fire resistance of materials & structures - modelling of fire scenario

Fire Resistance of Materials & Structures Modelling of Fire Scenario

Date of Submission

2016

Submitted by

Seyed Mohammad Sadegh Mousavi

836 154

Submitted to

Prof. P. G. Gambarova

Prof. R. Felicetti

Dr. P. Bamonte

Structural Assessment & Residual Bearing

Capacity, Fire & Blast Safety

Civil Engineering for Risk Mitigation

Politecnico di Milano

[ 2 n d H o m e w o r k - M o d e l l i n g o f f i r e s c e n a r i o ]

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Politecnico di Milano – Lecco Campus


Prof. R. Felicetti & Prof. P. G. Gambarova & Dr. P. Bamonte

Seyed Mohammad Sadegh Mousavi (836154)

Fire Resistance of Materials and Structures

Prof. R. Felicetti, Prof. P.G. Gambarova and Dr. P. Bamonte

2nd Homework - Modelling of the fire scenario

The figure below shows the plan of a library room, whose structural elements are to be checked (in terms of

bearing capacity, R criterion) in fire conditions. The dimensions of the room and windows are given in

centimeters; the height of the room is 3.50 m.

The active protection measures of the room are as follows:

· NO automatic fire suppression;

· NO independent water supplies;

· Automatic detection and alarm systems, by smoke;

· NO automatic transmission to Fire Brigade;

· NO on site Fire Brigade.

· The library is provided with safe access routes and fire-fighting devices.

The thermal characteristics of the walls, floor and ceiling (thick layers) are as follows:

· Mass per unit volume: ρ = 1100 · (1 + F/50) [kg/m3]

· Specific heat: c = 950 [J/ (kg K)]

· Thermal conductivity: λ = 0.5 · (1 - L/50) [W/ (m K)]

Evaluate the possible fire scenario, in terms of temperature-time curve, following:

a) The parametric approach given in the standard EN 1991-1-2 (with two alternative cooling stages);

b) The two/one-zone numerical model implemented in the Ozone 2.2.5 software according to the two

following hypotheses for the vents opening (according to the Luxenbourg Authorities):

- Scenario 1: windows are constantly 90% open from the beginning of the fire

- Scenario 2: double glazing failure: 50% opening beyond 200°C and 90% opening beyond 400°C F = number corresponding to the 3rd letter of the first name

L = number corresponding to the 3rd letter of the last name

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Thermal characteristics of walls, floor and ceiling:

F= 25 (Y), L= 21 (U)

Mass per unit volume :

𝜌 = 1100 (1 +25

50) = 1650 [

𝑘𝑔𝑚3⁄ ]

Specific Heat: c= 950 [J/(kgK)]

Thermal Conductivity:

𝜆 = 0.5 (1 −21

50) = 0.29 [𝑊

𝑚 𝐾⁄ ]

Opening Area: 𝐴𝑣 = 𝐵 × 𝐻𝑣 (𝑚2) (𝐻𝑣=Opening Height)

Segment Data

Floor Area 𝑨𝒇 8 × 12 = 96 𝑚2

Total area of the enclosure 𝑨𝒕 2 × (8 × 3.5 + 12 × 3.5 + 8 × 12) + 9 = 341 𝑚2

Average Height of openings 𝑯𝑽 1.5 𝑚

Area of vertical openings 𝑨𝒗 3 × 2 × 1.5 = 9 𝑚2

1. The Parametric Approach (given in standard EN1991-1-2)

Fire load density is the maximum energy released per 𝑚2.

𝑞𝑓,𝑘 =𝑄𝑓𝑖,𝑘

𝐴𝑓 (MJ/𝑚2) is refered to the area of the floor 𝐴𝑓.

𝑞𝑡 =𝑞𝑓,𝑑𝐴𝑓

𝐴𝑡(MJ/𝑚2) is refered to the total area 𝐴𝑡 of the enclosure (Walls, Openings & Ceiling included)

In case of the type of occupancy is known, 𝑞𝑓,𝑘 is provided by the tables in books & recommendations.

For library, value of characteristic fire load density (80% fractile) has been chosen from table in Fig.1:

𝑞𝑓,𝑘 = 1824 𝑀𝐽

𝑚2⁄

Under the assumption: 𝛿𝑞2 = 1

(Unit value of the danger of fire activation factor)

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Figure 1 – Type of occupancy

According to the Annex E (informative) EN 1991-Part 1-2, design fire load density is:

𝑞𝑓,𝑑 = 𝑞𝑓,𝑘 . 𝑚 . 𝛿𝑞1. 𝛿𝑞2. 𝛿𝑛 (𝑀𝐽

𝑚2⁄ )

Where:

m = Combustion factor, function of a type of fire load. For Cellulosic fire ≅ 0.8.

Danger of fire activation factors:

𝛿𝑞1 = Considering the compartment size.

𝛿𝑞2 = Considering the type of occupancy.

Figure 2 – Compartment floor area (At)

For 𝐴𝑓 = 96 𝑚2 → {𝛿𝑞1 = 1.33

𝛿𝑞2 = 1.0

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𝛿𝑛= Factors which consider the effect of the active fire fighting measures.

𝛿𝑛 = ∏ 𝛿𝑛𝑖

10

𝑖=1

Figure 3 – Active fire fighting measures

The active fire fighting measures of the room with respect to the Fig.3, are as follows:

NO Automatic fire suppression 𝛿𝑛1 = 1.0

NO Independent water supplies 𝛿𝑛2 = 1.0

Automatic detection & Alarm System, by Smoke {𝛿𝑛3 = 1.0 𝛿𝑛4 = 0.73

No Automatic transmission to fire bridge 𝛿𝑛5 =1.0

No on site fire bridge 𝛿𝑛7 = 0.78

Library provided with safe access route 𝛿𝑛8 = 1.0

Library provided with fire fighting devices 𝛿𝑛9 = 1.0

No smoke exhaust system 𝛿𝑛10 = 1.5

𝛿𝑛 = ∏ 𝛿𝑛𝑖

10

𝑖=1

= 0.73 × 0.78 × 1.5 = 0.8541

Design fire load density:

𝑞𝑓,𝑑 = 1824 × 0.8 × 1.33 × 1 × 0.8541 = 1657.58 (𝑀𝐽𝑚2⁄ )

Design fire load related to total area of enclosure: (Must be in the range 50 ≤ 𝑞𝑡,𝑑 ≤ 1000 𝑀𝐽𝑚2⁄ )

𝑞𝑡,𝑑 =𝑞𝑓,𝑑𝐴𝑓

𝐴𝑡=

1657.58 × 96

341= 466.65 (

𝑀𝐽𝑚2⁄ )

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Part a - Parametric fires according to Eurocode 1:

The Time-Temperature is a function of fire load, Ventilation and wall lining

The limitation of fire load is for compartments of floor area (𝐴𝑓) < 500 𝑚2

The limitation of height of the compartment < 4 m

The limitation of the wall lining, only vertical vent (no ceiling windows)

They have been worked out by interpolating the burning phase of the Swedish curves.

Temperature-time dependency for parametric fire is:

𝑇(℃) = 20 + 1325(1 − 0.324𝑒−0.2𝑡∗− 0.204𝑒−1.7𝑡∗

− 0.472𝑒−19𝑡∗)

Where:

𝑡∗ = Fictitious time, 𝑡∗ = Γ. t and t is the time in hours.

The sequence of step is:

1- Evaluate the wall factor (b) – (Square root of thermal inertia)

𝑏 = √𝜆𝜌𝑐 (100 < b < 2200)

𝑏𝑟𝑒𝑓 = 1160 (Reference value of thermal inertia)

b Factor - Thermal Inerta

Section Area (m^2) ρ [kg⁄m^3 ] c [J/Kg°C ] λ [W/m °C ] bi bi.Ai

Walls 140 1650 950 0.29 674 94391

Floor 96 1650 950 0.29 674 64725

Ceiling 96 1650 950 0.29 674 64725

Total 332 674.223 223842

(Opening Excluded) 𝑊𝑆1

2⁄

𝑚2°C

Figure 4 – Wall factor (b)

2- Evaluate Openin factor (O)

𝑂 = 𝐹𝑣 =𝐴𝑣√𝐻𝑣

𝐴𝑡=

9×√1.5

341= 0.0323 (0.02 < O < 0.20)

O = Opnenig (Ventilation) factor EN1991-2002 (𝐹𝑣 in Buchanan’s Book)

𝑂𝑟𝑒𝑓 = 0.4 (Reference value of the ventilation factor)

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3- Evaluate the factor (𝚪)

Γ = (

𝑂𝑂𝑟𝑒𝑓

𝑏𝑏𝑟𝑒𝑓

)

2

= (

0.03230.04

674.2231160

)

2

= 1.93

Γ = Distortion of the time scale that takes into account of the fact that fire is expected to be faster or

slower than in normal conditions.

So, Γ = 1.93 > 1.0 (high ventilation, low thermal inertia) will yield a faster heating phase compared to

the ISO curve (and vise versa).

4- Determine the shortest possible duration of the heating phase (𝒕𝒍𝒊𝒎) in hours:

According to the Fig.6 that is given from the minimum time for propagation (𝑡𝑙𝑖𝑚) in excel sheet and

code:

Minimum Time for Propagation (𝑡𝑙𝑖𝑚)

Slow 25

Medium 20

Fast 15

Figure 5 – Minimum time for propagation (𝒕𝒍𝒊𝒎)

So, In our case for the library (Fast fire growth rate) is 𝒕𝒍𝒊𝒎 = 𝟏𝟓 𝒎𝒊𝒏

Figure 6 – Fire growth rate cases

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5- Evaluate the duration of the ventilation-contorlled heating phase (𝒕𝒎𝒂𝒙) in hours

Time needed in case of reaching the maximum temperature that is the maximum between the ventilation

controlled time to burn the fire load (Kawagoe formula) and the fuel controlled minimum time, 𝑡𝑙𝑖𝑚.

𝑡𝑚𝑎𝑥 =2 × 10−3 × 𝑞𝑡,𝑑

𝑂=

2 × 10−3 × 467

0.0323= 2.89 ℎ𝑟𝑠

6- a) If 𝑡𝑚𝑎𝑥 > 𝑡𝑙𝑖𝑚 then the fire is ventilation controlled, as in this cases.

Determination the fictitious time to reach the maximum temperature, 𝑡𝑚𝑎𝑥∗ ,via the relevant time scale

factor Γ for ventilation controlled fire:

𝑡𝑚𝑎𝑥∗ =

0.0002×𝑞𝑡,𝑑

𝑂. Γ =

0.0002×467

0.0323× 1.93 = 5.581 hrs

𝑇𝑚𝑎𝑥 = 20 + 1325(1 − 0.324𝑒−0.2𝑡𝑚𝑎𝑥∗

− 0.204𝑒−1.7𝑡𝑚𝑎𝑥∗

− 0.472𝑒−19𝑡𝑚𝑎𝑥∗

) = 1204 ℃

Temperature during the heating phase, untill 𝑡 = 𝑡𝑚𝑎𝑥 is given by:

𝜃𝑔 = 20 + 1325(1 − 0.324𝑒−0.2𝑡∗− 0.204𝑒−1.7𝑡∗

− 0.472𝑒−19𝑡∗)

𝑡∗ = Γ × 𝑡

Temperaute during the cooling phase during the cooling down phase is given by: (EC1 & ISO)

𝜃𝑔 = 𝜃𝑚𝑎𝑥 − 625. (𝑡 − 𝑡𝑚𝑎𝑥). Γ 𝑓𝑜𝑟 𝑡𝑚𝑎𝑥∗ ≤ 0.5

𝜃𝑔 = 𝜃𝑚𝑎𝑥 − 250. (3 − 𝑡𝑚𝑎𝑥∗ ). (𝑡 − 𝑡𝑚𝑎𝑥). Γ 𝑓𝑜𝑟 0.5 < 𝑡𝑚𝑎𝑥

∗ < 2.0

𝜃𝑔 = 𝜃𝑚𝑎𝑥 − 250. (𝑡 − 𝑡𝑚𝑎𝑥). Γ 𝑓𝑜𝑟 2.0 ≤ 𝑡𝑚𝑎𝑥∗

Where 𝑡𝑚𝑎𝑥∗ = (

0.2×10−3×𝑞𝑡,𝑑

𝑂). Γ

According to the value of 𝑡𝑚𝑎𝑥∗ = 5.581 ℎ𝑟𝑠, the 3rd situation has been used.

Buchanan formula for cooling rate:

According to Buchanan, it should be more accurate to correct the cooling rate with a time scale

different from Γ. So Buchanan proposed different furmula for this issue.

𝑑𝑇

𝑑𝑡= (

𝑑𝑇

𝑑𝑡)

𝑟𝑒𝑓.

√𝑂0.04⁄

√𝑏1900⁄

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This is equivalent to using a second fictitious time, similar to that in the growth period, but in case of

better and accurare test results and computer simulations using square root rather than squared terms.

Thermal analysis should be performed taking into account also the cooling stage, as cooling is not

immediate inside the member and the damage can go up to the complete cooling of the member.

t/tmax* t* () real t. (h) T (°C) – EC1 P.F

0.00 0.0000 0.0000 20.0

0.05 0.2791 0.1444 767.7

0.10 0.5581 0.2887 856.4

0.15 0.8372 0.4331 916.8

0.20 1.1163 0.5775 961.1

0.25 1.3954 0.7218 995.0

0.30 1.6744 0.8662 1022.2

0.35 1.9535 1.0105 1044.8

0.40 2.2326 1.1549 1064.2

0.45 2.5116 1.2993 1081.4

0.50 2.7907 1.4436 1097.0

0.55 3.0698 1.5880 1111.2

0.60 3.3489 1.7324 1124.4

0.65 3.6279 1.8767 1136.6

0.70 3.9070 2.0211 1148.1

0.75 4.1861 2.1655 1158.9

0.80 4.4651 2.3098 1169.1

0.85 4.7442 2.4542 1178.7

0.90 5.0233 2.5985 1187.8

0.95 5.3024 2.7429 1196.3

1.00 5.5814 2.8873 1204.4

Figure 7 – EC1 Parametric Fire table

Figure 8 – ECI Time-Temperature fire curve comparing with ISO

0

200

400

600

800

1000

1200

1400

0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00

Te

mpe

ratu

re (

°C)

Time (hours)

EC1 parametric fire

ISO 834

EC1's cooling

Buchanan's cooling

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In the both ISO834 and EC1 time-temperature cases, there are a sharp increase in the time-temperature

curve during around the first 15 minutes. However, time scaling factor Γ accelerates the heating phase in

compression ISO834 fire. For EC1 fire, the time needed to reach maximum temperature is 2.8873h,

while for ISO834, that temperature at that time is around 10 percent less than EC1 fire.

According to the cooling stage and its plot, it is obvious that EC1 cooling is faster than the Buchanan’s

cooling. With respect to the slope calculation in excel, it provides that Buchanan’s cooling rate is

294.8°C/hour with cooling phase duration of 4.02h , while EC1 cooling rate is 483.3°C/hour with the

cooling phase duration of 2.45 hours.

O-ZONE

Part b – Time-Temperature Curve using O-Zone

To reach the aim of this homework, some implmentations were done in Ozone software. Ozone switches

autmatically from two zones [+localized fire] (Growth phase) to one zone (Fully developed fire).

Figure 9 – Zones

Figure 10 – Strategy

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In the next step, the compartment’s dimensions and wall openings were defined:

Figure 11 – Compartment’s Dimension

Definition of materials for floor, cleiling, walls- One layer of normal weight concerete with

thermal properties assigned. Openings, for the walls that contain them, are also defined.

Figure 12 – Materials Property

Openings: Walls 1 & 4 are defined in a same way:

Figure 13 – Walls 1 & 4

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Then, for the wall 2 (Fig. 14) was deifined an opening (window with its demension):

Figure 14 – Opening of wall 2

and also for wall 3 was defined two openings. As you can see in the following figure:

Figure 15 – Opening of wall 3

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Definition of the curve:

Parametric fire curve, according to EN 1991-1-2 has been chosen. Existing fire fighting measures are

checked and accounted for.

Figure 16 – Parametric Fire Curve

Definition of Paramaeters:

Calculation time was set to 8 hours, since we want to take cooling stage into account.

Two scenarios regarding openings have been defined:

Scenario 1: Time dependent openings (windows are constantly 90% opened from the beginning of the

fire).

Scenario 2: Temperature dependent openings - double glazing failure (50% opening beyond 200°C

and 90% opening beyond 400°C) - linear and stepwise.

As a result, 3 models were done with respect to the openings by changing the variation option:

1- Temperature dependent openings

Linear

Stepwise

2- Time dependent opening

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Figure 17 – Parameters

Results – Comparisions among different models

The following graph is a gas temperature comparison among the 3 different models. According the

trends and global point of view all the 3 curves tend to overlap.

Figure 18 – Localised Fire Curves

0

100

200

300

400

500

600

700

800

900

1000

1100

1200

1300

0 50 100 150 200 250 300 350 400 450 500

Tem

per

atu

re (

°C)

Time (min)

Time - Temperature Curve

Temp Dependent-Linear

Temp Dependent-Stepwise

Time Dependent

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Due to some flactuation in heating stage for three different cases in Fig. 18, it is necessary to check and

analyse the first few minutes more precisely. So, for reach to this aim the following graph (Fig. 19) will

be reperesented.

Figure 19 – Localised Fire Curves 2

According to the different scenarios regarding ventilation and openings, there are some differences

(flactuations) are dominant on the plot until around 8 min. while, all the curves will be almost the same

after that time.

For the temperature dependent openings (Linear & Stepwise) act very close to each other, but in case of

reaching the temperature of 500°C, linear temperature dependent openings is a bit faster than Stepwise

temperature dependent openings.

On the other hand, in case of time dependent scenario, there is a spike on the curve due to the failure of

the windows that it causes rapid decrease of the temperature because of fresh air is entering the

compartment and cools it and then immediately after that, again the temperature rise because of fresh air

increased the combustion.

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Comparison of EC1-Parametric Approach and Ozone fire evolution:

Figure 20 – Comparison between EC1 & Ozone Fire Evolution

The behavior of EuroCode parametric fire and Ozone fire are the same in the first minutes of fire or

clearly under the 500°C temperature, so having high burning rates.

When the temperature of 500°C is achieved in the Ozone, model will be switched from two zones (Pre-

flashover, growth period) to one zone (Fully developed fire).

The rate of burning in the Pre-flashover is generally governed by the nature of burning fuel surfaces,

while in the burning period (fully developed fire), the temperature and the radiant heat flux within the

room are so great that all exposed surfaces are burning and the RHR is governed by the available

ventilation.

Ozone model supposed lack of oxygen while in parametric fire model, there is no such an assumption.

According to the cooling stage, in the Ozone model it is not linear as in EC and Buchanan models, it is

faster down to 200°C and then it is happening at a slower rate down to room temperature.

0

200

400

600

800

1000

1200

1400

0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00

Te

mp

era

ture

(°C

)

Time [hours]

Comparison between EC1 & Ozone Fire Evolution

EC1 parametric fire

ISO 834

EC1's cooling

Buchanan's cooling

Time Dependent

Temp Dependent-Linear

Temp Dependent-Stepwise

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Results (Obtained by OZONE)

1st Scenario – Temperature Dependent Opening (Linear Variation)

Fire Area: The maximum fire area ( 96.00m²) is greater than 25% of the floor area ( 96.00m²). The fire load is uniformly distributed. Switch to one zone: Lower layer Height < 20.0% ocompartment height at time [s] 207.53 Fully engulfed fire: Temperature of zone in contact with fuel >300.0°C at time [s] 332.80

Peak: 1255 °C At: 171 min

Figure 21. Hot and Cold Zone Temperature

According to the model passes from 2 zones to 1 zone (around 3 min), so the cold zone stops at the beginning.

Peak: 48.00 MW At: 17.3 min

Figure 22. RHR Data and Computed

0

200

400

600

800

1000

1200

1400

0 50 100 150 200 250 300 350 400 450 500

Time [min]

Hot Zone

Cold Zone

Analysis Name: Library

Gas Temperature

0.0

5.0

10.0

15.0

20.0

25.0

30.0

35.0

40.0

45.0

50.0

0 50 100 150 200 250 300 350 400 450 500

Time [min]

RHR Data

RHR Computed


Rate of Heat Release

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According to the previous graph (Fig. 22), the theoretical Rate of Heat Release that is given by the code depends

on the type of compartment although calculated RHR related to the room’s envirinmental conditions and

ventilation factor of the openings.The area of the 2 curves should be the same while due to lack of Oxygen, at the

beginning there is low temperature. For theoretical RHR is around takes around 84 min and for computed RHR it

is around 310 min.

Figure 23. Zone Interface Elevation – Linear Variation

When the hot layer takes up more than 80 % of the total height of the compartment flashover will be happened

and as a result the seperation of 2 layers will be vanished.

Figure 24. Oxygen Mass – Linear Variation

The quantity of Oxygen in the room during the fire is change with time. According to the Fig. 24 at the beginning

the trend of Oxygen suddenly decrease because of the Oxygen is consumed by the combustion. At this step the

temperature is low but after breaking the windows and due to availablity of fresh air in the compartment that trend

is constant (zero) for some minutes and then Oxygen Mass tends to gradually increase in the room because the

combustile materials are consumed and they need less quantity of Oxygen for burning, that is Cooling Pahse.

0

0.5

1

1.5

2

2.5

3

3.5

4

0 0.5 1 1.5 2 2.5 3 3.5

[m]

Time [min]

Zone Interface Elevation - Linear

0

10

20

30

40

50

60

70

80

90

100

0 50 100 150 200 250 300 350 400 450 500

(kg)

Time (min)

Oxygen Mass - Linear

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2nd Scenario – Temperature Dependent Opening (Stepwise)






0

200

400

600

800

1000

1200

1400

0 50 100 150 200 250 300 350 400 450 500

Time [min]

Hot Zone

Cold Zone


Gas Temperature

0.0

5.0

10.0

15.0

20.0

25.0

30.0

35.0

40.0

45.0

50.0

0 50 100 150 200 250 300 350 400 450 500

Time [min]

RHR Data

RHR Computed



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Figure 27. Zone Interface Elevation – Stepwise Variation

Figure 28. Oxygen Mass – Stepwise Variation

0

0.5

1

1.5

2

2.5

3

3.5

4

0 0.5 1 1.5 2 2.5 3

[m]

Time [min]

Zone Interface Elevation - Stepwise

0

10

20

30

40

50

60

70

80

90

100

0 100 200 300 400 500

(kg)

Time (min)

Oxygen Mass - Stepwise

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3rd Scenario – Time Dependent Opening






0

200

400

600

800

1000

1200

1400

0 50 100 150 200 250 300 350 400 450 500

Time [min]

Hot Zone

Cold Zone


Gas Temperature

0.0

5.0

10.0

15.0

20.0

25.0

30.0

35.0

40.0

45.0

50.0

0 50 100 150 200 250 300 350 400 450 500

Time [min]

RHR Data

RHR Computed



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Figure 31. Zone Interface Elevation – Time-Dependent Opening

Figure 32. Oxygen Mass – Time-Dependent Opening

0

0.5

1

1.5

2

2.5

3

3.5

4

0 1 2 3 4 5 6 7

[m]

Time [min]

Zone Interface Elevation - Time Dependent Opening

0

10

20

30

40

50

60

70

80

90

100

0 100 200 300 400 500

(kg)

Time (min)

Oxygen Mass - Time Dependent Opening

fire resistance of materials & structures - modelling of fire scenario

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