STEEL STRUCTURE IN AN OPEN CAR PARK - TU Delft

STEEL STRUCTURE IN AN

OPEN CAR PARK

The influence of trapped smoke on the fire

resistance of steel beams

Master Thesis

Yan-Ying C. Wong

Delft University of Delft

Structural Engineering

Steel and Timber structures

STEEL CONSTRUCTION IN AN OPEN CAR PARK- Influence of trapped smoke on the fire resistance of the steel beams

Y.C.Wong i

This thesis has been performed as a partial fulfillment of the requirements for the degree of

Master of Science in Civil Engineering at Delft University of Technology

This thesis has been carried out in cooperation with

Bouwen met Staal (BmS)

Delft University of Technology (TU Delft)

Efectis Nederland

Author:

Name: Y.C.Wong (student number 4076915)

Institute: Delft University of Technology

Faculty of Civil Engineering & Geosciences

Structural Engineering - Steel and Timber structures

Email address: [email protected]

Graduation Committee:

Name: Prof.ir. F.S.K. Bijlaard




Name: Ir.R. Abspoel




Name: Dr.ir. A.F. Hamerlinck

Company: Bouwen met Staal

Senior Advisor

Name: Ir. R.A.P. van Herpen

Institute: Eindhoven University of Technology

Fellow Fire safety Engineering, Faculty of Architecture

Name: Ir. A.D. Lemaire

Company: Efectis Nederland

Senior Project Leader Fire Engineering

Name: Dr.ir. K.C. Terwel

Institute Delft University of Technology

Building Engineering

Name: Ir.L.J.M. Houben



Road and Railway Engineering

The photo used on the cover is from Universiteit Gent, photo Hilde Christiaens


Y.C.Wong ii

Preface

This study contains the research of the influence of smoke, originating from a car fire, on the

steel beams of an open car park. The study was done as a final fulfillment to obtain the degree of

Master of Science in Structural Engineering at the Delft University of Technology. The research

was done in cooperation with Bouwen met Staal and Efectis Nederland.

I am grateful for the assistance, advice and guidance of the graduation committee during this

research. Special thanks to Tony Lemaire for his patience, guidance and technical support which

are very valuable leading to the result of this research. My appreciation goes to Ruud van

Herpen for his invitations to the “Nationale Parkeerdag 2014” and the Expert class “Next

Generation” for an opportunity to learn even more about the topic I was graduating on. My

sincere gratitude also goes to Ralph Hamerlinck, whom gave advice and suggestions regarding

the car parks in the Netherlands.

Finally, I would like to thank my family and friends for the encouragement and the support

during this period. At last and the most important are my parents in Suriname for their support

and the opportunity to study in the Netherlands.

Y.C.Wong

Delft, Netherlands

November 2014


Y.C.Wong iii

Summary

A car in an open car park is on fire. The fire and the smoke unleash a heat that causes the

temperature to rise. The open car park is made out of a steel frame and to be designed for a fire

resistance of 60 minutes. This car fire is a local fire whereas flashover doesn’t occur. The crucial

point of the fire is when the steel frame reaches the critical temperature. If this occurs, the steel

will fail and might lead to the collapse of the building.

Because it is an open car park, it is assumed the natural ventilation will lead the smoke out of the

building very fast. But the smoke can be trapped between the beams, which are present below

the ceiling as a support structure for the floor system. The aim is to study whether the influence

of trapped smoke between beams in an open car park is significant or not. And is it necessary to

take the smoke into account during the design of an open car park when making use of the

Bouwen met Staal guideline (BmS- guide), a guideline for the design of the fire safety of an

open car park?

In this study the influence of the smoke on the steel structure of the open car park was

investigated by making use of a spreadsheet Car Park Fire (CaPaFi) and the software, Fire

Dynamic Simulator (FDS). CaPaFi is a spreadsheet which calculates the steel temperatures

without taking smoke into account. It is based on real car fire tests and the Eurocode. FDS is a

program that uses computational fluid dynamic calculations to run a simulation (model) of a car

fire in an open car park. It calculates the steel temperature of the steel beams taking the effect of

smoke into account. All the information for FDS is written in a script beforehand and run

afterwards.

A single car fire and a 3 car fire were modeled and studied. To verify the calculations in FDS

with CaPaFi, a single car fire model was put up. Because there were still some differences in the

results, 4 more models were set up with small adjustments in the first one to fine tune the model

(model 2 to 5). According to the study 95% of the car fires are limited to maximum 3 (fully)

burnt cars [1]. So, 3 car fires were also taken into account and the smoke. There were two cases

with 3 car fires: one with beam sticking out (model 6 with obstacles) and one with beams hidden

in the ceiling (model 7 without obstacles).

Based on the results of this study, it is found that the smoke which is trapped between the beams

can be neglected when making use of the BmS-guide to design the fire safety of an open car park

for the steel beams with a height smaller than 500mm. Also a reasonable explanation could not

be found of why the temperatures of the steel beams of FDS are lower than the ones calculated

by CaPaFi. And in a 3 car fire model points that are further away from the car fire can be

disregarded because their steel temperature calculated by FDS, even though higher than CaPaFi,

will never reach the critical temperature. At last, it is still unclear why the increased number of

soot doesn’t have any effect on the temperature of the steel beams in the single car fire model.

At last, information about each chapter is given:

Chapter 1 gives a brief introduction of the thesis, the objectives, preconditions and the

assumptions of this study. Finally the research strategy is presented.


Y.C.Wong iv

Chapter 2 provides information about the car park such as to distinguish between a closed and

open car park, the lay out, the dimensions of the beams and the type of floor systems that are

commonly used in the Netherlands.

Chapter 3 presents the different type of fires that can occur in a building and what type occurs in

an open car park. Then the cars which cause the fire are discussed. Finally the smoke that arises

from the fire is given.

Chapter 4 discusses the effects of heat on steel and what kind of fire safety measures can be

applied to protect the steel from the heat. Then simplified calculations are presented in

comparison with CaPaFi showing the effect of the heat of a single car fire and 3 car fires on a

steel beam within an open car park.

Chapter 5 is about the tools that can be used for this study. The choice for this study was making

use of computational fluid dynamic calculations that would be done by the FDS. The results

gained from the FDS were than compared with the results done by CaPaFi, which is a

spreadsheet that is used for calculating the steel temperatures of a beam in a car park. CaPaFi is

based on real car fire experiments and the Eurocode.

Chapter 6 is about the model set up in FDS which is divided into two parts: a single car fire with

a single beam and 3 car fires with 2 beams. The 3 car fires contain two cases, with beams

sticking out of the ceiling and without. The results of the comparison of the total heat fluxes and

the steel temperature of the beam between the different models are presented and the conclusions

are drawn.

Chapter 7, the final chapter of the study contains the conclusions and the recommendations

which can be used for further study and analysis.


Y.C.Wong v

Table of Contents

Preface............................................................................................................................................. ii

Summary ........................................................................................................................................ iii

Table of Symbols ......................................................................................................................... viii

Chapter 1 Introduction .................................................................................................................... 1

§1.1 General ................................................................................................................................ 1

§1.4 Objective ............................................................................................................................. 2

§1.5. Preconditions and assumptions of the study ...................................................................... 2

§1.6 Research strategy................................................................................................................. 3

Chapter 2 The car park .................................................................................................................... 5

§2.1 General ................................................................................................................................ 5

§2.2 The car park ......................................................................................................................... 5

§2.3 The layout of the car park ................................................................................................... 6

§2.4 The floor systems in a car park ......................................................................................... 10

Chapter 3 Fire and smoke ............................................................................................................. 13

§3.1 General .............................................................................................................................. 13

§3.2 Localized fire and a compartment fire .............................................................................. 13

§3.3 The combustible material .................................................................................................. 15

§3.4 The smoke ......................................................................................................................... 17

§3.4.1 Characteristics of the smoke ....................................................................................... 18

§3.4.2 The smoke movement ................................................................................................. 18

§3.4.3 Influence of smoke on the environment and humans ................................................. 18

§3.4.4 Measures against the smoke ....................................................................................... 18

Chapter 4 Effect of the high temperatures on the steel properties ................................................ 19

§4.1 General .............................................................................................................................. 19

§4.2 Heat transfer ...................................................................................................................... 19

§4.3. Influence of the temperature on the material properties .................................................. 21

§4.4 The simplified calculations of steel ................................................................................... 23

§4.5 Fire safety measures .......................................................................................................... 28

§4.5.1 Active measures .......................................................................................................... 28

§4.5.2 Passive measures ........................................................................................................ 28

Chapter 5 The tools to study thermal influences .......................................................................... 31

§5.1 General .............................................................................................................................. 31

§5.2 Models on thermal influences ........................................................................................... 31


Y.C.Wong vi

§5.3 Software ............................................................................................................................ 33

§5.3.1 Car Park Fire (CaPaFi) ............................................................................................... 33

§5.3.2 Fire Dynamic Simulator (FDS) .................................................................................. 36

Chapter 6 Modeling ...................................................................................................................... 37

§6.1 General .............................................................................................................................. 37

§6.2 Preparations for the verifications ...................................................................................... 37

§6.3 One car fire (Model 1 to 5)................................................................................................ 38

§6.3.1 Set up of model ........................................................................................................... 38

§6.3.2 Analysis of the results for model 1 to 5 ...................................................................... 42

§6.4 Three car fires (model 6 and model 7) ............................................................................. 52

§6.4.1 Set up 3 car fires ......................................................................................................... 52

§6.4.2 Analysis of the results for model 6 and 7 ................................................................... 55

Chapter 7 Conclusions and recommendations .............................................................................. 68

§7.1 Conclusions ....................................................................................................................... 68

§7.2 Recommendations ............................................................................................................. 68

§7.2.1 Recommendations with respect to further study ............................................................ 68

§7.2.2 Recommendations with respect to the software ............................................................. 69

References ..................................................................................................................................... 70

Appendices .................................................................................................................................... 74

Appendix 1 Size of the car [3] ...................................................................................................... 74

Appendix 2 Information TT-plates [26] ....................................................................................... 75

Appendix 3 Calculation of the section factor of some profiles [52] ............................................. 77

Appendix 4 Previous studies ......................................................................................................... 78

Appendix 5 Information about hollow core slab[14] .................................................................... 82

Appendix 6 Simplified calculations .............................................................................................. 83

Appendix 7 Profile of the fictitious beam ..................................................................................... 85

Appendix 8 Script of model 1 (FDS) ............................................................................................ 86

Appendix 9 Data total heat fluxes of Model 1 .............................................................................. 89

Appendix 10 Data temperatures of model 1 ................................................................................. 94

Appendix 11 Script model 2 for FDS ........................................................................................... 97

Appendix 12 Data Total heat fluxes for model 2 ........................................................................ 103

Appendix 13 Data temperature of model 2 ................................................................................. 112

Appendix 14 Comparison heat fluxes model 2,4 and CaPaFi .................................................... 116

Appendix 15 Comparison temperatures model 2,4 and CaPaFi ................................................. 121


Y.C.Wong vii

Appendix 16 Comparison Total heat fluxes model 2 and model 5 ............................................. 126

Appendix 17 Comparison Temperatures model 2 and model 5 ................................................. 135

Appendix 18 Convective heat transfer coefficient Model 5 ....................................................... 140

Appendix 19 Comparison Total heat fluxes model 2 and model 3 ............................................. 144

Appendix 20 Comparison temperatures model 2 and model 3 ................................................... 146

Appendix 21 Script of FDS (model 6) ........................................................................................ 150

Appendix 22 Data heat fluxes of model 6 .................................................................................. 159

Appendix 23 Data temperatures of model 6 ............................................................................... 170

Appendix 24 Script of FDS (model 7 hidden beams) ................................................................. 175

Appendix 25 Data heat fluxes of model 7 (hidden beams) ......................................................... 176

Appendix 26 Data temperatures model 7 (hidden beams) .......................................................... 187

Appendix 27 Comparison heat fluxes model 6 and 7 ................................................................. 192

Appendix 28 Comparison temperature model 6 and 7 ............................................................... 195


Y.C.Wong viii

Table of Symbols

Latin case letters

Am Perimeter of the area that is heated of the member [m]

ASB Asymmetric Slim for Beams

B1 The length of a parking unit (one side) [m]

B2 The length of a parking unit (two sides) [m]

Ca Specific heat of steel [J/kg K]

D Diameter of the fire [m]

H Distance between fire and ceiling [m]

or hpunt Total heat flux [W/m2]

hnet Net heat flux [W/m2]

hnet,c Net convective heat flux [W/m2]

hnet,r Net radiate heat flux [W/m2]

HRR Heat Release Rate [kW]

l Length [m]

Lf Flame length [m]

Lh Horizontal flame length [m]

min Minutes

P2 Depth of the double parking stroke

Q*D heat release coefficient related to the diameter D of the local fire

Q*H Heat release coefficient related to the height H of the compartment

r

Horizontal distance between the vertical axis of

the fire and the point along the ceiling where the thermal flux is calculated [m]

RHR Rate of heat release [W/m2]

s Seconds

T Temperature [oC]

t Time [in seconds or minutes]

THQ Top Hat Q-beams

Tm Surface temperature of the member [oC]

Tr Effective radiation temperature of the fire environment [oC]

tα Time constant [seconds]

V Cross- sectional area [m2]

W Width of the aisle [m]

y Dimensionless perimeter [-]

z' Vertical position of the vertical heat resource [m]


Y.C.Wong ix

Greek case letters

α Parking angle [ o ]

αc Convection coefficient [W/m2K]

εf Emissivity of the fire [-]

εm Emissivity of the member [-]

θg Temperature gas [oC]

θm Temperature member [oC]

κ1 Adaption factor for non-uniform temperature across the cross- section

κ2 adaption factor for non-uniform temperature along the beam

λa Thermal conductivity [W/mK]

ρ Density [kg/m3]

σ Constant of Stefan- Boltzmann [W/m2K

4]

Φ Configuration factor [-]


Y.C.Wong 1

Chapter 1 Introduction

In this chapter a brief introduction is given about the research, followed by the problem

statements, the objectives, the preconditions and the scope of this study and ending with the

research strategy.

§1.1 General

One of the most used construction material is steel. As for any material, even steel has its

advantages and disadvantages. One of those disadvantages is the deduction of the strength and

other properties when it is exposed to fire. Many architects and design recognized the

advantages of steel in the world of construction. The use of steel in the construction varies from

single- story industrial buildings to multi-story non-residential buildings [2]. An example of the

last named is a car park.

With a car park made out of steel, measures are taken to ensure the safety of users in case of fire.

In case of fire in the open car park, the surrounding area near the car that is on fire will heat up.

The fire in an open car park is short and local. There are some guidelines that will make sure of

the safety for design and construction. Because it is an open car park, it is assumed that the

smoke which is produced during the local fire will leave the area quickly (see Figure 1) due to

natural ventilation. The smoke rises up and gets to the ceiling and is hindered by the beams that

(partly) stick out, depending on which floor system is used. The beams’ height depends on the

type of floor system that is used. There is still uncertainty whether the smoke has an influence

(and at what rate) or not on the fire safety of the beams in a car park during a fire and therefore

the problem can be stated as:

What kind of influences will the smoke, trapped between the beams below the floor, have on

the steel frame of the open car park?

Figure 1 Sketch of the problem

Within a fire, a lot of chemical and physical reactions occur and the problem is very complex.

To gain more insight of the problem, the main question is divided in sub questions:

1. What is an open car park? (the size, the structure, material)

2. How does the heat spread through the space? How does it transfer from the open

area on to the structure?

3. How many heat/energy comes from the smoke?

4. Which size of the beam will hinder the free flow of the smoke?

5. Which methods are there available to model/calculate smoke?

6. How long does it take for the smoke to transfer the heat onto the structure? What

is the heat transfer with regard to the local fire model?


Y.C.Wong 2

7. Which preconditions can be stated with respect to the height of the beams to be

able to make use of CaPaFi and which must be written in the Guideline of the fire

safety for steel car parks (BmS -guideline) to limit the field of application?

§1.4 Objective

To research whether smoke, which is trapped between the beams, needs to be taken into account

during the fire safety design of the open car park when making use of the BmS -guideline.

§1.5. Preconditions and assumptions of the study

The preconditions are as followed:

- Fire resistance as written in Guideline of the fire safety for steel car parks [1]

- Only open car parks are researched and the enclosed car parks are not taken into account.

- The requirements which have been set up for this research regarding the car park are:

The main structure is made out of steel

Natural ventilation (without the help of mechanical ventilation)

No superstructure (upper structure) on top of the car park

The layout in the car park has a regular repetition of parking units

The minimum fire resistant requirement of an open car park is approximately 60

minutes [1]

- Only beams are checked in this process (no columns and floors)

Assumptions that are made:

- For an open car park, the worst case scenario in this case with the maximum of trapped

smoke is no wind. The wind is left out for this research during the whole process.

- There are only normal sized cars 1 that are making use of the open car parks (see

Appendix 1 Size of the car

- No new types of cars are included in this research such as hybrid and electric cars. Only

the ones that are mentioned in [4]

- Research shall only be done whereas the local fire occurs on a horizontal floor (no

research shall be done on floors with a slope)

1 Normal sized cars: A vehicle containing 4 or more wheels, not a plowing car or a disabled vehicle or a four-wheel

moped, designed for the transport of people containing not more than 8 seats not including the driver’s seat or a

camping car [in Appendix A of NEN 2443]. See Appendix 1 for the information.


Y.C.Wong 3

§1.6 Research strategy

This study involves two fields namely the thermal analysis and the structural analysis. Because

the time is limited, the thermal analysis is done thoroughly and the structural analysis is done in

a more simplified manner. To accumulate information about this topic, resources such as the

internet, papers, eBooks and articles are used.

Gaining insight for thermal analysis through full scale experiments are expensive and involves a

lot of significant work. These experiments are not used in the everyday building design but as a

scientist’s tool. Small scale experiments are often executed in a geometry scale where the

execution is easily done. Making use of the results gained from these small scale models other

mathematical models, hand calculated methods and even computer based models are derived

and/or assessed. However, not all experimental results are totally accurate because there are

measuring errors. And these measuring errors can be estimated for 30%. As mentioned before,

full-scale car fire experiments are usually very expensive to perform and require special facilities

for experimenting due to the damage it can caused to the structure and environment. Computer

simulated car fires are less expensive. A disadvantage is the long simulation time that is needed

to run the simulation although the technology of processors and computers has improved in the

last decades. [5], [6]

The car fire is a localized fire. In the Eurocodes the localized fire is described. In the BmS-guide

the spreadsheet Car Park Fire (CaPaFi) is used, which is based on the localized fire and data

gained from real experimental car fires [1], [7], [8]. In this study CaPaFi is used to verify

whether the models made in the software Fire Dynamics Simulator (FDS). CaPaFi doesn’t take

into account the smoke and FDS does. With these two tools insight is gained. With Smokeview

(SMV) graphic results can be seen which have been calculated by FDS.

For verification of the thermal analysis, the Eurocodes are used as reference. The Eurocodes that

have been used for this research are:

1. NEN-EN- 1991-1-2

2. NEN-EN- 1993-1-2

More information of CaPaFi and FDS are given in §5.3. Car Park Fire (CaPaFi) and details

about which version is used is as follow:

CaPaFi version 2.1

FDS version 6.0.1

In Figure 2 the steps carried out in the current study is given as a flow diagram.


Y.C.Wong 4

Figure 2 Flow chart of the research methodology


Y.C.Wong 5

Chapter 2 The car park

§2.1 General

In this chapter information about the car park is given such as the definition, the distinction

between an enclosed and open car park, the dimensions of a car park and the different floor

systems that can be used within a car park and its dimensions.

§2.2 The car park

A car park2 (also called a parking garage) is a building designed for parking cars which can be

made out of several floors. A distinction between car parks can be made:

A) An enclosed (closed) or integrated car park

An enclosed (closed) car park or “integrated” parking garage can be part of a big

building, have enclosed facades and/or located below the ground level (underground car

park). [9] From [10] it is shown that there has been a lot of research with respect to the

car fires in enclosed car parks. These studies involved around the smoke movement and

the fire development affected by the ventilation systems and it can be concluded that:

The fire will stop by itself in case of oxygen lack

If ambient air is drawn in, the fire can be re-ignited (also known as back draft)

Ventilation accelerates various stages of the fire

B) An open car park

An open car park can also be part of a building or a building itself with open facades.

The characteristics of an open car park are given in NEN2443 [3] (based on the

ventilation of carbon monoxide and the use of liquid propane gas):

At least two walls opposite from each other are open (it can’t be closed)

The maximum distance between two walls opposite from each other is 54m

The lowest floor is ≤ 1,3 m below ground level

The open sections in the walls are for each floor (area) ≥ 1/3 of the surface of all walls

and the walls that are confined to this floor (area) OR the openings in the two opposite

walls in each of these facades ≥ 2.5% of the gross floor area of the floor(area) AND

The ventilation (according to NEN 1087 [11]) must be at least 3*10-3

m3/s per m

2 used

surface (This is also an requirement of the Bouwbesluit (a Building decree used in the

Netherlands))

To ensure the natural ventilation, there are extra requirements or specifications [1]:

The requirement of the distance from one wall to the other is nuanced to: from each point

in the area in the car park the distance to a wall ≤ 27m

Only “The open sections in the walls are for each floor (area) ≥ 1/3 of the surface of all

walls and the walls that are confined to this floor (area)” stands, the other option about

the 2.5% is not applicable

When a wall with a length of ≥ 7.5m is closed over the entire height, a conservative

consideration on the basis of mirror symmetry is possible (in which it is assumed that the

number of cars on fire is doubled and no heat-exchange at the location of the reflecting

2 http://encyclopedia.thefreedictionary.com/parking+garage

http://encyclopedia.thefreedictionary.com/parking+garage


Y.C.Wong 6

surface takes place). At an angle with two closed walls over a length of ≥ 7.5m, this

mirror symmetry apply to both directions;

The free flow of hot combustion gasses above cars must not be enclosed on 4 sides by e.g.

high steel beams, closed wall sections that stick out of the floors or parapet

There must be a space of at least 500mm so that free flow is possible.

Since the amount of air is limited in an enclosed car park, the fire is limited to some point.

Within an enclosed car park, extra measures have been placed in to maintain the fire safety of

the people and the building itself. But for an open car park, whereas there is an unlimited amount

of fresh air this could lead to a short “big” fire. The focus of this study is on open car parks.

§2.3 The layout of the car park

There are many layouts for an open car park given in article 5.3.8.3 in [3]. There are two type of

car arrangements which are the herring bone shape (45o, 60

o, deep double parking) and parking

in the length (one side or double side). The dimensions can be found in the Table 1. For a public

(intensive use) a minimum unit width of 2.5 m is required.

Figure 3 Herring bone shape 45o [3]

Figure 4 Herring bone shape 60o [3]

Figure 5 Deep double parking [3]

W - Width of the aisle

P2 - Depth of the double parking stroke

- Direction of the car flow

For parking straight the minimum width of

the aisle (= W) is 4m.


Y.C.Wong 7

Figure 6 Parking in length (one side) [3]

Figure 7 Parking in length (two sides) [3]

B1 – The length of the parking unit (one side)

B2 – The length of the parking unit (two sides)

b – Width of a parking unit

W - Width of the aisle

α – Parking angle


Y.C.Wong 8

Table 1 The dimensions of the elements in an open and public car park [3]

Parking

angle (α)3

Depth of

a single

parking

stroke

(P1)

Depth of

a double

parking

stroke

(P2)

Depth of the

double

parking

Herrington

shape (P2)

Width of

the

aisle (W)

Width

parking

unit (b)

Length

of the

parking

unit

one side

(B1)

Length of

the

parking

unit

two side

(B2)

Figures Figure 6

Figure 5

Figure 3

and

Figure 4

Figure 3

till

Figure 7

Figure 6

and

Figure 7

Figure

6 Figure 7

[degrees] [m] [m] [m] [m] [m] [m] [m]

30.00 4.19 6.80 7.30 3.80 2.40 7.99 12.18

30.00 4.19 6.80 7.30 3.80 2.45 7.99 12.18

30.00 4.19 6.80 7.30 3.80 2.50 7.99 12.18

45.00 4.95 8.61 8.40 3.80 2.40 8.75 13.70

45.00 4.95 8.61 8.39 3.80 2.45 8.75 13.70

45.00 4.95 8.61 8.37 3.80 2.50 8.75 13.70

60.00 5.38 9.85 11.36 3.80 2.40 9.18 14.56

60.00 5.38 9.85 11.37 3.80 2.45 9.18 14.56

60.00 5.38 9.85 11.39 3.80 2.50 9.18 14.56

60.00 5.38 9.85 11.40 3.80 2.55 9.18 14.56

65.00 5.44 10.11 11.39 3.87 2.40 9.31 14.75

65.00 5.44 10.11 11.40 3.80 2.45 9.24 14.68

65.00 5.44 10.11 11.41 3.80 2.50 9.24 14.68

65.00 5.44 10.11 11.42 3.80 2.55 9.24 14.68

70.00 5.46 10.29 11.33 4.43 2.40 9.89 15.35

70.00 5.46 10.29 11.34 4.08 2.45 9.54 15.00

70.00 5.46 10.29 11.35 3.82 2.50 9.28 14.74

70.00 5.46 10.29 11.36 3.80 2.55 9.26 14.72

80.00 5.37 10.44

not

applicable

5.53 2.40 10.90 16.27

80.00 5.37 10.44 5.23 2.45 10.60 15.97

80.00 5.37 10.44 4.87 2.50 10.24 15.61

80.00 5.37 10.44 4.47 2.55 9.84 15.21

90.00 5.13 10.26

not

applicable

6.67 2.40 11.80 16.93

90.00 5.13 10.26 6.33 2.45 11.46 16.59

90.00 5.13 10.26 6.00 2.50 11.13 16.26

90.00 5.13 10.26 5.67 2.55 10.80 15.93

3 The angle in which the parking slots are located with respect to each other


Y.C.Wong 9

To have a sustainable design for the arrangements of the columns are also given as 3 examples

(See Figure 8 till Figure 10). All the sizes are given in m. This is to design column free.

Figure 8 Columns layout -1 [3]

Figure 9 Column layout -2 [3]

Figure 10 Column layout-3 [3]

In Figure 8 the columns placed in the

car park in a way that not big spans are

needed and more columns are needed.

In Figure 9 and Figure 10 the columns

are placed in such a manner that is it

easy to park the car and eye-sight for

the driver is better.

It can be concluded from the given layouts that for the x- direction the approximated length is

16m and in the y- direction it is between 5 – 8m. The governing case for the x – and y direction

are respectively columns layout 1 and 3.

For the minimum required free height (= the vertical distance between the floor or ground and de

lowest point of the upper structure) is minimum 2.3m and incidental areas (beneath beams and

(pipe) lines) is minimum 2.2m. [Article 5.5.1, [3]].

X

Y


Y.C.Wong 10

§2.4 The floor systems in a car park

The columns determine the possible spans in an open car park. The floor system depends on

many factors such as the height restriction and the structural layout (spacing between columns).

The available floor systems determine which beams should be used to be able to cover the span

and take up the loads that are present. The most common used floor systems in car parks in the

Netherlands are presented in different categories given in Figure 11 [12].

Figure 11 Categories of floors systems used in car parks in the Netherlands [12]

The different floor systems are briefly explained [12]:

1) Concrete hollow core slabs

The hollow core slabs prefabricated floor

elements, which have been prestressed and then

brought on site to be executed. The self-weight of

these floors are 50% lower than a massive floor

slab due to these hollow cores. They are able to

span over a length of 18m. The width of these

floors is standard 1.2m. The floors have a light

self-weight and support large loads too. An

example of this hollow core floor used on steel

beams for a car park is the Medimall car park in

Rotterdam. For the concrete hollow core slabs on

THQ- beams examples are car park at Tilburg , the

car park at the Martini hospital in Groningen,

Parking building Zuid in Eindhoven and the

Roermondsepoort in Venlo. [13] [14] [15] [16]

[17] [18].

Figure 12 Car park Medimall, Rotterdam

1) Hollow core slabs

On steel beams On THQ-beams

2) Composite decks/slabs

Low Composite decks/slabs

on steel beams

Deep Composite decks/slabs

On steel beams

On ASB beams (integrated)

3) Precast concrete plank

floors

With dowels Without dowels

4) TT - Plates


Y.C.Wong 11

2) Composite decks/ slabs

These floors obtain a steel metal sheet that acts

like a formwork for cast in situ concrete floors.

They are light weighted and easy to be executed.

Depending on the span there is a distinction

between low (with or without dowels) and high

composite floors (with or without propping). The

spans range from 3.25m to 9.60m. An example of

a car park with a low composite floor is Doorneind

Helmond. For the high composite floor

respectively on steel beams and on ASB beams are

car park Hoofddorp, car park Rijnstaat Hospital in

Arnhem and car park at the Bogaard in Rijswijk.

[13] [19] [20] [21] [22] [23] [24]

Figure 13 Car park Rijnstaat, Arnhem [22]

3) Precast concrete planks

Precast concrete planks are prefabricated

formwork elements where on site the concrete is

poured on top. These floors are used in residential

and non-residential structures. The maximum

length is 8.9m and the thickness varies from 50mm

to 90mm. An example of this type of floor system

the car park Gerechtsgebouw at the Wilheminapier

in Rotterdam. [13] [25].

Figure 14 Floor system car park

Gerechtsgebouw at the Wilheminapier in

Rotterdam [25]

4) TT-plates

This type of floor system is also used in car parks

such as split level car park. The spans range from

8 -16m, the effective width is 2.50m and the height

is 550mm or 770mm. A concrete layer can be

poured on top of the service. The flange thickness

of the TT-plates is variable depending how thick

the concrete topping is. (For sizes and information

see Appendix 2 Information TT-plates ). [26], [27]

Figure 15 TT –plates [26]

The fire safety of a parking garage is defined as the time that the building can withhold/

withstand without collapse and causing casualties. This is different in each country. From [1] it

can be concluded that car parks are required to have a fire resistance of 60 minutes for the main

construction. For car parks with fewer floors the requirement is at least 30 minutes. A fire safety

of an open car park fulfills the requirements as a safe building if the steel structure doesn’t fail

and the steel structure satisfies the safety requirements (if it is proven that it can withstand

scenarios in an equivalent safety analysis).


Y.C.Wong 12

Figure 16 Car Park “Medimall”

Figure 17 Car Park “Eindhoven” (Near the

airport)

Figure 18 Car Park “Q-Park Tilburg”

After visiting some open car parks in the

Netherlands (Figure 16, Figure 17 and Figure

18), the following can be concluded: column

layout 2 and 3 are the most common (Figure 9

and Figure 10) and the most user unfriendly

layout is number 1 (Figure 8).

Combining what was found in previous

paragraphs, layout 3 will be used for the study.

The main factor that sends out heat apart from the flames is the smoke. To have the largest

amount of heat it is therefore necessary to have as much smoke as possible (the bigger the

volume smoke, the more heat). The bigger the area where the smoke is trapped, the less dense it

is leading to possibly less heat production. This is still uncertain, therefore research and

investigation is needed.


Y.C.Wong 13

Chapter 3 Fire and smoke

§3.1 General

In this chapter, the distinction of different categories fires is given. The explanation of a car fire

and in which category a car fire is explained. A short elaboration about smoke, its movement and

hazards and the protection against smoke are presented.

§3.2 Localized fire and a compartment fire

To have a fire there are 3 components necessary:

A) The fuel (combustible material)

B) The oxygen (to sustain the combustion)

C) Heat or ignition source

These are given in the fire triangle. All three components

must be present at the same time and each of them has their

function in the reaction.

Figure 19 The fire triangle [http://www.academyfire.com/extinguisherguide.html]

The type of fire can be divided in a compartment fire and a localized fire.

A compartment fire can be described in 3 phases which is shown Figure 20 [28]:

1) Pre- flashover: The fire just started and can still effectively be put out if early warnings

are given. Only some of the material within the compartment is on fire.

2) Post flashover: in this stage the fire can either die out (lack of combustible material or

oxygen) or increase (sudden income fresh air inside room e.g. when a window breaks)

3) Flash over: All combustible material within the compartment is on fire and extinguishing

the fire in this stage is impossible. The flashover is around 600oC or with a radiation

intensity of 20 kW/m2. For models the flashover is around 500-600

oC and 15-20 kW/m

2

[28], [29].

Within a compartment fire, the whole compartment has a high temperature due to the fire.


Y.C.Wong 14

Figure 20 The temperature- time curve of a fire

A localized fire is characterized by the fact that the fire remains small or a fire within a very

large area where there is no flash over. The combustion products such as smoke and other hot

gasses will gather on the ceiling. This will cause the area to divide into a layer of smoke and one

without. In a zone model this is modeled as a hot and cold layer. The temperatures are assumed

to be overall the same within a layer. [28]

The fire in a car park can be categorized as a localized fire. In a car park with enough ventilation

or early intervention of the fire department there will be no flashover (low fire load density of

250 MJ/m2 [30]) and the fire is maintained. The fire is limited to one or a couple of cars. Fire

temperatures obtained from real fire test in an open car park from previous tests gives a good

indication how the development of the temperature is for a car fire. The fire in a car park

undergoes the following stages:

a) The ignition: This can be done on purpose (vandalism etc.) or accidently (heat in the

fuel/motor, cigarette in the car seat etc.). Once the ignition starts, part of the car will start

burning.

b) The growth: After ignition, the fire grows at a rate depending on the type of material, the

amount of oxygen. The whole car is burning and heat is spreading. This heat ignites a car

parked next to the fully burning car (fire spread).

c) Decay: The fire is starting to be smaller because there is no more material left to be

burned.

An example on how the temperature progress is within the time during a car fire can be seen in

Figure 21.


Y.C.Wong 15

Figure 21 Measured temperature of gasses (fire) [4]

To check whether a structure still meets the requirements of not failing, one makes use of the

standard fire curve. This curve (see Figure 20) is described with:

T= 20+ 345*log (8*t+1) Eq. (1)

with T= temperature in oC

t =time in minutes

Further elaboration on how to check the structures will be given in the other chapters.

§3.3 The combustible material

In case of a car fire the combustible material are the cars and the fuel within these cars in the car

park. Based on the amount of energy that a car releases during a fire, cars in Europe are divided

in 5 categories (examples of which cars are given in each category Table 2) with an energy

available to be released ranging from 6000 MJ to 12000 MJ in Table 3 [4].

Table 2 Definition of the European cars [4]


Y.C.Wong 16

Table 3 The average car mass, mass of the combustible materials and energy available to be released versus

category [4]

From [1], the following can be said:

Researches shows that more than 95% of the car fires are limited to maximum of 3 (fully)

burning vehicles

The flame spread from one vehicle to another vehicle (parked transversally) is

approximated 12 minutes (based on a category 3 car with an available energy of 9500 MJ)

[1] [4] For car parks with floors (levels) higher than 5m: after 12 minutes 2 cars are

burning and after 24 minutes 4 cars are burning.

The combustible material in a parking garage is the car itself, namely the tires, the interior of the

car, the fuel and the plastic car parts. There is time needed to have flame spread from one car to

another. The fire inside a car will die out if there is a lack of oxygen. The most common car fires

are due to casualties and overheated motors. Even this issue is almost ruled out because the car

producers are also responsible in getting good cars on the market [31].

From [32] an indication can be given how much the rate of the heat release is of different type of

cars. In this case, 3 cars were set on fire. In Table 4 and Table 5 the information of these cars and

the tanks are given.

Table 4 Cars in Full-scale Fire Experiment at VTT of 1994 [32]

Test no. Car model Mass before fire without

fuel [kg]

1

2

3

Ford Taunus 1.6

Datsun 160J Sedan

Datsun 180B Sedan

990

918

1102

Table 5 Fuel tank features [32]

Test

no.

Fuel tank Filler pipe

material

Fuel hose to engine

Material Location Material Connection to fuel tank

1

2

3

Steel

Steel

Steel

Beneath the boot

Between the back of

the rear seat and the

boot

Beneath the boot

Steel

Plastic

Plastic

Steel

Plastic

Plastic

Top of the tank

Bottom of the tank

Top of the tank


Y.C.Wong 17

Figure 22 Rate of heat release measured in the

car fire experiments [32]

The results of these tests are given in Figure 22 and

it’s ignition at t = 2 min. The peaks correspond to the

burning of different parts of the car and are indicated

by the arrows.

Table 6 Information about Figure 22 [32]

Test

Arrow

1

Arrow

2

Arrow

3

1 1/3 of

windscreen

collapse,

increasing

fire in the

passenger

cabin

Fuel is

burning from

the filler pipe

mouth

2 Windscreen

collapse,

flashover in

the

passenger

cabin

Burning

liquid is

dropping

from the rear

part of car

3 Flashover

in the

passenger

cabin

Flames from

the fuel tank

where the

plastic filler

pipe has

melted

Melted

plastics from

a pool fire

under the rear

part

According to [32] 59% of the car fires started from the engine area and 35% from the

passenger’s area. Fire spreads faster from engine to the passenger’s cabin then the other way

around. Temperatures measured in the experiments vary from 400-800oC.

In this research the focus will mainly be on vehicles described in Table 2 and the electric cars

and hydrogen or hybrid cars are disregarded. It should be mentioned with the search of cleaner

and sustainable energy the use of more hydrogen and electric cars will be more common.

Research of tunnel fires with hydrogen car has already begun. [33]

§3.4 The smoke

When the ignition has started, a smoke layer will develop and the heat production process starts.

The amount of energy is expressed in the rate of heat release (RHR [in W/m2]) and a time

constant (tα [s]). The RHR is dependent on the type of combustion material and the amount of

oxygen.


Y.C.Wong 18

§3.4.1 Characteristics of the smoke

The smoke within a closed compartment can be divided into layers: cold and hot layer. Each

layer has its own characteristics [34]:

1. Hot layer: the temperature in this part of the layer causes the natural buoyancy of the

smoke to lift up itself toward the ceiling while clean or a little polluted air is drawn into

the lower part.

2. Cold layer: In this layer the mixing and all forms of heat transfers reduce the effect of the

driving force whereas the buoyancy won’t lift up so much smoke. Wind and stack effects,

mechanical heat, ventilating and other air moving systems control the smoke movement.

The layers in an open car park will not be distributed very accurately. The hot layer will be

located between the beams and the cold layer under the beams to a certain extent (certain

height). The area and surroundings where the burning car is located will be warm. The further

away from the source the colder it gets.

§3.4.2 The smoke movement

A phenomenon called back-layering can also occur. During fires, jet fans are used to drive the

smoke onto one side. But if the driven force is too low, the smoke flow might go back (air flow

going in the upstream direction) which is called back-layering. [35] This usually occurs in tunnel

fires, but it can also occur in car parks. Some back-layering is allowed in car parks. Researches

have been done to study this phenomenon in large closed car parks. [36]

§3.4.3 Influence of smoke on the environment and humans

The emissions from car fires have been examined. A detailed investigation of full-scale

simulated car fires (3 separate full scale fire tests: fire ignited and developed in the engine

compartment, fire ignited in the coupe and extinguished in the early phases and a fire ignited in a

coupe which spread out to the entire vehicle) was done, including characterizing the gas phase

components, particulates and run-off water from extinguishing activities. It is concluded out of

these researches that these emissions have potentially negative effect on the environment or a

toxic effect on humans if it were produced in significant quantities. During the fire, the smoke is

the biggest problem and leads to the death of people. The most toxic effects are those coming

from carbon monoxide, fumes and vapors. The smoke is the main hazard against humans. [37]

[38] [39]

§3.4.4 Measures against the smoke

There are different methods to keep the smoke under control in the car park. It is necessary to

keep the smoke under control so that people can safely escape from the building and for the

firemen to enter the building to extinguish the fire at an early stage. The smoke can influence the

sight of the people and also the oxygen which the people inhale. The measures that can be taken

to control the smoke flow during the design stage [39]:

- Natural or mechanical ventilation

- Positions of the escape/ fighting stairs

- Escape distances

To some distinct these measurements can remove the smoke during the fire away from the car

parks.


Y.C.Wong 19

Chapter 4 Effect of the high temperatures on the steel properties

§4.1 General

Within this chapter, the car park and the fire are brought together. What will happen? The effects

of the high temperatures on the steel are discussed. Different types of heat transfers are discussed

and the formulas on how to determine these. Afterwards, the effects on the material properties of

steel are discussed. In the last part, the simplified calculations are given and the reason why it is

necessary to research the influence of the smoke.

§4.2 Heat transfer

On the surfaces that are exposed to the fire, heat transfer occurs. The heat transfer from a fire on

to a steel member is illustrated in Figure 23 and is known in 3 forms [29] [30]:

Figure 23 Different type of heat transfer4

1. Conduction: the amount of heat transfer from hot to cold object is proportional to the

temperature gradient, the contact area and the conductivity. Since it is about the steel car

park, the steel’s thermal conductivity

is used and given in NEN-1993-1-2 [40].

For 20oC ≤ < 800

oC Eq. ( 2a)

For 800oC ≤ < ≤ 1200

oC Eq. ( 2b)

Where

4Picture obtained from http://schoolworkhelper.net/thermal-energy-transfer-conduction-convection-radiation/

http://schoolworkhelper.net/thermal-energy-transfer-conduction-convection-radiation/


Y.C.Wong 20

Figure 24 Thermal conductivity of steel vs. temperature [40]

And furthermore the specific heat is a property influenced by the temperature.

The determination of the specific heat Ca of steel [J/kg K] according to [40]:

For

Eq. (3a )

For

Eq. (3b )

For

Eq. ( 3c)

For

Eq. (3d )

Where

Figure 25 Specific heat of steel vs. temperature [40]


Y.C.Wong 21

2. Convection: this is heat flow in a gas or fluid. The amount of heat that is transferred is

proportional to the difference in temperature, the contact area and the convection

coefficient. The convective heat transfer according to [40]

Eq.(4)

[

]

[oC]

[oC]

3. Radiation: the amount of radiation is dependent on the material of which the radiator is

made out of, a constant σ (Stefan- Boltzmann constant) and the temperature of this

object. The heat flux coming from the radiation according to [40]

Eq.(5)

[– ]

[– ]

[

]

Summarizing to net heat flux (

Eq.(6)

§4.3. Influence of the temperature on the material properties

The yield strength of steel will decrease as the temperature rises. This can lead to a failure.

Theoretically if the stress is known due to the loads, the temperature of steel can be calculated

when it fails. This temperature is known as the critical temperature [29]. The loss of strength

starts at approximately 400oC. Around 550

oC only 60% of its strength is left for hot rolled

sections. Decrease of the strength is the strongest between 400oC and 800

oC. The limiting

temperature in which structural steel member would withstand before collapse varies according

to the temperature profile and the load. [41]


Y.C.Wong 22

Figure 26 Strength factor steel vs. temperature [41]

Depending on how the steel element was designed, it can be that the element doesn’t necessarily

have to fail. For example if the element is designed to just carry the load at room temperature, it

will probably fail during the fire or afterwards. This doesn’t have to be the case if the element

was a bit over dimensioned [29].

Figure 27 Steeltemperature and the stadard fire curve [29]

The extent in which the object is warmed up depends on a section factor [29] [30]. It is

calculated:

Am/V Eq.(7)

With: Am = the perimeter of the area that is heated [m]

V= the cross- sectional area [m2]

In Appendix 3 Calculation of the section factor of some profiles [52] there is more info about the

different shapes and there calculation method with for with and without fire protection. The

smaller the section factor, the slower it heats up (see Figure 27). This information is provided by

the producers.


Y.C.Wong 23

§4.4 The simplified calculations of steel

A building is designed to withstand loads such as the self-weight, the live loads and the wind

loads. Even during a casualty such as a fire. In previous studies of Liew et al. and the paper

about the car park Medimall, the steel structure was able to withstand the fire with or without

addition of fire protection. For more detailed information about these cases see Appendix 4

Previous studies. The same matter was done in a simplified manner with a beam which is simply

supported. This beam is located in an open car park. Areas where this beam needs to be checked

against failure are:

1. The area where the maximum moment occurs (in the middle of the beam): in this area a

car is never parked here, but it could be that a fire can start there.

2. The area where the fire occurs (where the car is parked): Although the biggest moment

capacity isn’t in this area, the heat might cause the moment capacity to reduce

significantly and lead to failure.

The dimensions for the beam are taken from the car park Medimall in Rotterdam. In §2.3 it was

concluded that the biggest span was approximately 16m. Due to this reason, the direction of the

floor system and span given in Medimall are changed: the hollow core sections will span across

4.8m (effective width) and the beams across 14.75m. It is chosen to start with HEB 500 (S355)

and making use of hollow core slabs (type 150-8 of Dycore, see Appendix 5 Information about

hollow core slab. The fire is at 2m from the left support, which approximate the center of the car.

In Figure 28 the beam and the position of the fire are given.

Figure 28 Fire occurring in the middle of the beam (Dimensions are in mm)

The critical temperature of the beam is calculated (see Appendix

6 Simplified calculations) and the temperatures of the steel beam

during the car fire are determined by Car Park Fire (CaPaFi).

In practice the temperature in the cross- section of the beam

differs. The topside of the beam is put against the slab floor in

and the bottom of the beam is exposed to the heat of the car fire

(Figure 29). The differences in the temperature throughout the

cross- section of the beam are corrected by the factor κ1 in the

x

y

Figure 29 Heated I-section


Y.C.Wong 24

NEN-EN- 1993-1-2. The temperature of the beam throughout the cross-section is than being

averaged. Since the beam is simply supported the factor κ2 will be 1.

In Figure 30, Figure 32 and Figure 34 the beam is represented by the green dots in CaPaFi. Point

1 and 4 are the points at the support. Point 2 is the point at x= 2m and point 3 is the middle of the

beam, x= 7.375m. The car is given as the red square. The steel temperatures are calculated and

plotted in graphs given in Figure 31, Figure 33 and Figure 35.

Figure 30 Beam is illustrated with green points: point 1 and 4 are at the supports, point 2 at 2m and point 3

in the middle of the beam; car fire is the red square. [Source: CaPaFi]

Car fire at 2m away from the left support of the beam


Y.C.Wong 25

Figure 31 Temperature of different positions of the beam with the car fire at x=2m [Source: CaPaFi]


in the middle of the beam; car fire is the red square. [Source: CaPaFi]

618

73

0

50

100

150

200

250

300

350

400

450

500

550

600

650

0 600 1200 1800 2400 3000 3600 4200 4800 5400 6000 6600 7200

Tem

p [

°C]

Time [sec]

Temperature field of the beam (fire at x=2m)

Pos 1

Pos 2

Pos 3

Pos 4

Car fire in the middle of the beam


Y.C.Wong 26

Figure 33 Temperature of different positions of the beam with the car fire in the middle of the beam [Source:

CaPaFi]

All the results of the simplified calculations and the ones done by CaPaFi are given in Table 7.

Table 7 Overview of the critical temperatures (hand calculations5) and the beam’s temperature of CaPaFi

Location Critical temperature

[oC]

Beam’s temperature

with fire at 2m [oC]

Beam’s temperature

with fire in middle [oC]

X = 2.00m 712 618 73

X= 7.38m 628 73 618

From Table 7 it can be concluded that the temperature of the beam in both situations are lower

than the critical temperature, so the beam would not fail. But in both cases the influence of the

smoke that is trapped between the beams can cause the temperature to be higher. For the

situation given in red in Table 7, the smoke might cause the temperature to be higher than 628oC.

That’s why it is necessary to check the influence of the smoke.

Another situation that can occur is that there is more than 1 car parked near the support. These

cars are about 2.5m apart from each other. It is assumed that the first car right (red car in Figure

34) under the beam ignites first and then the blue car and at last the pink one (Figure 34). As

shown Figure 35 the temperature of the beam at position 2 reaches 734oC which is higher than

the critical temperature. This beam needs to be re-designed again with fire protection or enlarged

to a bigger profile. As expected, for more than 1 car fire the temperature will be much higher

than in the case of 1 car fire.

5 See Appendix 6 Simplified calculations

73

618

0

50

100

150

200

250

300

350

400

450

500

550

600

650

0 600 1200 1800 2400 3000 3600 4200 4800 5400 6000 6600 7200

Tem

p [

°C]

Time [sec]

Temperature field of the beam (fire at x=7.375m)

Pos 1

Pos 2

Pos 3

Pos 4


Y.C.Wong 27


in the middle of the beam; car fires are the red, blue and pink square [Source: CaPaFi]

Figure 35 Temperature of different positions of the beam with 3car fire at 2m from the left support [Source:

CaPaFi]

734

141

0

50

100

150

200

250

300

350

400

450

500

550

600

650

700

750

800

0 600 1200 1800 2400 3000 3600 4200 4800 5400 6000 6600 7200

Tem

p [

°C]

Time [sec]

Temperature field of the beam ( 3 fires at x=2m)

Pos 1

Pos 2

Pos 3

Pos 4

3 Car fires at 2m from the left support of the beam


Y.C.Wong 28

§4.5 Fire safety measures

To protect a building, in this case a car park, against fire there are many measures that can be

taken. These measures can be divided into active (fire and smoke detectors, sprinklers etc.) and

passive measures (special applied materials such as paint, coatings, protection of the steel by

concrete surroundings etc.). In this paragraph it is elaborated on these measures.

§4.5.1 Active measures

Active measures are measures that actively respond to the fire. These are:

1. Fire and smoke detectors [42]

Fire detectors: Their functions are to detect and locate the fire at an early stage, alert the

occupants and the fire brigade and activate the fire control systems.

Smoke detectors: these systems detect the presence of smoke. The detection can be done

through ionization (electrical conductivity of air ionized by radioactive element), optical

detection (attenuated or scattered light) or long distance light beam (attenuated light).

Disadvantage of these smoke detectors are that it is very sensitive (smoking).

2. Sprinklers

There are many types and classes sprinklers, it functionality ranging from industrial

buildings to car parks. They can detect the fire in an early stage (smoke/ small fire) and

suppress or extinguish it and sound the alarm. The continuous development of the

sprinklers ensures that there is a high reliability and sensitive in responding to the fire.

When there is a fire, water is sprinkled and thus keeping the fire small, have control over

the smoke and flames. Regular checkups and maintenance is required for the optimal

functioning of the sprinkler system. [43]

In recent years, there are new ventilation systems developed which combined with an electronic

fire detection are considered as an addition to extinguish fire at an early stage, and CAN’T

replace the sprinkler system.

§4.5.2 Passive measures

Passive measures are measures that don’t need activation in order to function, such as insulation

material and planning an escape route.

To protect the steel against the heat there are many methods, fire insulation of the load bearing

structures [41]. In Figure 36 an outline of the different types of fire protected steel is given.


Y.C.Wong 29

Figure 36 Outline of fire protected steel [41]

The methods for protecting the steel against fire are described below [41]:

i. Intumescent coatings: A material that will be inert at low temperatures and will insulate

the steel during high temperatures (starts a chemical reaction at a temperature of 200oC -

250oC). This material will swell and acts as an expanded layer with low conductivity.

These materials are subdivided into two groups:

- Thin film: This type is water based or solvent based (used for cellulosic fire conditions).

These are applicable for buildings with a fire resistance requirement of 30 to 90 minutes.

Some of these materials nowadays can also reach 120 minutes. Water based ones can be

applied on- site and solvent based ones are used for area which are dry and heated.

Expansion ratio is about 50:1 (1mm coating expands to 50mm).

- Thick film: first developed for off-shore and hydrocarbon industries but nowadays also

applicable for buildings. They are epoxy based and have a higher dry film thickness than

the thin ones. Expansion ratio is lower and is about 5:1.

ii. Boards: A system that is used to protect the necessary areas and it is not hidden. They are

applied on painted and unpainted steelwork. They are divided in two groups:

- Lightweight (150-250 kg/m3): used not decorative finishes and are cheaper than heavy

weights.

- Heavy weight (700-950 kg/m3): used for decorative finishes.

iii. Sprays: It can cover up complex shapes elements and the costs don’t rise significantly as

the thickness of the elements thickens. They are not applicable in areas where the

aesthetic is necessary. Spraying is a wet trade, so it might influence other site operations.

Fire protected steel

Reactive

Thin film intumenscent

coatings

On site applied

Off site applied

Thick film intumescent

coatings

On site applied

Off site applied

Non- Reactive

Boards

Light weight Heavy weight

Sprays


Y.C.Wong 30


Y.C.Wong 31

Chapter 5 The tools to study thermal influences

§5.1 General

As quoted in [6]: “Fire processes are a very complicated and complex phenomenon consisting of

combustion, radiation, turbulence, fluid dynamics and other physical and chemical processes. A

good knowledge about complex phenomena and processes occurring during fire in different

environments is a significant component of fire safety. As fire itself is very complicated

phenomenon, interdisciplinary approach to the problem is required.”

There are many tools nowadays to predict the smoke and fire spread. These tools make use of a

model, which is a simplified “version” of the reality, to calculate and predict what will happen

with the use of formulas. The model used within the simulations can model and simulate and

visualize the spreading of fire and smoke. An estimation of the environmental damages caused

by the fire can even be given. The benefits of a model are mentioned in the §1.6. [6].

Making use of a model requires skills and knowledge. The software that is used will always give

a solution. It is therefore important that the user defines what data and boundaries to give to the

software and how to model the situation as good as possible. Verification must always be done

with literature cases or other cases [29].

In this chapter a brief explanation is given, the different methods to study the thermal effects on

the steel structure and the software that will be used for this research.

§5.2 Models on thermal influences

Over the years many models have been developed to describe the behavior of the fire and its

influences in the environment. With these models researches with respect to the fire and its

behavior can be researched more thoroughly. Depending on the accuracy of the results that one

wants to obtain and the best model for describing the fire a model is chosen.

Some of the models that are known for the description of fire presented with a short explanation:

1) Empirical correlations:

- Very easy to use

- Applicable for a certain case and limited in the range of conditions

- Examples are the Thomas’ Plume equation

2) Zone models:

- They are based on analytical and semi-analytical considerations

- It divides the interested area into zones, which are described by a simply set of

parameters and semi-empirical laws and these parameters are averaged for the

specific area

- Boundary conditions are used when there is a change between the areas

- Examples: CFAST and OZone

Requirements that must be fulfilled in order to use this model are given in NEN 6055 (article

7.1.2). Zone models are not suitable for modeling fire in car parks because they are limited to

small areas (smoke cools down too fast), works with average temperatures and underestimates


Y.C.Wong 32

the temperature of the upper layer. Furthermore in a zone model it is very difficult to take into

account the natural ventilation or mechanical ventilation and the horizontal spreading of the

smoke can’t be taken into account [44]

3) CFD (Computational Fluid Dynamics) or field models:

They are based on local physical quantities laws (e.g. mass, momentum, energy and

different type of concentrations)

It is an accurate and scientifically method

This model provides the ability to model the evolution of the fire at any time and any

point of a specific area

Very time consuming

They also take into account the turbulence effects of the smoke and therefore can be

divided in two categories namely the Reynolds-Averaged Navier- Stokes (RANS) and

Large Eddy Simulations (LES) and the Direct Numerical Simulation (DNS) [29] [45]

A) The RANS: this model describes the turbulent quantities based on the time

interval which can cause the situation to change. The intervals can be around 1s- 5s. An

example of such a model is the k-ε model. [29]

B) The LES: This model will only take into account the small and fast vortices.

The large vortices are calculated with the fundamental equations. This model is very

accurate and requires really small time intervals (0.01s -0.1s) and is therefore time

consuming. [29]

C) The DNS: This is the most accurate tool to simulate fluid turbulence. It can

compute and solve Navier- Stokes equations in a very fine spatial mesh with very small

time steps and the smallest turbulent and fastest fluctuations. But the computational cost

of DNS is very high. The resources required to calculate DNS exceeds the capacity of

most powerful computers currently available [45]

The presentation of a CFD model can be given in a table chart or a graphic layout.

Within the graphic layout there are two options: the vector plots and the contour plot.

Examples are: FDS, Jasmine and Fluent

With CFD modeling, the fire in a car park can be modeled more realistic. More

parameters can be taken into account such as the heat transfer by convection, conduction

and radiation etc. [44].

Since CFD modeling provides more accuracy and more realistic for a car park, computational

model software was needed. The choice was for FDS (Fire Dynamic Simulator). The reason for

this:

It’s a free software

Its specialty is smoke and its movements

It is widely used by engineers to plan out escape routes, fire simulations etc.


Y.C.Wong 33

§5.3 Software

To analyze the thermal effects on the steel structure of a car park the spreadsheet Car Park Fire

(CaPaFi) can be used. This spreadsheet has its limits and can’t take into account the influence of

smoke, but it is based on a local fire model of the Eurocode and has a database of results from

real car fire experiments. To gain more accurate information and also taking into the smoke it is

better to make use of computational fluid dynamics software. This shall be discussed in the

paragraphs.

§5.3.1 Car Park Fire (CaPaFi)

CaPaFi is an excel spreadsheet made to calculate the temperature of the elements in a large

enclosed or open car park due to a car fire whereas the walls are far enough from the fire to

avoid any influence on the heat distribution. The formulas are based on the NEN-EN- 1991-1-2

[46]. As it is known that a car fire is a localized fire, one shall make use of Annex C of the

previous mentioned NEN.

A brief explanation is given as follow:

1. The spreadsheet can calculate the temperature of the steel beams with maximum 5 local

fire sources

2. It is only valid in cases where the fires has an influence on the ceiling

3. The given rates of heat releases are calibrated on cars and are based on real

measurements (One of these is for example Hs (= height of the fire) is 0.3m [1])

4. The model used is as shown in Figure 37.

Figure 37 Localized fire when Lf > H ( The fires have

influence on the ceiling [46]

Legend:

H [m]- Distance between fire and ceiling

D [m]- Diameter of the fire

r [m]- Horizontal distance between the

vertical axis of the fire and the point

along the ceiling where the thermal flux

is calculated

Lh [m]- Horizontal flame length

Lf [m]- Flame length

If the fire reaches the ceiling (Lf ≥ H), the heat flux [W/m2] received by the area exposed to the

fire is as followed:

If y ≤ 0.30 Eq. (8a)

If 0.30 < y < 1.00 Eq. (8b)

If y ≥1.00 Eq. (8c)


Y.C.Wong 34

Where

y is a dimensionless parameter calculated as

Eq.(9)

r is the horizontal distance [m] between the vertical axis of the fire and the point along the

ceiling where the thermal flux is calculated (see Figure 37)

H is the distance [m] between the fire source and the ceiling (see Figure 37)

Lh is the horizontal flame length [m] (see Figure 37) and follows the relation of:

Eq.(10)

(A non-dimensional rate of heat release) Eq.(11)

z’ is the vertical position of the virtual heat source [m] and is given by:

When Eq. (12a)

When Eq.(12b)

Whereas Eq.(13)

And the net heat flux [W/m

2] received by the fire exposed surface area at the level of the

ceiling is calculated:

Eq. (14)

With :

From Eq. (14) it can be deduced that is the net heat flux to a beam with a temperature of 20oC.


Y.C.Wong 35

The heat release of the car which is used in CaPaFi is given in Figure 38. For more than 1 car,

the heat releases are also determined and CaPaFi can reach a maximum of 5 cars (Figure 39).

These are not input data but already written within the spreadsheet.

Figure 38 Heat release of a car [6, CaPaFi]

Figure 39 Heat release of 5 cars[6,CaPaFi]


Y.C.Wong 36

§5.3.2 Fire Dynamic Simulator (FDS)

Fire Dynamic Simulator (FDS) is a computational fluid dynamics (CFD) model of the fire-

driven fluid flow. Navier- Stokes equations suitable for low- speed (Ma6 < 0.3), thermally –

driven flow with an emphasis on smoke and heat transport from fires are solved numerically. [47]

The formulated equations and numerical algorithm are given in the FDS Technical Reference

Guide [48], whereas the verification and validation of the model are conferred in the FDS

Verification and Validation Guide. [49] [50]. Smokeview (SMV) is a separate program used to

display the results of the FDS simulation graphically. Because FDS make use of syntax

commands and for some cases it is much more convenient to have a graphical layout of the

model which has to be written in syntax command.

From [47] the formulas are obtained which it uses to do the computational fluid dynamics. These

are as followed:

Quantity Formula

Heat flux radiation Eq.(15)

Heat flux convection Eq.(16)

Heat net flux

Eq.(17)

With:

[oC]

[oC]

[oC]

Combining equations 15, 16 and 17 one obtains a heat flux as in CaPaFi given in equation 8:

Eq.(18)

The comparisons can now be made for FDS with CaPaFi by comparing Eq.(14) and Eq. (18).

In FDS devices are put up to measure the hnet,d and the temperature of the member and then use

these information to calculate the . With this a comparison of the heat fluxes can be made with

CaPaFi to verify the model which will be set up in FDS. This will be given in chapter §6.3.

The default settings of FDS were used. Information about these default settings can be found in

the FDS Technical Reference Guide volume1: Mathematical Model.

6 Ma or M: Mach number, a dimensionless number representing the ratio of the speed of the medium and the speed

of the sound in that medium.


Y.C.Wong 37

Chapter 6 Modeling

§6.1 General

In this chapter the focus is on the models itself. Before modeling one has to make certain that the

models are calculating according to the Eurocodes and that the reality is given correctly. In the

process, CaPaFi have been analyzed on how it calculates the temperature of the steel structure

and the models which are set up in FDS are then verified with CaPaFi.

§6.2 Preparations for the verifications

To verify FDS, a case has to be put up where the beams and the positions of the measuring

points must be the same. FDS has its limits in modeling small sized things in terms of the

meshes. The smaller the meshes the longer it takes to gain results. Furthermore with the chosen

mesh it can be that some modeled obstacles can be round up. For the first trial, an actual

HEA500 was being modeled in FDS. This beam has the shape of an HEA in CaPaFi and in FDS

it contains a shape of a U-profile. The reason for the shape as a U is the sides which are exposed

to the fire in FDS. This three sided exposure is taken into account by CaPaFi with its section

factor. 7 With the information about its sections factor, the thickness was calculated and resulted

in a thickness of 16mm. Of course, other models were made as well and up on checking these,

the rounding up phenomenon was discovered. (The height of a HEA500 = 490mm and that was

rounded up to 500 mm). A fictitious profile is set up for this purpose.

Figure 40 Fictitious beam (Left =CaPaFi, Right = FDS)

The calculations and information about the fictitious beam can be found in Appendix 7 Profile of

the fictitious beam. As shown in Figure 40 the U-profile seems to allow heat to be stored

between the legs of the U-profile, but one must keep in mind the buildup heat is prevented by a

dummy obstacle. Furthermore, the heating effects of FDS are measured in 1 direction within the

obstacle. This means that for the U-profile, the temperature is measured on each side in its local

cross-section (z-direction for the legs and the x- direction for the under flange). This fictitious

7 Section factor is the ratio between the surface area that is heated up and the volume of the profile. (see Eq. (7))

x

z


Y.C.Wong 38

beam can be “translated” back into a real beam with the ratio calculation between the section

factor and the boxed section factor. The calculated section factor for the beam is the same as the

section factor of the U-profile.

The modeling can be divided in two parts:

a) There is 1 car on fire within the car park with 1 beam: this model was used for fine

tuning a model made in FDS to gain the more or less the same results of CaPaFi.

b) There are 3 cars on fire within the car park with 2 beams

More on these models and their results will be presented in the following paragraphs.

§6.3 One car fire (Model 1 to 5)

§6.3.1 Set up of model

A simple model is being set up in CaPaFi which is given the name model 1 and this case is then

set up in FDS. The set up in CaPaFi is shown in Figure 41 and the input parameters for this case

are shown Table 8. The green dots display the position of the measuring points on the beam and

the red square the position of the car with respect to the beam. In this case, the beam is directly

above the car.

Figure 41 Position of the beam with respect to the car in CaPaFi

Table 8 Input data for CaPaFi for models

Quantity Unit Model 1 and 3 Model 2,4,5

Hf (=Height of ceiling) m 2.8 2.8

Hb (=Height of the beam) m 0.5 0.5

Coefficient Beam - 0.85 0.85

Am/V m-1

92 54

Am/V(box) m-1

65 37


Y.C.Wong 39

The model that has been set up in FDS is written in a script and can be found in Appendix 8

Script of model 1 (FDS). The space where the simulation takes place has the dimensions of 12m

by 12m by 2.8m (x, y and z direction). The reason for choosing a square box is to also test the

fire for symmetry since the CaPaFi model is a circular fire, meaning that the heating process

should be symmetric too. The height is 2.8m according to the average height of a car park.

The next step is to define how big the mesh should be within this space. The more accurate the

results, the smaller the mesh (the grids within the model) must be. The disadvantage of this is the

long simulation time. It has been chosen to make the grids 10cm by 10 cm by 10cm (x, y and z

direction). The space has 6 planes which have been described with boundary conditions (see

Figure 42). The planes of X=0, X=12, Y=0 and Y= 12m are open, because it’s an open car park.

The planes for Z=0 and Z=2.8 are put to “INERT”, which means that the ceiling and the floor

stays at the ambient temperature of 20oC. The reason for this decision was that the focus was on

the steel beam.

Figure 42 The space of the model

Figure 43 Sideview of the model 1 (Dimensions in mm)

After that, the fire and it properties are described. The maximum fire area is calculated with the

given fire diameter (D) in CaPaFi as followed: . The

maximum heat release rate in CaPaFi is 8.30MW at t= 25 min= 1500s. The size of a car is about

4.8m by 2m, so the rate of heat release for this car is:

. This heat

release rate was put on the cubic car in FDS with the dimension 3.0m by 3.0m (to approximate a

circular fire as in CaPaFi) by 0.3m.


Y.C.Wong 40

The height is 0.3m, because in CaPaFi, this is set to 0.3m. The height between the fire and the

ceiling is equal to 2.0m (Figure 43). The fire pool description is from an example that was

provided by Efectis. The properties of the beam have been done according to the Eurocodes

regarding the thermal properties and the shape (found in respectively in §4.2 and §6.2).

Devices are defined to measure the temperature of the steel member, the temperature of the gas,

the net heat flux for the position 1, 2, 3 and 4 (just like in CaPaFi on the same position). There

are also other devices for measuring the radiation and convective heat fluxes (Figure 44).

Figure 44 Top view of model 1 with the coordinates in FDS

The heat release curve of a car fire (Figure 38) shows that the heat release is stable from t= 4min

till t= 16min and then reaches its highest value at t= 25min, therefore the model has been

simulated till t= 25+ min. (=1500+ s) to see whether the heat fluxes originating from radiation

and convection on to the beam is correct.

The same set up is used for model 2, 3, 4 and 5 with minor modification for fine tuning the

model, because the results that were gained from the model didn’t match up with the model of

CaPaFi. The changes are presented in Table 9.


Y.C.Wong 41

Table 9 Overview of model 1 to 5 and briefly summarized

Model 1 2 3 4 5

Soot-yield 0.037 0.037 0.074 0.2 0.037

Number of cars 1 1 1 1 1

Number of beams 1 1 1 1 1

Thickness of the beam

[m]

0.016 0.032 0.016 0.032 0.032

Burning surface area

car [m2]

21.6 12.6 12.6 12.6 12.6

Center to center

distance beams and

carfire(s) [m]

0 0 0 0 0

Area (hxbxh) [m] 12x12x2.8 12x12x2.8 12x12x2.8 12x12x2.8 12x12x2.8

Number of meshes 1 1 1 1 1

Grid size [cm] 10x10x10 10x10x10 10x10x10 10x10x10 10x10x10

Ceiling Inert concrete concrete concrete concrete

Floors Inert concrete concrete concrete concrete

αc,steel [W/m2 K] 35 35 35 35 FDS

calculates

αc,concrete [W/m2 K] Not

applicable

FDS

calculates

FDS

calculates

FDS

calculates

FDS

calculates

Table 10 Comparison Matrix

Models 1 2 3 4 5

2

3 x

4 x

5 x

The checklist for the analysis of each model is:

Comparison HRR of the car for CaPaFi and FDS

Heat fluxes of the different positions of the beam for CaPaFi and FDS

Temperature of the different position of the beam for CaPaFi and FDS

And for some models the convective factor has to be checked with the Eurocode

Legend of Table 10

not applicable

x Comparison


Y.C.Wong 42

§6.3.2 Analysis of the results for model 1 to 5

The results and the comparison (data input for the charts) of CaPaFi and FDS are given in tables

in appendices. Only the governing cases/positions are discussed in the report and the rest can be

found in the appendixes. The governing cases/ positions are the ones which are the most heated

area. The equations 15, 16 and 17 have been used to calculate the total heat fluxes. The same

procedures of data analysis are done for model 2, 3, 4 and 5.

Note: The total heat fluxes in FDS (Eq. 18) = in CaPaFi (Eq.14).

The first model was analyzed. The total heat fluxes and the temperatures of model 1 of the other

positions can be found in Appendix 9 Data total heat fluxes of Model 1 and Appendix 10 Data

temperatures of model 1. Due to an error this model is not valid for comparison with other

models, but it was used to fine tune the other models. The fine tuning for model 2:

1. The burning area was set to burn on the top side and the 4 sides (surface area would

be .

2. The ceiling and the floor was put to inert, which means that the ceiling and the floor stays

at the ambient temperature of 20oC. For the next scenario it is decided to change this to a

concrete ceiling and floor. This was done because a real car park consists of concrete

floors and ceiling. The concrete properties concrete specific heat and conductivity are

obtained from NEN-EN-1992-1-2.

The emissivity of concrete was left as

the default setting of FDS 0.9, and not

making use of 0.7 as stated in the

Eurocodes.

3. There are more devices put up

to check the symmetry of the model

for the beam. The points can be seen

in Figure 45. The total heat fluxes of

points 2 and 8 should be the same, and

for the pairs of 3 -9 and 4 - 10. The

points 5 till 12 are points that are

below the ceiling measuring the

assigned quantities of the concrete

ceiling.

Figure 45 Top view of model 2 with the coordinates


Y.C.Wong 43

The script for the second model is given in Appendix 11 Script model 2 for FDS for FDS, the

results and comparisons of the heat fluxes and temperatures are given in Appendix 12 Data Total

heat fluxes for model 2and Appendix 13 Data temperature of model 2.

Figure 46 Heat Release Rate 1 car for model 2 (FDS vs. CaPaFi)

In Figure 46 it can clearly be concluded that the HRR is configured correctly. The HRR curve

given in CaPaFi and the one of FDS is almost a match, with only minor fluctuations after t=

1000s. Also the maximum value at t= 1500s is a bit higher for the FDS curve that the one of

CaPaFi. This can be the case since the burning surface of FDS was put to 12.6m2, whereas

CaPaFi is 12.01m2.

Figure 47 Total heat fluxes position 1 for model 2 (FDS vs. CaPaFi)

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

0 200 400 600 800 1000 1200 1400 1600 1800

HR

R [

kW]

Time [s]

Heat release rate of 1 car (model 2)

FDS

CaPaFi

0

20

40

60

80

100

120

140

0 200 400 600 800 1000 1200 1400 1600

Tota

l he

at f

luxe

s [k

W/m

2]

Time [s]

Total heat fluxes position 1 (model 2)

FDS Pos1

CaPaFi Pos1


Y.C.Wong 44

Figure 48 Total heat fluxes for position 2 and 8 for model 2 (FDS vs. CaPaFi)

Figure 49 Temperature of the steel beam for position 1 for model 2 (FDS vs. CaPaFi)

Figure 50 Temperature of the steel beam for position 2 for model 2 (FDS vs. CaPaFi)

0

20

40

60

80

100

120

140

0 200 400 600 800 1000 1200 1400 1600

Tota

l he

at f

luxe

s [k

W/m

2 ]

Time [s]

Total heat fluxes Position 2 and 8 (model 2)

FDS Pos2

CaPaFi Pos2

FDS Pos8

0.00

100.00

200.00

300.00

400.00

500.00

0 200 400 600 800 1000 1200 1400 1600

Tem

pe

ratu

re [

oC

]

Time [s]

Temperature position 1 (model 2)

Temp.FDSPos1

Temp.CaPaFiPos1

0.00

100.00

200.00

300.00

400.00

500.00

0 200 400 600 800 1000 1200 1400 1600

Tem

pe

ratu

re [

oC

]

Time [s]


Temp.FDSPos2

Temp.CaPaFiPos2


Y.C.Wong 45

From the analysis of the heat fluxes the following can be concluded:

1) Although the HRR of the car in FDS is more or less correct with CaPaFi, the total heat

fluxes for the beam still isn’t correct. For position 1 of model 2, the total heat flux is at

the beginning of the fire more or less the same as CaPaFi, but at higher heat releases of

the car fire the total heat fluxes are much higher than CaPaFi (Figure 47). As for position

2, which is a bit further away from the center of the heat fluxes at lower heat release rates

of the car is lower than CaPaFi and at higher heat releases the opposite happens (Figure

48). In Figure 48 there is no graph put for CaPaFi for position 8, because this is identical

as position 2 of CaPaFi. For the other positions, see Appendix 12 Data Total heat fluxes

for model 2.

2) For position 2 and position 8 the symmetry was checked, to see whether the fire was

simulated good enough as a circular fire as stated in CaPaFi. In the results of Figure 47

the green line is more or less the same as the blue one. It can be concluded that the

symmetry was done correctly.

3) In Figure 49 and Figure 50 it can be concluded that the temperature matches the total

heat fluxes again. From t= 200s and onward, both the total heat fluxes and the

temperature show a big difference between the model in FDS and CaPaFi. For the

temperature plots of the other positions, see Appendix 13 Data temperature of model 2.

Because the total heat fluxes and the temperature of the steel beams in the model are lower than

the one given in CaPaFi, the next step is to see whether if a more homogeneous smoke layer

would make a difference. The soot-yield of the model 4 was enlarged to gain a more

homogeneous smoke. The soot-yield number gives the amount of small particles within the

smoke. The higher the number, the more particles there are within the smoke, the more

homogeneous the heat is divided within the smoke layer. The same script is used as the one for

model 2, with only a soot-yield number 0.2 for model 4. The results are presented in Table 11

and Table 12 (numerically), because the differences between each model are not that significant

to be seen within a graph. Only for position 1 and 2 the heat fluxes and temperature are

presented. The rest of the results can be found in Appendix 14 Comparison heat fluxes model 2,4

and CaPaFi and Appendix 15 Comparison temperatures model 2,4 and CaPaFi.

From these tables, it can be concluded that for the heat fluxes it really doesn’t matter whether the

soot-yield is higher or not, the differences between each model is very little. The same can be

said about the temperatures of the beam between these two models. For a too high soot-yield

(model 4) the steel temperatures are more or less the same as model 2.


Y.C.Wong 46

Table 11 Comparison heat fluxes of model 2,4 and CaPaFi

Total Heat

fluxes Position 1 Position 2

t [s] Model 2 Model 4 CaPaFi Model 2 Model 4 CaPaFi

0 0.00 0.00 0.00 0.00 0.00 0.00

61 5.60 5.20 20.39 2.90 2.66 5.91

120 12.79 12.64 33.39 5.11 5.14 10.80

181 20.06 18.75 39.98 7.44 6.84 17.77

240 37.20 33.28 44.33 9.63 8.44 23.92

301 32.64 37.84 44.33 9.25 9.32 23.92

360 31.38 34.32 44.33 10.63 9.98 23.92

420 34.47 34.65 44.33 10.19 10.27 23.92

480 29.80 37.77 44.33 11.04 10.63 23.92

540 34.42 36.85 44.33 9.82 8.56 23.92

600 36.82 32.36 44.33 10.68 10.39 23.92

660 31.99 32.57 44.33 10.38 9.27 23.92

720 29.92 35.60 44.33 10.83 8.79 23.92

780 28.61 38.73 44.33 10.55 10.93 23.92

841 30.09 37.98 44.33 9.89 8.80 23.92

900 28.08 28.54 44.33 9.82 9.95 23.92

961 28.58 36.10 44.33 10.04 8.97 23.92

1020 42.82 52.99 48.79 12.96 15.16 30.13

1081 59.68 56.32 52.07 22.97 19.84 34.61

1140 63.55 60.91 54.67 22.40 21.25 38.09

1201 78.43 71.92 56.82 27.34 28.65 40.95

1260 81.22 74.56 58.68 28.29 29.64 43.36

1321 90.36 95.00 60.31 46.13 29.23 45.46

1380 93.84 93.17 61.77 42.43 40.22 47.32

1441 91.92 112.80 63.09 54.89 60.61 48.99

1500 126.68 123.35 68.85 58.45 63.08 56.04


Y.C.Wong 47

Table 12 Comparison temperatures of model 2,4 and CaPaFi

Temperatures Position 1 Position 2


0 20 20 20 20 20 20

61 23 23 21 21 21 20

120 29 29 33 24 24 24

181 40 39 52 28 27 30

240 55 55 73 32 32 40

301 70 73 95 37 37 53

360 85 89 116 42 41 65

420 98 104 137 47 45 77

480 110 118 156 51 49 88

540 123 131 175 55 53 99

600 134 142 193 59 57 110

660 144 153 210 63 60 120

720 154 164 227 66 63 130

780 163 175 243 70 66 140

841 172 184 259 73 69 149

900 181 193 274 76 72 158

961 188 200 289 79 74 167

1020 203 215 303 83 78 176

1081 222 234 318 91 85 187

1140 242 253 334 99 93 201

1201 264 275 351 109 104 215

1260 286 298 368 120 113 230

1321 310 324 385 135 124 246

1380 335 349 402 150 139 262

1441 361 377 419 168 158 278

1500 396 414 435 194 182 295


Y.C.Wong 48

Figure 51 Comparison temperature of model 2, 4 and CaPaFi for position 1

Figure 52 Comparison temperature of model 2, 4 and CaPaFi for position 2

From Figure 51 and Figure 52 one can see that the temperature for positions that are further

away from the fire are still not the same yet as the one presented in CaPaFi, so for the next

model (model 5) adjustments have been made to the steel beam. The convection coefficient of

the steel beam is not defined in the model and it is set to be calculated by FDS itself to see

whether the model is much more stabilized then the previous ones. Parts of the results are given

in the next two figures.

0

100

200

300

400

500

0 200 400 600 800 1000 1200 1400 1600

Tem

pe

ratu

re [

oC

]

Time [s]

Temperature Position 1

Model 2

Model 4

CaPaFi

0

100

200

300

400

500

0 200 400 600 800 1000 1200 1400 1600

Tem

pe

ratu

re [

oC

]

Time [s]


Model 2

Model 4

CaPaFi


Y.C.Wong 49

Figure 53 Comparison heat fluxes model 2, model 5 and CaPaFi for position 1

Figure 54 Comparison heat fluxes model 2, model 5 and CaPaFi for position 2

From Figure 53 and Figure 54 it can be concluded that the heat fluxes are even lower than the

ones in model 2. With this being said, it can also be deduced that the temperature of the beam in

FDS will be much lower than the ones in CaPaFi. Furthermore, the differences also are bigger

for positions further apart from the fire source. In Appendix 18 Convective heat transfer

coefficient Model 5 the average convection coefficient of steel is calculated which is between

0.86 and 27 W/m2K. This value is much lower than the one written for steel in the Eurocode (35

W/m2K).

At last model 3 has been checked with model 2. In model 3, the thickness of the beam is half the

size (16mm) of model 2 (32mm). The soot-yield is also 2x the one given in model 2. The results

are given in Appendix 19 Comparison Total heat fluxes model 2 and model 3 and Appendix 20

Comparison temperatures model 2 and model 3. As expected, the temperatures of model 3 are

higher because the thickness of the beam is thinner.

0

20

40

60

80

100

120

140

0 200 400 600 800 1000 1200 1400 1600

Tota

l he

at f

luxe

s [k

W/m

2]

Time [s]

Total heat fluxes comparison Position 1

Model 2

Model 5

CaPaFi

0

20

40

60

80

100

120

140

0 200 400 600 800 1000 1200 1400 1600

Tota

l he

at f

luxe

s [k

W/m

2]

Time [s]

Total heat fluxes comparison position 2

Model 2

Model 5

CaPaFi


Y.C.Wong 50

After going through each model, it can be found that model 2 is the closest to CaPaFi. An

overview is given in Table 13 with the differences of each model compared to each other and

their conclusions.


Y.C.Wong 51

Table 13 Summary of all 5 models, the differences and their conclusions

Model Soot-

yield

Thickness

[m]

αc,steel

[W/m2K]

Results/

comparisons

appendix

(ces)

Conclusions

(Compared to

Model 2)

Conclusions

(Compared to CaPaFi)

2

0.037

0.032

35

12, 13

(A) The total heat fluxes for the point directly above

the fire are at the beginning more or less the same, and

in the end much higher. The total heat fluxes for point

2-8, all were lower than CaPaFi.

(B) The temperatures of the beam for all positions

were lower than the ones calculated in CaPaFi.

(C) The symmetry of the positions 2-8, 3-9 and 4-10 is

modeled correctly.

3

0.074

0.016

35

19, 20

(A) The temperature of model 3 are higher than

model 2 because the thickness of the beam is thinner.

(B) The symmetry of the positions 2-8, 3-9 and 4-10

is modeled correctly.

This comparison was not made, due to a calculation

mistake the shadow factor was not taken into account

leading to a thinner beam of 0.016m.

4

0.2

0.032

35

14, 15

There are no significant differences in the total heat

fluxes and the temperatures, even with a higher soot-

yield. (See table 13 and 14)

The total heat fluxes and the temperatures of model 4

are more or less the same as model 2. In both models

these results are still lower than the ones that are

calculated by CaPaFi.

5

0.037

0.032

FDS

calculates

16, 17, 18

The total heat fluxes and the temperatures of model 5

are a bit lower than the ones in model 2. This is

caused by the lower αc,steel calculated by FDS.

(A) The calculated average αc,steel is between 0.86 and

27 W/m2 K which is lower than 35 W/m

2 K in the

Eurocode.

(B) Model 2 is still much closer to CaPaFi than model

5 for both the total heat fluxes and the temperatures of

the beam.


Y.C.Wong 52

Since all the models did have some improvements and is still not totally in accordance with the

one set up in CaPaFi, it has been decided to go further with 3 cars. According to the study 95%

of the car fires are limited to maximum 3 (fully) burnt cars [1]. In §4.6 showed that the

temperature of the beam will be much higher when there is more than 1 car burning. With this

information, a model with 3 cars is set up in FDS and being more realistic with 3 cars, the model

might be even closer to CaPaFi. These new models with 3 cars are given the name model 6 and

model 7. Model 6 is with beams sticking out of the ceiling and model 7 is without the beams

sticking out. Elaboration on these two models is in the next paragraph.

§6.4 Three car fires (model 6 and model 7)

§6.4.1 Set up 3 car fires

The car in the previous models (1 car fire for models 2, 3, 4 and 5) was 12.6 m2 which was a

square. To model three car fires next to each other the shape of the car has to be changed. In

practice the cars in a car park are parked next to each other with a space of approximately 2.5m.

This “square car” would be too big with its dimensions of 3x3m. The most suitable size of the

rectangular car is 4.8m by 1.8m with a height of 0.3m. For this car, only the top and the 4 sides

are taken into account as burning surface and the surface area is exactly 12.6m2.

Because there are three fires, the space where this takes place has to be increased too. There

must be sufficient air going through the space as the previous models 2, 3, 4 and 5. The ratio of

the openings is approximate two times the previous space. The space can’t be too large because

the run time increases too. The space where 1 car fire took place was about 4*12m*2.8m

=134.4m2 and for the 3 car fires it’s about 268m

2 leading to a space of 24m by 24m.

For the three car fires 2 models had been set up where as in model 6 the beams stick out from the

ceiling and for model 7 the beams are hidden in the ceilings. For simplicity model 6 will be

named with obstacles beams and model 7 without obstacles. The run time for these two models

is set to 2500s because it is necessary that all three cars reach their maximum heat release rate.

To make sure that the run time is as short as possible to reach the 2500s the space of 24m by

24m was divided into 5 meshes, whereas the area around the fire and the 2 beams with a heart to

heart distance of 16m was with a smaller mesh of 10cm, all the other space is made with a mesh

of 20cm.

In Figure 55 the beams are displayed as green points 1-8 and the cars are given in little blocks.

This is top view of model 6 and 7 in CaPaFi. The order in which the cars burned is given in

white numbers. The same model is set up in FDS (Figure 56 and Figure 57). The side views of

the models are also given Figure 58 and Figure 59. In model 6 where the beams stick out of the

floor, the temperature at the side of the beam which is facing the fire is also measured. This is to

check what the influences with respect to the temperatures are.


Y.C.Wong 53

Figure 55 Positions of the beams and the cars modeled in CaPaFi for model 6 and 7

Figure 56 Model 6 (3 cars with obstacles)

Figure 57 Model 7 in FDS (3 cars without obstacles)

Figure 58 Side views of model 6 (all dimensions are in mm)


Y.C.Wong 54

Figure 59 Side views of model 7 (all dimensions are in mm)

Table 14 Data input for CaPaFi for model 6 and model 7

Quantity Unit Model 6 Model 7

Hf (=Height of ceiling) m 2.8 2.3

Hb (=Height of the beam) m 0.5 0.001

Coefficient Beam - 1 1

Am/V m-1

54 54

Am/V(box) m-1

37 37

The input parameters for CaPaFi for model 6 and 7 are given in Table 14. The reason why the

ceiling height of model 7 for CaPaFi is 2.3m and not 2.8 is because in FDS the ceiling is pulled

down in order to create the hidden beam effect. The space was kept the same as model 6 to keep

as many factors constant as possible.

An overview of model 6 and 7 is given in Table 15 and the differences between models are

marked out in red. In the end this is needed to check if there is really a difference between a one

car fire and three car fires within an open car park.


Y.C.Wong 55

Table 15 Overview of differences Model 2, 6 and 7

Model 2 6 7

Soot-yield 0.037 0.037 0.037 Number of cars 1 3 3 Number of beams 1 2 2 Thickness of the

beams [m] 0.032 0.032 0.032

Center to center

distance beams

and carfire(s) [m]

0 2.65

and 13.05

2.65

and 13.05

Area (hxbxh) [m] 12x12x2.8 24x24x2.8 24x24x2.8 Number of meshes 1 5 5 Grid size [cm] 10x10x10 10x10x10

and

4x20x20x20

10x10x10

and

4x20x20x20 Ceiling concrete concrete concrete Floors concrete concrete concrete

αc,steel 35 35 35

αc,concrete FDS

calculates

FDS

calculates

FDS

calculates

Table 16 Comparison Matrix

Models 2 3 4 5 6 7

2

3 x

4 x

5 x

6 x

7 x x

§6.4.2 Analysis of the results for model 6 and 7

The heat release rate according to CaPaFi of each car is given in Figure 60. The heat release of

the model 6 and 7, which are obtained from FDS are given in Figure 61 and Figure 62. As can be

seen these figures the shape of the graphs are different. The reason for the shape in Figure 61

and Figure 62 in FDS compared to Figure 39 of CaPaFi is that FDS sums up the total heat

release rate of all 3 cars. This can be verified.

To verify the heat releases of FDS with CaPaFi, the heat releases of the cars is determined for

CaPaFi and FDS at t= 1500s= 25 min. For CaPaFi the sum of the heat release is 8.3MW +3.96

MW +2.4 MW =14.66 MW. For FDS the heat release is at t= 1501s 14165.882 kW = 14.17 MW.

For more verification, see Table 17. The differences are not that significant meaning that the

HRR was modeled correctly.

Legend of Table 16

not applicable

x Comparison


Y.C.Wong 56

Figure 60 Heat release of each car in CaPaFi (Source: CaPaFi)

Table 17 Verification HRR model 6 and model 7 with CaPaFi

Time

[min]

HRR CaPaFi

[MW]

HRR FDS with

obstacles

[MW]

HRR FDS without

obstacles

[MW]

16 1.4+2.4= 3.8 3.84 3.76

24 5.5+3.44+0= 8.94 9.05 8.88

25 14.66 14.42 14.17

Figure 61 Heat Release Rate of the 3 burning cars (model 6)

0

2000

4000

6000

8000

10000

12000

14000

16000

0 500 1000 1500 2000 2500 3000

HR

R [

kW]

Time [s]

Sum of HRR of 3 cars (with obstacles)

HRR- with obstacles (M6)

CaPaFi


Y.C.Wong 57

Figure 62 Heat Release Rate of 3 burning cars (model 7)

After the verification of the heat releases of the cars, the next step is to check whether the total

heat fluxes of the beams and the temperature are done correctly.

Starting with model 6, the total heat fluxes were compared for each of the positions with CaPaFi.

From Figure 63 and Figure 64 it can be concluded that the total heat fluxes are still qualitative

good and quantitative bad. One can also see that the total heat fluxes have turned around for

positions that are further apart from the car fire: the total heat fluxes of FDS are higher than the

ones in CaPaFi. It should be mentioned that the total heat fluxes are very low for points that are

further apart from the car fire (the maximum is around 5 kW/m2). More results about the heat

fluxes of model 6 of the other positions can be found in Appendix 22 Data heat fluxes of model

6.

From Figure 65 and Figure 66 it can be concluded that the temperature is also not the same as

CaPaFi, but the temperature does follow the trend of the total heat fluxes. In position 2 both the

total heat flux and the temperature in FDS are higher than the one given in CaPaFi. The

temperatures of the positions that are further away from the fire (Figure 66) are very low

compared to position 2 and will never reach the critical temperature.

0

2000

4000

6000

8000

10000

12000

14000

16000

0 500 1000 1500 2000 2500 3000

HR

R [

kW]

Time [s]

Sum HRR of 3 burning cars (Without obstacles)

HRR- without obstacles(M7)

CaPaFi


Y.C.Wong 58

Figure 63 Total heat fluxes of position 2 of model 6 (with obstacles)

Figure 64 Total heat fluxes of position 5 of model 6(with obstacles)

Figure 65 Temperature of Position 2 of model 6 (with obstacles)

0

10

20

30

40

50

60

70

0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 2400 2600

Tota

l He

at f

luxe

s [k

W/m

2 ]

Time[s]


FDS

CaPaFi

0

10

20

30

40

50

60

70

0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 2400 2600

Tota

l He

at f

luxe

s [k

W/m

2 ]

Time[s]

Total heat fluxes Position 5 (model 6)

FDS

CaPaFi

0

50

100

150

200

250

300

350

400

0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 2400 2600

Tem

pe

ratu

re [

oC

]

Time [s]

Temperature Position 2 (model 6)

FDS

CaPaFi


Y.C.Wong 59

Figure 66 Temperature of Position 5 of model 6(with obstacles)

After model 6, model 7 is also analyzed which is the one without beams. The total heat fluxes

shown in Figure 67 is already much closer to the ones in CaPaFi, only the heat up is much

slower in FDS. In Figure 68 where position 5 is much further apart from the car fire, the total

heat fluxes of FDS is higher than the one in CaPaFi just as the same case as Model 6.

Figure 67 Total heat fluxes of position 1 of model 7(without obstacles)

0

50

100

150

200

250

300

350

400

0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 2400 2600

Tem

pe

ratu

re [

oC

]

Time[s]


FDS

CaPaFI

0

10

20

30

40

50

60

70

0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 2400 2600

Tota

l He

at f

luxe

s [k

W/m

2]

Time [s]

Total Heat fluxes Position 2 (model 7)

FDS

CaPaFi


Y.C.Wong 60

Figure 68 Total heat fluxes of position 5 of model 7 (without obstacles)

Figure 69 Temperature of position 1 of model 7(without obstacles)

Figure 70 Temperature of position 5 of model 7(without obstacles)

0

10

20

30

40

50

60

70

0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 2400 2600

He

at f

luxe

s [k

W/m

2 ]

Time [s]

Total heat fluxes of Position 5 (model 7)

FDS

CaPaFi

0

50

100

150

200

250

300

350

400

0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 2400 2600

Tem

pe

ratu

re [

oC

]

Time [s]


FDS

CaPaFi

0

50

100

150

200

250

300

350

400

0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 2400 2600

Tem

pe

ratu

re [

oC

]

Time [s]


FDS

CaPaFi


Y.C.Wong 61

Afterwards, the temperatures are compared. Where in position 2 of model 7 the total heat flux

was a bit lower in heating up (at the maximum at t= 1500s differs 4 kW/m2), the temperature in

FDS is almost half the value of CaPaFi (Figure 69).

Finally both models are also compared to see the effect of with beams and without beams with

respect to CaPaFi. The total heat fluxes between CaPaFi of model 6 and model 7 are the same,

with a minimum difference in the range of one hundredth. It can be concluded from Figure 71

that model 7 is much closer to CaPaFi. Of course for positions further from the fire source had

the effect that the ones in FDS were much higher than the ones in CaPaFi (Figure 72), but still

very low in value.

Figure 71 Total heat fluxes comparison between model 6, model 7 and CaPaFi (position 2)

Figure 72 Total heat fluxes comparison between model 6, model 7 and CaPaFi (position 5)

It can be concluded the total heat fluxes for the model with obstacles is much lower than the one

without obstacles. This is very unusual. Therefor the temperatures between these two models are

also compared.

0

10

20

30

40

50

60

0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 2400 2600

Tota

l he

at f

luxe

s [k

W/m

2]

Time [s]


With obstacles(M6)

Withoutobstacles (M7)

CaPaFi

0

10

20

30

40

50

60

0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 2400 2600

Tota

l he

at f

luxe

s [k

W/m

2]

Time [s]


With obstacles(M6)


CaPaFi


Y.C.Wong 62

Figure 73 Temperature comparison between model 6 and 7 (position 2)

Figure 74 Temperature comparison between model 6 and 7 (position 5)

The same effect can be seen with the temperatures. The model with the obstacles has a lower

temperature than the without obstacles. This shouldn’t be the case. The reason for this is as

followed:

In Figure 75 and Figure 76 the smoke’s movement is given in blue arrows. In model 6 the

ceiling is higher and the smoke travels along the ceiling and then nearing the beam it moves

downwards (point C) and then flowing across the lower side of the beam (Point B). This causes

the temperature to be lower than the without obstacles. In model 7 is lowered in the middle,

causing the flame length to bend along the ceiling spreading the heat more out and causes higher

temperature at the lower part of the beam (point E). This can be seen with the visual effects in

Smokeview in the Table 18. In the last picture where t = 1530s the heat is spread along the beam

in model 6, whereas in model 7 this is spread across the whole area.

0

50

100

150

200

250

300

350

400

0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 2400 2600

Tem

pe

ratu

re [

oC

]

Time [s]

Position 2 Comparison Model 6 and 7

With obstacles(M6)


CaPaFi

0

50

100

150

200

250

300

350

400

0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 2400 2600

Tem

pe

ratu

re [

oC

]

Time [s]


With obstacles(M6)


CaPaFi


Y.C.Wong 63

Table 18 Snap shots of the graphic results of model 6 and 7 in Smokeview

With obstacles (model 6) Without obstacles (model 7)

Figure 75 Movement smoke (model 6) Figure 76 Movement smoke (model 7)


Y.C.Wong 64

The temperatures of these two models are given Figure 77 and Figure 78. The temperature at

points A and D (see Figure 77 and Figure 78) were not measured and couldn’t be found via

Smokeview too (it was at the intersection of 2 meshes causing Smokeview not to be able to view

it). The temperature of the side given in Figure 77 and Figure 78 are the temperature measured in

point C.

Figure 77 Temperature comparison position 2

Figure 78 Temperature comparison position 5

As expected, the temperature of the side of beam is much closer to the one of CaPaFi and a bit

higher than the one of without obstacles. This is because CaPaFi calculates its temperature and

the total heat fluxes at the lowest point of the beam (point B and E). For the case where there is

an obstacle if the temperature of point A is known this would be very low with respect to point C.

Taking the average temperature of point A, B and C this temperature would be more or less the

same as point E of the model without obstacles (the purple line in Figure 84 and Figure 85).

From this it can be concluded that the smoke doesn’t affect the temperature of the steel beam for

0

50

100

150

200

250

300

350

400

0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 2400 2600

Tem

pe

ratu

re [

oC

]

Time [s]


With obstacles(M6)

Without obstacles(M7)

With obstacles Side(M6)

CaPaFi

0

50

100

150

200

250

300

350

400

0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 2400 2600

Tem

pe

ratu

re [

oC

]

Time [s]


With obstacles (M6)

Without obstacles(M7)

With obstacles Side(M6)

CaPaFi


Y.C.Wong 65

beams of 500mm. So for smaller beams (< 500mm) the smoke shall have no influence either.

Although for points that are further away from the fire (Figure 85) the temperatures are higher

than the ones in CaPaFi, it still isn’t significant because the temperature doesn’t reach the critical

temperature. The temperature comparisons of model 6 and 7 of the other positions can be found

in Appendix 28 Comparison temperature model 6 and 7.

At last, a single car fire model (model 2) will be compared with the 3 cars fires (model 6- with

obstacles and model 7- without obstacles). Comparison of these models that have been set up in

FDS and run is not possible. The reason is the beam’s placement, even though the burning area

of the cars and the defined properties of the beam are the same. In the single car fire the beam is

directly above the fire and in the 3 car fires model these beams are 2.65m away from the fires.

The flame and the smoke within the single car fire will first hit the beam first and spread out

whereas within the 3 car fires models, the flame and the smoke will first hit the ceiling and then

spread sideways to the beam. This will cause the heating up of the beam to be different and can’t

be compared to each other. See Table 19 for the positioning of the beam and the smoke’s

movements.

To be able to compare these models, it is recommended to reposition the beam with respect to

the fires in the same plane to be able to compare the steel temperatures of the beam (see Figure

79). The beam is given in green color.

Figure 79 Top view position of the beam in model 2, 6, 7 and the recommended position of the beam

(dimensions in mm)

Finally, an overview of the conclusions of the comparisons for model 6, model 7 and CaPaFi are

presented in Table 20.


Y.C.Wong 66

Table 19 Comparison model 2, 6 and 7: Positioning beam and the smoke’s movement (dimensions are in mm)

Models Positions x-z plane Smoke’s movement

Single car

fire

(model 2)

3 car fires-

with

obstacles

(model 6)

3 car fires-

without

obstacles

(model 7)

Legend:

Smoke’s movement


Y.C.Wong 67

Table 20 Overview and summary of model 6, model 7, model 2 and CaPaFi comparisons

Model Appendices

Conclusions

(Compared to model 6)

Conclusions

(Compared to CaPaFi)

6 (with obstacles,

3 car fires)

21, 22 (A)The total heat fluxes for points that are closer to the fire are

lower than CaPaFi. For points that are further away from the fire

the total heat fluxes are higher than CaPaFi.

(B)The temperatures for the points closer to the fire are lower

than CaPaFi, but don’t reach the critical temperature. Points

further away from the fire have higher temperatures than CaPaFi,

but are relatively low compared to points that are closer to the

fire.

(C)The average temperature of the beam calculated by measuring

the side temperature and the temperature at the lowest point is

more or less the same as CaPaFi.

7 (without

obstacles,

3 car fires)

24, 25 The total heat fluxes and temperatures are higher

than model 6. This has to do with the movement

of the smoke (Table 18, explanation on page 63)

For more results see appendices 27 and 28 for all

positions.

(A)The total heat fluxes for the points that are closer to the fire

are closer to CaPaFi, almost matching it. For points that are

further away from the fire the total heat fluxes are higher than

model 6 and CaPaFi.

(B)The temperatures for the points closer to the fire are lower

than CaPaFi, but don’t reach the critical temperature. Points

further away from the fire have higher temperatures than CaPaFi

and model 6, but are relatively low compared to points that are

closer to the fire.


Y.C.Wong 68

Chapter 7 Conclusions and recommendations

In this chapter the final conclusions are given of the research that has been performed. As

finalization the recommendations are presented for further research on this topic.

§7.1 Conclusions

The objective of this research was to determine whether the smoke, trapped between the beams,

needs to be taken into account during the design of the fire safety of an open car park when

making use of the guideline for car parks (Bouwen met Staal guideline (BmS-guide)).

As mentioned before, there were single car fire models and 3 car fire models put up in FDS and

then compared with CaPaFi. The following can be concluded:

1. When making use of the BmS-guide to design the fire safety of an open car park,

the influence of the smoke trapped between the beams is negligible and therefore

doesn’t have to be taken into account for beams with a height smaller than

500mm. The average temperature obtained in FDS for the steel beams sticking

out is more or less then the same as the temperature of the beam hidden in the

ceiling.

2. The temperatures of the steel beams of FDS are lower than the ones calculated by

CaPaFi and a reasonable explanation could not be found during this research.

Even if the reason is found why this occurs, conclusion 1 with respect to the

model with beams sticking out and the model without beams, which are related to

each other, will not change if the models of FDS are fine-tuned closer to the ones

in CaPaFi.

3. In a 3 car fire model, the points that are further away from the car fire can be

disregarded because their steel temperature calculated with FDS, even though

higher than CaPaFi, will never reach the critical temperature.

4. It is still unclear why the increased number of soot doesn’t have any effect on the

temperature of the steel beams in the single car fire model.

§7.2 Recommendations

§7.2.1 Recommendations with respect to further study

1. The reason why FDS calculates the steel temperatures lower than CaPaFi can be

researched more in detail than in the present study. To gain more insight whether the

calculations of FDS are better than CaPaFi or not, the FDS results should be compared to

the results of the real car fires, which form the basis of CaPaFi.

2. There is still research to be done to check what the influences of smoke are, trapped

between beams that are higher than 500mm. The significant limit of the height in which


Y.C.Wong 69

case the smoke should or shouldn’t be taken into account during design still has to be

found.

3. To gain better insight of how much the influence of the smoke is on the steel beams in

the car park it is recommended to use a better model with 4 beams surrounding the 3 car

fires.

4. It is still not clear why the difference of the total heat fluxes and the temperatures isn’t

significant between model 4 (soot-yield =0.2) and model 2 (soot-yield =0.037). There

should be a study to check why this had occurred.

5. After modeling in FDS to gain information about the thermal load, the next step is to

model the steel beam with the thermal load in the software, making use of the finite

element methods to gain proper insight of the effects of the smoke on the beam itself

(taking into account the height of the beam, the shape of the beam, the cross section and

the height).

6. Since there are new type of cars such as hybrid, electric cars etc., it is recommended to

also research the smoke effects and the car fire heat effects on the beam (het heat releases

rates, the new material, burning time) of these cars.

§7.2.2 Recommendations with respect to the software

7. Although CaPaFi was renewed in 2010 to make use of the Eurocodes, the software itself

was not working totally correctly with the new versions of Microsoft office 2010 and

higher. The temperatures graphs which were supposed to be plot after the calculation

didn’t show up. It is recommended that CaPaFi is renewed each time there is a new

Microsoft office to keep the use of CaPaFi user friendly.

8. For large models made in FDS, it is not possible to stop the model and resume the

simulation at another time. This problem only occurs when running FDS in a windows

operating system. For OS and Linux this doesn’t occur.


Y.C.Wong 70

References

[1] A.F Hamerlinck, A. Breunese, L.M Noordijk, D.W.L Jansen, and N.J van Oerle, Richtlijn

Brandveiligheid Stalen Parkeergarages. Zoetermeer, November 2011.

[2] BSCA and SCI Tata Steel. Steelconstruction.info. [Online].

http://www.steelconstruction.info

[3] Nederlandse Normalisatie-instituut, NEN 2443 Parkeren en stallen van personenauto's op

terreinen en in garages., Maart 2013.

[4] Bin Zhao and Joel Kruppa. (2002) Structural behavior of an open car park under real fire

scenarios. [Online]. http://www.civil.canterbury.ac.nz/sif/paper23.pdf

[5] Jörgen Carlsson, "Fire Modelling Using CFD- An introduction for Fire Safety Engineers,"

Lund Institute of Science and Technology, Lund University, Lund, Report 5025, 1999.

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Dynamics," in Advanced in Modeling of Fluid Dynamics., 2012, ch. 9. [Online].

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Y.C.Wong 73

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van staalconstructies voor gebouwen volgens Eurocode 3, 1st ed. Zoetermeer, The

Netherlands: Bouwenmetstaal, 2010.


Y.C.Wong 74

Appendices

Appendix 1 Size of the car [3]

Characteristics of the vehicle Value Percentile

Length 4.88 m 95%

Width without rearview

mirrors

1.83 m 95%

Height 1.73 m 95%

Numbers of axles 2

Numbers of tires 4

Width of the track 1.56 m 95%

Turning circle (between walls) 11.58 m 95%

Weight (empty) 1491 kg 95%

Weight (maximum) 2189 kg 95%

Capacity 110 kW/150 pk 95%

Deceleration 5.2 m/s2


Y.C.Wong 75

Appendix 2 Information TT-plates [26]


Y.C.Wong 76


Y.C.Wong 77

Appendix 3 Calculation of the section factor of some profiles [52]

Shape Discription Section factor (Am/V)

Open cross -section

with four sides exposed

to fire

Corner profile with

four sides exposed to

fire

Strip- or staff steel with

four sides exposed to

fire

Round tube with four

sides to exposed to fire

Rectangular tube or

welded rectangular

tube with a constant

thickness with four

sides to exposed to fire

I-section with welded

side plates with four

sides exposed to the

fire

Open cross-section

with three sides

exposed to fire

Open cross- section

with 1 side exposed to

fire


Y.C.Wong 78

Appendix 4 Previous studies

The study and modeling of Liew et al. (2002) [51] showed the structural response of the frame in

a multistory car park before and after the fire. The plan view and the loads are given in Figure 80.

The results of before the fire (ambient temperature) are as follow:

- Midspan beam deflection is 17mm < span/360 = 36mm

- Maximum sway deflection at first story is 7mm < height/ 300 = 9.3 mm

The structure’s design satisfies both the ultimate and serviceability limit states at ambient

temperature. The resistance of the frame reaches its limits at load factor 1.481. Two fire

scenarios were set up to test the frame. The most critical column and the most critical loaded

beam were chosen. For both scenarios, the collapse was not observed. The fire service load are

1.0 DL + 1.0 IL (DL = Dead load, IL = Imposed Load).

Figure 80 (a) Plan view of multistory car park (b) elevation and load of the frame on Gridline B [51]


Y.C.Wong 79

Scenario 1: Car fire near column

Figure 81 Simulation of a car fire near column [51]

The results are given in Figure 83. After cooling down, the residual displacement is 27.5mm

which is less than 36mm (span/360). In Figure 85 the horizontal displacement of node A is

given. Node A is at the first story level (see Figure 80(b)). The maximum air temperature is

reached around t= 12min and at t= 33 min when the fuel tank and the compartment is on fire.

The maximum sway deflection is 36mm. The residual sway displacement is 20mm (1/140 of the

height).

Scenario 2: Car fire in the middle of a beam (mid span)

Figure 82 Simulation of car fire in the middle of beam [51]

In Figure 84 it shows that the moment initially decreases due to thermal bowing. The deflection

of the beam increased to a maximum of 138mm, and after the fire the residual deflection is about

113mm. The compression force increases when the temperature rises and decreases when the

cool down starts. The maximum deflection of the beam is 48mm and the residual deflection is

about 31mm (1/90 story height).

The results of the study are presented in Figure 83 till Figure 86.


Y.C.Wong 80

Figure 83 Midspan deflection of the heated beam

[51]

Figure 84 Midspan moment of the heated beam [51]

Figure 85 Horizontal displacement Node A [51]

Figure 86 Axial force of the heated beam [51]

It can be concluded that fire scenario 2 is more critical (Maximum and residual frame deflection

are respectively 33.3% and 55% higher than scenario 1). After post fire analysis (Analysis of the

stability of the structure after fire, so that inspection and repairs could safely be carried out) it

can be concluded that the frame collapse at a load factor of 1.444 and for the midspan fire 1.415.

Both are a bit lower than what the British standards requires (1.4 DL +1.6 IL, BSI 1990a). And

in an advanced analysis it shows that the structure has an adequate factor of safety to have

repairs and inspection work carried out. The imposed load that exists during the repair doesn’t

exceed the limit.

For another car park, Medimall, located in Rotterdam (the Netherlands) there also have been

checked whether the critical areas will reach the critical temperature during fire. This car park

has the measurements of 295x35x13m. The results have been presented and all of the beams and

columns passed the unity check. The value of the unity check must be ≤ 1.0 in order to satisfy

the requirements. These checks have been done without taking into the account the influence of

the smoke. The results are presented in Table 21 and Table 22. [28]


Y.C.Wong 81

Table 21 Results of the calculation of the beam according to natural fire scenarios and the governing u.c. with

redistributed moments taking into account the temperature curve along the length of the beam [28]

Steel profile Location Max. steel temperature [oC] U.C.

HEM 240 Middle beam 609 0.63

HEB300 Middle beam 721 0.54

HEB320 Middle beam 667 0.57

HEA300 Edge beam 691 0.89

HEA320 Edge beam

(1st – 3

rd floor)

688 0.98

HEA320 Edge beam

(4th

floor)

688 0.83

HEB300 Edge beam

(4th

floor)

721 0.69

HEM260 On the ramp 611 0.59

HEM280 On the ramp 608 0.86

HEA240 On the ramp 612 0.37

HEA200 On the ramp 628 0.71

Table 22 Results of the column’s calculation with the maximum steel temperature (natural fire curve) and

the critical steel temperature [28]

Steel Profile Location Max. steel

temperature [oC]

Critical steel

temperature [oC]

K220 Axis D and B

(axis 19-29)

538 586

K220 Axis D and B

(other axis)

495 563

K250 Axis B

(axis 5-9,34-38,44,54-58

538 575

K250 Axis B(45,47) 538 561

K300 Axis B (axis 33,41) 449 530

K300 Axis B (axis 4,10,12, 29,

43,49,53,59)

538 528

K300 Axis B (axis 2, 16) 566 528

K220 Axis A (on the ramp) 558 740

In both examples of previous studies showed that these structures are safe and will be able to

withstand the fire for the amount of time that it was designed for, without any protection added.

Additional fire protection by using concrete was added to the columns in Medimall (given in red,

Table 22). In both these cases there was no smoke taken into account.


Y.C.Wong 82

Appendix 5 Information about hollow core slab[14]

Fixed data:

- Calculations according NEN-EN 1992-1-1 and NEN-EN-1992-1-2

- Load category A,B and G

- Momentary factor Ψ = 0.4/0.5/0.3 (Category A)

- Momentary factor Ψ = 0.5/0.5/0.3 (Category B)

- Momentary factor Ψ = 0.7/0.5/0.3 (Category G)

- Fire resistance (see graph)

- Environmental class XC1-XC3

- Permanent load =1.20 kN/m2

- End deflection ≤ 0.004 Lt

- Additional deflection ≤ 0.002 Lt

- Pressure layer (top layer) C20/25 50mm thick

- Service class 2


Y.C.Wong 83

Appendix 6 Simplified calculations

Assumed that the temperature is thoroughly equally divided over the whole beam and the

temperature is the same in cross- section and in the longitudinal direction, the simplified method

given in [52] can be used.

Method 1 (According to [52])

[1])

(

) oC=

3 (

) oC

(For unprotected beam exposed to three sides, with concrete slab on side four)

(For all other cases)

At T= 712 oC the beam will fail (critical temperature).

Method 2 (according to the Eurocode)

From NEN-EN-1993-1-2, §4.2.3.3:

x

y


Y.C.Wong 84

*

+ Eq. (7)

Parameters are given to take into account the non-uniform temperature in the cross-section. This

factor is given in 4.2.3.3 of the mentioned Eurocode given in equation (4.10):

Eq.(8)

(For unprotected beam exposed to three sides, with concrete slab on side four)

(For all other cases)

Out of Eq. (7) and (8) can be derived:

[

]

=0.44

With the temperature for failure can be found with linear interpolation from table 3.1 of

NEN-EN-1993-1-2, which is 612.5 oC (critical temperature).

The moment M at position at x= 2m is determined:

*

+

With the temperature for failure can be found with linear interpolation from table 3.1 of

NEN-EN-1993-1-2, which 717 oC (critical temperature).

The input data for CaPaFi for beam HEB500:


Y.C.Wong 85

Appendix 7 Profile of the fictitious beam

tf =50 mm

tw=12 mm

h= 500 mm

b =300mm

(

)

Thickness calculation for the U-profile

In CaPaFi the ksh = 0.9 * (

)

and this factor is used to calculate the temperature change of

the steel beam. This 0.9 has to be taken into account to for FDS.

FDS : 0.9* (

)

(

)


Y.C.Wong 86

Appendix 8 Script of model 1 (FDS)

The script itself is written in uppercase because all the commands in FDS are written uppercase

and FDS is case sensitive. The remarks are written between ----- or behind the /. The script starts

with &HEAD CHID / and ends with &TAIL/.

&HEAD CHID='test5', TITLE='test5'/ For 1 car fire (named model 1)

&TIME T_END=3000/

&MISC RESTART=.TRUE./

---- Fuel (From the example of Efectis of the half car) ---

&REAC ID='EFECTIS_HEPTANE',

FYI='SFPE',

FUEL='REAC_FUEL',

FORMULA='C7H16',

HRRPUA_SHEET=0.0,

CO_YIELD=0.01,

SOOT_YIELD=0.037,

HEAT_OF_COMBUSTION=4.46E4,

IDEAL=.TRUE./

------ Spaces ------

&MESH IJK=120,120,28, XB=0,12,0,12,0,2.8/ with a mesh of 10cm

------ The car and properties ----- HRR is for a car with a surface of 9.6m2 but with 4 sides burning

&SURF ID='car1',

color='RED',

HRRPUA= 864.583,

RAMP_Q='car1_fire'/

&RAMP ID='car1_fire', T=0, F=0.0/


&RAMP ID='car1_fire', T=960, F=0.169 /





&RAMP ID='car1_fire', T=2800, F=0 /

&OBST XB=4.5,7.5,4.5,7.5,0,0.3, SURF_ID='car1'/


Y.C.Wong 87

----- Properties of the steel beams ------

&MATL ID='STEEL_EURO',

SPECIFIC_HEAT_RAMP='STEEL_EURO_SPECIFIC_HEAT_RAMP',

CONDUCTIVITY_RAMP='STEEL_EURO_CONDUCTIVITY_RAMP',

DENSITY=7850.0,

EMISSIVITY=0.7/

&RAMP ID='STEEL_EURO_SPECIFIC_HEAT_RAMP', T=0.0, F=0.425/

&RAMP ID='STEEL_EURO_SPECIFIC_HEAT_RAMP', T=580, F=0.738/













&RAMP ID='STEEL_EURO_CONDUCTIVITY_RAMP', T=0.0, F=54.0/













&SURF ID='STEEL1',

MATL_ID = 'STEEL_EURO',

HEAT_TRANSFER_COEFFICIENT=35,

THICKNESS= 0.016

RGB=105,105,105/

&OBST XB=5.85,6.15, 0.0,12, 2.3,2.8, RGB= 105,105,105,

SURF_ID6='STEEL1','STEEL1','INERT','INERT','STEEL1','INERT'/ beam described as an U-profile

with the properties of “my profile”

--- Walls ---

&VENT SURF_ID='INERT', MB='ZMIN',RGB= 165,42,42 / floor

&VENT SURF_ID='INERT', MB='ZMAX',RGB= 165,42,42 / ceiling


Y.C.Wong 88

&VENT SURF_ID='OPEN',MB='YMIN', COLOR='INVISIBLE'/ front wall

&VENT SURF_ID='OPEN',MB='YMAX' , COLOR='INVISIBLE'/ back wall

&VENT SURF_ID='OPEN',MB= 'XMIN', COLOR='INVISIBLE'/ left wall

&VENT SURF_ID='OPEN',MB= 'XMAX' , COLOR='INVISIBLE'/ right wall

--- Devices to measure things----

&DEVC ID='INC-FLUX1', QUANTITY='INCIDENT HEAT FLUX', XYZ= 6, 6, 2.3, IOR= -3/




&DEVC ID='NET-FLUX1', QUANTITY='NET HEAT FLUX', XYZ= 6, 6, 2.3, IOR=-3/




&DEVC ID='RAD-FLUX1', QUANTITY='NET HEAT FLUX', XYZ= 6, 6, 2.3, IOR=-3/




&DEVC ID='CONV-FLUX1', QUANTITY='NET HEAT FLUX', XYZ= 6, 6, 2.3, IOR=-3/




&DEVC ID='Tmember-1', QUANTITY ='WALL TEMPERATURE', XYZ= 6, 6, 2.3, IOR=-3/




&DEVC ID='Tgas-1',QUANTITY='GAS TEMPERATURE', XYZ= 6, 6, 2.3, IOR=-3/




--- Slices to be shown in smoke view---

&SLCF PBZ=2.3, QUANTITY='TEMPERATURE'/

&SLCF PBX=1, QUANTITY='TEMPERATURE'/


&SLCF PBY=6, QUANTITY='TEMPERATURE'/


&BNDF QUANTITY='WALL TEMPERATURE' /

&TAIL/


Y.C.Wong 89

Appendix 9 Data total heat fluxes of Model 1

Position 1

Total heat

fluxes

FDS CaPaFi

t[s] hnet

[kW/m2]

Tmember [

oC]

ε*boltzmann*

ΔT(W/m2)

α*ΔT

[W/m2]

hpunt

[kW/m2]

q"Tot

[kW/m²]

0.00 0.00 20.00 0.00 0.00 0.00 0.00

60.00 6.09 24.48 18.32 156.63 6.27 20.39

120.00 19.50 39.41 85.71 679.32 20.27 33.39

180.00 32.77 64.45 222.55 1555.83 34.55 39.98

240.00 50.39 101.49 488.95 2852.09 53.74 44.33

300.00 48.62 138.72 849.47 4155.23 53.63 44.33

360.00 48.80 172.02 1266.38 5320.67 55.39 44.33

420.00 38.43 202.07 1732.22 6372.47 46.54 44.33

480.00 33.22 229.47 2241.51 7331.58 42.80 44.33

540.00 40.16 253.68 2766.43 8178.92 51.10 44.33

600.00 36.59 274.40 3277.00 8904.07 48.77 44.33

661.00 29.94 290.67 3720.55 9473.29 43.14 44.33

721.00 36.05 306.83 4201.19 10039.12 50.29 44.33

781.00 31.44 321.06 4658.67 10536.94 46.63 44.33

841.00 30.00 333.05 5070.97 10956.86 46.02 44.33

901.00 32.46 344.46 5486.46 11356.20 49.30 44.33

961.00 35.29 354.35 5865.56 11702.19 52.86 44.33

1021.00 37.28 369.24 6471.58 12223.49 55.97 48.79

1081.00 49.53 391.14 7442.52 12989.99 69.97 52.07

1141.00 51.95 413.99 8563.15 13789.63 74.31 54.67

1201.00 69.76 441.55 10072.28 14754.33 94.59 56.82

1261.00 62.93 470.13 11832.39 15754.42 90.51 58.68

1321.00 74.34 500.98 13975.21 16834.38 105.15 60.31

1381.00 78.21 531.33 16348.19 17896.58 112.46 61.77

1441.00 78.37 560.98 18941.00 18934.32 116.24 63.09

1501.00 92.23 594.42 22216.20 20104.64 134.55 68.85

1561.00 71.70 619.85 24974.07 20994.66 117.67 65.17


Y.C.Wong 90

Position 2

Total heat

fluxes

FDS CaPaFi

t[s] hnet

[kW/m2]

Tmember [

oC]

ε*boltzmann*

ΔT(W/m2)

α*ΔT

[W/m2]

hpunt

[kW/m2]

q"Tot

[kW/m²]

0.00 0.00 20.00 0.00 0.00 0.00 0.00

60.00 3.21 22.20 8.92 77.12 3.30 5.91

120.00 5.79 27.99 33.29 279.59 6.11 10.80

180.00 7.68 36.19 70.33 566.59 8.32 17.77

240.00 10.38 47.30 125.44 955.44 11.47 23.92

300.00 12.08 58.45 186.82 1345.67 13.61 23.92

360.00 12.27 69.09 251.48 1718.18 14.24 23.92

420.00 8.85 78.53 314.08 2048.38 11.22 23.92

480.00 9.98 87.46 378.21 2361.13 12.72 23.92

540.00 10.84 95.24 438.08 2633.51 13.91 23.92

600.00 10.93 102.40 496.62 2884.11 14.31 23.92

661.00 8.21 108.44 548.64 3095.34 11.85 23.92

721.00 10.14 114.28 601.41 3299.87 14.04 23.92

781.00 10.85 120.10 656.35 3503.36 15.01 23.92

841.00 9.17 125.26 707.20 3684.00 13.56 23.92

901.00 8.90 129.71 752.72 3839.96 13.50 23.92

961.00 10.17 133.85 796.32 3984.62 14.95 23.92

1021.00 13.08 140.40 868.27 4214.14 18.16 30.13

1081.00 20.03 152.06 1004.83 4621.95 25.65 34.61

1141.00 36.43 170.40 1243.84 5264.08 42.93 38.09

1201.00 24.62 188.70 1513.66 5904.49 32.04 40.95

1261.00 31.61 213.02 1925.51 6755.74 40.29 43.36

1321.00 40.54 239.94 2459.31 7697.79 50.70 45.46

1381.00 39.97 265.86 3059.25 8605.00 51.64 47.32

1441.00 59.55 295.45 3858.48 9640.65 73.05 48.99

1501.00 87.08 335.84 5170.25 11054.33 103.30 56.04

1561.00 70.33 368.21 6428.17 12187.34 88.95 51.58


Y.C.Wong 91

Position 3

Total heat

fluxes

FDS CaPaFI

t[s] hnet

[kW/m2]

Tmember

[oC]

ε*boltzmann*

ΔT(W/m2)

α*ΔT

[W/m2]

Hpunt

[kW/m2]

q"Tot

[kW/m²]

q"Tot

[kW/m²]

0.00 0.00 20.00 20.00 0.00 0.00 0.00 0.00

60.00 0.61 20.55 20.06 2.22 19.33 0.63 1.34

120.00 1.73 22.06 20.89 8.34 72.18 1.81 2.62

180.00 1.97 24.16 22.43 17.00 145.61 2.13 3.81

240.00 2.80 26.98 24.60 28.92 244.19 3.07 4.96

300.00 3.15 29.80 27.31 41.23 343.09 3.53 4.96

360.00 2.74 32.33 29.95 52.51 431.38 3.22 4.96

420.00 2.22 34.62 33.00 63.00 511.61 2.80 4.96

480.00 2.30 36.92 35.00 73.78 592.18 2.96 4.96

540.00 2.36 38.82 37.00 82.84 658.56 3.10 4.96

600.00 3.21 40.67 40.00 91.87 723.50 4.03 4.96

661.00 2.22 42.28 42.00 99.83 779.83 3.10 4.96

721.00 2.54 43.83 44.00 107.60 834.00 3.48 4.96

781.00 2.45 45.35 47.00 115.34 887.22 3.46 4.96

841.00 1.89 46.75 49.00 122.60 936.39 2.95 4.96

901.00 2.36 48.10 51.00 129.64 983.48 3.47 4.96

961.00 2.13 49.19 53.00 135.40 1021.59 3.29 4.96

1021.00 3.01 50.97 55.00 144.96 1083.97 4.24 6.57

1081.00 4.31 53.61 58.00 159.40 1176.26 5.64 8.12

1141.00 5.88 57.11 62.00 179.10 1298.74 7.36 9.65

1201.00 4.89 60.92 66.00 201.32 1432.36 6.52 11.14

1261.00 6.04 65.06 71.00 226.28 1577.16 7.84 12.63

1321.00 6.56 69.60 77.00 254.71 1735.86 8.55 15.77

1381.00 7.74 74.37 84.00 285.90 1903.03 9.93 18.43

1441.00 9.78 80.24 92.00 326.00 2108.30 12.21 20.79

1501.00 18.90 89.16 102.00 390.95 2420.57 21.71 30.42

1561.00 9.97 97.08 116.00 452.78 2697.82 13.12 24.38


Y.C.Wong 92

Position 4

Total heat

fluxes

FDS CaPaFi

t[s] hnet

[kW/m2]

Tmember

[oC]

ε*boltzmann*

ΔT(W/m2)

α*ΔT

[W/m2]

Hpunt

[kW/m2]

q"Tot

[kW/m²]

q"Tot

[kW/m²]

0.00 0.00 20.00 20.00 0.00 0.00 0.00 0.00

60.00 0.07 20.06 20.02 0.22 1.95 0.07 0.47

120.00 0.13 20.20 20.31 0.79 6.92 0.14 0.94

180.00 0.15 20.46 20.87 1.85 16.13 0.17 1.40

240.00 0.29 20.82 21.67 3.30 28.76 0.32 1.84

300.00 0.25 21.26 22.68 5.09 44.27 0.30 1.84

360.00 0.26 21.55 23.67 6.25 54.28 0.32 1.84

420.00 0.29 21.84 25.00 7.44 64.45 0.36 1.84

480.00 0.22 22.16 26.00 8.74 75.64 0.30 1.84

540.00 0.36 22.44 26.00 9.88 85.35 0.46 1.84

600.00 0.55 22.71 27.00 11.01 94.98 0.66 1.84

661.00 0.24 22.98 28.00 12.12 104.46 0.36 1.84

721.00 0.21 23.22 29.00 13.08 112.58 0.33 1.84

781.00 0.31 23.43 30.00 13.96 120.01 0.45 1.84

841.00 0.36 23.60 31.00 14.68 126.10 0.50 1.84

901.00 0.32 23.79 32.00 15.46 132.67 0.46 1.84

961.00 0.34 23.97 32.00 16.19 138.78 0.49 1.84

1021.00 0.34 24.23 33.00 17.31 148.18 0.51 2.46

1081.00 0.54 24.70 34.00 19.26 164.51 0.72 3.07

1141.00 1.36 25.51 36.00 22.68 192.90 1.58 3.67

1201.00 1.57 26.54 37.00 27.05 228.87 1.83 4.25

1261.00 1.37 27.73 39.00 32.18 270.67 1.67 4.82

1321.00 1.96 29.36 42.00 39.26 327.49 2.33 5.39

1381.00 1.49 30.94 44.00 46.29 382.97 1.92 5.96

1441.00 1.82 32.83 47.00 54.81 449.16 2.32 6.52

1501.00 4.25 35.29 50.00 66.14 535.30 4.85 9.60

1561.00 1.94 37.24 55.00 75.31 603.50 2.61 7.51


Y.C.Wong 93

0

20

40

60

80

100

120

140

0 200 400 600 800 1000 1200 1400 1600

Tota

l he

at f

lux

[kW

/m2 ]

Time [s]

Total Heat fluxes Position 1(model 1)

FDS

CaPaFi

0

20

40

60

80

100

120

140

0 200 400 600 800 1000 1200 1400 1600

Tota

l He

at f

lux

[kW

/m2 ]

Time [s]


FDS

CaPaFi

0

20

40

60

80

100

120

140

0 200 400 600 800 1000 1200 1400 1600

Tota

l He

at f

lux

[kW

/m2 ]

Time [s]

Total Heat fluxes Postion 3 (model 1)

FDS

CaPaFi

0

20

40

60

80

100

120

140

0 200 400 600 800 1000 1200 1400 1600

Tota

l He

at f

lux

[kW

/m2]

Time [s]


FDS

CaPaFi


Y.C.Wong 94

Appendix 10 Data temperatures of model 1

Temperature Member [oC]

Position 1 Position 2 Position 3 Position 4

t[s] FDS CaPaFi FDS CaPaFi FDS CaPaFi FDS CaPaFi

0 20.00 20.00 20.00 20.00 20.00 20.00 20.00 20.00

60 24.48 21.00 22.20 20.00 20.55 20.00 20.06 20.00

120 39.41 33.00 27.99 24.00 22.06 21.00 20.20 20.00

180 64.45 52.00 36.19 30.00 24.16 22.00 20.46 21.00

240 101.49 73.00 47.30 40.00 26.98 25.00 20.82 22.00

300 138.72 95.00 58.45 53.00 29.80 27.00 21.26 23.00

360 172.02 116.00 69.09 65.00 32.33 30.00 21.55 24.00

420 202.07 137.00 78.53 77.00 34.62 33.00 21.84 25.00

480 229.47 156.00 87.46 88.00 36.92 35.00 22.16 26.00

540 253.68 175.00 95.24 99.00 38.82 37.00 22.44 26.00

600 274.40 193.00 102.40 110.00 40.67 40.00 22.71 27.00

661 290.67 210.00 108.44 120.00 42.28 42.00 22.98 28.00

721 306.83 227.00 114.28 130.00 43.83 44.00 23.22 29.00

781 321.06 243.00 120.10 140.00 45.35 47.00 23.43 30.00

841 333.05 259.00 125.26 149.00 46.75 49.00 23.60 31.00

901 344.46 274.00 129.71 158.00 48.10 51.00 23.79 32.00

961 354.35 289.00 133.85 167.00 49.19 53.00 23.97 32.00

1021 369.24 303.00 140.40 176.00 50.97 55.00 24.23 33.00

1081 391.14 318.00 152.06 187.00 53.61 58.00 24.70 34.00

1141 413.99 334.00 170.40 201.00 57.11 62.00 25.51 36.00

1201 441.55 351.00 188.70 215.00 60.92 66.00 26.54 37.00

1261 470.13 368.00 213.02 230.00 65.06 71.00 27.73 39.00

1321 500.98 385.00 239.94 246.00 69.60 77.00 29.36 42.00

1381 531.33 402.00 265.86 262.00 74.37 84.00 30.94 44.00

1441 560.98 419.00 295.45 278.00 80.24 92.00 32.83 47.00

1501 594.42 435.00 335.84 295.00 89.16 102.00 35.29 50.00


Y.C.Wong 95

0

100

200

300

400

500

600

700

0 200 400 600 800 1000 1200 1400 1600

Tem

pe

ratu

re [

oC

]

Time [s]


FDS

CaPaFi

0

100

200

300

400

500

600

700

0 200 400 600 800 1000 1200 1400 1600

Tem

pe

ratu

re [

oC

]

Time [s]


FDS

CaPaFi

0

100

200

300

400

500

600

700

0 200 400 600 800 1000 1200 1400 1600

Tem

pe

ratu

re [

oC

]

Time [s]


FDS

CaPaFi


Y.C.Wong 96

0

100

200

300

400

500

600

700

0 200 400 600 800 1000 1200 1400 1600

Tem

pe

ratu

re [

oC

]

Time [s]


FDS

CaPaFi


Y.C.Wong 97

Appendix 11 Script model 2 for FDS

&HEAD CHID='test6', TITLE='test6'/ For 1 car fire (model 2)

&TIME T_END=3600/

&MISC RESTART=.TRUE./

----Fuel (From an example of Efectis of a half car and info from SFPE) ---


FYI='SFPE',

FUEL='REAC_FUEL',

FORMULA='C7H16',

HRRPUA_SHEET=0.0,

CO_YIELD=0.01,

SOOT_YIELD=0.037,


IDEAL=.TRUE./

------ Spaces ------

&MESH IJK=120,120,28, XB=0,12,0,12,0,2.8/ The space where the simulation takes place,

with meshes of 10cm

------ The car and its properties -----

&SURF ID='car1',

color='RED',

HRRPUA= 658.730,

RAMP_Q='car1_fire'/ Fire surface is now used is 12.6m2 (3*3+4*3*0.3=12.6m2)










Y.C.Wong 98

&OBST XB=4.5,7.5,4.5,7.5,0,0.3, SURF_ID6='car1','car1','car1','car1','INERT','car1'/ (The

upper side and the 4 sides of the box are going to be on fire)

------ Properties of the steel beam ------




DENSITY=7850.0,

EMISSIVITY=0.7/




























&SURF ID='STEEL1',



Y.C.Wong 99


THICKNESS= 0.016

RGB=105,105,105/

&OBST XB=5.85,6.15, 0.0,12, 2.3,2.8, RGB= 105,105,105,

SURF_ID6='STEEL1','STEEL1','INERT','INERT','STEEL1','INERT'/ (The beam is the

fictitious beam with the properties of “My Profile”)

--- Concrete properties used for the ceiling and the floors----

&MATL ID='CONCRETE_EURO',

SPECIFIC_HEAT_RAMP='CONCRETE_EURO_SPECIFIC_HEAT_RAMP',

CONDUCTIVITY_RAMP='CONCRETE_EURO_CONDUCTIVITY_RAMP',

DENSITY=2500/

&RAMP ID='CONCRETE_EURO_SPECIFIC_HEAT_RAMP', T=20, F=0.9/













&RAMP ID='CONCRETE_EURO_SPECIFIC_HEAT_RAMP', T=1200,F=1.1/

&RAMP ID='CONCRETE_EURO_CONDUCTIVITY_RAMP', T=20.0, F=1.951/













Y.C.Wong 100



&SURF ID='CONCRETE',

MATL_ID = 'CONCRETE_EURO',

THICKNESS=0.4

RGB=84,255,159/

---Ceiling and the floor --

&VENT SURF_ID='CONCRETE', MB='ZMIN'/ floor

&VENT SURF_ID='CONCRETE', MB='ZMAX'/ ceiling

--- 4 sides (walls) ---

&VENT SURF_ID='OPEN',MB='YMIN', COLOR='INVISIBLE'/ front wall

&VENT SURF_ID='OPEN',MB='YMAX' , COLOR='INVISIBLE'/ back wall

&VENT SURF_ID='OPEN',MB= 'XMIN', COLOR='INVISIBLE'/ left wall

&VENT SURF_ID='OPEN',MB= 'XMAX' , COLOR='INVISIBLE'/ right wall

--- Devices ----

(Devices 5,6,7,11,12 are on the ceiling and devices 1,2,3,4,8,9,10 are on the bottom of the steel

member)




&DEVC ID='INC-FLUX4', QUANTITY='INCIDENT HEAT FLUX', XYZ= 6, 11, 2.3, IOR= -

3/




3/




3/


3/


3/

---12 (counts of the devices)


Y.C.Wong 101













----24 (counts of the devices)




























Y.C.Wong 102













-----60 (counts of the devices)











&DEVC ID='Tgas-11',QUANTITY='GAS TEMPERATURE',XYZ= 5, 6, 2.8, IOR=-3/


-----72 (counts of the devices)

--- Slices ---










&TAIL/


Y.C.Wong 103

Appendix 12 Data Total heat fluxes for model 2

Position 1 (model 2)

Total heat

fluxes

FDS CaPaFi

t

[s]

Hnet

[kW/m2]

Tmember

[oC]

ε*boltzmann*ΔT

[W/m2]

α*ΔT

[W/m2]

Hpunt

[kW/m2]

qtot

[kW/m²]

0 0.00 20.00 0.00 0.00 0.00 0.00

60 5.17 23.54 14.40 123.77 5.31 20.39

120 12.96 33.38 57.31 468.36 13.48 33.39

180 20.04 50.47 142.29 1066.62 21.25 39.98

240 28.97 76.25 298.51 1968.73 31.24 44.33

300 29.00 103.06 502.16 2907.06 32.41 44.33

360 26.59 126.35 718.20 3722.18 31.03 44.33

420 26.52 149.14 969.61 4519.97 32.01 44.33

480 22.64 168.31 1214.98 5190.72 29.05 44.33

540 23.59 185.91 1470.43 5806.95 30.87 44.33

600 24.11 199.83 1694.34 6294.18 32.10 44.33

660 24.40 213.18 1928.44 6761.36 33.09 44.33

720 24.41 225.26 2157.57 7184.13 33.75 44.33

780 25.94 236.48 2385.92 7576.90 35.90 44.33

840 22.98 246.85 2610.65 7939.65 33.53 44.33

900 22.38 255.09 2799.14 8228.00 33.41 44.33

960 22.83 262.68 2980.98 8493.94 34.30 44.33

1020 33.45 276.66 3336.20 8983.01 45.77 48.79

1080 52.18 300.94 4021.21 9832.81 66.03 52.07

1140 44.61 327.63 4881.49 10767.00 60.25 54.67

1200 42.54 353.13 5817.81 11659.51 60.02 56.82

1260 49.17 381.63 7008.82 12657.09 68.83 58.68

1320 59.64 412.56 8489.83 13739.71 81.87 60.31

1380 62.76 442.72 10140.25 14795.23 87.70 61.77

1440 74.54 475.01 12154.20 15925.30 102.62 63.09

1500 92.61 515.38 15066.76 17338.24 125.02 68.85


Y.C.Wong 104


Total heat

fluxes

FDS CaPaFi

t

[s]

hnet

[kW/m2]

Tmember

[oC]

ε*boltzmann*ΔT

[W/m2]

α*ΔT

[W/m2]

hpunt

[kW/m2]

qtot

[kW/m²]

0 0.00 20.00 0.00 0.00 0.00 0.00

60 2.70 21.72 6.93 60.14 2.77 5.91

120 5.33 26.20 25.60 216.97 5.57 10.80

180 6.78 32.65 53.96 442.61 7.28 17.77

240 9.86 41.05 93.72 736.68 10.69 23.92

300 8.90 49.61 137.66 1036.44 10.07 23.92

360 7.61 57.76 182.82 1321.44 9.12 23.92

420 8.16 65.19 227.08 1581.73 9.96 23.92

480 7.62 71.61 267.73 1806.49 9.70 23.92

540 7.83 77.40 306.37 2009.10 10.15 23.92

600 8.14 82.69 343.37 2194.15 10.68 23.92

660 7.15 87.31 377.11 2355.97 9.88 23.92

720 6.93 92.17 413.97 2525.90 9.87 23.92

780 6.99 96.80 450.50 2687.88 10.13 23.92

840 8.03 100.97 484.60 2833.82 11.35 23.92

900 6.46 104.31 512.81 2950.93 9.92 23.92

960 7.15 107.79 542.94 3072.66 10.77 23.92

1020 9.56 112.60 585.94 3240.87 13.38 30.13

1080 12.79 121.26 667.66 3544.16 17.00 34.61

1140 14.48 132.05 777.20 3921.72 19.18 38.09

1200 23.69 147.11 945.49 4448.91 29.09 40.95

1260 33.29 167.02 1197.47 5145.68 39.63 43.36

1320 29.54 185.97 1471.30 5808.92 36.82 45.46

1380 35.85 210.93 1887.59 6682.58 44.42 47.32

1440 46.18 235.86 2372.83 7555.08 56.11 48.99

1500 48.46 269.84 3159.39 8744.29 60.36 56.04


Y.C.Wong 105


Total heat

fluxes

FDS CaPaFi

t

[s]

hnet

[kW/m2]

Tmember

[oC]

ε*boltzmann*ΔT

[W/m2]

α*ΔT

[W/m2]

hpunt

[kW/m2]

qtot

[kW/m²]

0 0.00 20.00 0.00 0.00 0.00 0.00

60 0.83 20.44 1.77 15.48 0.85 1.34

120 1.18 21.56 6.29 54.61 1.24 2.62

180 1.92 23.28 13.35 114.89 2.05 3.81

240 2.40 25.39 22.16 188.62 2.61 4.96

300 2.44 27.62 31.68 266.62 2.74 4.96

360 2.23 29.73 40.92 340.62 2.61 4.96

420 2.27 31.67 49.56 408.55 2.72 4.96

480 2.39 33.35 57.17 467.26 2.91 4.96

540 2.15 34.88 64.23 520.92 2.74 4.96

600 2.29 36.32 70.96 571.33 2.93 4.96

660 1.69 37.62 77.10 616.65 2.39 4.96

720 1.58 38.98 83.63 664.27 2.33 4.96

780 1.89 40.27 89.92 709.58 2.69 4.96

840 1.74 41.48 95.87 751.93 2.59 4.96

900 1.47 42.48 100.82 786.77 2.36 4.96

960 1.87 43.46 105.74 821.13 2.79 4.96

1020 2.25 44.75 112.27 866.18 3.22 6.57

1080 3.52 46.93 123.51 942.51 4.59 8.12

1140 3.55 49.44 136.76 1030.50 4.71 9.65

1200 4.63 52.55 153.58 1139.33 5.92 11.14

1260 6.43 56.33 174.65 1271.45 7.88 12.63

1320 5.43 60.27 197.47 1409.50 7.03 15.77

1380 6.47 64.80 224.67 1567.99 8.27 18.43

1440 7.10 69.46 253.84 1731.11 9.08 20.79

1500 6.95 75.37 292.60 1938.08 9.18 30.42


Y.C.Wong 106


Total heat

fluxes

FDS CaPaFi

t

[s]

hnet

[kW/m2]

Tmember

[oC]

ε*boltzmann*ΔT

[W/m2]

α*ΔT

[W/m2]

hpunt

[kW/m2]

qtot

[kW/m²]

0 0.00 20.00 0.00 0.00 0.00 0.00

60 0.09 20.04 0.17 1.51 0.09 0.47

120 0.11 20.15 0.61 5.38 0.12 0.94

180 0.14 20.34 1.35 11.78 0.16 1.40

240 0.30 20.61 2.44 21.32 0.32 1.84

300 0.37 20.90 3.63 31.57 0.41 1.84

360 0.38 21.19 4.77 41.52 0.43 1.84

420 0.15 21.42 5.73 49.75 0.21 1.84

480 0.22 21.62 6.52 56.58 0.28 1.84

540 0.24 21.81 7.33 63.50 0.31 1.84

600 0.21 22.01 8.12 70.32 0.29 1.84

660 0.17 22.19 8.87 76.73 0.25 1.84

720 0.20 22.42 9.82 84.86 0.29 1.84

780 0.43 22.61 10.58 91.37 0.54 1.84

840 0.23 22.76 11.19 96.57 0.34 1.84

900 0.29 22.91 11.83 101.97 0.41 1.84

960 0.11 23.03 12.32 106.15 0.22 1.84

1020 0.40 23.28 13.33 114.68 0.52 2.46

1080 0.48 23.64 14.82 127.27 0.63 3.07

1140 0.56 24.10 16.76 143.60 0.72 3.67

1200 0.78 24.85 19.90 169.86 0.97 4.25

1260 1.31 25.76 23.74 201.69 1.54 4.82

1320 1.01 26.90 28.58 241.37 1.28 5.39

1380 2.21 28.20 34.19 286.85 2.53 5.96

1440 1.38 29.68 40.68 338.78 1.76 6.52

1500 2.78 31.72 49.77 410.17 3.24 9.60


Y.C.Wong 107


Total heat

fluxes

FDS CaPaFi

t

[s]

hnet

[kW/m2]

Tmember

[oC]

ε*boltzmann*ΔT

[W/m2]

α*ΔT

[W/m2]

hpunt

[kW/m2]

qtot

[kW/m²]

0 0.00 20.00 0.00 0.00 0.00 0.00

60 3.02 21.83 7.41 64.22 3.09 5.91

120 5.75 26.50 26.89 227.61 6.00 10.80

180 7.34 33.64 58.49 477.37 7.87 17.77

240 10.79 42.94 103.14 803.01 11.70 23.92

300 9.53 52.41 152.81 1134.41 10.82 23.92

360 8.93 61.69 205.87 1459.15 10.59 23.92

420 9.30 69.64 254.96 1737.24 11.29 23.92

480 8.19 76.47 300.01 1976.46 10.46 23.92

540 8.21 82.82 344.30 2198.71 10.75 23.92

600 8.80 88.71 387.53 2404.70 11.59 23.92

660 7.24 93.92 427.62 2587.16 10.25 23.92

720 7.53 98.78 466.59 2757.35 10.75 23.92

780 7.38 103.72 507.74 2930.13 10.82 23.92

840 7.31 107.87 543.63 3075.41 10.93 23.92

900 6.84 111.80 578.69 3212.96 10.63 23.92

960 7.92 115.96 617.03 3358.63 11.89 23.92

1020 10.08 121.88 673.65 3565.63 14.32 30.13

1080 14.78 131.77 774.22 3911.84 19.47 34.61

1140 18.33 144.70 917.31 4364.53 23.62 38.09

1200 25.03 160.48 1110.89 4916.97 31.06 40.95

1260 35.40 180.55 1389.42 5619.22 42.41 43.36

1320 31.32 201.78 1727.31 6362.39 39.41 45.46

1380 50.60 228.73 2226.60 7305.65 60.13 47.32

1440 41.54 256.36 2829.13 8272.65 52.65 48.99

1500 67.74 293.42 3799.52 9569.63 81.11 56.04


Y.C.Wong 108


Total heat

fluxes

FDS CaPaFi

t

[s]

hnet

[kW/m2]

Tmember

[oC]

ε*boltzmann*ΔT

[W/m2]

α*ΔT

[W/m2]

hpunt

[kW/m2]

qtot

[kW/m²]

0 0.00 20.00 0.00 0.00 0.00 0.00

60 0.90 20.46 1.85 16.18 0.92 1.34

120 1.63 21.66 6.69 58.02 1.70 2.62

180 1.71 23.47 14.12 121.38 1.84 3.81

240 2.72 25.78 23.83 202.45 2.95 4.96

300 2.06 28.12 33.84 284.03 2.37 4.96

360 2.64 30.54 44.48 368.80 3.06 4.96

420 2.76 32.62 53.85 441.74 3.26 4.96

480 2.17 34.42 62.09 504.71 2.74 4.96

540 2.09 36.16 70.18 565.48 2.72 4.96

600 2.50 37.79 77.91 622.58 3.20 4.96

660 1.56 39.15 84.44 670.16 2.32 4.96

720 1.38 40.44 90.75 715.53 2.19 4.96

780 1.69 41.88 97.85 765.90 2.55 4.96

840 2.18 43.00 103.44 805.14 3.09 4.96

900 2.21 44.17 109.31 845.81 3.16 4.96

960 2.08 45.27 114.93 884.41 3.08 4.96

1020 2.48 46.74 122.53 935.91 3.54 6.57

1080 3.68 49.04 134.61 1016.36 4.83 8.12

1140 3.86 51.87 149.83 1115.36 5.12 9.65

1200 4.63 55.07 167.55 1227.45 6.02 11.14

1260 5.48 58.74 188.53 1356.02 7.03 12.63

1320 4.96 62.91 213.18 1501.84 6.68 15.77

1380 6.84 67.47 241.23 1661.41 8.74 18.43

1440 6.53 72.41 272.94 1834.40 8.63 20.79

1500 10.88 79.00 317.39 2065.10 13.26 30.42


Y.C.Wong 109


Total heat

fluxes

FDS CaPaFi

t

[s]

hnet

[kW/m2]

Tmember

[oC]

ε*boltzmann*ΔT

[W/m2]

α*ΔT

[W/m2]

hpunt

[kW/m2]

qtot

[kW/m²]

0 0.00 20.00 0.00 0.00 0.00 0.00

60 0.09 20.04 0.18 1.54 0.09 0.47

120 0.11 20.16 0.64 5.62 0.11 0.94

180 0.20 20.37 1.49 12.97 0.21 1.40

240 0.34 20.62 2.47 21.57 0.37 1.84

300 0.28 20.94 3.78 32.90 0.31 1.84

360 0.30 21.24 5.01 43.56 0.35 1.84

420 0.34 21.54 6.22 54.00 0.40 1.84

480 0.31 21.80 7.26 62.91 0.38 1.84

540 0.26 22.05 8.29 71.76 0.34 1.84

600 0.24 22.22 8.99 77.73 0.33 1.84

660 0.27 22.42 9.80 84.70 0.36 1.84

720 0.52 22.62 10.64 91.86 0.62 1.84

780 0.21 22.77 11.23 96.87 0.32 1.84

840 0.21 22.93 11.91 102.63 0.32 1.84

900 0.18 23.10 12.60 108.51 0.30 1.84

960 0.42 23.27 13.29 114.32 0.55 1.84

1020 0.86 23.55 14.45 124.14 1.00 2.46

1080 0.41 23.87 15.80 135.51 0.56 3.07

1140 0.95 24.39 17.98 153.80 1.12 3.67

1200 1.10 25.14 21.09 179.77 1.30 4.25

1260 1.62 26.23 25.75 218.22 1.86 4.82

1320 1.03 27.41 30.78 259.33 1.32 5.39

1380 1.53 28.67 36.26 303.53 1.87 5.96

1440 1.88 30.19 42.95 356.73 2.28 6.52

1500 2.01 32.18 51.83 426.14 2.48 9.60


Y.C.Wong 110

0

20

40

60

80

100

120

140

0 200 400 600 800 1000 1200 1400 1600

Tota

l he

at f

luxe

s [k

W/m

2 ]

Time [s]

Heat fluxes position 1 (model 2)

FDS Pos1

CaPaFi Pos1

0

20

40

60

80

100

120

140

0 200 400 600 800 1000 1200 1400 1600

Tota

l he

at f

luxe

s [k

W/m

2 ]

Time [s]

Heat fluxes Position 2 and 8 (model 2)

FDS Pos2

CaPaFi Pos2

FDS Pos8

0

20

40

60

80

100

120

140

0 200 400 600 800 1000 1200 1400 1600

Tota

l he

at f

luxe

s [k

W/m

2 ]

Time [s]

Heat fluxes position 3 and 9 (model 2)

FDS pos3

CaPaFi Pos3

FDS Pos9


Y.C.Wong 111

0

20

40

60

80

100

120

140

0 200 400 600 800 1000 1200 1400 1600

Tota

l he

at f

luxe

s [k

W/m

2 ]

Time [s]

Heat fluxes position 4 and 10 (model 2)

FDS Pos4

CaPaFi Pos4

FDS Pos10


Y.C.Wong 112

Appendix 13 Data temperature of model 2

Temperature of the steel beam [oC]

Position 1 Position 2 Position 3 Position 4

t [s] FDS CaPaFi FDS CaPaFi FDS CaPaFi FDS CaPaFi

0 20.00 20 20.00 20 20.00 20 20.00 20

61 22.68 21 21.33 20 20.34 20 20.03 20

120 28.94 33 23.98 24 21.06 21 20.11 20

181 39.56 52 27.81 30 22.06 22 20.23 21

240 54.65 73 32.48 40 23.24 25 20.39 22

301 70.01 95 37.34 53 24.42 27 20.54 23

360 84.69 116 42.11 65 25.65 30 20.70 24

420 97.87 137 46.50 77 26.79 33 20.83 25

480 110.41 156 50.85 88 27.91 35 20.97 26

540 122.54 175 54.75 99 28.96 37 21.13 26

600 134.02 193 58.86 110 30.02 40 21.26 27

660 144.00 210 62.52 120 31.02 42 21.40 28

720 154.14 227 66.36 130 31.95 44 21.53 29

780 163.42 243 69.78 140 32.85 47 21.65 30

841 172.29 259 72.86 149 33.66 49 21.75 31

900 180.68 274 76.17 158 34.58 51 21.85 32

961 188.32 289 79.12 167 35.36 53 21.94 32

1020 202.61 303 83.50 176 36.43 55 22.11 33

1081 222.32 318 90.51 187 37.98 58 22.36 34

1140 242.49 334 98.56 201 39.79 62 22.75 36

1201 264.39 351 108.54 215 41.95 66 23.26 37

1260 286.23 368 120.25 230 44.21 71 23.74 39

1321 310.13 385 135.39 246 46.93 77 24.39 42

1380 335.14 402 150.40 262 49.67 84 25.15 44

1441 361.23 419 168.44 278 52.82 92 26.07 47

1500 395.98 435 193.52 295 57.24 102 27.40 50


Y.C.Wong 113

Temperature of the steel beam [oC]

Position 8 Position 9 Position 10

t [s] FDS CaPaFi FDS CaPaFi FDS CaPaFi

0 20.00 20 20.00 20 20.00 20

61 21.43 20 20.38 20 20.04 20

120 24.22 24 21.09 21 20.11 20

181 28.43 30 22.18 22 20.24 21

240 33.72 40 23.47 25 20.44 22

301 38.98 53 24.79 27 20.60 23

360 44.09 65 26.00 30 20.75 24

420 49.12 77 27.24 33 20.90 25

480 53.89 88 28.50 35 21.07 26

540 58.01 99 29.51 37 21.21 26

600 62.45 110 30.64 40 21.34 27

660 66.48 120 31.67 42 21.46 28

720 70.43 130 32.77 44 21.60 29

780 73.88 140 33.69 47 21.69 30

841 77.44 149 34.52 49 21.83 31

900 80.78 158 35.47 51 21.94 32

961 84.21 167 36.38 53 22.06 32

1020 88.88 176 37.51 55 22.25 33

1081 97.66 187 39.29 58 22.49 34

1140 105.83 201 41.16 62 22.82 36

1201 117.15 215 43.57 66 23.39 37

1260 130.67 230 46.06 71 24.02 39

1321 148.44 246 49.02 77 24.70 42

1380 165.25 262 52.11 84 25.66 44

1441 184.54 278 55.39 92 26.63 47

1500 210.22 295 59.73 102 28.02 50

0

100

200

300

400

500

0 200 400 600 800 1000 1200 1400 1600

Tem

pe

ratu

re [

oC

]

Time [s]


Temp.FDSPos1

Temp.CaPaFiPos1


Y.C.Wong 114

0

100

200

300

400

500

0 200 400 600 800 1000 1200 1400 1600

Tem

pe

ratu

re [

oC

]

Time [s]


Temp.FDSPos2

Temp.CaPaFiPos2

0

100

200

300

400

500

0 200 400 600 800 1000 1200 1400 1600

Tem

pe

ratu

re [

oC

]

Time [s]


Temp.FDS Pos3

Temp.CaPaFi Pos3

0

100

200

300

400

500

0 200 400 600 800 1000 1200 1400 1600

Tem

pe

ratu

re [

oC

]

Time [s]


Temp.FDS Pos4

Temp.CaPaFiPos4


Y.C.Wong 115

0

100

200

300

400

500

0 200 400 600 800 1000 1200 1400 1600

Tem

pe

ratu

re [

oC

]

Time [s]


Temp.FDSPos8

Temp.CaPaFi Pos8

0

100

200

300

400

500

0 200 400 600 800 1000 1200 1400 1600

Tem

pe

ratu

re [

oC

]

Time [s]


Temp.FDSPos9

Temp.CaPaFiPos9

0

100

200

300

400

500

0 200 400 600 800 1000 1200 1400 1600

Tem

pe

ratu

re [

oC

]

Time [s]


Temp.FDSPos10

Temp.CaPaFiPos10


Y.C.Wong 116

Appendix 14 Comparison heat fluxes model 2,4 and CaPaFi

Total heat

fluxes

Position 3 Position 4

Model 2 [kW/m

2]

Model 4 [kW/m

2]

CaPaFi [kW/m

2]

Model 2 [kW/m

2]

Model 4 [kW/m

2]

CaPaFi [kW/m

2]

t [s] 0.00 0.00 0.00 0.00 0.00 0.00

0 0.75 0.80 1.34 0.08 0.04 0.47

61 1.26 1.55 2.62 0.20 0.10 0.94

120 1.94 2.18 3.81 0.26 0.20 1.40

181 2.45 1.80 4.96 0.24 0.68 1.84

240 2.25 2.15 4.96 0.36 0.32 1.84

301 2.53 2.26 4.96 0.27 0.34 1.84

360 3.02 2.62 4.96 0.26 0.21 1.84

420 2.76 2.57 4.96 0.34 0.31 1.84

480 2.58 2.19 4.96 0.82 0.23 1.84

540 2.71 2.65 4.96 0.30 0.22 1.84

600 2.94 2.84 4.96 0.79 0.31 1.84

660 2.42 2.20 4.96 0.39 0.26 1.84

720 2.84 2.32 4.96 0.45 0.21 1.84

780 2.23 2.41 4.96 0.25 0.29 1.84

841 2.62 2.42 4.96 0.25 0.28 1.84

900 2.67 2.39 4.96 0.25 0.43 1.84

961 3.40 3.34 6.57 0.46 0.42 2.46

1020 4.45 4.74 8.12 0.49 0.68 3.07

1081 4.95 4.65 9.65 1.26 0.89 3.67

1140 5.68 5.66 11.14 1.84 0.85 4.25

1201 6.14 6.60 12.63 1.26 1.99 4.82

1260 7.35 5.85 15.77 1.79 0.94 5.39

1321 6.94 6.59 18.43 1.58 1.63 5.96

1380 9.13 8.29 20.79 1.59 2.37 6.52

1441 11.10 9.31 30.42 2.99 1.83 9.60

1500


Y.C.Wong 117

Total heat

fluxes


Model 2 [kW/m

2]

Model 4 [kW/m

2]

CaPaFi [kW/m

2]

Model 2 [kW/m

2]

Model 4 [kW/m

2]

CaPaFi [kW/m

2] t[s]

0 0.00 0.00 0.00 0.00 0.00 0.00

61 3.11 3.12 5.91 0.96 0.87 1.34

120 5.50 5.98 10.80 1.20 1.48 2.62

181 8.22 7.31 17.77 2.03 2.08 3.81

240 10.93 9.09 23.92 2.42 2.71 4.96

301 9.41 9.74 23.92 2.49 2.85 4.96

360 10.48 10.85 23.92 2.31 2.64 4.96

420 11.39 10.16 23.92 2.59 2.27 4.96

480 10.29 10.46 23.92 2.84 2.68 4.96

540 10.95 10.21 23.92 2.53 2.25 4.96

600 10.47 9.68 23.92 2.76 2.90 4.96

660 10.77 11.38 23.92 2.67 2.67 4.96

720 11.71 10.50 23.92 3.16 2.76 4.96

780 11.03 9.77 23.92 3.02 2.33 4.96

841 10.71 10.90 23.92 2.29 3.07 4.96

900 11.10 9.42 23.92 2.80 2.54 4.96

961 12.49 10.70 23.92 3.51 2.64 4.96

1020 13.98 14.37 30.13 3.06 3.67 6.57

1081 24.48 14.56 34.61 4.75 3.98 8.12

1140 25.06 21.52 38.09 5.10 5.24 9.65

1201 28.74 32.97 40.95 5.89 5.68 11.14

1260 33.74 23.46 43.36 6.93 5.29 12.63

1321 52.27 40.08 45.46 8.81 7.20 15.77

1380 42.72 56.06 47.32 7.30 8.27 18.43

1441 49.30 44.59 48.99 8.14 7.80 20.79

1500 75.38 92.60 56.04 11.22 13.19 30.42


Y.C.Wong 118

Total heat

fluxes Position 10

t [s] Model 2 [kW/m

2]

Model 4 [kW/m

2]

CaPaFi [kW/m

2]

0 0.00 0.00 0.00

61 0.07 0.17 0.47

120 0.13 0.17 0.94

181 0.17 0.18 1.40

240 0.72 0.30 1.84

301 0.31 0.25 1.84

360 0.26 0.25 1.84

420 0.43 0.26 1.84

480 0.66 0.31 1.84

540 0.50 0.47 1.84

600 0.48 0.31 1.84

660 0.33 0.31 1.84

720 0.41 0.33 1.84

780 0.26 0.31 1.84

841 0.33 0.49 1.84

900 0.36 0.34 1.84

961 0.38 0.26 1.84

1020 0.58 0.39 2.46

1081 0.54 1.01 3.07

1140 0.66 0.65 3.67

1201 1.25 0.98 4.25

1260 1.69 1.80 4.82

1321 1.65 1.40 5.39

1380 1.94 1.45 5.96

1441 1.82 2.40 6.52

1500 2.66 2.30 9.60

0

20

40

60

80

100

120

140

0 200 400 600 800 1000 1200 1400 1600

Tota

l He

at f

luxe

s [k

W/m

2 ]

Time [s]

Position 1

Model 2

Model 4

CaPaFi


Y.C.Wong 119

0

20

40

60

80

100

120

140

0 200 400 600 800 1000 1200 1400 1600

Tota

l He

at f

luxe

s [k

W/m

2 ]

Time [s]

Position 2

Model 2

Model 4

CaPaFi

0

20

40

60

80

100

120

140

0 200 400 600 800 1000 1200 1400 1600

Tota

l He

at f

luxe

s [k

W/m

2 ]

Time [s]

Position 3

Model 2

Model 4

CaPaFi

0

20

40

60

80

100

120

140

0 200 400 600 800 1000 1200 1400 1600

Tota

l He

at f

luxe

s [k

W/m

2]

Time [s]

Position 4

Model 2

Model 4

CaPaFi


Y.C.Wong 120

0

20

40

60

80

100

120

140

0 200 400 600 800 1000 1200 1400 1600

Tota

l He

at f

luxe

s [k

W/m

2]

Time [s]

Position 8

Model 2

Model 4

CaPaFi

0

20

40

60

80

100

120

140

0 200 400 600 800 1000 1200 1400 1600

Tota

l He

at f

luxe

s [k

W/m

2 ]

Time [s]

Position 9

Model 2

Model 4

CaPaFi

0

20

40

60

80

100

120

140

0 200 400 600 800 1000 1200 1400 1600Tota

l He

at f

luxe

s [k

W/m

2]

Time [s]

Position 10

Model 2

Model 4

CaPaFi


Y.C.Wong 121

Appendix 15 Comparison temperatures model 2,4 and CaPaFi

Temperatures Position 3

Position 4

t [s] Model2 Model4 CaPaFi Model 2 Model 4 CaPaFi

0 20 20 20 20 20 20

61 20 20 20 20 20 20

120 21 21 21 20 20 20

181 22 22 22 20 20 21

240 23 23 25 20 20 22

301 24 24 27 21 21 23

360 26 25 30 21 21 24

420 27 26 33 21 21 25

480 28 28 35 21 21 26

540 29 29 37 21 21 26

600 30 29 40 21 21 27

660 31 30 42 21 21 28

720 32 31 44 22 21 29

780 33 32 47 22 22 30

841 34 33 49 22 22 31

900 35 34 51 22 22 32

961 35 34 53 22 22 32

1020 36 35 55 22 22 33

1081 38 37 58 22 22 34

1140 40 39 62 23 23 36

1201 42 41 66 23 23 37

1260 44 43 71 24 24 39

1321 47 45 77 24 24 42

1380 50 48 84 25 25 44

1441 53 50 92 26 26 47

1500 57 54 102 27 27 50


Y.C.Wong 122



0 20 20 20 20 20 20

61 21 21 20 20 20 20

120 24 24 24 21 21 21

181 28 28 30 22 22 22

240 34 33 40 23 23 25

301 39 38 53 25 25 27

360 44 43 65 26 26 30

420 49 47 77 27 27 33

480 54 51 88 28 28 35

540 58 55 99 30 29 37

600 62 59 110 31 30 40

660 66 63 120 32 31 42

720 70 66 130 33 32 44

780 74 70 140 34 33 47

841 77 73 149 35 34 49

900 81 76 158 35 35 51

961 84 79 167 36 35 53

1020 89 83 176 38 37 55

1081 98 90 187 39 38 58

1140 106 99 201 41 40 62

1201 117 109 215 44 42 66

1260 131 120 230 46 44 71

1321 148 136 246 49 47 77

1380 165 157 262 52 50 84

1441 185 172 278 55 53 92

1500 210 202 295 60 57 102


Y.C.Wong 123


t [s] Model 2 Model 4 CaPaFi

0 20 20 20

61 20 20 20

120 20 20 20

181 20 20 21

240 20 20 22

301 21 21 23

360 21 21 24

420 21 21 25

480 21 21 26

540 21 21 26

600 21 21 27

660 21 21 28

720 22 22 29

780 22 22 30

841 22 22 31

900 22 22 32

961 22 22 32

1020 22 22 33

1081 22 22 34

1140 23 23 36

1201 23 23 37

1260 24 24 39

1321 25 25 42

1380 26 25 44

1441 27 26 47

1500 28 28 50

0

100

200

300

400

500

0 200 400 600 800 1000 1200 1400 1600

Tem

pe

ratu

re [

oC

]

Time [s]

Position 1

Model 2

Model 4

CaPaFi


Y.C.Wong 124

0

100

200

300

400

500

0 200 400 600 800 1000 1200 1400 1600

Tem

pe

ratu

re [

oC

]

Time [s]

Position 2

Model 2

Model 4

CaPaFi

0

100

200

300

400

500

0 200 400 600 800 1000 1200 1400 1600

Tem

pe

ratu

re [

oC

]

Time [s]

Position 3

Model 2

Model 4

CaPaFi

0

100

200

300

400

500

0 200 400 600 800 1000 1200 1400 1600

Tem

pe

ratu

re [

oC

]

Time [s]

Position 4

Model 2

Model 4

CaPaFi


Y.C.Wong 125

0

100

200

300

400

500

0 200 400 600 800 1000 1200 1400 1600

Tem

pe

ratu

re [

oC

]

Time [s]

Position 8

Model 2

Model 4

CaPaFi

0

100

200

300

400

500

0 200 400 600 800 1000 1200 1400 1600

Tem

pe

ratu

re [

oC

]

Time [s]

Position 9

Model 2

Model 4

CaPaFi

0

100

200

300

400

500

0 200 400 600 800 1000 1200 1400 1600

Tem

pe

ratu

re [

oC

]

Time [s]

Position 10

Model 2

Model 4

CaPaFi


Y.C.Wong 126

Appendix 16 Comparison Total heat fluxes model 2 and model 5

The heat fluxes of model 2 are already presented in Appendix 9. Only the ones of model 5 will

be presented here and the rest of the graphs of the different positions.


FDS CaPaFi

t[s]

hnet

[kW/m2]

Tmember

[oC]

ε*boltzmann*ΔT

[W/m2]

α*ΔT

[W/m2]

hpunt

[kW/m2]

qtot

[kW/m²]

0 0.00 20.00 0.00 0.00 0.00 0.00

61 2.43 21.11 4.48 12.25 2.45 20.39

120 7.85 24.75 19.48 52.28 7.92 33.39

180 13.90 31.83 50.28 130.16 14.08 39.98

241 21.51 43.13 104.10 254.48 21.87 44.33

300 21.01 55.59 170.47 391.47 21.57 44.33

361 20.48 66.12 232.81 507.31 21.22 44.33

420 22.94 76.97 303.44 626.72 23.87 44.33

480 16.36 87.24 376.53 739.59 17.47 44.33

540 22.89 97.33 454.80 850.63 24.20 44.33

600 23.07 107.31 538.68 960.36 24.57 44.33

661 17.12 115.64 614.07 1052.09 18.79 44.33

720 19.74 123.83 692.96 1142.15 21.57 44.33

781 28.09 134.25 800.64 1256.74 30.15 44.33

840 15.73 141.71 883.03 1338.82 17.95 44.33

900 14.79 149.75 976.94 1427.28 17.19 44.33

961 17.82 158.95 1091.12 1528.46 20.44 44.33

1020 33.21 172.28 1270.01 1675.06 36.16 48.79

1081 39.85 190.62 1543.93 1876.84 43.27 52.07

1140 44.60 209.32 1858.76 2082.56 48.54 54.67

1201 47.54 230.36 2259.35 2313.91 52.11 56.82

1261 47.84 252.46 2738.02 2557.02 53.13 58.68

1320 64.24 277.62 3361.56 2833.77 70.43 60.31

1381 69.40 303.23 4090.69 3115.58 76.61 61.77

1440 76.15 330.47 4980.08 3415.16 84.54 63.09

1500 91.08 363.69 6240.56 3780.56 101.11 68.85

1560 75.02 391.44 7456.45 4085.85 86.56 65.17


Y.C.Wong 127


FDS CaPaFi

t[s]

hnet

[kW/m2]

Tmember

[oC]

ε*boltzmann*ΔT

[W/m2]

α*ΔT

[W/m2]

hpunt

[kW/m2]

qtot

[kW/m²]

0 0.00 20.00 0.00 0.00 0.00 0.00

61 1.52 20.67 2.70 17.66 1.54 5.91

120 3.11 22.30 9.30 60.46 3.18 10.80

180 4.62 24.74 19.43 124.66 4.77 17.77

241 6.10 28.07 33.66 212.33 6.35 23.92

300 6.68 31.73 49.84 308.61 7.04 23.92

361 6.29 35.24 65.91 400.91 6.75 23.92

420 6.18 38.60 81.78 489.10 6.75 23.92

480 6.64 41.91 97.99 576.29 7.31 23.92

540 6.34 45.19 114.53 662.50 7.12 23.92

600 5.95 48.24 130.38 742.72 6.83 23.92

661 5.88 51.41 147.34 826.09 6.85 23.92

720 6.09 54.48 164.22 906.70 7.16 23.92

781 6.09 57.56 181.71 987.88 7.26 23.92

840 5.64 60.57 199.23 1066.99 6.91 23.92

900 5.52 63.42 216.27 1141.98 6.88 23.92

961 6.24 66.41 234.59 1220.46 7.70 23.92

1020 8.87 70.42 259.98 1325.98 10.45 30.13

1081 11.15 75.85 295.82 1468.87 12.92 34.61

1140 13.07 82.88 344.75 1653.80 15.07 38.09

1201 16.47 91.50 408.82 1880.51 18.76 40.95

1261 18.84 102.27 495.47 2163.61 21.50 43.36

1320 33.03 115.37 611.50 2508.19 36.15 45.46

1381 28.98 129.46 750.14 2878.92 32.61 47.32

1440 33.03 146.00 932.46 3313.85 37.28 48.99

1500 65.67 167.44 1203.18 3877.67 70.76 56.04

1560 35.52 185.60 1465.60 4355.22 41.34 51.58


Y.C.Wong 128


FDS CaPaFi

t[s]

hnet

[kW/m2]

Tmember

[oC]

ε*boltzmann*ΔT

[W/m2]

α*ΔT

[W/m2]

hpunt

[kW/m2]

qtot

[kW/m²]

0 0.00 20.00 0.00 0.00 0.00 0.00

61 0.36 20.16 0.64 1.00 0.36 1.34

120 0.72 20.52 2.07 3.26 0.73 2.62

180 0.94 21.02 4.10 6.42 0.95 3.81

241 1.23 21.72 6.96 10.87 1.25 4.96

300 1.39 22.45 9.94 15.46 1.42 4.96

361 1.32 23.18 12.93 20.03 1.35 4.96

420 1.26 23.89 15.88 24.51 1.30 4.96

480 1.35 24.58 18.78 28.88 1.40 4.96

540 1.25 25.28 21.69 33.25 1.31 4.96

600 1.18 25.95 24.54 37.49 1.24 4.96

661 1.20 26.63 27.44 41.78 1.26 4.96

720 1.25 27.32 30.39 46.11 1.33 4.96

781 1.34 27.98 33.25 50.28 1.42 4.96

840 1.27 28.65 36.16 54.49 1.36 4.96

900 1.23 29.28 38.91 58.45 1.33 4.96

961 1.22 29.92 41.73 62.48 1.32 4.96

1020 1.70 30.75 45.41 67.70 1.81 6.57

1081 2.17 31.88 50.48 74.82 2.29 8.12

1140 2.46 33.19 56.43 83.08 2.60 9.65

1201 2.92 34.76 63.68 93.01 3.08 11.14

1261 3.60 36.56 72.09 104.34 3.77 12.63

1320 3.57 38.46 81.12 116.30 3.76 15.77

1381 4.24 40.66 91.79 130.13 4.46 18.43

1440 4.78 42.94 103.13 144.54 5.03 20.79

1500 7.14 45.89 118.14 163.12 7.42 30.42

1560 4.49 48.76 133.11 181.16 4.80 24.38


Y.C.Wong 129


FDS CaPaFi

t[s]

hnet

[kW/m2]

Tmember

[oC]

ε*boltzmann*ΔT

[W/m2]

α*ΔT

[W/m2]

hpunt

[kW/m2]

qtot

[kW/m²]

0 0.00 20.00 0.00 0.00 0.00 0.00

61 0.04 20.02 0.08 -0.02 0.04 0.47

120 0.07 20.06 0.23 -0.05 0.07 0.94

180 0.11 20.11 0.46 -0.10 0.11 1.40

241 0.16 20.20 0.79 -0.18 0.16 1.84

300 0.15 20.28 1.12 -0.25 0.16 1.84

361 0.16 20.37 1.49 -0.33 0.16 1.84

420 0.16 20.46 1.83 -0.41 0.16 1.84

480 0.16 20.54 2.16 -0.48 0.16 1.84

540 0.16 20.62 2.50 -0.56 0.16 1.84

600 0.15 20.71 2.85 -0.64 0.16 1.84

661 0.15 20.79 3.19 -0.72 0.15 1.84

720 0.16 20.88 3.55 -0.80 0.17 1.84

781 0.15 20.96 3.88 -0.87 0.16 1.84

840 0.15 21.05 4.21 -0.94 0.15 1.84

900 0.17 21.13 4.56 -1.02 0.18 1.84

961 0.15 21.21 4.89 -1.09 0.16 1.84

1020 0.22 21.33 5.35 -1.20 0.22 2.46

1081 0.30 21.50 6.03 -1.35 0.31 3.07

1140 0.46 21.71 6.92 -1.54 0.46 3.67

1201 0.56 21.99 8.06 -1.79 0.57 4.25

1261 0.64 22.34 9.49 -2.11 0.65 4.82

1320 0.71 22.72 11.05 -2.45 0.72 5.39

1381 0.90 23.18 12.92 -2.86 0.91 5.96

1440 1.09 23.68 15.01 -3.31 1.11 6.52

1500 1.24 24.35 17.79 -3.91 1.26 9.60

1560 1.00 25.03 20.63 -4.52 1.01 7.51


Y.C.Wong 130


FDS CaPaFi

t[s]

hnet

[kW/m2]

Tmember

[oC]

ε*boltzmann*ΔT

[W/m2]

α*ΔT

[W/m2]

hpunt

[kW/m2]

qtot

[kW/m²]

0 0.00 20.00 0.00 0.00 0.00 0.00

61 1.50 20.70 2.82 7.05 1.51 5.91

120 3.35 22.42 9.82 24.29 3.39 10.80

180 5.07 25.01 20.55 50.17 5.14 17.77

241 6.61 28.69 36.34 87.07 6.73 23.92

300 7.18 32.49 53.24 125.12 7.35 23.92

361 6.79 36.15 70.14 161.80 7.02 23.92

420 6.90 39.69 87.07 197.29 7.19 23.92

480 7.31 43.38 105.35 234.29 7.64 23.92

540 7.10 46.97 123.70 270.20 7.49 23.92

600 6.65 50.45 142.14 305.08 7.09 23.92

661 6.51 53.88 160.94 339.53 7.01 23.92

720 6.32 57.23 179.79 373.01 6.88 23.92

781 6.61 60.67 199.84 407.55 7.22 23.92

840 7.14 63.90 219.15 439.83 7.80 23.92

900 6.18 66.96 238.04 470.52 6.89 23.92

961 6.17 70.15 258.29 502.55 6.94 23.92

1020 9.17 74.56 287.13 546.66 10.01 30.13

1081 13.05 81.30 333.50 614.25 14.00 34.61

1140 15.13 89.55 393.88 696.86 16.22 38.09

1201 25.48 99.77 474.69 799.29 26.75 40.95

1261 26.99 111.42 575.28 916.04 28.48 43.36

1320 22.23 123.60 690.61 1038.03 23.95 45.46

1381 30.43 140.99 874.86 1212.32 32.52 47.32

1440 45.49 157.14 1068.06 1374.15 47.93 48.99

1500 54.65 184.01 1441.40 1643.40 57.74 56.04

1560 58.89 206.13 1802.26 1864.98 62.56 51.58


Y.C.Wong 131


FDS CaPaFi

t[s]

hnet

[kW/m2]

Tmember

[oC]

ε*boltzmann*ΔT

[W/m2]

α*ΔT

[W/m2]

hpunt

[kW/m2]

qtot

[kW/m²]

0 0.00 20.00 0.00 0.00 0.00 0.00

61 0.35 20.17 0.69 1.10 0.36 1.34

120 0.85 20.56 2.24 3.58 0.85 2.62

180 1.07 21.09 4.40 7.01 1.08 3.81

241 1.35 21.86 7.52 11.93 1.37 4.96

300 1.52 22.64 10.72 16.94 1.55 4.96

361 1.40 23.42 13.92 21.92 1.43 4.96

420 1.31 24.17 17.06 26.75 1.35 4.96

480 1.59 24.95 20.32 31.75 1.64 4.96

540 1.30 25.70 23.48 36.55 1.36 4.96

600 1.36 26.44 26.62 41.28 1.43 4.96

661 1.34 27.20 29.87 46.13 1.42 4.96

720 1.43 27.94 33.06 50.87 1.51 4.96

781 1.31 28.64 36.11 55.36 1.40 4.96

840 1.40 29.35 39.25 59.96 1.50 4.96

900 1.35 30.06 42.38 64.51 1.46 4.96

961 1.37 30.77 45.53 69.05 1.48 4.96

1020 1.87 31.69 49.62 74.91 1.99 6.57

1081 2.48 32.93 55.24 82.87 2.62 8.12

1140 2.73 34.34 61.72 91.93 2.88 9.65

1201 3.44 36.05 69.70 102.90 3.61 11.14

1261 3.50 37.90 78.43 114.72 3.69 12.63

1320 3.67 39.92 88.20 127.71 3.89 15.77

1381 4.23 42.30 99.94 142.97 4.48 18.43

1440 4.86 44.69 111.97 158.26 5.13 20.79

1500 7.10 48.21 130.23 180.84 7.42 30.42

1560 5.88 51.44 147.52 201.55 6.23 24.38


Y.C.Wong 132


t[s]

hnet

[kW/m2]

Tmember

[oC]

ε*boltzmann*ΔT

[W/m2]

α*ΔT

[W/m2]

hpunt

[kW/m2]

qtot

[kW/m²]

0 0.00 20.00 0.00 0.00 0.00 0.00

61 0.05 20.02 0.09 0.08 0.05 0.47

120 0.08 20.06 0.26 0.22 0.08 0.94

180 0.12 20.13 0.51 0.43 0.12 1.40

241 0.23 20.22 0.89 0.76 0.23 1.84

300 0.19 20.31 1.26 1.07 0.19 1.84

361 0.17 20.41 1.65 1.41 0.17 1.84

420 0.17 20.51 2.03 1.73 0.18 1.84

480 0.18 20.60 2.41 2.05 0.19 1.84

540 0.18 20.70 2.81 2.39 0.19 1.84

600 0.17 20.79 3.17 2.69 0.17 1.84

661 0.17 20.89 3.56 3.02 0.18 1.84

720 0.17 20.98 3.93 3.33 0.18 1.84

781 0.16 21.07 4.30 3.65 0.17 1.84

840 0.17 21.16 4.68 3.97 0.18 1.84

900 0.19 21.26 5.07 4.29 0.20 1.84

961 0.19 21.35 5.45 4.61 0.20 1.84

1020 0.25 21.48 5.97 5.05 0.26 2.46

1081 0.38 21.66 6.71 5.67 0.39 3.07

1140 0.43 21.90 7.69 6.49 0.44 3.67

1201 0.55 22.20 8.91 7.51 0.57 4.25

1261 0.68 22.57 10.40 8.75 0.70 4.82

1320 1.00 22.99 12.17 10.21 1.02 5.39

1381 0.88 23.47 14.12 11.83 0.90 5.96

1440 1.02 24.01 16.38 13.68 1.05 6.52

1500 1.46 24.77 19.57 16.28 1.49 9.60

1560 1.47 25.49 22.58 18.71 1.51 7.51

0

20

40

60

80

100

120

140

0 200 400 600 800 1000 1200 1400 1600

Tota

l he

at f

luxe

s [k

W/m

2 ]

Time [s]


Model 2

Model 5

CaPaFi


Y.C.Wong 133

0

20

40

60

80

100

120

140

0 200 400 600 800 1000 1200 1400 1600

Tota

l he

at f

luxe

s [k

W/m

2 ]

Time [s]

Total heat fluxes comparison position 2

Model 2

Model 5

CaPaFi

0

20

40

60

80

100

120

140

0 200 400 600 800 1000 1200 1400 1600

Tota

l he

at f

luxe

s [k

W/m

2]

Time [s]


Model 2

Model 5

CaPaFi

0

20

40

60

80

100

120

140

0 200 400 600 800 1000 1200 1400 1600

Tota

l he

at f

luxe

s [k

W/m

2 ]

Time [s]


Model 2

Model 5

CaPaFi


Y.C.Wong 134

0

20

40

60

80

100

120

140

0 200 400 600 800 1000 1200 1400 1600

Tota

l he

at f

luxe

s [k

W/m

2 ]

Time [s]


Model 2

Model 5

CaPaFi

0

20

40

60

80

100

120

140

0 200 400 600 800 1000 1200 1400 1600

Tota

l he

at f

luxe

s [k

W/m

2 ]

Time [s]


Model 2

Model 5

CaPaFi

0

2

4

6

8

10

12

0 200 400 600 800 1000 1200 1400 1600

Tota

l he

at f

luxe

s [k

W/m

2 ]

Time [s]

Total heat fluxes Position 10

Model 2

Model 5

CaPaFi


Y.C.Wong 135

Appendix 17 Comparison Temperatures model 2 and model 5

Temperatures Position 1 Position 2 Position 3

t [s]

Model

2

Model

5 CaPaFi

Model

2

Model

5 CaPaFi

Model

2

Model

5 CaPaFi

0 20.00 20.00 20 20.00 20.00 20 20.00 20.00 20

61 22.68 21.11 21 21.33 20.67 20 20.34 20.16 20

120 28.94 24.75 33 23.98 22.30 24 21.06 20.52 21

181 39.56 31.83 52 27.81 24.74 30 22.06 21.02 22

240 54.65 43.13 73 32.48 28.07 40 23.24 21.72 25

301 70.01 55.59 95 37.34 31.73 53 24.42 22.45 27

360 84.69 66.12 116 42.11 35.24 65 25.65 23.18 30

420 97.87 76.97 137 46.50 38.60 77 26.79 23.89 33

480 110.41 87.24 156 50.85 41.91 88 27.91 24.58 35

540 122.54 97.33 175 54.75 45.19 99 28.96 25.28 37

600 134.02 107.31 193 58.86 48.24 110 30.02 25.95 40

660 144.00 115.64 210 62.52 51.41 120 31.02 26.63 42

720 154.14 123.83 227 66.36 54.48 130 31.95 27.32 44

780 163.42 134.25 243 69.78 57.56 140 32.85 27.98 47

841 172.29 141.71 259 72.86 60.57 149 33.66 28.65 49

900 180.68 149.75 274 76.17 63.42 158 34.58 29.28 51

961 188.32 158.95 289 79.12 66.41 167 35.36 29.92 53

1020 202.61 172.28 303 83.50 70.42 176 36.43 30.75 55

1081 222.32 190.62 318 90.51 75.85 187 37.98 31.88 58

1140 242.49 209.32 334 98.56 82.88 201 39.79 33.19 62

1201 264.39 229.60 351 108.54 91.29 215 41.95 34.73 66

1260 286.23 252.46 368 120.25 102.27 230 44.21 36.56 71

1321 310.13 278.15 385 135.39 116.53 246 46.93 38.60 77

1380 335.14 303.23 402 150.40 129.46 262 49.67 40.66 84

1441 361.23 330.47 419 168.44 146.00 278 52.82 42.94 92

1500 395.98 363.69 435 193.52 167.44 295 57.24 45.89 102


Y.C.Wong 136


t [s]

Model

2

Model

5 CaPaFi

Model

2

Model

5 CaPaFi

Model

2

Model

5 CaPaFi

0 20.00 20.00 20.00 20.00 20.00 20 20.00 20.00 20

61 20.03 20.02 20.00 21.43 20.70 20 20.38 20.17 20

120 20.11 20.06 20.00 24.22 22.42 24 21.09 20.56 21

181 20.23 20.11 21.00 28.43 25.01 30 22.18 21.09 22

240 20.39 20.20 22.00 33.72 28.69 40 23.47 21.86 25

301 20.54 20.28 23.00 38.98 32.49 53 24.79 22.64 27

360 20.70 20.37 24.00 44.09 36.15 65 26.00 23.42 30

420 20.83 20.46 25.00 49.12 39.69 77 27.24 24.17 33

480 20.97 20.54 26.00 53.89 43.38 88 28.50 24.95 35

540 21.13 20.62 26.00 58.01 46.97 99 29.51 25.70 37

600 21.26 20.71 27.00 62.45 50.45 110 30.64 26.44 40

660 21.40 20.79 28.00 66.48 53.88 120 31.67 27.20 42

720 21.53 20.88 29.00 70.43 57.23 130 32.77 27.94 44

780 21.65 20.96 30.00 73.88 60.67 140 33.69 28.64 47

841 21.75 21.05 31.00 77.44 63.90 149 34.52 29.35 49

900 21.85 21.13 32.00 80.78 66.96 158 35.47 30.06 51

961 21.94 21.21 32.00 84.21 70.15 167 36.38 30.77 53

1020 22.11 21.33 33.00 88.88 74.56 176 37.51 31.69 55

1081 22.36 21.50 34.00 97.66 81.30 187 39.29 32.93 58

1140 22.75 21.71 36.00 105.83 89.55 201 41.16 34.34 62

1201 23.26 21.98 37.00 117.15 99.19 215 43.57 36.00 66

1260 23.74 22.34 39.00 130.67 111.42 230 46.06 37.90 71

1321 24.39 22.74 42.00 148.44 123.79 246 49.02 39.98 77

1380 25.15 23.18 44.00 165.25 140.99 262 52.11 42.30 84

1441 26.07 23.68 47.00 184.54 157.14 278 55.39 44.69 92

1500 27.40 24.35 50.00 210.22 184.01 295 59.73 48.21 102


Y.C.Wong 137

0

50

100

150

200

250

300

350

400

450

0 200 400 600 800 1000 1200 1400 1600

Tem

pe

ratu

re [

oC

]

Time[s]


Model2

Model5

CaPaFi


t [s]

Model

2

Model

5 CaPaFi

0 20.00 20.00 20

61 20.04 20.02 20

120 20.11 20.06 20

181 20.24 20.13 21

240 20.44 20.22 22

301 20.60 20.31 23

360 20.75 20.41 24

420 20.90 20.51 25

480 21.07 20.60 26

540 21.21 20.70 26

600 21.34 20.79 27

660 21.46 20.89 28

720 21.60 20.98 29

780 21.69 21.07 30

841 21.83 21.16 31

900 21.94 21.26 32

961 22.06 21.35 32

1020 22.25 21.48 33

1081 22.49 21.66 34

1140 22.82 21.90 36

1201 23.39 22.20 37

1260 24.02 22.57 39

1321 24.70 22.99 42

1380 25.66 23.47 44

1441 26.63 24.01 47

1500 28.02 24.77 50


Y.C.Wong 138

0

50

100

150

200

250

300

350

400

450

0 200 400 600 800 1000 1200 1400 1600

Tem

pe

ratu

re [

oC

]

Time [s]


Model2

Model5

CaPaFi

0

50

100

150

200

250

300

350

400

450

0 200 400 600 800 1000 1200 1400 1600

Tem

pe

ratu

re [

oC

]

Time [s]


Model2

Model5

CaPaFi

0

50

100

150

200

250

300

350

400

450

0 200 400 600 800 1000 1200 1400 1600

Tem

pe

ratu

re [

oC

]

Time [s]


Model2

Model5

CaPaFi


Y.C.Wong 139

0

50

100

150

200

250

300

350

400

450

0 200 400 600 800 1000 1200 1400 1600

Tem

pe

ratu

re [

oC

]

Time [s]


Model2

Model5

CaPaFi

0

50

100

150

200

250

300

350

400

450

0 200 400 600 800 1000 1200 1400 1600

Tem

pe

ratu

re [

oC

]

Time [s]


Model2

Model5

CaPaFi

0

50

100

150

200

250

300

350

400

450

0 200 400 600 800 1000 1200 1400 1600

Tem

pe

ratu

re [

oC

]

Time [s]


Model2

Model5

CaPaFi


Y.C.Wong 140

Appendix 18 Convective heat transfer coefficient Model 5

The calculation of the convection coefficient of the steel for model 5 is presented. This is done to

verify the calculated value by FDS with the Eurocodes. The value in the yellow block is the

averaged value of the convection coefficient.


t[s]

qconv

[kW/m2]

Tgas

[oC]

Tmember

[oC]

αC

[W/m2 K]

qconv

[kW/m2]

Tgas

[oC]

Tmember

[oC]

αC

[W/m2 K]

0 0 20 20 --- 0 20 20 ---

61 0.83 133.78 21.11 7.36 0.83 68.15 20.67 17.46

120 1.83 229.32 24.75 8.97 1.83 92.77 22.30 26.03

181 2.92 321.73 32.11 10.07 2.92 145.79 24.82 24.10

241 4.49 443.00 43.13 11.22 4.49 129.37 28.07 44.28

301 4.07 427.58 55.66 10.95 4.07 131.78 31.79 40.74

361 4.08 438.05 66.12 10.97 4.08 161.73 35.24 32.27

420 4.35 467.48 76.97 11.15 4.35 127.75 38.60 48.83

480 2.86 372.01 87.24 10.03 2.86 200.33 41.91 18.03

540 4.15 474.65 97.33 11.00 4.15 178.59 45.19 31.11

600 4.17 485.41 107.31 11.02 4.17 141.92 48.24 44.48

661 3.07 416.14 115.64 10.23 3.07 157.08 51.41 29.08

720 3.00 412.87 123.83 10.39 3.00 165.42 54.48 27.07

781 4.62 540.16 134.25 11.37 4.62 164.72 57.56 43.07

840 2.38 389.48 141.71 9.60 2.38 157.54 60.57 24.54

900 1.89 358.08 149.75 9.07 1.89 139.99 63.42 24.67

961 2.45 412.02 158.95 9.70 2.45 176.90 66.41 22.21

1020 4.69 583.95 172.28 11.39 4.69 216.18 70.42 32.17

1081 5.33 643.70 190.62 11.77 5.33 255.67 75.85 29.65

1140 5.29 659.40 209.32 11.75 5.29 269.00 82.88 28.42

1200 4.96 659.37 229.60 11.53 4.96 341.98 91.29 19.77

1261 4.89 677.15 252.46 11.52 4.89 397.69 102.27 16.56

1320 6.27 789.96 277.62 12.23 6.27 644.32 115.37 11.85

1381 5.86 789.47 303.23 12.05 5.86 523.34 129.46 14.87

1440 6.16 832.88 330.47 12.27 6.16 596.28 146.00 13.69

1500 7.00 921.92 363.69 12.55 7.00 925.52 167.44 9.24

1560 4.06 756.44 391.44 11.11 4.06 626.32 185.60 9.20

10.82

26.28


Y.C.Wong 141


t[s]

qconv

[kW/m2]

Tgas

[oC]

Tmember

[oC]

αC

[W/m2 K]

qconv

[kW/m2]

Tgas

[oC]

Tmember

[oC]

αC

[W/m2 K]

0 0 20 20 --- 0 20 20 ---

61 0.05 34.32 20.16 3.70 0.00 21.11 20.16 1.91

120 0.14 48.90 20.52 4.88 0.00 21.16 20.52 2.69

181 0.24 64.65 21.04 5.61 0.01 23.70 21.04 3.17

241 0.16 52.96 21.72 5.26 0.02 26.84 21.72 3.89

301 0.27 70.10 22.48 5.74 0.00 22.03 22.48 -7.25

361 0.29 73.79 23.18 5.73 0.02 26.30 23.18 5.48

420 0.17 55.65 23.89 5.31 0.01 24.68 23.89 13.34

480 0.32 77.59 24.58 5.97 0.01 24.45 24.58 -77.94

540 0.23 64.30 25.28 5.82 0.01 24.90 25.28 -31.21

600 0.12 51.55 25.95 4.70 0.01 23.56 25.95 -2.58

661 0.15 52.86 26.63 5.72 0.00 22.74 26.63 -0.96

720 0.20 63.45 27.32 5.50 0.01 25.78 27.32 -8.52

781 0.32 81.05 27.98 6.11 0.01 25.28 27.98 -4.13

840 0.28 76.87 28.65 5.82 0.01 24.35 28.65 -1.79

900 0.12 53.39 29.28 5.16 0.01 24.99 29.28 -2.52

961 0.16 60.10 29.92 5.31 0.00 22.88 29.92 -0.43

1020 0.32 84.15 30.75 5.94 0.01 24.29 30.75 -1.03

1081 0.49 101.80 31.88 7.02 0.03 30.25 31.88 -17.08

1140 0.44 95.47 33.19 6.99 0.06 37.15 33.19 16.25

1200 0.66 125.37 34.73 7.25 0.03 29.91 34.73 -5.65

1261 0.94 152.23 36.56 8.13 0.08 40.59 36.56 19.94

1320 0.75 135.81 38.46 7.66 0.16 53.77 38.46 10.48

1381 0.99 165.36 40.66 7.97 0.21 61.37 40.66 10.06

1440 1.33 197.84 42.94 8.56 0.34 79.18 42.94 9.47

1500 2.05 254.62 45.89 9.84 0.28 71.75 45.89 10.65

1560 0.67 137.96 48.76 7.52 0.15 53.53 48.76 31.40

6.28

-0.86


Y.C.Wong 142


t[s]

qconv

[kW/m2]

Tgas

[oC]

Tmember

[oC]

αC

[W/m2 K]

qconv

[kW/m2]

Tgas

[oC]

Tmember

[oC]

αC

[W/m2 K]

0 0 20 20 --- 0 20 20 ---

61 0.29 62.26 20.70 6.90 0.03 28.05 20.17 3.20

120 0.69 106.57 22.42 8.21 0.23 60.53 20.56 5.67

181 1.29 162.93 25.10 9.33 0.24 61.98 21.11 5.84

241 1.01 138.71 28.69 9.16 0.23 63.06 21.86 5.61

301 1.11 154.14 32.52 9.16 0.26 69.15 22.66 5.61

361 1.37 179.71 36.15 9.56 0.28 71.84 23.42 5.73

420 1.03 151.26 39.69 9.23 0.12 49.97 24.17 4.61

480 1.59 208.04 43.38 9.65 0.41 85.92 24.95 6.73

540 1.42 191.17 46.97 9.85 0.20 60.76 25.70 5.60

600 1.19 178.34 50.45 9.27 0.22 66.26 26.44 5.53

661 0.93 155.03 53.88 9.18 0.17 58.83 27.20 5.31

720 0.84 149.98 57.23 9.08 0.29 78.26 27.94 5.85

781 1.01 167.41 60.67 9.50 0.20 60.39 28.64 6.37

840 1.38 205.25 63.90 9.76 0.25 73.00 29.35 5.67

900 0.79 152.11 66.96 9.29 0.18 60.99 30.06 5.78

961 0.94 177.19 70.15 8.76 0.21 68.86 30.77 5.49

1020 1.55 235.85 74.56 9.60 0.41 91.54 31.69 6.90

1081 2.31 307.81 81.30 10.21 0.61 115.74 32.93 7.43

1140 2.45 326.59 89.55 10.33 0.62 124.18 34.34 6.95

1200 3.81 442.04 99.19 11.12 0.52 111.57 36.00 6.91

1261 4.77 518.48 111.42 11.71 0.63 118.08 37.90 7.91

1320 3.19 422.28 123.60 10.69 0.71 132.25 39.92 7.68

1381 4.60 526.91 140.99 11.91 0.80 145.68 42.30 7.74

1440 7.30 723.54 157.14 12.88 1.08 174.81 44.69 8.29

1500 8.23 801.47 184.01 13.33 2.13 266.32 48.21 9.77

1560 7.12 760.15 206.13 12.85 1.37 211.42 51.44 8.57

10.02

6.41


Y.C.Wong 143

Position 10

t[s]

qconv

[kW/m2]

Tgas

[oC]

Tmember

[oC]

αC

[W/m2 K]

0 0 20 20 ---

61 0.00 20.87 20.02 1.58

120 0.00 21.47 20.06 1.72

181 0.00 21.89 20.13 1.83

241 0.07 36.85 20.22 4.27

301 0.01 24.37 20.32 2.50

361 0.01 23.22 20.41 2.15

420 0.01 23.40 20.51 2.19

480 0.01 23.56 20.60 2.24

540 0.02 27.03 20.70 2.90

600 0.01 23.28 20.79 2.11

661 0.00 22.96 20.89 2.03

720 0.00 23.10 20.98 2.33

781 0.00 22.13 21.07 1.57

840 0.00 23.04 21.16 1.95

900 0.01 24.85 21.26 2.63

961 0.02 28.03 21.35 3.51

1020 0.02 27.30 21.48 2.75

1081 0.06 36.62 21.66 4.29

1140 0.02 29.83 21.90 3.08

1200 0.16 52.99 22.20 5.05

1261 0.09 42.37 22.57 4.34

1320 0.42 84.13 22.99 6.83

1381 0.13 49.93 23.47 5.06

1440 0.21 61.22 24.01 5.70

1500 0.42 85.68 24.77 6.83

1560 0.50 95.16 25.49 7.23

3.41


Y.C.Wong 144

Appendix 19 Comparison Total heat fluxes model 2 and model 3

Total heat

fluxes Position 1 Position 2 Position 3 Position 4

t [s]

Model

2

Model

3

Model

2

Model

3

Model

2

Model

3

Model

2

Model

3

0 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

61 5.60 5.58 2.90 2.96 0.75 0.80 0.08 0.07

120 12.79 14.02 5.11 5.69 1.26 1.44 0.20 0.15

181 20.06 21.75 7.44 7.00 1.94 2.01 0.26 0.19

240 37.20 29.21 9.63 9.61 2.45 2.80 0.24 0.36

301 32.64 28.32 9.25 9.20 2.25 2.45 0.36 0.27

360 31.38 32.38 10.63 11.62 2.53 3.40 0.27 0.36

420 34.47 34.76 10.19 11.38 3.02 3.13 0.26 0.22

480 29.80 34.70 11.04 9.81 2.76 2.64 0.34 0.27

540 34.42 31.09 9.82 9.82 2.58 2.73 0.82 0.32

600 36.82 33.37 10.68 9.52 2.71 2.11 0.30 0.44

660 31.99 34.25 10.38 9.82 2.94 2.37 0.79 0.34

720 29.92 31.03 10.83 9.81 2.42 2.97 0.39 0.32

780 28.61 30.85 10.55 9.03 2.84 2.39 0.45 0.31

841 30.09 31.16 9.89 9.88 2.23 2.47 0.25 0.25

900 28.08 30.09 9.82 9.92 2.62 2.33 0.25 0.35

961 28.58 28.45 10.04 10.86 2.67 3.18 0.25 0.33

1020 42.82 52.85 12.96 14.56 3.40 4.17 0.46 0.48

1081 59.68 63.40 22.97 17.76 4.45 4.38 0.49 0.82

1140 63.55 63.12 22.40 21.21 4.95 4.47 1.26 0.74

1201 78.43 76.09 27.34 26.35 5.68 5.70 1.84 0.95

1260 81.22 74.35 28.29 25.96 6.14 5.94 1.26 1.42

1321 90.36 75.18 46.13 38.54 7.35 7.41 1.79 1.84

1380 93.84 92.24 42.43 36.49 6.94 7.91 1.58 1.93

1441 91.92 84.00 54.89 44.68 9.13 8.38 1.59 2.12

1500 126.68 125.09 58.45 57.00 11.10 10.17 2.99 2.94


Y.C.Wong 145

Total heat

fluxes Position 8 Position 9 Position 10

t [s] Model 2 Model 3

Model

2

Model

3

Model

2

Model

3

0 0.00 0.00 0.00 0.00 0.00 0.00

61 3.11 3.07 0.96 0.68 0.07 0.08

120 5.50 5.54 1.20 1.72 0.13 0.16

181 8.22 8.29 2.03 1.83 0.17 0.21

240 10.93 10.07 2.42 2.38 0.72 0.23

301 9.41 10.48 2.49 2.35 0.31 0.24

360 10.48 12.84 2.31 3.13 0.26 0.31

420 11.39 10.62 2.59 2.77 0.43 0.27

480 10.29 11.74 2.84 3.22 0.66 0.28

540 10.95 11.11 2.53 2.79 0.50 0.31

600 10.47 10.79 2.76 2.49 0.48 0.29

660 10.77 11.52 2.67 3.36 0.33 0.31

720 11.71 12.11 3.16 3.36 0.41 0.37

780 11.03 9.78 3.02 2.37 0.26 0.26

841 10.71 11.84 2.29 3.64 0.33 0.47

900 11.10 10.44 2.80 2.39 0.36 0.32

961 12.49 11.58 3.51 2.96 0.38 0.48

1020 13.98 16.41 3.06 4.12 0.58 0.42

1081 24.48 19.76 4.75 4.24 0.54 0.60

1140 25.06 30.98 5.10 5.24 0.66 0.75

1201 28.74 32.85 5.89 6.58 1.25 0.79

1260 33.74 39.72 6.93 7.29 1.69 1.47

1321 52.27 36.51 8.81 7.14 1.65 2.09

1380 42.72 46.35 7.30 9.03 1.94 2.21

1441 49.30 79.69 8.14 10.81 1.82 2.56

1500 75.38 98.84 11.22 15.96 2.66 2.66


Y.C.Wong 146

Appendix 20 Comparison temperatures model 2 and model 3

Temperatures Position 1 Position 2 Position 3 Position 4

t [s]

Model

2

Model

3

Model

2

Model

3

Model

2

Model

3

Model

2

Model

3

0 20 20 20 20 20 20 20 20

61 23 24 21 22 20 20 20 20

120 29 33 24 26 21 22 20 20

181 40 51 28 33 22 23 20 20

240 55 76 32 41 23 25 20 21

301 70 104 37 49 24 27 21 21

360 85 129 42 57 26 30 21 21

420 98 150 47 65 27 31 21 21

480 110 170 51 71 28 33 21 22

540 123 186 55 77 29 35 21 22

600 134 202 59 82 30 36 21 22

660 144 215 63 88 31 38 21 22

720 154 227 66 92 32 39 22 22

780 163 237 70 96 33 40 22 22

841 172 247 73 100 34 41 22 23

900 181 255 76 103 35 42 22 23

961 188 263 79 107 35 43 22 23

1020 203 278 83 112 36 45 22 23

1081 222 302 91 122 38 47 22 23

1140 242 327 99 133 40 49 23 24

1201 264 353 109 147 42 52 23 25

1260 286 382 120 165 44 56 24 26

1321 310 413 135 185 47 60 24 27

1380 335 443 150 208 50 64 25 28

1441 361 472 168 234 53 69 26 30

1500 396 516 194 265 57 75 27 31


Y.C.Wong 147


t [s]

Model

2

Model

3

Model

2

Model

3

Model

2

Model

3

0 20 20 20 20 20 20

61 21 22 20 20 20 20

120 24 26 21 22 20 20

181 28 34 22 24 20 20

240 34 42 23 26 20 21

301 39 52 25 28 21 21

360 44 61 26 30 21 21

420 49 68 27 32 21 21

480 54 76 28 34 21 22

540 58 81 30 36 21 22

600 62 88 31 37 21 22

660 66 93 32 39 21 22

720 70 99 33 41 22 23

780 74 103 34 42 22 23

841 77 107 35 43 22 23

900 81 110 35 44 22 23

961 84 114 36 45 22 23

1020 89 120 38 46 22 23

1081 98 130 39 49 22 24

1140 106 144 41 51 23 24

1201 117 162 44 55 23 25

1260 131 182 46 59 24 26

1321 148 202 49 63 25 27

1380 165 228 52 67 26 29

1441 185 261 55 73 27 30

1500 210 299 60 80 28 32

0

100

200

300

400

500

600

0 200 400 600 800 1000 1200 1400 1600

Tem

pe

ratu

re [

oC

]

Time[s]


Model 2

Model 3


Y.C.Wong 148

0

100

200

300

400

500

600

0 200 400 600 800 1000 1200 1400 1600

Tem

pe

ratu

re [

oC

]

Time[s]


Model 2

Model 3

0

100

200

300

400

500

600

0 200 400 600 800 1000 1200 1400 1600

Tem

pe

ratu

re [

oC

]

Time[s]


Model 2

Model 3

0

100

200

300

400

500

600

0 200 400 600 800 1000 1200 1400 1600

Tem

pe

ratu

re [

oC

]

Time[s]


Model 2

Model 3


Y.C.Wong 149

0

100

200

300

400

500

600

0 200 400 600 800 1000 1200 1400 1600

Tem

pe

ratu

re [

oC

]

Time[s]


Model 2

Model 3

0

100

200

300

400

500

600

0 200 400 600 800 1000 1200 1400 1600

Tem

pe

ratu

re [

oC

]

Time[s]


Model 2

Model 3

0

100

200

300

400

500

600

0 200 400 600 800 1000 1200 1400 1600

Tem

pe

ratu

re [

oC

]

Time[s]


Model 2

Model 3


Y.C.Wong 150

Appendix 21 Script of FDS (model 6)

&HEAD CHID='model6', TITLE='model6'/ For 3 cars with obstacles: 2 beams

&TIME T_END=2500/

MISC RESTART=.TRUE.

----Fuel (UIT HET VOORBEELD V DE HALVE AUTO OOK UIT SFPE) ---


FYI='SFPE',

FUEL='REAC_FUEL',

FORMULA='C7H16',

HRRPUA_SHEET=0.0,

CO_YIELD=0.01,

SOOT_YIELD=0.037,


IDEAL=.TRUE./

------ Spaces------

&MESH IJK=150,160,28, XB=0,15,0,16,0,2.8/ With the cars 10cm mesh ->150,160,28)

&MESH IJK=22.5,120,14, XB=-4.5,0,-4,20,0,2.8/Mesh 2 (meshes of 20cm )

&MESH IJK=22.5,120,14, XB=15,19.5,-4,20,0,2.8/ Mesh 3 (meshes of 20cm)

&MESH IJK=75,20,14, XB=0,15,-4,0,0,2.8/ Mesh 4 (meshes of 20cm)

&MESH IJK=75,20,14, XB=0,15,16,20,0,2.8/ Mesh 5 (meshes of 20cm)

------ Cars and the properties -----

&SURF ID='car1',

color='RED',

HRRPUA= 658.730,

RAMP_Q='car1_fire'/ (OPPERVLAKTE DAT IN BRAND STAAT IS 12.6M2 WANT 4.8X1.8+

2x4.8x0.3+ 2x1.8x0.3)









&SURF ID='car2',

RGB=34,139,34,

HRRPUA= 658.730,

RAMP_Q='car2_fire'/ (Green car, burning surface is 12.6M2: 4.8X1.8+ 2x4.8x0.3+ 2x1.8x0.3)


Y.C.Wong 151










&SURF ID='car3',

RGB=255,0,255,

HRRPUA= 658.730,

RAMP_Q='car3_fire'/ (Magenta car, burning surface is 12.6M2: 4.8X1.8+ 2x4.8x0.3+ 2x1.8x0.3)










&OBST XB= 6.6, 8.4, 0.4,5.2, 0,0.3, SURF_ID6='car1','car1','car1','car1','INERT','car1'/ (top side and the sides are

on fire)

&OBST XB= 4.1,5.9, 0.4,5.2, 0,0.3, SURF_ID6='car2','car2','car2','car2','INERT','car2'/ (top side and the sides are

on fire)

&OBST XB= 9.1,10.9, 0.4,5.2, 0,0.3, SURF_ID6='car3','car3','car3','car3','INERT','car3'/ top side and the sides are

on fire)

------ Properties of steel beams ------




DENSITY=7850.0,

EMISSIVITY=0.7/














Y.C.Wong 152
















&SURF ID='STEEL1',



THICKNESS= 0.032

RGB=105,105,105/

&OBST XB= 0,15, 0,0.3, 2.3,2.8, RGB= 105,105,105,

SURF_ID6='INERT','INERT','STEEL1','STEEL1','STEEL1','INERT'/ fictitious beam "my profile"

&OBST XB= 0,15, 15.7,16, 2.3,2.8, RGB= 105,105,105,

SURF_ID6='INERT','INERT','STEEL1','STEEL1','STEEL1','INERT'/ fictitious beam "my profile"

--- Concrete properties ----

&MATL ID='CONCRETE_EURO',

SPECIFIC_HEAT_RAMP='CONCRETE_EURO_SPECIFIC_HEAT_RAMP',

CONDUCTIVITY_RAMP='CONCRETE_EURO_CONDUCTIVITY_RAMP',

DENSITY=2500/














&RAMP ID='CONCRETE_EURO_SPECIFIC_HEAT_RAMP', T=1200,F=1.1/


Y.C.Wong 153















&SURF ID='CONCRETE',

MATL_ID = 'CONCRETE_EURO',

THICKNESS=0.4

RGB=84,255,159/

---Floor and ceiling --

&VENT SURF_ID='CONCRETE', MB='ZMIN'/ floor

&VENT SURF_ID='CONCRETE', MB='ZMAX'/ ceiling

--- walls ---

&VENT SURF_ID='OPEN',MB='YMIN', COLOR='INVISIBLE'/ front side

&VENT SURF_ID='OPEN',MB='YMAX' , COLOR='INVISIBLE'/ back side

&VENT SURF_ID='OPEN',MB= 'XMIN', COLOR='INVISIBLE'/ left side

&VENT SURF_ID='OPEN',MB= 'XMAX' , COLOR='INVISIBLE'/ right side

--- Devices ----

Devices 5,6,7,11,12 on the ceiling terwijl 1,2,3,4,8,9,10 are on the member ----

&DEVC ID='INC-FLUX1', QUANTITY='INCIDENT HEAT FLUX', XYZ= 2 , 0.15 , 2.3, IOR= -3/

&DEVC ID='INC-FLUX2', QUANTITY='INCIDENT HEAT FLUX', XYZ= 6.3, 0.15 , 2.3, IOR= -3/

&DEVC ID='INC-FLUX3', QUANTITY='INCIDENT HEAT FLUX', XYZ= 8.8, 0.15 , 2.3, IOR= -3/

&DEVC ID='INC-FLUX4', QUANTITY='INCIDENT HEAT FLUX', XYZ= 13 , 0.15 , 2.3, IOR= -3/

&DEVC ID='INC-FLUX5', QUANTITY='INCIDENT HEAT FLUX', XYZ= 2 , 15.85, 2.3, IOR= -3/

&DEVC ID='INC-FLUX6', QUANTITY='INCIDENT HEAT FLUX', XYZ= 6.3, 15.85, 2.3, IOR= -3/


&DEVC ID='INC-FLUX8', QUANTITY='INCIDENT HEAT FLUX', XYZ= 13 , 15.85, 2.3, IOR= -3/

&DEVC ID='INC-FLUX9', QUANTITY='INCIDENT HEAT FLUX', XYZ= 0, 2.8, 2.8, IOR= -3/









&DEVC ID='INC-FLUX18', QUANTITY='INCIDENT HEAT FLUX', XYZ= 7.5, 8, 2.8, IOR= -3/


Y.C.Wong 154





&DEVC ID='INC-FLUX23', QUANTITY='INCIDENT HEAT FLUX', XYZ= 7.5, 12, 2.8, IOR= -3/



&DEVC ID='INC-FLUX26', QUANTITY='INCIDENT HEAT FLUX', XYZ= 2, 0.3, 2.6, IOR= 2/


&DEVC ID='INC-FLUX28', QUANTITY='INCIDENT HEAT FLUX', XYZ= 6.3, 0.3, 2.6, IOR= 2/









---36

&DEVC ID='NET-FLUX1', QUANTITY='NET HEAT FLUX', XYZ= 2, 0.15, 2.3, IOR=-3/

&DEVC ID='NET-FLUX2', QUANTITY='NET HEAT FLUX', XYZ= 6.3, 0.15, 2.3, IOR=-3/
















&DEVC ID='NET-FLUX18', QUANTITY='NET HEAT FLUX', XYZ= 7.5, 8, 2.8, IOR=-3/





&DEVC ID='NET-FLUX23', QUANTITY='NET HEAT FLUX', XYZ= 7.5, 12, 2.8, IOR=-3/



&DEVC ID='NET-FLUX26', QUANTITY='NET HEAT FLUX', XYZ= 2, 0.3, 2.6, IOR= 2/


&DEVC ID='NET-FLUX28', QUANTITY='NET HEAT FLUX', XYZ= 6.3, 0.3, 2.6, IOR= 2/






Y.C.Wong 155

&DEVC ID='NET-FLUX33', QUANTITY='NET HEAT FLUX', XYZ= 2, 15.7, 2.6, IOR= -2/

&DEVC ID='NET-FLUX34', QUANTITY='NET HEAT FLUX', XYZ= 6.3, 15.7, 2.6, IOR= -2/

&DEVC ID='NET-FLUX35', QUANTITY='NET HEAT FLUX', XYZ= 8.8, 15.7, 2.6, IOR= -2/

&DEVC ID='NET-FLUX36', QUANTITY='NET HEAT FLUX', XYZ= 13, 15.7, 2.6, IOR= -2/

----72

&DEVC ID='RAD-FLUX1', QUANTITY='RADIATIVE HEAT FLUX', XYZ= 2, 0.15, 2.3, IOR=-3/

&DEVC ID='RAD-FLUX2', QUANTITY='RADIATIVE HEAT FLUX', XYZ= 6.3, 0.15, 2.3, IOR=-3/














&DEVC ID='RAD-FLUX16', QUANTITY='RADIATIVE HEAT FLUX', XYZ= 2, 8, 2.8, IOR=-3/


&DEVC ID='RAD-FLUX18', QUANTITY='RADIATIVE HEAT FLUX', XYZ= 7.5, 8, 2.8, IOR=-3/





&DEVC ID='RAD-FLUX23', QUANTITY='RADIATIVE HEAT FLUX', XYZ= 7.5, 12, 2.8, IOR=-3/



&DEVC ID='RAD-FLUX26', QUANTITY='RADIATIVE HEAT FLUX', XYZ= 2, 0.3, 2.6, IOR= 2/


&DEVC ID='RAD-FLUX28', QUANTITY='RADIATIVE HEAT FLUX', XYZ= 6.3, 0.3, 2.6, IOR= 2/





&DEVC ID='RAD-FLUX33', QUANTITY='RADIATIVE HEAT FLUX', XYZ= 2, 15.7, 2.6, IOR= -2/

&DEVC ID='RAD-FLUX34', QUANTITY='RADIATIVE HEAT FLUX', XYZ= 6.3, 15.7, 2.6, IOR= -2/

&DEVC ID='RAD-FLUX35', QUANTITY='RADIATIVE HEAT FLUX', XYZ= 8.8, 15.7, 2.6, IOR= -2/

&DEVC ID='RAD-FLUX36', QUANTITY='RADIATIVE HEAT FLUX', XYZ= 13, 15.7, 2.6, IOR= -2/

----108

&DEVC ID='CONV-FLUX1', QUANTITY='CONVECTIVE HEAT FLUX', XYZ= 2, 0.15, 2.3, IOR=-3/

&DEVC ID='CONV-FLUX2', QUANTITY='CONVECTIVE HEAT FLUX', XYZ= 6.3, 0.15, 2.3, IOR=-3/








Y.C.Wong 156








&DEVC ID='CONV-FLUX16', QUANTITY='CONVECTIVE HEAT FLUX', XYZ= 2, 8, 2.8, IOR=-3/


&DEVC ID='CONV-FLUX18', QUANTITY='CONVECTIVE HEAT FLUX', XYZ= 7.5, 8, 2.8, IOR=-3/





&DEVC ID='CONV-FLUX23', QUANTITY='CONVECTIVE HEAT FLUX', XYZ= 7.5, 12, 2.8, IOR=-3/



&DEVC ID='CONV-FLUX26', QUANTITY='CONVECTIVE HEAT FLUX', XYZ= 2, 0.3, 2.6, IOR= 2/


&DEVC ID='CONV-FLUX28', QUANTITY='CONVECTIVE HEAT FLUX', XYZ= 6.3, 0.3, 2.6, IOR= 2/





&DEVC ID='CONV-FLUX33', QUANTITY='CONVECTIVE HEAT FLUX', XYZ= 2, 15.7, 2.6, IOR= -2/

&DEVC ID='CONV-FLUX34', QUANTITY='CONVECTIVE HEAT FLUX', XYZ= 6.3, 15.7, 2.6, IOR= -2/

&DEVC ID='CONV-FLUX35', QUANTITY='CONVECTIVE HEAT FLUX', XYZ= 8.8, 15.7, 2.6, IOR= -2/

&DEVC ID='CONV-FLUX36', QUANTITY='CONVECTIVE HEAT FLUX', XYZ= 13, 15.7, 2.6, IOR= -2/

-------144

&DEVC ID='Tmember-1', QUANTITY ='WALL TEMPERATURE', XYZ= 2, 0.15, 2.3, IOR=-3/

&DEVC ID='Tmember-2', QUANTITY ='WALL TEMPERATURE', XYZ= 6.3, 0.15, 2.3, IOR=-3/
















&DEVC ID='Tmember-18', QUANTITY ='WALL TEMPERATURE', XYZ= 7.5, 8, 2.8, IOR=-3/






Y.C.Wong 157

&DEVC ID='Tmember-23', QUANTITY ='WALL TEMPERATURE', XYZ= 7.5, 12, 2.8, IOR=-3/



&DEVC ID='Tmember-26', QUANTITY='WALL TEMPERATURE', XYZ= 2, 0.3, 2.6, IOR= 2/


&DEVC ID='Tmember-28', QUANTITY='WALL TEMPERATURE', XYZ= 6.3, 0.3, 2.6, IOR= 2/





&DEVC ID='Tmember-33', QUANTITY='WALL TEMPERATURE', XYZ= 2, 15.7, 2.6, IOR= -2/

&DEVC ID='Tmember-34', QUANTITY='WALL TEMPERATURE', XYZ= 6.3, 15.7, 2.6, IOR= -2/

&DEVC ID='Tmember-35', QUANTITY='WALL TEMPERATURE', XYZ= 8.8, 15.7, 2.6, IOR= -2/

&DEVC ID='Tmember-36', QUANTITY='WALL TEMPERATURE', XYZ= 13, 15.7, 2.6, IOR= -2/

------180

&DEVC ID='Tgas-1',QUANTITY='GAS TEMPERATURE', XYZ= 2, 0.15, 2.3, IOR=-3/

&DEVC ID='Tgas-2',QUANTITY='GAS TEMPERATURE', XYZ= 6.3, 0.15, 2.3, IOR=-3/
















&DEVC ID='Tgas-18',QUANTITY='GAS TEMPERATURE', XYZ= 7.5, 8, 2.8, IOR=-3/





&DEVC ID='Tgas-23',QUANTITY='GAS TEMPERATURE', XYZ= 7.5, 12, 2.8, IOR=-3/



&DEVC ID='Tgas-26', QUANTITY='GAS TEMPERATURE', XYZ= 2, 0.3, 2.6, IOR= 2/


&DEVC ID='Tgas-28', QUANTITY='GAS TEMPERATURE', XYZ= 6.3, 0.3, 2.6, IOR= 2/





&DEVC ID='Tgas-33', QUANTITY='GAS TEMPERATURE', XYZ= 2, 15.7, 2.6, IOR= -2/

&DEVC ID='Tgas-34', QUANTITY='GAS TEMPERATURE', XYZ= 6.3, 15.7, 2.6, IOR= -2/

&DEVC ID='Tgas-35', QUANTITY='GAS TEMPERATURE', XYZ= 8.8, 15.7, 2.6, IOR= -2/

&DEVC ID='Tgas-36', QUANTITY='GAS TEMPERATURE', XYZ= 13, 15.7, 2.6, IOR= -2/

-----216


Y.C.Wong 158

-- Slices ---






&SLCF PBX=6.3, QUANTITY='TEMPERATURE'/







&SLCF PBY=0.4, QUANTITY='TEMPERATURE'/






&TAIL/

The locations of where the measuring points are given below for model 6:

Dark blue dots: points on the ceiling

Green dots: points on the lower part of the beam


Y.C.Wong 159

Appendix 22 Data heat fluxes of model 6

Left blank on purpose


Y.C.Wong 160

Position 1.00 (model 6)

t[s] hnet [kW/m2] tmember ε*boltzmann*ΔT[W/m

2] α*ΔT [W/m

2]

hpunt

[kW/m2]

0.00 0.00 20.00 0.00 0.00 0.00

60.00 0.29 20.12 0.48 4.20 0.29

120.00 0.50 20.42 1.69 14.79 0.51

180.00 1.03 20.93 3.75 32.67 1.07

240.00 1.16 21.45 5.85 50.83 1.21

300.00 1.08 22.15 8.69 75.19 1.16

360.00 1.27 22.85 11.59 99.91 1.38

420.00 2.03 23.59 14.64 125.76 2.17

480.00 0.92 24.21 17.19 147.23 1.08

540.00 1.25 24.78 19.61 167.46 1.44

600.00 1.81 25.49 22.57 191.99 2.02

660.00 1.46 26.08 25.11 212.95 1.70

720.00 1.22 26.66 27.55 233.01 1.48

780.00 2.82 27.72 32.15 270.36 3.13

840.00 2.53 29.13 38.27 319.54 2.89

900.00 3.46 30.53 44.47 368.67 3.88

960.00 3.14 32.23 52.09 428.16 3.62

1020.00 4.51 33.93 59.82 487.46 5.06

1080.00 3.42 35.41 66.70 539.49 4.02

1140.00 4.02 36.70 72.73 584.40 4.68

1200.00 2.80 37.91 78.50 626.92 3.51

1260.00 3.49 39.58 86.54 685.31 4.26

1320.00 4.27 41.40 95.43 748.86 5.12

1380.00 5.32 43.64 106.63 827.33 6.26

1440.00 5.57 45.88 118.06 905.71 6.60

1500.00 8.59 48.75 133.09 1006.34 9.73

1560.00 6.71 52.14 151.30 1124.78 7.99

1620.00 8.33 55.04 167.40 1226.47 9.73

1680.00 6.40 57.05 178.78 1296.78 7.87

1740.00 6.93 59.42 192.46 1379.63 8.50

1800.00 7.14 61.86 206.91 1465.23 8.82

1860.00 6.38 63.90 219.15 1536.33 8.13

1920.00 3.66 64.85 224.99 1569.82 5.45

1980.00 4.74 66.51 235.26 1627.98 6.61

2040.00 2.50 67.27 240.01 1654.62 4.40

2100.00 2.32 67.87 243.76 1675.48 4.24

2160.00 3.17 68.32 246.60 1691.25 5.11

2220.00 2.08 68.79 249.56 1707.57 4.03

2280.00 1.62 68.84 249.86 1709.26 3.58

2340.00 1.52 68.96 250.66 1713.67 3.48

2400.00 2.53 69.25 252.47 1723.60 4.51

2460.00 3.01 69.84 256.27 1744.40 5.02

2500.00 3.91 70.22 258.70 1757.64 5.93


Y.C.Wong 161



2]

α*ΔT

[W/m2] hpunt [kW/m

2]

0.00 0.00 20.00 0.00 0.00 0.00

60.00 0.56 20.26 1.02 8.95 0.57

120.00 1.06 20.80 3.19 27.84 1.09

180.00 1.50 21.61 6.50 56.44 1.57

240.00 1.92 22.65 10.76 92.83 2.02

300.00 2.48 23.81 15.52 133.20 2.63

360.00 1.79 24.82 19.75 168.57 1.97

420.00 2.32 26.00 24.75 209.98 2.55

480.00 2.20 27.02 29.10 245.62 2.48

540.00 1.91 27.98 33.23 279.16 2.22

600.00 2.34 29.05 37.93 316.89 2.70

660.00 2.34 29.98 42.00 349.24 2.73

720.00 1.54 30.87 45.97 380.46 1.97

780.00 7.60 34.37 61.85 502.93 8.16

840.00 7.65 37.96 78.72 628.54 8.36

900.00 7.04 41.42 95.55 749.71 7.88

960.00 7.38 44.55 111.28 859.41 8.35

1020.00 7.44 48.16 129.97 985.68 8.56

1080.00 9.63 52.38 152.64 1133.32 10.91

1140.00 9.64 56.97 178.34 1294.09 11.11

1200.00 10.36 61.65 205.61 1457.63 12.02

1260.00 11.76 66.74 236.70 1636.07 13.63

1320.00 12.22 71.86 269.34 1815.15 14.31

1380.00 13.69 77.69 308.32 2019.06 16.02

1440.00 17.18 84.74 358.14 2265.74 19.80

1500.00 22.97 94.68 433.62 2613.80 26.02

1560.00 24.79 105.96 527.02 3008.75 28.33

1620.00 17.78 112.99 589.54 3254.67 21.63

1680.00 17.30 119.35 649.18 3477.30 21.42

1740.00 21.16 126.53 720.02 3728.45 25.61

1800.00 16.00 132.18 778.55 3926.19 20.71

1860.00 15.33 136.67 826.88 4083.45 20.24

1920.00 12.49 140.16 865.57 4205.73 17.56

1980.00 10.84 143.00 897.69 4304.92 16.04

2040.00 9.06 145.15 922.57 4380.40 14.37

2100.00 8.01 146.61 939.62 4431.43 13.38

2160.00 7.29 147.64 951.78 4467.53 12.71

2220.00 6.29 148.08 956.96 4482.82 11.73

2280.00 5.34 148.17 958.01 4485.91 10.78

2340.00 5.27 148.37 960.41 4492.97 10.72

2400.00 5.62 148.38 960.50 4493.24 11.07

2460.00 7.18 149.47 973.55 4531.48 12.68

2500.00 6.27 149.37 972.39 4528.11 11.77


Y.C.Wong 162



2] α*ΔT [W/m

2] hpunt [kW/m

2]

0.00 0.00 20.00 0.00 0.00 0.00

60.00 0.59 20.25 0.99 8.67 0.60

120.00 1.00 20.77 3.07 26.79 1.03

180.00 1.62 21.56 6.30 54.70 1.68

240.00 1.86 22.52 10.19 88.05 1.96

300.00 1.89 23.49 14.22 122.19 2.02

360.00 1.93 24.48 18.35 156.93 2.11

420.00 1.76 25.42 22.29 189.71 1.97

480.00 1.84 26.36 26.27 222.52 2.09

540.00 1.87 27.21 29.95 252.52 2.15

600.00 1.62 28.03 33.47 281.06 1.93

660.00 1.74 28.85 37.02 309.59 2.08

720.00 1.90 29.63 40.45 336.90 2.27

780.00 4.54 31.74 49.86 410.83 5.00

840.00 4.86 34.22 61.19 497.87 5.42

900.00 4.87 36.37 71.17 572.85 5.51

960.00 3.78 38.58 81.70 650.27 4.51

1020.00 5.63 41.03 93.60 735.88 6.46

1080.00 5.38 43.51 105.96 822.69 6.30

1140.00 6.02 46.09 119.16 913.15 7.05

1200.00 6.85 48.81 133.42 1008.51 7.99

1260.00 5.96 51.68 148.80 1108.75 7.22

1320.00 6.55 54.60 164.94 1211.15 7.93

1380.00 6.23 58.01 184.31 1330.48 7.75

1440.00 9.83 62.23 209.11 1478.09 11.52

1500.00 22.82 73.16 277.83 1860.45 24.96

1560.00 24.30 85.21 361.63 2282.48 26.95

1620.00 16.20 92.50 416.58 2537.67 19.16

1680.00 14.99 98.50 464.31 2747.60 18.20

1740.00 15.06 104.15 511.44 2945.32 18.52

1800.00 13.66 109.33 556.56 3126.64 17.34

1860.00 11.92 113.55 594.68 3274.29 15.79

1920.00 11.62 117.35 630.09 3407.21 15.66

1980.00 9.50 120.43 659.54 3514.90 13.68

2040.00 9.19 123.01 684.82 3605.39 13.48

2100.00 8.92 125.14 705.98 3679.74 13.30

2160.00 8.73 127.22 727.03 3752.59 13.21

2220.00 8.01 129.01 745.46 3815.42 12.57

2280.00 7.60 130.68 762.82 3873.86 12.24

2340.00 7.86 132.61 783.11 3941.26 12.59

2400.00 9.33 134.74 805.88 4015.76 14.15

2460.00 14.85 140.06 864.37 4201.98 19.91

2500.00 12.03 141.33 878.71 4246.54 17.15


Y.C.Wong 163



2] α*ΔT [W/m

2] hpunt [kW/m

2]

0.00 0.00 20.00 0.00 0.00 0.00

60.00 0.39 20.14 0.56 4.93 0.39

120.00 0.46 20.45 1.80 15.67 0.48

180.00 0.66 20.85 3.41 29.72 0.70

240.00 1.14 21.41 5.70 49.47 1.20

300.00 0.80 21.88 7.59 65.81 0.87

360.00 1.01 22.35 9.50 82.14 1.10

420.00 0.82 22.75 11.18 96.42 0.93

480.00 1.31 23.24 13.16 113.23 1.43

540.00 1.00 23.63 14.79 127.03 1.14

600.00 0.69 23.97 16.22 139.09 0.84

660.00 0.98 24.36 17.84 152.66 1.15

720.00 0.96 24.67 19.13 163.44 1.14

780.00 1.60 25.42 22.29 189.72 1.81

840.00 1.87 26.34 26.19 221.84 2.12

900.00 1.18 27.09 29.42 248.21 1.45

960.00 1.68 28.03 33.48 281.12 1.99

1020.00 1.74 28.85 37.05 309.84 2.09

1080.00 2.00 29.79 41.18 342.73 2.38

1140.00 2.74 30.86 45.92 380.07 3.17

1200.00 3.01 31.96 50.87 418.69 3.48

1260.00 2.72 33.22 56.57 462.68 3.24

1320.00 4.12 34.66 63.17 512.93 4.70

1380.00 2.78 35.99 69.39 559.62 3.41

1440.00 3.58 37.53 76.67 613.52 4.27

1500.00 5.02 40.03 88.73 701.10 5.81

1560.00 5.24 42.85 102.67 799.72 6.14

1620.00 4.25 44.61 111.56 861.31 5.23

1680.00 4.28 46.38 120.66 923.27 5.33

1740.00 4.23 47.72 127.65 970.26 5.33

1800.00 3.16 49.12 135.05 1019.25 4.31

1860.00 2.76 50.38 141.78 1063.31 3.96

1920.00 3.64 51.56 148.18 1104.76 4.89

1980.00 2.01 52.26 151.97 1129.05 3.30

2040.00 2.20 52.92 155.58 1152.08 3.51

2100.00 2.09 53.81 160.55 1183.52 3.44

2160.00 2.64 54.72 165.57 1215.03 4.02

2220.00 3.43 55.50 169.97 1242.47 4.85

2280.00 2.80 56.35 174.76 1272.12 4.24

2340.00 2.51 57.59 181.85 1315.53 4.01

2400.00 4.36 59.53 193.13 1383.63 5.93

2460.00 6.81 62.46 210.47 1486.07 8.50

2500.00 8.41 64.65 223.75 1562.72 10.19


Y.C.Wong 164



2] α*ΔT [W/m

2] hpunt [kW/m

2]

0.00 0.00 20.00 0.00 0.00 0.00

60.00 0.03 20.01 0.03 0.24 0.03

120.00 0.17 20.12 0.46 4.04 0.17

180.00 0.30 20.29 1.15 10.04 0.32

240.00 0.36 20.49 1.95 17.03 0.38

300.00 0.41 20.73 2.92 25.44 0.44

360.00 0.47 20.97 3.90 33.96 0.51

420.00 0.48 21.18 4.75 41.29 0.53

480.00 0.56 21.40 5.66 49.15 0.62

540.00 0.54 21.62 6.55 56.79 0.60

600.00 0.44 21.79 7.24 62.79 0.51

660.00 0.48 21.99 8.04 69.64 0.56

720.00 0.59 22.18 8.83 76.35 0.67

780.00 1.49 22.82 11.42 98.53 1.60

840.00 1.38 23.48 14.18 121.85 1.51

900.00 1.52 24.22 17.23 147.57 1.69

960.00 1.65 24.93 20.23 172.59 1.84

1020.00 1.63 25.67 23.36 198.53 1.85

1080.00 1.70 26.48 26.80 226.81 1.96

1140.00 1.84 27.33 30.46 256.71 2.13

1200.00 1.96 28.28 34.57 289.96 2.29

1260.00 2.04 29.24 38.76 323.49 2.40

1320.00 2.28 30.29 43.39 360.16 2.68

1380.00 2.66 31.39 48.31 398.77 3.10

1440.00 2.98 32.57 53.62 439.98 3.47

1500.00 4.14 34.50 62.47 507.58 4.71

1560.00 4.17 36.35 71.08 572.21 4.81

1620.00 3.32 37.79 77.94 622.82 4.03

1680.00 3.03 39.17 84.54 670.92 3.78

1740.00 4.16 41.04 93.67 736.33 4.99

1800.00 3.03 42.58 101.34 790.42 3.92

1860.00 3.02 43.92 108.07 837.30 3.96

1920.00 3.23 44.92 113.17 872.37 4.22

1980.00 2.15 45.71 117.22 899.99 3.17

2040.00 2.48 46.52 121.40 928.31 3.53

2100.00 2.80 47.25 125.19 953.79 3.88

2160.00 2.27 47.81 128.12 973.33 3.37

2220.00 2.49 48.52 131.87 998.27 3.62

2280.00 2.32 49.14 135.15 1019.92 3.48

2340.00 2.09 49.76 138.43 1041.49 3.27

2400.00 1.93 50.20 140.82 1057.05 3.13

2460.00 2.33 50.79 143.98 1077.61 3.55

2500.00 1.87 51.12 145.76 1089.12 3.10


Y.C.Wong 165



2] α*ΔT [W/m

2] hpunt [kW/m

2]

0.00 0.00 20.00 0.00 0.00 0.00

60.00 0.04 20.01 0.03 0.30 0.04

120.00 0.18 20.10 0.41 3.61 0.18

180.00 0.27 20.27 1.07 9.34 0.28

240.00 0.46 20.46 1.82 15.93 0.47

300.00 0.59 20.70 2.81 24.50 0.61

360.00 0.51 20.90 3.63 31.58 0.55

420.00 0.45 21.11 4.46 38.84 0.50

480.00 0.37 21.32 5.32 46.22 0.42

540.00 0.46 21.55 6.25 54.28 0.52

600.00 0.35 21.72 6.95 60.24 0.42

660.00 0.46 21.93 7.78 67.41 0.53

720.00 0.43 22.12 8.58 74.23 0.52

780.00 1.44 22.78 11.28 97.33 1.55

840.00 1.34 23.59 14.62 125.61 1.48

900.00 1.71 24.36 17.85 152.76 1.88

960.00 1.73 25.13 21.09 179.72 1.93

1020.00 1.66 25.93 24.47 207.67 1.89

1080.00 1.78 26.80 28.18 238.13 2.04

1140.00 1.97 27.76 32.29 271.56 2.28

1200.00 2.41 28.76 36.66 306.67 2.76

1260.00 2.26 29.78 41.11 342.16 2.65

1320.00 2.86 30.91 46.13 381.73 3.29

1380.00 2.59 32.00 51.03 419.99 3.06

1440.00 2.67 33.16 56.28 460.48 3.19

1500.00 4.73 35.26 65.97 533.99 5.33

1560.00 3.89 37.36 75.85 607.48 4.57

1620.00 3.79 39.13 84.35 669.53 4.54

1680.00 3.70 40.87 92.85 730.54 4.52

1740.00 4.13 42.66 101.74 793.26 5.02

1800.00 4.09 44.46 110.78 855.96 5.06

1860.00 3.09 45.77 117.49 901.80 4.11

1920.00 3.42 47.00 123.90 945.14 4.49

1980.00 3.54 48.05 129.37 981.68 4.65

2040.00 2.69 48.82 133.46 1008.80 3.83

2100.00 2.94 49.67 137.97 1038.44 4.12

2160.00 2.85 50.37 141.73 1062.99 4.06

2220.00 2.36 51.01 145.15 1085.22 3.59

2280.00 2.26 51.69 148.86 1109.13 3.52

2340.00 2.16 52.15 151.37 1125.22 3.43

2400.00 1.96 52.67 154.23 1143.46 3.26

2460.00 2.04 53.11 156.64 1158.83 3.35

2500.00 1.76 53.36 158.00 1167.43 3.08


Y.C.Wong 166



2] α*ΔT [W/m

2] hpunt [kW/m

2]

0.00 0.00 20.00 0.00 0.00 0.00

60.00 0.01 20.01 0.02 0.21 0.01

120.00 0.20 20.11 0.45 3.91 0.21

180.00 0.35 20.29 1.16 10.11 0.36

240.00 0.39 20.49 1.96 17.09 0.41

300.00 0.32 20.69 2.77 24.18 0.34

360.00 0.53 20.93 3.74 32.54 0.56

420.00 0.43 21.14 4.59 39.89 0.48

480.00 0.39 21.35 5.45 47.32 0.44

540.00 0.41 21.58 6.37 55.27 0.47

600.00 0.32 21.76 7.09 61.47 0.39

660.00 0.49 21.98 7.98 69.14 0.57

720.00 0.46 22.16 8.76 75.77 0.55

780.00 1.24 22.79 11.33 97.75 1.35

840.00 1.62 23.58 14.58 125.29 1.76

900.00 1.75 24.34 17.74 151.84 1.92

960.00 1.52 25.12 21.04 179.33 1.72

1020.00 1.59 25.93 24.47 207.67 1.82

1080.00 2.02 26.81 28.19 238.23 2.28

1140.00 1.88 27.70 32.02 269.34 2.18

1200.00 2.06 28.67 36.25 303.45 2.40

1260.00 2.40 29.66 40.61 338.17 2.78

1320.00 2.21 30.67 45.07 373.40 2.63

1380.00 2.42 31.73 49.83 410.62 2.88

1440.00 2.53 32.87 54.97 450.37 3.04

1500.00 3.89 34.97 64.62 523.82 4.48

1560.00 4.44 37.20 75.12 602.07 5.11

1620.00 4.11 38.92 83.34 662.22 4.86

1680.00 3.94 40.60 91.51 720.97 4.75

1740.00 4.87 42.60 101.42 790.99 5.76

1800.00 4.05 44.42 110.60 854.72 5.02

1860.00 3.30 45.74 117.34 900.81 4.32

1920.00 2.99 46.93 123.52 942.55 4.06

1980.00 3.17 47.86 128.36 974.95 4.27

2040.00 2.54 48.75 133.07 1006.24 3.68

2100.00 2.69 49.54 137.27 1033.86 3.86

2160.00 2.77 50.31 141.39 1060.79 3.97

2220.00 2.19 50.92 144.70 1082.26 3.42

2280.00 2.55 51.64 148.61 1107.48 3.81

2340.00 2.08 52.02 150.67 1120.76 3.36

2400.00 2.10 52.47 153.14 1136.54 3.39

2460.00 1.73 52.92 155.59 1152.15 3.04

2500.00 1.90 53.18 157.01 1161.16 3.22


Y.C.Wong 167



2] α*ΔT [W/m

2] hpunt [kW/m

2]

0.00 0.00 20.00 0.00 0.00 0.00

60.00 0.05 20.01 0.03 0.24 0.05

120.00 0.25 20.13 0.53 4.61 0.25

180.00 0.34 20.29 1.17 10.22 0.36

240.00 0.40 20.49 1.98 17.31 0.42

300.00 0.54 20.77 3.07 26.79 0.57

360.00 0.53 21.01 4.07 35.42 0.57

420.00 0.54 21.25 5.04 43.85 0.59

480.00 0.39 21.50 6.06 52.59 0.45

540.00 0.44 21.73 6.97 60.45 0.50

600.00 0.54 21.93 7.80 67.58 0.61

660.00 0.38 22.15 8.69 75.20 0.47

720.00 0.46 22.37 9.62 83.12 0.55

780.00 1.35 22.94 11.95 103.02 1.46

840.00 1.42 23.69 15.05 129.19 1.56

900.00 1.62 24.36 17.83 152.53 1.79

960.00 1.46 25.03 20.63 175.88 1.65

1020.00 1.31 25.69 23.45 199.28 1.54

1080.00 1.46 26.43 26.60 225.21 1.71

1140.00 1.79 27.25 30.08 253.65 2.08

1200.00 1.94 28.07 33.66 282.55 2.26

1260.00 2.04 28.98 37.62 314.37 2.40

1320.00 2.13 29.95 41.89 348.37 2.52

1380.00 2.12 30.90 46.08 381.36 2.54

1440.00 2.33 31.94 50.79 418.06 2.79

1500.00 4.11 33.90 59.70 486.57 4.66

1560.00 3.98 35.78 68.39 552.16 4.60

1620.00 3.49 37.42 76.18 609.87 4.18

1680.00 3.18 38.93 83.38 662.48 3.93

1740.00 4.18 40.76 92.28 726.47 5.00

1800.00 4.18 42.52 101.04 788.37 5.07

1860.00 3.00 43.79 107.41 832.70 3.94

1920.00 2.86 44.78 112.43 867.31 3.84

1980.00 3.05 45.72 117.25 900.22 4.07

2040.00 2.24 46.44 120.96 925.31 3.28

2100.00 2.66 47.15 124.68 950.34 3.73

2160.00 2.26 47.75 127.83 971.41 3.36

2220.00 2.08 48.32 130.78 991.03 3.20

2280.00 1.87 48.89 133.80 1011.03 3.02

2340.00 1.73 49.26 135.77 1024.00 2.89

2400.00 1.51 49.63 137.78 1037.22 2.69

2460.00 1.86 50.01 139.76 1050.18 3.05

2500.00 1.75 50.33 141.53 1061.67 2.96


Y.C.Wong 168

0

10

20

30

40

50

60

70

0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 2400 2600

Tota

l He

at f

luxe

s [k

W/m

2 ]

Time[s]

Total heat fluxes Position 1 (Model6)

FDS

CaPaFi

0

10

20

30

40

50

60

70

0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 2400 2600

Tota

l He

at f

luxe

s [k

W/m

2 ]

Time[s]


FDS

CaPaFi

0

10

20

30

40

50

60

70

0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 2400 2600Tota

l He

at f

luxe

s [k

W/m

2]

Time[s]

Total heat fluxes Position3 (model6)

FDS

CaPaFi

0

10

20

30

40

50

60

70

0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 2400 2600

Tota

l He

at f

luxe

s [k

W/m

2 ]

Time[s]


FDS

CaPaFi


Y.C.Wong 169

0

10

20

30

40

50

60

70

0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 2400 2600

Tota

l He

at f

luxe

s [k

W/m

2 ]

Time[s]


FDS

CaPaFi

0

10

20

30

40

50

60

70

0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 2400 2600

Tota

l He

at f

luxe

s [k

W/m

2 ]

Time[s]

Total heat flux Position 6 (model 6)

FDS

CaPaFi

0

10

20

30

40

50

60

70

0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 2400 2600

Tota

l He

at f

luxe

s [k

W/m

2]

Time[s]


FDS

CaPaFi

0

10

20

30

40

50

60

70

0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 2400 2600

Tota

l He

at f

luxe

s [k

W/m

2 ]

Time[s]

Total heat fluxes Postion 8 (model 6)

FDS

CaPaFi


Y.C.Wong 170

Appendix 23 Data temperatures of model 6


t[s] FDS CaPaFi FDS CaPaFi FDS CaPaFi

0 20.00 20.00 20.00 20.00 20.00 20.00

60 20.12 20.04 20.26 20.08 20.25 20.03

120 20.42 20.60 20.80 21.08 20.77 20.44

180 20.93 21.64 21.61 22.94 21.56 21.21

240 21.45 23.14 22.65 25.56 22.52 22.32

300 22.15 25.03 23.81 28.84 23.49 23.72

360 22.85 26.86 24.82 32.02 24.48 25.08

420 23.59 28.65 26.00 35.12 25.42 26.42

480 24.21 30.40 27.02 38.14 26.36 27.72

540 24.78 32.10 27.98 41.08 27.21 28.99

600 25.49 33.76 29.05 43.94 28.03 30.23

660 26.08 35.38 29.98 46.72 28.85 31.43

720 26.66 36.96 30.87 49.44 29.63 32.61

780 27.72 38.61 34.37 52.54 31.74 34.23

840 29.13 41.38 37.96 60.51 34.22 40.76

900 30.53 44.09 41.42 68.23 36.37 47.10

960 32.23 46.72 44.55 75.71 38.58 53.24

1020 33.93 49.34 48.16 83.05 41.03 59.23

1080 35.41 52.51 52.38 91.18 43.51 65.51

1140 36.70 56.21 56.97 100.03 46.09 72.05

1200 37.91 60.39 61.65 109.54 48.81 78.83

1260 39.58 65.03 66.74 119.70 51.68 85.83

1320 41.40 70.11 71.86 130.78 54.60 93.03

1380 43.64 75.61 77.69 143.33 58.01 100.50

1440 45.88 81.76 84.74 157.90 62.23 109.10

1500 48.75 88.88 94.68 174.78 73.16 119.36

1560 52.14 100.33 105.96 198.97 85.21 136.92

1620 55.04 108.24 112.99 220.41 92.50 154.15

1680 57.05 114.31 119.35 238.17 98.50 170.96

1740 59.42 120.18 126.53 255.87 104.15 188.61

1800 61.86 126.56 132.18 276.21 109.33 209.98

1860 63.90 131.64 136.67 291.99 113.55 226.90

1920 64.85 135.53 140.16 302.61 117.35 238.70

1980 66.51 138.85 143.00 311.41 120.43 248.89

2040 67.27 141.61 145.15 318.40 123.01 257.42

2100 67.87 143.84 146.61 323.94 125.14 265.00

2160 68.32 145.64 147.64 328.66 127.22 272.47

2220 68.79 147.02 148.08 332.56 129.01 279.82

2280 68.84 147.96 148.17 335.65 130.68 287.47

2340 68.96 148.51 148.37 337.97 132.61 295.69

2400 69.25 148.95 148.38 340.00 134.74 304.47

2460 69.84 149.34 149.47 341.86 140.06 313.92

2500 70.22 149.80 149.37 343.87 141.33 322.71


Y.C.Wong 171

Temperature Position 4 Position 5 Position 6

Time[s] FDS CaPaFi FDS CaPaFi FDS CaPaFi

0 20.00 20.00 20.00 20.00 20.00 20.00

60 20.14 20.01 20.01 20.00 20.01 20.00

120 20.45 20.10 20.12 20.03 20.10 20.03

180 20.85 20.28 20.29 20.08 20.27 20.08

240 21.41 20.55 20.49 20.15 20.46 20.16

300 21.88 20.89 20.73 20.24 20.70 20.26

360 22.35 21.22 20.97 20.34 20.90 20.36

420 22.75 21.55 21.18 20.43 21.11 20.45

480 23.24 21.87 21.40 20.51 21.32 20.55

540 23.63 22.18 21.62 20.60 21.55 20.64

600 23.97 22.48 21.79 20.68 21.72 20.73

660 24.36 22.78 21.99 20.77 21.93 20.82

720 24.67 23.07 22.18 20.85 22.12 20.90

780 25.42 23.46 22.82 20.94 22.78 21.00

840 26.34 25.04 23.48 21.16 23.59 21.26

900 27.09 26.59 24.22 21.37 24.36 21.51

960 28.03 28.09 24.93 21.58 25.13 21.76

1020 28.85 29.57 25.67 21.78 25.93 22.00

1080 29.79 31.13 26.48 22.02 26.80 22.28

1140 30.86 32.78 27.33 22.29 27.76 22.59

1200 31.96 34.50 28.28 22.58 28.76 22.92

1260 33.22 36.29 29.24 22.91 29.78 23.29

1320 34.66 38.15 30.29 23.25 30.91 23.68

1380 35.99 40.10 31.39 23.63 32.00 24.10

1440 37.53 42.36 32.57 24.05 33.16 24.58

1500 40.03 45.22 34.50 24.55 35.26 25.14

1560 42.85 51.57 36.35 25.30 37.36 26.02

1620 44.61 57.58 37.79 25.96 39.13 26.79

1680 46.38 63.28 39.17 26.52 40.87 27.47

1740 47.72 69.07 41.04 27.08 42.66 28.16

1800 49.12 75.67 42.58 27.73 44.46 28.95

1860 50.38 81.19 43.92 28.25 45.77 29.59

1920 51.56 85.72 44.92 28.65 47.00 30.09

1980 52.26 89.92 45.71 29.00 48.05 30.52

2040 52.92 93.80 46.52 29.30 48.82 30.91

2100 53.81 97.41 47.25 29.57 49.67 31.24

2160 54.72 101.29 47.81 29.81 50.37 31.56

2220 55.50 105.40 48.52 30.03 51.01 31.86

2280 56.35 109.73 49.14 30.22 51.69 32.13

2340 57.59 114.28 49.76 30.40 52.15 32.38

2400 59.53 119.08 50.20 30.57 52.67 32.64

2460 62.46 124.45 50.79 30.74 53.11 32.90

2500 64.65 130.52 51.12 30.91 53.36 33.15


Y.C.Wong 172


Time[s] FDS CaPaFi FDS CaPaFi

0 20.00 20.00 20.00 20.00

60 20.01 20.00 20.01 20.00

120 20.11 20.03 20.13 20.02

180 20.29 20.07 20.29 20.05

240 20.49 20.14 20.49 20.10

300 20.69 20.23 20.77 20.16

360 20.93 20.32 21.01 20.23

420 21.14 20.41 21.25 20.29

480 21.35 20.49 21.50 20.35

540 21.58 20.57 21.73 20.40

600 21.76 20.66 21.93 20.46

660 21.98 20.73 22.15 20.52

720 22.16 20.81 22.37 20.57

780 22.79 20.90 22.94 20.63

840 23.58 21.15 23.69 20.83

900 24.34 21.40 24.36 21.02

960 25.12 21.63 25.03 21.20

1020 25.93 21.87 25.69 21.38

1080 26.81 22.14 26.43 21.58

1140 27.70 22.43 27.25 21.81

1200 28.67 22.75 28.07 22.04

1260 29.66 23.09 28.98 22.30

1320 30.67 23.46 29.95 22.57

1380 31.73 23.85 30.90 22.86

1440 32.87 24.30 31.94 23.20

1500 34.97 24.83 33.90 23.60

1560 37.20 25.68 35.78 24.26

1620 38.92 26.43 37.42 24.86

1680 40.60 27.11 38.93 25.40

1740 42.60 27.79 40.76 25.96

1800 44.42 28.58 42.52 26.60

1860 45.74 29.22 43.79 27.12

1920 46.93 29.72 44.78 27.53

1980 47.86 30.16 45.72 27.90

2040 48.75 30.55 46.44 28.23

2100 49.54 30.89 47.15 28.52

2160 50.31 31.22 47.75 28.80

2220 50.92 31.54 48.32 29.08

2280 51.64 31.84 48.89 29.36

2340 52.02 32.12 49.26 29.63

2400 52.47 32.41 49.63 29.90

2460 52.92 32.71 50.01 30.19

2500 53.18 32.99 50.33 30.47


Y.C.Wong 173

0

100

200

300

400

0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 2400 2600

Tem

pe

ratu

re [

oC

]

Time[s]


FDS

CaPaFi

0

100

200

300

400

0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 2400 2600

Tem

pe

ratu

re [

oC

]

Time [s]


FDS

CaPaFi

0

100

200

300

400

0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 2400 2600

Tem

pe

ratu

re [

oC

]

Time[s]


FDS

CaPaFi

0

100

200

300

400

0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 2400 2600

Tem

pe

ratu

re [

oC

]

Time [s]


FDS

CaPaFI


Y.C.Wong 174

0

100

200

300

400

0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 2400 2600

Tem

pe

ratu

re [

oC

]

Time[s]


FDS

CaPaFI

0

100

200

300

400

0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 2400 2600

Tem

pe

ratu

re[o

C]

Time[s]


FDS

CaPaFI

0

100

200

300

400

0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 2400 2600

Tem

pe

ratu

re[o

C]

Time [s]


FDS

CaPaFI

0

100

200

300

400

0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 2400 2600

Tem

pe

artu

re [

oC

]

Time [s]


FDS

CaPaFI


Y.C.Wong 175

Appendix 24 Script of FDS (model 7 hidden beams)

The script of model 7 is the same as model 6, only difference is that the beams are next to the

ceiling and not sticking out, and the measuring points from 26-36 are not applicable because the

beams are not sticking out.

The positions of the points on the beam are given in the picture below.

Dark blue dots: points on the ceiling

Green dots: points on the lower part of the beam


Y.C.Wong 176

Appendix 25 Data heat fluxes of model 7 (hidden beams)

Left blank on purpose


Y.C.Wong 177



2]

α*ΔT

[W/m2]

hpunt

[kW/m2]

0.00 0.00 20.00 0.00 0.00 0.00

60.00 0.89 20.37 1.48 12.90 0.90

120.00 1.49 21.09 4.38 38.14 1.53

180.00 1.88 22.05 8.29 71.76 1.96

240.00 2.47 23.34 13.58 116.78 2.60

300.00 3.07 24.64 18.99 162.25 3.25

360.00 2.16 25.78 23.80 202.16 2.38

420.00 2.10 26.89 28.54 241.09 2.37

480.00 2.03 27.90 32.89 276.40 2.34

540.00 2.22 28.98 37.59 314.16 2.57

600.00 2.12 29.99 42.07 349.74 2.51

660.00 2.47 31.10 46.99 388.50 2.90

720.00 2.36 32.11 51.52 423.73 2.83

780.00 4.43 33.80 59.21 482.83 4.98

840.00 4.71 36.45 71.58 575.87 5.35

900.00 6.31 38.70 82.27 654.46 7.05

960.00 3.64 40.33 90.20 711.62 4.44

1020.00 4.66 42.76 102.23 796.66 5.56

1080.00 4.66 44.88 112.96 870.89 5.64

1140.00 3.88 46.84 123.05 939.41 4.94

1200.00 4.44 49.03 134.55 1015.96 5.59

1260.00 5.34 51.28 146.61 1094.64 6.58

1320.00 6.89 54.10 162.11 1193.36 8.24

1380.00 6.34 56.86 177.72 1290.27 7.81

1440.00 9.49 61.14 202.62 1440.04 11.14

1500.00 9.96 65.42 228.50 1589.77 11.78

1560.00 7.48 69.15 251.86 1720.24 9.45

1620.00 7.16 72.25 271.86 1828.66 9.27

1680.00 8.62 76.18 298.06 1966.39 10.89

1740.00 22.62 82.29 340.54 2180.30 25.14

1800.00 9.20 85.89 366.58 2306.12 11.87

1860.00 8.32 88.39 385.14 2393.57 11.10

1920.00 7.45 90.59 401.79 2470.50 10.32

1980.00 5.74 92.00 412.67 2520.04 8.67

2040.00 5.75 93.35 423.16 2567.22 8.74

2100.00 4.68 94.15 429.46 2595.37 7.71

2160.00 3.50 94.83 434.80 2619.05 6.55

2220.00 4.45 95.26 438.20 2634.06 7.52

2280.00 2.75 95.24 438.03 2633.28 5.83

2340.00 3.23 95.07 436.74 2627.60 6.29

2400.00 2.64 94.92 435.54 2622.30 5.70

2460.00 2.33 94.71 433.82 2614.69 5.38

2500.00 2.48 94.51 432.30 2607.94 5.52


Y.C.Wong 178



2] α*ΔT [W/m

2] hpunt [kW/m

2]

0.00 0.00 20.00 0.00 0.00 0.00

60.00 1.24 20.57 2.28 19.91 1.26

120.00 2.18 21.72 6.93 60.13 2.25

180.00 3.08 23.39 13.80 118.69 3.21

240.00 3.69 25.23 21.48 182.95 3.90

300.00 3.60 27.12 29.52 249.05 3.88

360.00 3.63 28.96 37.51 313.49 3.98

420.00 3.65 30.77 45.53 377.07 4.07

480.00 3.67 32.44 53.03 435.40 4.16

540.00 3.43 34.03 60.29 491.10 3.98

600.00 3.44 35.59 67.52 545.59 4.05

660.00 3.36 37.00 74.14 594.89 4.03

720.00 3.14 38.30 80.35 640.47 3.86

780.00 10.39 43.21 104.46 812.20 11.31

840.00 10.28 48.29 130.62 990.00 11.40

900.00 10.45 53.19 157.09 1161.66 11.77

960.00 9.67 57.80 183.07 1322.94 11.18

1020.00 11.40 62.88 213.00 1500.76 13.11

1080.00 11.82 68.24 246.06 1688.27 13.75

1140.00 12.77 74.27 285.20 1899.39 14.95

1200.00 15.09 80.78 329.81 2127.28 17.55

1260.00 15.68 87.72 380.11 2370.06 18.43

1320.00 18.61 95.65 441.32 2647.76 21.70

1380.00 20.30 104.93 518.14 2972.72 23.79

1440.00 23.39 116.21 619.40 3367.49 27.38

1500.00 48.68 136.55 825.54 4079.17 53.59

1560.00 46.33 154.28 1032.26 4699.94 52.06

1620.00 26.39 163.20 1146.35 5011.90 32.55

1680.00 22.84 170.71 1248.13 5274.90 29.36

1740.00 32.34 180.88 1394.38 5630.91 39.37

1800.00 21.39 187.43 1493.92 5860.17 28.74

1860.00 15.91 191.50 1557.95 6002.62 23.47

1920.00 14.69 194.53 1606.68 6108.59 22.40

1980.00 10.17 196.22 1634.32 6167.78 17.97

2040.00 9.25 197.22 1650.74 6202.65 17.10

2100.00 7.37 197.60 1657.04 6215.97 15.24

2160.00 6.72 197.29 1651.85 6205.01 14.58

2220.00 4.56 196.18 1633.55 6166.13 12.36

2280.00 4.72 194.91 1612.91 6121.99 12.46

2340.00 4.13 193.59 1591.49 6075.77 11.79

2400.00 5.20 192.67 1576.62 6043.46 12.82

2460.00 8.30 192.87 1579.84 6050.47 15.93

2500.00 6.35 192.48 1573.59 6036.85 13.96


Y.C.Wong 179



2] α*ΔT [W/m

2] hpunt [kW/m

2]

0.00 0.00 20.00 0.00 0.00 0.00

60.00 1.26 20.58 2.32 20.24 1.29

120.00 2.18 21.69 6.84 59.30 2.25

180.00 2.98 23.21 13.06 112.44 3.11

240.00 3.61 24.96 20.33 173.44 3.80

300.00 3.37 26.75 27.97 236.42 3.64

360.00 3.18 28.39 35.03 293.64 3.51

420.00 3.51 30.00 42.08 349.87 3.90

480.00 3.42 31.61 49.29 406.45 3.88

540.00 2.89 32.94 55.28 452.78 3.40

600.00 2.84 34.29 61.47 500.04 3.40

660.00 3.34 35.80 68.49 552.89 3.96

720.00 3.00 37.07 74.48 597.34 3.68

780.00 4.26 38.85 83.00 659.72 5.00

840.00 4.59 40.86 92.79 730.12 5.41

900.00 3.90 42.58 101.30 790.16 4.79

960.00 3.82 44.28 109.90 849.92 4.78

1020.00 5.22 46.26 120.06 919.27 6.26

1080.00 6.00 48.78 133.21 1007.15 7.14

1140.00 5.85 51.48 147.71 1101.72 7.10

1200.00 7.36 54.70 165.48 1214.50 8.74

1260.00 7.81 58.11 184.85 1333.75 9.33

1320.00 7.67 61.65 205.61 1457.62 9.34

1380.00 8.60 65.64 229.81 1597.23 10.43

1440.00 9.76 69.71 255.46 1739.97 11.75

1500.00 39.40 89.38 392.58 2428.13 42.22

1560.00 34.11 107.55 540.86 3064.40 37.71

1620.00 22.78 115.87 616.19 3355.49 26.76

1680.00 22.46 123.46 689.24 3621.02 26.77

1740.00 18.34 129.59 751.46 3835.69 22.92

1800.00 17.03 135.82 817.63 4053.75 21.90

1860.00 12.60 139.90 862.56 4196.33 17.66

1920.00 10.56 143.44 902.79 4320.48 15.78

1980.00 12.52 146.49 938.17 4427.13 17.89

2040.00 10.84 148.70 964.33 4504.50 16.31

2100.00 9.32 150.62 987.33 4571.55 14.87

2160.00 7.90 152.12 1005.56 4624.04 13.53

2220.00 8.66 153.58 1023.57 4675.35 14.36

2280.00 8.25 155.06 1041.91 4727.08 14.02

2340.00 8.87 156.76 1063.19 4786.43 14.72

2400.00 10.44 158.88 1090.27 4860.96 16.39

2460.00 14.49 163.08 1144.85 5007.90 20.64

2500.00 9.07 163.78 1154.09 5032.38 15.25


Y.C.Wong 180



2] α*ΔT [W/m

2] hpunt [kW/m

2]

0.00 0.00 20.00 0.00 0.00 0.00

60.00 0.76 20.34 1.35 11.77 0.77

120.00 1.20 21.04 4.18 36.34 1.24

180.00 1.94 22.09 8.44 73.08 2.02

240.00 2.04 23.29 13.40 115.31 2.17

300.00 2.27 24.48 18.36 156.95 2.45

360.00 2.41 25.72 23.57 200.29 2.63

420.00 2.30 26.90 28.58 241.41 2.57

480.00 2.31 27.93 33.06 277.72 2.62

540.00 2.09 29.06 37.96 317.06 2.44

600.00 2.44 30.17 42.86 355.97 2.84

660.00 1.91 31.03 46.68 386.04 2.34

720.00 1.76 31.92 50.69 417.33 2.23

780.00 2.65 33.28 56.84 464.72 3.17

840.00 2.73 34.71 63.44 514.95 3.31

900.00 3.40 36.28 70.74 569.63 4.04

960.00 3.26 37.75 77.74 621.39 3.96

1020.00 3.61 39.27 85.06 674.61 4.37

1080.00 4.31 41.13 94.10 739.40 5.14

1140.00 4.85 43.27 104.76 814.31 5.77

1200.00 5.96 45.72 117.27 900.32 6.98

1260.00 6.67 48.46 131.54 996.07 7.80

1320.00 6.85 51.02 145.22 1085.64 8.08

1380.00 5.60 53.82 160.57 1183.64 6.94

1440.00 7.13 57.07 178.91 1297.56 8.60

1500.00 6.05 59.56 193.31 1384.69 7.63

1560.00 7.98 62.47 210.52 1486.34 9.68

1620.00 5.06 64.43 222.41 1555.04 6.84

1680.00 4.36 66.18 233.20 1616.37 6.21

1740.00 4.53 68.12 245.35 1684.30 6.46

1800.00 5.14 69.59 254.65 1735.53 7.13

1860.00 4.27 70.63 261.36 1772.11 6.30

1920.00 3.94 71.87 269.39 1815.40 6.02

1980.00 3.30 72.77 275.32 1847.10 5.42

2040.00 3.30 73.85 282.45 1884.89 5.46

2100.00 3.90 74.85 289.09 1919.76 6.11

2160.00 5.65 76.40 299.52 1973.93 7.92

2220.00 4.16 77.38 306.19 2008.19 6.47

2280.00 5.86 79.05 317.69 2066.60 8.24

2340.00 5.20 80.42 327.29 2114.77 7.65

2400.00 6.17 82.55 342.37 2189.24 8.70

2460.00 14.85 87.57 379.03 2364.98 17.60

2500.00 6.47 87.88 381.33 2375.78 9.23


Y.C.Wong 181



2] α*ΔT [W/m

2] hpunt [kW/m

2]

0.00 0.00 20.00 0.00 0.00 0.00

60.00 0.19 20.04 0.14 1.25 0.19

120.00 0.42 20.27 1.10 9.61 0.43

180.00 0.74 20.64 2.55 22.26 0.77

240.00 0.77 21.03 4.14 36.04 0.81

300.00 0.80 21.47 5.94 51.60 0.86

360.00 0.87 21.88 7.57 65.64 0.94

420.00 0.81 22.26 9.15 79.16 0.89

480.00 0.72 22.61 10.59 91.41 0.83

540.00 0.82 22.99 12.16 104.77 0.94

600.00 0.73 23.32 13.53 116.37 0.86

660.00 0.73 23.65 14.87 127.72 0.87

720.00 0.73 23.98 16.27 139.44 0.88

780.00 1.71 24.78 19.59 167.29 1.89

840.00 1.75 25.70 23.47 199.47 1.98

900.00 1.83 26.56 27.15 229.73 2.08

960.00 1.81 27.39 30.71 258.76 2.10

1020.00 2.01 28.30 34.65 290.60 2.34

1080.00 1.76 29.17 38.46 321.05 2.12

1140.00 2.04 30.18 42.88 356.17 2.44

1200.00 2.70 31.33 48.02 396.53 3.15

1260.00 2.52 32.46 53.10 435.94 3.01

1320.00 2.81 33.79 59.18 482.61 3.35

1380.00 3.22 35.09 65.19 528.12 3.81

1440.00 3.40 36.55 72.02 579.15 4.05

1500.00 4.38 38.67 82.14 653.50 5.11

1560.00 4.98 40.98 93.36 734.13 5.80

1620.00 4.64 42.92 103.02 802.19 5.54

1680.00 4.15 44.80 112.51 867.85 5.13

1740.00 4.81 46.78 122.71 937.15 5.87

1800.00 4.28 48.69 132.76 1004.15 5.41

1860.00 3.71 50.04 139.97 1051.53 4.91

1920.00 3.08 51.04 145.34 1086.39 4.31

1980.00 3.26 52.10 151.13 1123.66 4.53

2040.00 2.64 53.03 156.19 1155.94 3.95

2100.00 3.03 53.68 159.78 1178.69 4.37

2160.00 2.87 54.43 163.96 1204.98 4.24

2220.00 2.75 55.02 167.30 1225.85 4.15

2280.00 2.03 55.57 170.35 1244.83 3.45

2340.00 2.59 56.35 174.76 1272.08 4.04

2400.00 2.55 57.01 178.56 1295.41 4.03

2460.00 2.65 57.83 183.28 1324.21 4.16

2500.00 3.84 58.70 188.29 1354.55 5.39


Y.C.Wong 182



2] α*ΔT [W/m

2] hpunt [kW/m

2]

0.00 0.00 20.00 0.00 0.00 0.00

60.00 0.14 20.03 0.10 0.88 0.14

120.00 0.41 20.24 0.97 8.51 0.42

180.00 0.56 20.55 2.21 19.25 0.58

240.00 0.72 20.95 3.81 33.19 0.76

300.00 0.80 21.36 5.47 47.56 0.85

360.00 0.72 21.72 6.95 60.25 0.79

420.00 0.72 22.09 8.46 73.24 0.80

480.00 0.75 22.45 9.93 85.80 0.84

540.00 0.71 22.81 11.39 98.24 0.82

600.00 0.61 23.11 12.65 108.97 0.73

660.00 0.68 23.45 14.04 120.70 0.82

720.00 0.69 23.76 15.32 131.48 0.83

780.00 2.18 24.73 19.39 165.61 2.37

840.00 1.65 25.74 23.63 200.80 1.87

900.00 2.04 26.76 27.99 236.58 2.31

960.00 1.72 27.70 32.06 269.64 2.03

1020.00 2.15 28.75 36.60 306.19 2.49

1080.00 2.27 29.83 41.34 343.99 2.65

1140.00 2.31 30.99 46.52 384.78 2.74

1200.00 2.65 32.30 52.37 430.34 3.13

1260.00 2.50 33.56 58.11 474.46 3.03

1320.00 3.13 34.99 64.72 524.58 3.72

1380.00 3.62 36.54 71.97 578.79 4.27

1440.00 3.58 38.09 79.33 632.99 4.30

1500.00 5.34 40.76 92.32 726.77 6.16

1560.00 5.82 43.48 105.86 821.97 6.75

1620.00 5.28 46.05 118.96 911.81 6.31

1680.00 4.68 48.10 129.67 983.66 5.79

1740.00 4.87 50.27 141.17 1059.35 6.07

1800.00 6.11 52.51 153.35 1137.90 7.40

1860.00 4.59 54.11 162.18 1193.81 5.95

1920.00 4.34 55.48 169.88 1241.90 5.75

1980.00 4.02 56.91 177.95 1291.68 5.49

2040.00 3.37 57.99 184.16 1329.55 4.88

2100.00 3.39 58.93 189.63 1362.62 4.94

2160.00 3.36 59.93 195.46 1397.55 4.96

2220.00 3.30 60.85 200.87 1429.70 4.93

2280.00 3.13 61.73 206.11 1460.57 4.80

2340.00 3.29 62.57 211.14 1489.97 5.00

2400.00 3.24 63.42 216.27 1519.71 4.97

2460.00 3.07 64.27 221.43 1549.42 4.84

2500.00 3.00 64.98 225.76 1574.18 4.80


Y.C.Wong 183



2] α*ΔT [W/m

2] hpunt [kW/m

2]

0.00 0.00 20.00 0.00 0.00 0.00

60.00 0.15 20.03 0.11 0.97 0.16

120.00 0.41 20.25 1.02 8.88 0.42

180.00 0.56 20.56 2.25 19.66 0.58

240.00 0.74 20.96 3.84 33.47 0.78

300.00 0.78 21.38 5.57 48.36 0.84

360.00 0.77 21.76 7.12 61.71 0.84

420.00 0.73 22.14 8.66 74.94 0.81

480.00 0.76 22.51 10.16 87.78 0.85

540.00 0.68 22.85 11.59 99.90 0.79

600.00 0.70 23.18 12.94 111.39 0.82

660.00 0.71 23.54 14.40 123.76 0.85

720.00 0.72 23.84 15.66 134.33 0.87

780.00 1.90 24.67 19.13 163.39 2.08

840.00 2.11 25.72 23.56 200.18 2.34

900.00 1.91 26.65 27.53 232.84 2.17

960.00 1.99 27.67 31.92 268.54 2.29

1020.00 1.99 28.63 36.08 302.05 2.33

1080.00 2.23 29.74 40.96 340.94 2.61

1140.00 2.37 30.88 45.99 380.67 2.80

1200.00 2.41 32.03 51.15 420.90 2.88

1260.00 2.41 33.27 56.79 464.36 2.93

1320.00 2.66 34.52 62.56 508.25 3.24

1380.00 3.56 35.90 68.97 556.44 4.19

1440.00 3.09 37.31 75.65 605.98 3.77

1500.00 5.93 40.03 88.70 700.89 6.72

1560.00 5.80 42.69 101.86 794.06 6.69

1620.00 5.34 44.92 113.15 872.21 6.33

1680.00 5.78 47.22 125.03 952.69 6.86

1740.00 5.55 49.45 136.82 1030.90 6.72

1800.00 5.28 51.71 149.00 1109.99 6.54

1860.00 4.58 53.38 158.13 1168.27 5.90

1920.00 4.59 54.92 166.69 1222.05 5.98

1980.00 4.17 56.31 174.54 1270.74 5.62

2040.00 2.94 57.47 181.19 1311.51 4.43

2100.00 3.20 58.49 187.08 1347.27 4.74

2160.00 3.18 59.37 192.20 1378.04 4.75

2220.00 3.71 60.46 198.57 1416.07 5.33

2280.00 3.18 61.19 202.92 1441.78 4.82

2340.00 3.05 61.86 206.88 1465.10 4.72

2400.00 3.10 62.64 211.56 1492.40 4.80

2460.00 3.11 63.34 215.76 1516.74 4.84

2500.00 3.29 64.03 219.95 1540.96 5.06


Y.C.Wong 184



2] α*ΔT [W/m

2] hpunt [kW/m

2]

0.00 0.00 20.00 0.00 0.00 0.00

60.00 0.19 20.04 0.15 1.33 0.19

120.00 0.46 20.29 1.16 10.12 0.47

180.00 0.62 20.61 2.44 21.25 0.65

240.00 0.84 21.04 4.18 36.40 0.88

300.00 0.75 21.47 5.92 51.41 0.80

360.00 0.77 21.85 7.48 64.86 0.84

420.00 0.79 22.26 9.14 79.02 0.88

480.00 0.83 22.63 10.68 92.20 0.93

540.00 0.64 22.96 12.04 103.77 0.76

600.00 0.75 23.32 13.52 116.33 0.88

660.00 0.75 23.66 14.91 128.04 0.89

720.00 0.67 23.99 16.28 139.53 0.82

780.00 1.52 24.67 19.15 163.62 1.70

840.00 1.92 25.56 22.89 194.68 2.14

900.00 1.48 26.33 26.17 221.68 1.72

960.00 1.89 27.20 29.88 251.96 2.17

1020.00 2.18 28.03 33.47 281.03 2.49

1080.00 1.82 28.83 36.95 309.00 2.16

1140.00 1.94 29.78 41.14 342.39 2.32

1200.00 2.08 30.71 45.27 374.96 2.50

1260.00 2.16 31.64 49.41 407.38 2.62

1320.00 2.31 32.67 54.06 443.37 2.81

1380.00 2.66 33.76 59.05 481.63 3.20

1440.00 2.73 34.94 64.49 522.83 3.32

1500.00 4.39 37.14 74.82 599.87 5.07

1560.00 4.16 39.42 85.74 679.56 4.92

1620.00 3.79 41.24 94.66 743.39 4.63

1680.00 4.35 42.98 103.30 804.15 5.25

1740.00 3.98 44.98 113.43 874.14 4.97

1800.00 3.90 46.68 122.24 933.94 4.95

1860.00 3.02 48.03 129.28 981.09 4.13

1920.00 3.38 49.32 136.08 1026.05 4.54

1980.00 3.41 50.38 141.78 1063.36 4.62

2040.00 3.11 51.32 146.84 1096.14 4.35

2100.00 3.26 52.23 151.79 1127.94 4.54

2160.00 3.15 53.01 156.12 1155.48 4.47

2220.00 2.81 53.78 160.37 1182.40 4.16

2280.00 2.82 54.46 164.16 1206.26 4.19

2340.00 2.51 55.04 167.40 1226.48 3.91

2400.00 2.59 55.64 170.75 1247.33 4.00

2460.00 2.86 56.46 175.41 1276.10 4.32

2500.00 3.92 57.30 180.23 1305.64 5.41


Y.C.Wong 185

0.00

5.00

10.00

15.00

20.00

25.00

30.00

0 500 1000 1500 2000 2500 3000Tota

l He

at f

luxe

s [k

W/m

2 ]

Time [s]


FDS

CaPaFi

0.00

20.00

40.00

60.00

80.00

0 500 1000 1500 2000 2500 3000

Tota

l He

at f

luxe

s [k

W/m

2 ]

Time [s]


FDS

CaPaFi

0.00

10.00

20.00

30.00

40.00

50.00

60.00

0 500 1000 1500 2000 2500 3000

Tota

l He

atfl

uxe

s [k

W/m

2]

Time [s]


FDS

CaPaFi

0.00

5.00

10.00

15.00

20.00

25.00

0 500 1000 1500 2000 2500 3000

Tota

l He

at f

luxe

s [k

W/m

2 ]

Time [s]


FDS

CaPaFi


Y.C.Wong 186

0.00

2.00

4.00

6.00

8.00

0 500 1000 1500 2000 2500 3000

Tota

l He

at f

luxe

s [k

W/m

2 ]

Time [s]


FDS

CaPaFi

0.00

2.00

4.00

6.00

8.00

0 500 1000 1500 2000 2500 3000

Tota

l He

at f

luxe

s [k

W/m

2 ]

Time [s]


FDS

CaPaFi

0.00

2.00

4.00

6.00

8.00

0.00 500.00 1000.00 1500.00 2000.00 2500.00 3000.00

Tota

l He

atfl

uxe

s [k

W/m

2]

Time [s]


FDS

CaPaFi

0.00

1.00

2.00

3.00

4.00

5.00

6.00

0.00 500.00 1000.00 1500.00 2000.00 2500.00 3000.00

Tota

l He

at f

luxe

s [k

W/m

2 ]

Time [s]


FDS

CaPaFi


Y.C.Wong 187

Appendix 26 Data temperatures model 7 (hidden beams)



0 20.00 20.00 20.00 20.00 20.00 20.00

60 20.37 20.04 20.57 20.08 20.58 20.03

120 21.09 20.60 21.72 21.08 21.69 20.44

180 22.05 21.64 23.39 22.94 23.21 21.21

240 23.34 23.14 25.23 25.57 24.96 22.32

300 24.64 25.03 27.12 28.84 26.75 23.72

360 25.78 26.86 28.96 32.03 28.39 25.09

420 26.89 28.65 30.77 35.13 30.00 26.42

480 27.90 30.40 32.44 38.15 31.61 27.72

540 28.98 32.10 34.03 41.08 32.94 28.99

600 29.99 33.76 35.59 43.95 34.29 30.23

660 31.10 35.38 37.00 46.73 35.80 31.44

720 32.11 36.96 38.30 49.45 37.07 32.62

780 33.80 38.61 43.21 52.55 38.85 34.23

840 36.45 41.39 48.29 60.53 40.86 40.77

900 38.70 44.09 53.19 68.25 42.58 47.10

960 40.33 46.73 57.80 75.73 44.28 53.25

1020 42.76 49.35 62.88 83.07 46.26 59.24

1080 44.88 52.52 68.24 91.20 48.78 65.53

1140 46.84 56.22 74.27 100.05 51.48 72.07

1200 49.03 60.40 80.78 109.57 54.70 78.85

1260 51.28 65.04 87.72 119.73 58.11 85.85

1320 54.10 70.12 95.65 130.82 61.65 93.05

1380 56.86 75.63 104.93 143.37 65.64 100.52

1440 61.14 81.77 116.21 157.95 69.71 109.13

1500 65.42 88.90 136.55 174.83 89.38 119.38

1560 69.15 100.35 154.28 199.03 107.55 136.96

1620 72.25 108.26 163.20 220.47 115.87 154.19

1680 76.18 114.33 170.71 238.24 123.46 171.01

1740 82.29 120.20 180.88 255.95 129.59 188.66

1800 85.89 126.58 187.43 276.29 135.82 210.04

1860 88.39 131.67 191.50 292.08 139.90 226.96

1920 90.59 135.55 194.53 302.70 143.44 238.77

1980 92.00 138.87 196.22 311.50 146.49 248.96

2040 93.35 141.63 197.22 318.50 148.70 257.49

2100 94.15 143.87 197.60 324.04 150.62 265.08

2160 94.83 145.67 197.29 328.76 152.12 272.54

2220 95.26 147.04 196.18 332.65 153.58 279.89

2280 95.24 147.99 194.91 335.74 155.06 287.55

2340 95.07 148.53 193.59 338.07 156.76 295.78

2400 94.92 148.98 192.67 340.09 158.88 304.55

2460 94.71 149.37 192.87 341.95 163.08 341.01

2500 94.51 149.82 192.48 343.96 163.78 322.80


Y.C.Wong 188



0 20.00 20.00 20.00 20.00 20.00 20.00

60 20.34 20.01 20.04 20.00 20.03 20.00

120 21.04 20.10 20.27 20.03 20.24 20.03

180 22.09 20.28 20.64 20.08 20.55 20.08

240 23.29 20.55 21.03 20.15 20.95 20.16

300 24.48 20.89 21.47 20.24 21.36 20.26

360 25.72 21.22 21.88 20.34 21.72 20.36

420 26.90 21.55 22.26 20.43 22.09 20.45

480 27.93 21.87 22.61 20.51 22.45 20.55

540 29.06 22.18 22.99 20.60 22.81 20.64

600 30.17 22.48 23.32 20.68 23.11 20.73

660 31.03 22.78 23.65 20.77 23.45 20.82

720 31.92 23.07 23.98 20.85 23.76 20.90

780 33.28 23.46 24.78 20.94 24.73 21.00

840 34.71 25.04 25.70 21.16 25.74 21.26

900 36.28 26.59 26.56 21.37 26.76 21.51

960 37.75 28.09 27.39 21.58 27.70 21.76

1020 39.27 29.57 28.30 21.78 28.75 22.00

1080 41.13 31.13 29.17 22.02 29.83 22.28

1140 43.27 32.78 30.18 22.29 30.99 22.59

1200 45.72 34.50 31.33 22.58 32.30 22.92

1260 48.46 36.29 32.46 22.91 33.56 23.29

1320 51.02 38.16 33.79 23.25 34.99 23.68

1380 53.82 40.10 35.09 23.63 36.54 24.10

1440 57.07 42.37 36.55 24.05 38.09 24.58

1500 59.56 45.23 38.67 24.55 40.76 25.14

1560 62.47 51.57 40.98 25.30 43.48 26.02

1620 64.43 57.58 42.92 25.96 46.05 26.79

1680 66.18 63.29 44.80 26.52 48.10 27.47

1740 68.12 69.07 46.78 27.08 50.27 28.16

1800 69.59 75.68 48.69 27.73 52.51 28.95

1860 70.63 81.20 50.04 28.25 54.11 29.59

1920 71.87 85.73 51.04 28.65 55.48 30.09

1980 72.77 89.93 52.10 29.00 56.91 30.52

2040 73.85 93.81 53.03 29.30 57.99 30.91

2100 74.85 97.42 53.68 29.57 58.93 31.24

2160 76.40 101.30 54.43 29.81 59.93 31.56

2220 77.38 105.41 55.02 30.03 60.85 31.86

2280 79.05 109.75 55.57 30.22 61.73 32.13

2340 80.42 114.29 56.35 30.40 62.57 32.38

2400 82.55 119.10 57.01 30.57 63.42 32.64

2460 87.57 124.47 57.83 30.74 64.27 32.90

2500 87.88 130.54 58.70 30.91 64.98 33.15


Y.C.Wong 189


t[s] FDS CaPaFi FDS CaPaFi

0 20.00 20.00 20.00 20.00

60 20.03 20.00 20.04 20.00

120 20.25 20.03 20.29 20.02

180 20.56 20.07 20.61 20.05

240 20.96 20.14 21.04 20.10

300 21.38 20.23 21.47 20.16

360 21.76 20.32 21.85 20.23

420 22.14 20.41 22.26 20.29

480 22.51 20.49 22.63 20.35

540 22.85 20.57 22.96 20.40

600 23.18 20.66 23.32 20.46

660 23.54 20.73 23.66 20.52

720 23.84 20.81 23.99 20.57

780 24.67 20.90 24.67 20.63

840 25.72 21.15 25.56 20.83

900 26.65 21.40 26.33 21.02

960 27.67 21.63 27.20 21.20

1020 28.63 21.87 28.03 21.38

1080 29.74 22.14 28.83 21.58

1140 30.88 22.43 29.78 21.81

1200 32.03 22.75 30.71 22.04

1260 33.27 23.09 31.64 22.30

1320 34.52 23.46 32.67 22.57

1380 35.90 23.85 33.76 22.86

1440 37.31 24.30 34.94 23.20

1500 40.03 24.83 37.14 23.60

1560 42.69 25.68 39.42 24.26

1620 44.92 26.43 41.24 24.86

1680 47.22 27.11 42.98 25.40

1740 49.45 27.79 44.98 25.96

1800 51.71 28.58 46.68 26.60

1860 53.38 29.22 48.03 27.12

1920 54.92 29.72 49.32 27.53

1980 56.31 30.16 50.38 27.90

2040 57.47 30.55 51.32 28.22

2100 58.49 30.89 52.23 28.52

2160 59.37 31.22 53.01 28.80

2220 60.46 31.54 53.78 29.08

2280 61.19 31.84 54.46 29.36

2340 61.86 32.12 55.04 29.63

2400 62.64 32.41 55.64 29.90

2460 63.34 32.70 56.46 30.19

2500 64.03 32.99 57.30 30.47


Y.C.Wong 190

0.00

50.00

100.00

150.00

200.00

0 500 1000 1500 2000 2500 3000

Tem

pe

artu

re [

oC

]

Time [s]


FDS

CaPaFi

0.00

100.00

200.00

300.00

400.00

0 500 1000 1500 2000 2500 3000

Tem

pe

ratu

re [

oC

]

Time [s]


FDS

CaPaFi

0.00

100.00

200.00

300.00

400.00

0 500 1000 1500 2000 2500 3000

Tem

pe

ratu

re [

oC

]

Time [s]


FDS

CaPaFi

0.00

50.00

100.00

150.00

0 500 1000 1500 2000 2500 3000

Tem

pe

ratu

re [

oC

]

Time [s]


FDS

CaPaFi


Y.C.Wong 191

0.00

20.00

40.00

60.00

80.00

0 10 20 30 40 50

Tem

pe

ratu

re [

oC

]

Time [s]


FDS

CaPaFi

0.00

20.00

40.00

60.00

80.00

0 10 20 30 40 50

Tem

pe

ratt

ure

[oC

]

Time[s]


FDS

CaPaFi

0.00

20.00

40.00

60.00

80.00

0 500 1000 1500 2000 2500 3000

Tem

pe

ratu

re [

oC

]

Time [s]


FDS

CaPaFi

0.00

20.00

40.00

60.00

80.00

0 10 20 30 40 50

Tem

pe

rrat

ure

[oC

]

Time [s]


FDS

CaPaFi


Y.C.Wong 192

Appendix 27 Comparison heat fluxes model 6 and 7

The data used for the graphs are presented in the previous appendices.

0

5

10

15

20

25

30

0 500 1000 1500 2000 2500 3000

Tota

l he

at f

luxe

s [k

W/m

2 ]

Time [s]


With obstacles (M6)

Without Obstacles (M7)

CaPaFi

0

20

40

60

80

0 500 1000 1500 2000 2500 3000

Tota

l he

at f

luxe

s [k

W/m

2 ]

Time [s]


With obstacles (M6)

Without obstacles (M7)

CaPaFi

0

10

20

30

40

50

60

0 500 1000 1500 2000 2500 3000

Tota

l he

at f

luxe

s [k

W/m

2 ]

Time [s]


With obstacles (M6)


CaPaFi


Y.C.Wong 193

0

5

10

15

20

25

0 500 1000 1500 2000 2500 3000

Tota

l he

at f

luxe

s [k

W/m

2]

Time [s]


With obstacles (M6)


CaPaFi

0

2

4

6

8

0 500 1000 1500 2000 2500 3000

Tota

l he

at f

luxe

s [k

W/m

2 ]

Time [s]


With obstacles (M6)


CaPaFi

0

2

4

6

8

0 500 1000 1500 2000 2500 3000

Tota

l he

at f

luxe

s [k

W/m

2 ]

Time [s]


With obstacles (M6)


CaPaFi


Y.C.Wong 194

0

2

4

6

8

0 500 1000 1500 2000 2500 3000

Tota

l he

at f

luxe

s [k

W/m

2]

Time [s]


With obstacles (M6)


CaPaFi

0

1

2

3

4

5

6

0 500 1000 1500 2000 2500 3000

Tota

l he

at f

luxe

s [k

W/m

2 ]

Time [s]


With obstacles (M6)


CaPaFi


Y.C.Wong 195

Appendix 28 Comparison temperature model 6 and 7

The data used for the graphs are presented in the previous appendices.

0

20

40

60

80

100

120

140

160

0 500 1000 1500 2000 2500 3000

Tem

pe

ratu

re [

oC

]

Time [s]


With obstacles (M6)


With obstacles Side (M6)

CaPaFi

0

50

100

150

200

250

300

350

400

0 500 1000 1500 2000 2500 3000

Tem

pe

ratu

re [

oC

]

Axis Title


With obstacles (M6)



CaPaFi

0

50

100

150

200

250

300

350

0 500 1000 1500 2000 2500 3000

Tem

pe

ratu

re [

oC

]

Time [s]


With obstacles (M6)



CaPaFi


Y.C.Wong 196

0

20

40

60

80

100

120

140

0 500 1000 1500 2000 2500 3000

Tem

pe

ratu

re [

oC

]

Time [s]


With obstacles (M6)



CaPaFi

0

10

20

30

40

50

60

70

0 500 1000 1500 2000 2500 3000

Tem

pe

ratu

re [

oC

]

Time [s]


With obstacles (M6)



CaPaFi

0

10

20

30

40

50

60

70

0 500 1000 1500 2000 2500 3000

Tem

pe

ratu

re [

oC

]

Time [s]


With obstacles (M6)



CaPaFi


Y.C.Wong 197

0

10

20

30

40

50

60

70

0 500 1000 1500 2000 2500 3000

Tem

pe

ratu

re [

oC

]

Time [s]


With obstacles (M6)



CaPaFi

0

10

20

30

40

50

60

70

0 500 1000 1500 2000 2500 3000

Tem

pe

ratu

re [

oC

]

Time [s]


With obstacles (M6)



CaPaFi

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