𝑉=

𝐸𝑥𝑝𝑜𝑠𝑒𝑑 𝑠𝑢𝑟𝑓𝑎𝑐𝑒 𝑎𝑟𝑒𝑎 𝑝𝑒𝑟 𝑢𝑛𝑖𝑡 𝑙𝑒𝑛𝑔𝑡ℎ

𝑉𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑚𝑒𝑚𝑏𝑒𝑟 𝑝𝑒𝑟 𝑢𝑛𝑖𝑡 𝑙𝑒𝑛𝑔𝑡ℎ

(4.11)

The section factor is explained well and graphically shown in Section 5.1 of the Euro-nomogram, and

shown in Figure 4.6. The effect of different section factors is demonstrated below in Figure 4.7.

Stockier members have lower section factors and heat up less quickly.

Figure 4.6: Section factors depending on the protection material used and presence of a slab above.

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Figure 4.7: Heating curves for various beam sizes (Hp/A ratios) in a standard fire test (Corus Construction &

Industrial, 2006)

Unprotected Steelwork 1.14.2

Since the Canadian code steelwork design guidelines (CSA, 2009) are being adopted for member

design it is proposed that the Canadian heat transfer equations also be used, as will possibly be the

case for the next version of SANS 10162-1. However, the difference in results between the two codes

is generally less than a few percent to not a concern. Heat transfer equations for all codes are typically

based upon simplified, lumped mass transfer equations.

In a time period Δt the change in the temperature of unprotected steelwork is given by the

commentary on the Canadian CSA S16 (CISC, 2010) code as:

∆𝑇𝑠𝑡𝑒𝑒𝑙 =

𝑎

𝑐𝑠𝑡𝑒𝑒𝑙(𝜌𝑠𝑡𝑒𝑒𝑙𝐴𝑚/𝑉

)(𝑇𝐹 − 𝑇𝑠𝑡𝑒𝑒𝑙)∆𝑡 (4.12)

The coefficient of heat transfer, a, is:

𝑎 = 𝑎𝑐 + 𝑎𝑟

(4.13)

where:

𝑎𝑟 =5.67 × 10−8𝜖𝐹

𝑇𝐹 − 𝑇𝑠𝑡𝑒𝑒𝑙(𝑇𝐹

4 − 𝑇𝑠𝑡𝑒𝑒𝑙4 )

(4.14)

with symbols defined above as:

Am/V is the unprotected section factor (see above) (m-1

)

ac is the convective radiative heat transfer coefficient, approximated as 25W/mºC

ar is the radiative heat transfer coefficient (W/mºC)

csteel is the specific heat of the steel (J/kgºC)

D is the exposed perimeter of the member (m)

M is the mass per unit length of the member (kg/m)

TF is the fire or gas temperature (ºC)

Tsteel is the steel temperature (ºC)

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ΔT is the temperature rise in an unprotected section in the time period (°C)

Δt is the time step, limited to 5 seconds for accuracy reasons (sec)

εF is a parameter accounting for the emissivity of the fire and view factor

𝜌𝑠𝑡𝑒𝑒𝑙 is the density of the steelwork (kg/m3)

The following guidelines are provided for estimating the emissivity factor:

Type of Assembly εf

Column, exposed on all sides 0.7

Floor beam: imbedded in the concrete floor slab,

with only bottom flange of beam exposed to fire 0.5

Floor beam, with concrete slab resting on top

flange of beam:

- Flange width : beam depth ratio ≥ 0.5 0.5

- Flange width : beam depth ratio < 0.5 0.7

Box girder and lattice girder 0.7

Table 4.3: Guidelines for estimating the emissivity factor

It should be noted that in this equation the rate of heat change is proportional to the difference in steel

and gas temperatures to the power of 4. Thus, there is a rapid increase in radiative heat transfer as the

temperature in a room rises.

The two modes of heat transfer from the gas into the steelwork are:

a) Conduction which is the transportation of molecular energy,

b) Radiation which is the transfer of electromagnetic energy

Protected Steelwork 1.14.3

To reduce the rate at which steelwork temperature rises it is often advisable to protect steelwork with

various passive protection systems. These have discussed previously. The change in temperature

during the time period Δt for a protected steel member is given by:

When: 𝑐𝑆𝑡𝑒𝑒𝑙 (𝜌𝑠𝑡𝑒𝑒𝑙

𝐴𝑝/𝑉) > 2𝑑𝑝𝜌𝑝𝑐𝑝 (the thermal capacity of the insulation is much less than that of the

steel and can be ignored)

∆𝑇𝑆𝑡𝑒𝑒𝑙 =

𝑘𝑝

𝑐𝑠𝑡𝑒𝑒𝑙𝑑𝑝 (𝜌𝑠𝑡𝑒𝑒𝑙𝐴𝑝/𝑉

)(𝑇𝐹 − 𝑇𝑆𝑡𝑒𝑒𝑙)∆𝑡 (4.15)

Otherwise (when the thermal capacity of the insulation must be considered):

∆𝑇𝑆𝑡𝑒𝑒𝑙 =𝑘𝑝

𝑑𝑝

[

𝑇𝐹 − 𝑇𝑆𝑡𝑒𝑒𝑙

𝑐𝑠𝑡𝑒𝑒𝑙 (𝜌𝑠𝑡𝑒𝑒𝑙𝐴𝑝/𝑉

) +𝑐𝑝𝜌𝑝𝑑𝑝

2 ]

∆𝑡 (4.16)

where:

Ap/V is the protected section factor (see above) (m-1

)

cp is the specific heat of the coating (J/kgºC)

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ρp is the coating density (kg/m3)

dp is the coating thickness (m)

kp is the thermal conductivity of the coating (W/mºC)

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EXAMPLE: HEAT TRANSFER EQUATIONS

QUESTION:

1) What temperature does the column on Gridline B3 and primary beam on Gridline B reach for

the fire curve generated in 0. Generate time-temperature curves to show the behaviour.

Consider the following for each member:

a. The member being bare steel.

b. Protection by being boxed out with 12mm gypsum board.

ANSWER 1:

a) Column of GL. B3 - Unprotected

i) For a UC 203x203x46 bare column: Ap / V = 205m-1

(Section 5.2, Euro-Nomogram).

𝜌

𝐴𝑚 / 𝑉=

7850𝑘𝑔/𝑚3

205𝑚−1 = 38.3𝑘𝑔/𝑚2 (useful conversion equation)

ii) εF = 0.7 for a column exposed on all sides.

iii) Time increment to be used: 5 seconds.

iv) At the first time increment: TF = 45.1°C, from Example spreadsheet.

𝑎𝑟 =5.67×10−8𝜖𝐹

𝑇𝐹−𝑇𝑠(𝑇𝐹

4 − 𝑇𝑠4) =

5.67×10−8×0.7

45.1−20(45.14 − 204) = 0.006276

∆𝑇𝑠 =𝑎

𝑐𝑠(𝜌𝑠𝑡𝑒𝑒𝑙𝐴𝑝/𝑉

)(𝑇𝐹 − 𝑇𝑠)∆𝑡 =

25+0.00832

600×38.3(45.1 − 20) × 5 = 0.136°𝐶

Thus, the temperature at the end of the first time period is: 20.14°C. The remaining

steps have been carried out in a spreadsheet to generate the graph below.

b) For the cladded column:

ii) Perimeter of the boxed out section

𝐴𝑝

𝑉=

𝐵𝑜𝑎𝑟𝑑 𝐼𝑛𝑡𝑒𝑟𝑛𝑎𝑙 𝑃𝑒𝑟𝑖𝑚𝑒𝑡𝑒𝑟

𝑆𝑡𝑒𝑒𝑙 𝐴𝑟𝑒𝑎=

4𝑠𝑖𝑑𝑒𝑠 × (0.203𝑚)

5.88 × 10−3𝑚2= 138.1𝑚−1

iii) For gypsum board: cp = 1700 J/kgºC. ρp = 800kg/m3. dp = 0.012m. kp = 0.20W/m°C.

iv) 𝑐𝑆𝑀

𝐷= 22980 < 2𝑑𝑝𝜌𝑝𝑐𝑝 =32640. Thus, equation (4.16) must be used.

∆𝑇𝑆 =𝑘𝑝

𝑑𝑝[

𝑇𝐹 − 𝑇𝑆

𝑐𝑠𝑀𝐷 +

𝑐𝑝𝜌𝑝𝑑𝑝

2

]∆𝑡 =0.20

0.012[

45.1 − 20

600 ×7850138.1 +

1700 × 800 × 0.0122

]5 = 0.0494°𝐶

The remainder of the calculations have been carried out as shown in the graph below.

Maximum temperatures – Unprotected: 837.6°C

- Protected: 582.4°C

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Figure 4.8: Temperatures of the protected and unprotected UC 203x203x46 column.

ANSWER 2:

a) Primary Beam on Gl. B, unprotected:

i) For a UB 533x210x82 bare column: Ap / V = 180m-1


ii) Flange width : beam depth = 210 / 533 = 0.39 < 0.5, so εF = 0.7

b) Perimeter of the boxed out section:

iii) Ap / V = 120m-1


See the curves below for the temperature.

Maximum temperatures – Unprotected: 827.32°C

- Protected: 562.3°C

Figure 4.9: Temperatures of the protected and unprotected UC 533x210x82 beam.

0

100

200

300

400

500

600

700

800

900

1000

0 20 40 60 80 100 120

Tem

pe

ratu

re (

°C)

Time (min)

EN 1-1-2 Fire

Unprotected

Protected

0

100

200

300

400

500

600

700

800

900

1000

0 20 40 60 80 100 120

Tem

pe

ratu

re (

°C)

Time (min)

EN 1-1-2 Fire

Unprotected

Protected

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TUTORIAL: HEAT TRANSFER EQUATIONS

Using the fire curve that you generated from the last tutorial generate time-temperature graphs and

determine the maximum temperatures for a UC 305x305x97 grade S355JR exposed on all sides in the

firecell with:

a) No passive fire protection.

b) 24mm vermiculite boards, boxing out the entire section.

Submit a graph showing the temperature development with time.

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5 Member Design for Fires

1.15 Prescriptive Design

The simplest rules available for the prescriptive design of steelwork occur in SANS 10400. The

thicknesses of coatings are given to provide certain fire resistances. These guidelines will not be

considered as there are a number of fairly simple guides which provide much better design

information.

1.16 The “Yellow Book”

A guide to consider for passive protection fire design is the “Yellow Book” published by the

Association for Specialist Fire Protection (ASFP, 2010) (available free at www.asfp.org.uk). The

design is based upon limiting the temperature of steelwork to the “critical temperature” as listed

below, which depends on the load ratio. The critical temperature is defined as “The temperature at

which failure of the structural steel element is expected to occur against a given load level”. Example

6 below is taken from the Yellow Book to illustrate how coating thickness might be determined.

EXAMPLE: YELLOW BOOK FIRE PROTECTION

http://www.asfp.org.uk/

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Table 5.1: Limiting temperatures for the design of protected steelwork according to the "Yellow Book" (ASFP, 2010)

1.17 Euro-Nomogram

Another good resource for determining the thickness of passive protection is the Euro-Nomogram

published by the ECCS. It is contained on the following pages. It can be freely downloaded after

registering online with the ECCS as part of the document “Explanatory Document for ECCS No 89 -

Euro-Nomogram - Fire Resistance of Steel Structures” (ECCS, 1999).

Examples are given in the Nomogram regarding how to use it. On the following page a useful exert

from the Nomogram which provides the section factors of various steel members and for different

protection conditions is provided.

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EXAMPLE: COATING THICKNESS TO THE EURO-NOMOGRAM

QUESTION: Determine the thickness of boxed out gypsum boards required to give the column from

the previous example a 60 minute fire rating (SANS 10400).

ANSWER: For the profile Ap/V = 138.1m-1

(140 in the Euro-Nomogram). The column is exposed on

all 4 sides and is important for overall stability, so K = 1.2.

From the Red Book the strength of a UC 203x203x46 with a 4m effective length: Cr = 1067kN.

Thus, using the fire load from Example 3 of 551kN, the degree of utilisation is:

𝜇0 =𝐶𝐹𝐿𝑆

𝐶𝑟 =

551𝑘𝑁

1067𝑘𝑁= 0.52

Now to go the Nomogram: Enter the graph on the left at 𝜇0 = 0.52. Go up to K=1.2. On the right

enter the Nomogram at a fire resistance of 60 min. Go up to meet the line projected across from

K=1.2. From this we approximately get: 𝐴𝑝𝜆𝑝

𝑉𝑑𝑝= 1350𝑊/𝑚3𝐾.

By substituting the gypsum board value𝜆𝑝 = 0.20 we get: dp = 20.5mm.

Thus, an approximately 20mm thick board will be sufficient.

TUTORIAL: EURO-NOMOGRAM COATING THICKNESS

Determine the thickness of passive protection for a UC 305x305x97 of grade S355JR requiring 60min

fire rating. Consider it to be important for stability. Vermiculite boards will be used to fully box out

the column, which is exposed on all sides.

1.18 Design to SANS 10162-1: Fire Design Annex

In 2015 South Africa’s steel design code, SANS 10162-1, is being updated. Along with various other

updates and changes it is getting a fire design annex, which the discussions below are based on. The

annex has been created from the Canadian code CSA S16, and edited by the authors of this course.

Tensile Resistance 1.18.1

The tension resistance of a member is determined in the same way that it is done an ambient

temperature, but with the reduced yield strength of members.

Compressive Resistance 1.18.2

The compressive resistance at temperature T is given by:

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𝐶𝑟(𝑇) = (1 + 𝜆(𝑇)2𝑑𝑛)−1/𝑑𝑛

𝐴𝑓𝑦(𝑇) (5.1)

𝜆(𝑇) =𝐾𝐿

𝑟√

𝑓𝑦(𝑇)

𝜋2𝐸(𝑇)= √

𝑓𝑦(𝑇)

𝑓𝑒(𝑇) (5.2)

with:

d equals 0.6

n equals 1.34 for general steelwork

Figure 5.1 shows the failure stress for columns when at ambient temperature, 500°C and 800°C. It can

be seen that the strength of members degrades very quickly with increasing temperature.

Figure 5.1: Compressive failure stress of columns according to CSA S16

Bending Resistance 1.18.3

The resistance of a member in bending under lateral-torsional buckling is given as:

𝑀𝑟(𝑇) = 0.12𝑀𝑝(𝑇) + 0.88𝑀𝑝(𝑇) (1 − (

0.12𝑀𝑝(𝑇)

𝑀𝑐𝑟(𝑇))0.5

)𝜁(𝑇)

(5.3)

where

Mp(T) is the plastic moment at elevated temperature, T

Mcr (T) is the elastic critical load at elevated temperature T, given by:

𝑀𝑢(𝑇) =

𝜔2𝜋

𝐿√𝐸(𝑇)𝐼𝑦𝐺(𝑇)𝐽 + 𝐼𝑦𝐶𝑤 (

𝜋𝐸(𝑇)

𝐿)2 (5.4)

where

ω2 is a factor to account for the bending moment shape. This can be taken as defined in

Table 5.4 of the Red Book.

𝜁(𝑇) =

𝑇 + 800

500≤ 2.4 (5.5)

For a fully restrained beam the resistance can simply be calculated as the plastic or elastic section

modulus (depending on what class it is) multiplied by the reduced yield strength of the steelwork.

0

50

100

150

200

250

300

350

0 50 100 150 200

Cr(

T)/A

- F

ailu

re S

tre

ss (

MP

a)

KL/r - Slenderness Ratio

20°C

500°C

800°C

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The lateral-torsional buckling resistance of a UB 406x178x54 is shown in the figure below.

Figure 5.2: Lateral-torsional buckling resistance of a UB 406x178x54 beam at different temperatures

Combined Axial Force and Flexure 1.18.4

Beam-columns are to be designed in the same manner as done at ambient temperature with the

reduced member capacities as defined above.

EXAMPLE: SANS 10162-1 STEEL DESIGN EXAMPLE

QUESTION: Check the design capacity of the UC 203x203x46 column in the fire compartment at

the fire limit state. Obtain maximum temperatures from Example 5, considering both the protected

and unprotected member.

ANSWER:

Obtain the reduction factor for fy and E from Table 3.5 by interpolation.

UC 203x203x46 Details:

Maximum Temperature:

ky,θ: kE,θ: fy((T)

(MPa): E(T)

(GPa):

Bare steel 837.6°C 0.091 0.082 32.3MPa 16.4GPa

Protected – 12mm gypsum

582.4°C 0.525 0.361 186.4MPa 72.2GPa

𝜆(837.6°C) =𝐾𝐿

𝑟√

𝑓𝑦(𝑇)

𝜋2𝐸(𝑇)=

1.0×4000

51.2√

32.3

𝜋2×16400= 1.10

𝐶𝑟(837.6°C) = (1 + 𝜆(𝑇)2𝑑𝑛)−

1𝑑𝑛𝐴𝑓𝑦(𝑇) = (1 + (1.10)2×0.6×1.34)−1/(0.6×1.34) × 5880 × 32.3

= 72.4𝑘𝑁

0

50

100

150

200

250

300

350

400

450

0.0 2.0 4.0 6.0 8.0 10.0

Mr

- B

en

din

g re

sist

ance

(kN

m)

KL - Effective length (m)

20°C

500°C

800°C

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Using the same equations: 𝐶𝑟(582.4) = 358𝑘𝑁 for the protected member. Thus, the column is

insufficient for the 551kN load calculated earlier for the FLS.

However, note that for the Eurocode the effective length can be reduced to 0.5 of the original because

of the cool columns above and below acting as fixities. For the top floor of a building a factor of 0.7

should be used. If an effective length of 0.5L is used the resistance will increase to around 674kN for

the protected member. This would be sufficient for resistance.

TUTORIAL: STEEL RESISTANCES

QUESTIONS:

1) Determine the capacity of a UC305x305x97 grade S355JR column which is 5m long and at

750°C. What would the capacity be is the effective length was halved as per the Eurocodes for

columns between intermediate floors in buildings?

2) Determine the bending resistance of a 5m long UB 406x140x39 grade S355JR beam at

650°C. Consider the beam to be unbraced along its full length, so the effective length can be

taken as 1.0. The beam carries a UDL and is simply-supported.

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6 Introduction to Advanced Design Methods

1.19 Overview of Advanced Design / Performance-based methods

In this section a brief overview of performance-based design methods, primarily for composite floors,

is presented. These methods allow for significant savings in the amount of passive fire protection

required and produce safer structures. Since the calculation procedures can be quite lengthy the

philosophy of the design methods will be discussed rather than the actual equations and maths.

Readers should refer to the references if they wish to use these methods in practice.

1.20 Global structural behaviour considerations

Up until now only single elements have been considered when carrying out designs. However,

elements will generally be influenced by the members around them. The following are important

factors that can influence the forces in an element (ECCS, 2001):

1. Restraint effects. High forces, buckling, localised plastification and other such factors can be

results from the restrained expansion of members.

2. P-Δ Effects. The nonlinear behaviour and large deformations that result in a structure in a

severe fires causes second-order effects. In simplified analysis methods this is typically

neglected.

3. Internal force redistribution. In natural fire conditions force redistribution often occurs as

parts of a structure yield.

4. Membrane effects, as discussed below for composite floors.

5. Alternative loads paths are created whereby weakened members transfer loads to adjacent

structural elements, or sometime even to secondary elements not designed to carry loads (e.g.

internal brickwork).

6. Lateral-torsional buckling which might not be an issue at ambient temperatures can become

an issue in severe fires.

7. Joint behaviour becomes very complex as large deformations can cause pinned connections to

become almost fixed, and local buckling can occur.

The figures below show a number of examples which demonstrate how analyses of structures can

potentially be conducted using advanced design methods (Franssen & Vila Real, 2010).

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Figure 6.1:Examples of advanced design models that consider global and local behaviour (Franssen & Vila Real,

2010)

When considering the global analysis and design of a structure Figure 6.2 shows various aspects that

should be addressed, or could be utilised to satisfy structural performance.

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Figure 6.2: Considerations when designing a structure using performance-based methods

1.21 Background to Composite Floor Design Methods

One great challenge that exists with regards to the performance based design of steel structures in fire

is that the modelling and analysis of structures is complicated, only a relatively small number of full-

scale tests have been conducted to validate models against, and there are few industry accepted

methods which are commonly used for doing designs. However, significant advances have been made

in structural fire engineering since the series of full-scale fire tests done at BRE’s Large Building Test

Facility at Cardington from 1993 to 2003 (European Joint Research Program, 1999). In these tests a

purpose-built 8 storey building was progressively burnt down to investigate the behaviour of steel and

composite buildings at elevated temperatures.

The tests demonstrated that the interaction between members has a significant effect on overall

structural fire behaviour (Lennon, 2011). It is interesting to note no structural collapses were observed

during tests, even when the atmosphere temperature reached 1200ºC, and the temperature of exposed

steel beams reached 1150ºC (Bailey, 2002). Current design codes (BS5950-8, EN1994-1-2) predicted

that the beams would fail at temperatures of around 680ºC, showing that practice does not fully match

codes at this stage. Figure 6.3 shows a photo of a failed beams and a buckled column as observed at

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the Cardington tests. The floor deflections were substantial but the floors exhibited catenary-type

tensile behaviour which greatly enhanced the capacity of the floors, as shown in Figure 6.4.

Following on from the tests Bailey (2000a, 2000b; 2008; 2004a) developed a method for calculating

the capacity of composite floors when catenary actions occurs in severe fires. Various improvements

have been made by him and others to the method as research has continued. Prof Charles Clifton

(2014; 2006; 2013) from New Zealand developed the Slab Panel Method (SPM) based on Bailey’s

work, and additional research conducted by his group. An overview of the philosophy of the

methodology used by Bailey and Clifton will now be presented. In 2014 a research project at

Stellenbosch University by Geldenhuys (2014) investigated the SPM’s suitability for South Africa

and it was found that it can be used as is, with only possible minor changes to the fire loading such

that it matches local codes.

Figure 6.3: Failed column and beams at the Cardington fire tests (Lamont, 2001)

Figure 6.4: Large deflections observed in the composite floors during the Cardington tests (Lamont, 2001)

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1.22 Composite floor design methods

The general principle behind methods for composite floors in severe fires is to protect the primary

beams and columns in a structure, but allow the secondary beams to fail in case of a fire. This allows

the unprotected beams and slab to “fail” and substantially deflect causing catenary action to occur

This can result in substantial savings, where up to 50% of beams do not need passive protection.

Figure 6.5 shows the typical layout and failure mechanism observed in a composite floor when it fails

during a fire. Figure 6.6 is an example of a floor where passive protection has only be applied on

selected beam elements.

Figure 6.5: Layout for the SPM. The typical crack pattern associated with the inelastic, large-deflection behaviour of

composite slabs at elevated temperatures is shown (Clifton, 2006)

Figure 6.6: Application of the SPM or Bailey's method can lead to only primary beams and columns needing passive

protection, as demonstrated in the picture (Bailey, 2002)

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Outline of Technical Details 1.22.1

At ambient temperatures the manner that loads are transmitted through a composite building involves:

The slab -> Secondary beams -> primary beams -> columns.

When severe fire conditions occur and the interior secondary beams are unprotected, they lose most of

their strength and the load path above cannot be maintained. The beams form plastic hinges and the

load-carrying mechanism changes to a two-way spanning system, as illustrated by Figure 6.7. Here

the load carrying path becomes:

The slab panel -> primary supporting beams -> columns.

From this it can be seen that the secondary beams no longer play a major role, and simply form part of

the sagging slab panel system. However, it is essential that primary beams are protected as these carry

the sagging slab panels. The progression of the load carrying setup from ambient to fully developed

catenary action is shown below.

Under ultimate load conditions at ambient temperature, yield-line behaviour develops first and then

tensile membrane enhancement, which occurs as the plastic hinges form. But under severe fire

conditions, tensile membrane enhancement occurs first – i.e. the floor capacity increases as it becomes

a hanging catenary. In the event of a fully developed fire, the SPM performs as follows:

1. The slab and the unprotected secondary beams may undergo considerable permanent

deformation.

2. The primary support beams and columns undergo much less permanent deformation

compared to that within the panel.

3. The load-carrying capacity and the integrity of the floor system are preserved.

4. Both local and global collapse is prevented.

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Figure 6.7: Development of catenary action and plastic hinges in a composite slab (Bailey, 2004a)

Calculation Procedure 1.22.2

The calculation procedure followed to calculate the capacity of a floor complying to the SPM

procedure is:

1. Determine the total floor load (dead and live) at the fire limit state.

2. Calculate the fire severity based on the fire loads, and building characteristics. Convert this to

an equivalent standard fire time.

3. Determine the temperature of the slab concrete, rebar and steel beams. Various equations and

tables are provided for this purpose.

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4. Evaluate the yieldline load-carrying moment capacity in each direction for hogging and

sagging.

5. Calculate the yieldline load-carrying capacity based on the actual support conditions but

ignoring tensile membrane action.

6. Determine the deflections that would occur in the slab panel as these have a significant

influence on the magnitude of the tensile membrane action.

7. Find the tensile membrane enhancement factor and multiply this by the yieldline load

carrying capacity to determine the total capacity of the floor.

8. Check that the total capacity of the floor is greater than the total floor load.

9. Check the shear capacity.

10. Ensure that sufficient reinforcement is provided to preserve integrity (no cracks opening up in

the floor).

1.23 Detailing Requirements Necessary for the SPM

A variety of detailing requirements must be adhered to for tensile membrane action to be able to

occur. The following are a basic summary of some of the guidelines contained in report R4-131:2006

by Clifton:

- Rebar used must be sufficiently ductile to allow for the development of plastic hinges

- Columns and primary beams must be passively protected or have sufficient capacity in fire

conditions (as is sometimes the case in seismic resisting frames) such that load can be carried.

The full length of beams, full height of columns, and the connection elements of secondary

beams must be passively protected if protection is required.

- Steel connections must allow for sufficient inelastic rotation up to the maximum temperature.

- Decking must be fastened to beams as specified in the technical reports.

- Hooks must be placed on rebar at edge panels to allow sufficient connection between the slab

and beams, and reinforcement lap requirements must be adhered to.

EXAMPLE: FLOOR DESIGN USING THE SPM SOFTWARE

QUESTION: For floor layout of the structures shown in Example 1 check the floor capacity and size

the rebar to ensure adequate capacity during a fire.

ANSWER:

Input values will be taken from the previous examples and used as values for the SPM software,

namely:

- FLS Load: w∗ = G + 𝛼𝑄 = 3.2𝑘𝑃𝑎 + 0.5 × 3.4𝑘𝑃𝑎 = 4.9𝑘𝑃𝑎

- 𝑏 = 1849.1 𝐽/𝑚2𝑠0.5𝐾

- 𝑞𝑓,𝑑 = 540.5 𝑀𝐽/𝑚2

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Let us divide our floor into three separate slab panel sections, as shown below. Note that of the 29

beams only 12 are passively protected, or 41%, which means a substantial savings in protection costs.

By adjusting the rebar in the slab we can obtain a solution that satisfies both the bending and shear

requirements of the system, as detailed below. Basically the summary of the calculations is:

- Design floor load: 4.9kPa

- Floor capacity: 5.04kPa. OK

- Design shear load: 18.38kN.m

- Floor shear capacity: 24.75kN/m. OK

- Rebar: Mesh ref. 395 (8mm bars at 200 each way)

Y12-200 interior support bars in the X-direction

Y12-450 trough bars

The rebar specific is similar (possibly a bit higher) to that which would be found in a typical

composite floor when fire resistance is not considered. Hence, additional capacity has been obtained

in fire conditions with significantly less passive protection that typically used.

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NOTE: The UB 406x140x46 beams on the sides which at ambient temperatures function as secondary

beams and are now part of the slab panel system may need to be checked to ensure that they have

sufficient capacity, and might need to be increased in size.

Calculations from the SPM are provided on the following pages.

TUTORIAL: TENSILE MEMBRANE BEHAVIOUR

Download the MACS+ or TSLAB software. Redesign the slab in the example above but considering

that the live load now comes from a storage area so the full imposed load must be taken for the FLS

case. Adjust rebar and the floor thickness to suit the design. Panel layouts may need to be adjusted

depending on what the software used can accommodate.

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1.24 Software for advanced design

Other software systems that have been produced for advanced design of structures in fire include:

TSLAB: This is a spreadsheet that has been developed in the UK by the Steel Construction Institute

(SCI) and is based upon Bailey’s tensile membrane design method for composite structures. It appears

that it is no longer being updated.

MACS+: MACS+ is a package freely distributed by Arcelor Mittal and its name stands for

Membrane Action of Composite Structures in Case of Fire (Vassart & Zhao, 2012). It used to be

known as FRACOF and has also been built upon Bailey’s (2000a, 2000b) membrane action method

for designing composite slabs. Cellular and protected steel supporting beams can be considered. It has

many similarities to the SPM software.

VULCAN: This is a commercially available software package for the design of structures in fire. It

has been produced by Sheffield University over many years through numerous research projects.

SAFIR: SAFIR is an advanced finite element structural engineering software package specifically

developed for structures in fire. It has been developed by Franssen at the University of Liege.

ABAQUS or DIANA: ABAQUS and DIANA are general purpose, powerful, finite-element

programs that can consider the nonlinear behaviour of structures. Various researchers have used these

packages for analysing structures in fire, or for validating other models. It can be quite time-

consuming to setup and run models in these packages.

Arcelor Mittal - Fire Calculations Download Centre: A number of free software packages are

provided on Arcelor-Mittal’s website http://amsections.arcelormittal.com. These modules cover

aspects such as composite design, column design, beam design etc.

http://amsections.arcelormittal.com/

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7 References

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