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Performance-Based Design of Structural Fire Resistance
Morgan J. Hurley, P.E.Society of Fire Protection Engineers
Brian Y. Lattimer, Ph.D.Hughes Associates, Inc.
Presentation Overview
• Historical perspective• Elements of performance-based design
approach• Calculation of fire boundary conditions
– Enclosure fires– Localized fires
Historical Perspective
• Fire resistance specified based on ASTM E-119 “standard fire”
• ASTM E-119 specifies furnace temperature and thermal endpoint criteria
• Codes specify required “ratings”
ASTM E-119 Endpoint Criteria
• Must maintain applied load or• Average of measured temperatures must not
exceed specified limits
Basis for Code Requirements
Application
• Select an assembly that has been tested• Use engineering calculations, e.g.,
ASCE/SFPE 29-99
Limitations• “Standard” fire does not consider all of the factors
that would influence fire severity• Single elements tested in isolation, without
considering structural performance• Air temperature in furnace measured
– Radiation from walls dominant mode of heat transfer
• Ratings based on mass per unit area in typical occupancies– Mass not necessarily indicative of severity
Limitations
• Convection
• Radiation
( )sg TThq −=′′&
( )44sTTq −=′′ σ&
Performance-Based Design Approach
• Estimate fire exposures• Perform heat transfer analysis to determine
thermal response• Perform structural analysis
Why Performance-Based Design?
• Better knowledge of fire safety provided by a design
• Apply best available science• Tailor safety to building use and
characteristics
Scenarios Considered
Heat Transfer
• Generally use finite element or finite difference approach
• Conservatively assume ε = 1 (ε expected to vary between 0.65 for small enclosures to 0.95 for realistic fires.)
• hc ≈ 10 – 30 W/m2K• For insulated members – assume surface
temperature = fire temperature
Compartment Fires
Time
Tem
pera
ture
Dev
elop
men
t
Flas
hove
r
Fully Developed
Cooling Phase
Significant effect on structure
Time
Tem
pera
ture
Dev
elop
men
t
Flas
hove
r
Fully Developed
Cooling Phase
Significant effect on structure
Compartment Fires
Ao
C.V.
T
fm&
δ k, ρ, c
Ho
m&
om&
ρ0, T0
Factors
• Fuel Load (mf)• Ventilation (Ao, Ho)• Enclosure thermal properties (k, ρ, C, A)
Compartment Fire Modeling
• Several predictive methods available – most are algebraic correlations
• Assumptions– Fuel distributed uniformly over floor– Vents in walls– Natural ventilation only– Large fires– Uniform conditions throughout enclosure
Compartment Fire Models
• Most models based on wood cribs, which may be conservative for enclosure fires
• Long, narrow, ventilation controlled enclosures – assumption of uniform conditions breaks down
• FDS holds some promise – CFD modeling + heat transfer and combustion
Eurocode Parametric Method
( )*** 197.12.0 472.0204.0324.011325 ttt eeeT −−− −−−=
Lie’s Parametric Method
5.0
1236.0/1.0 600)]1(4)1()1(3[)10(250
23.0
⎟⎟⎠
⎞⎜⎜⎝
⎛+−+−−−= −−−⎟
⎟⎠
⎞⎜⎜⎝
⎛−⎟
⎟⎠
⎞⎜⎜⎝
⎛
oo
tttt
AHA
AHA
oo
HAACeeee
AHA
Toooo
Tanaka
31
0000
32
0000
6.1
−
∞∞
∞
∞⎟⎟⎠
⎞⎜⎜⎝
⎛⎟⎟⎠
⎞⎜⎜⎝
⎛=⎟⎟
⎠
⎞⎜⎜⎝
⎛ −=
∆HAcg
AhHATcg
QT
TTT
T k
ρρ
&
Magnusson and ThelanderssonCurves
Harmathy
( ) ( ) ( ) ( )⎥⎦⎤
⎢⎣⎡ −−−+−∆+∆= 4
04
0 368.0932.01 TT
ATTcmmHHm
Aq o
focvfE σζβ &&&
41
42
1
0 2⎪⎭
⎪⎬⎫
⎪⎩
⎪⎨⎧
⎥⎥⎦
⎤
⎢⎢⎣
⎡⎟⎠⎞
⎜⎝⎛++≈
πκτ
ση kq
Tq
T EE
Babrauskas
54321 *****)1452( θθθθθoo TTT −+=
• θ1 - Stoiciometry• θ2 – Steady-state heat loss to walls• θ3 – Transient wall losses• θ4 – Radiation loss through vent• θ5 – Combustion efficiency
Ma and Mäkeläinen
0.0
0.2
0.4
0.6
0.8
1.0
1.2
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0
Time Ratio (t / tm)
Tem
pera
ture
Rat
io (T
g / T
gm)
δ = 0.5, 1.0
δ = 0.8, 1.6
CIB – Temperature
0
200
400
600
800
1000
1200
0 10 20 30 40 50A/AoHo1/2 (m-1/2)
T (°
C)
CIB Data
CIB Curve
CIB – Burning Rate
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0 10 20 30 40 50 60
A/AoHo (m^-1/2)
R/A
oHo(
D/W
)^1/
2 (k
g/s-
m^5
/2)
121
221
211
441
Curve Fit
Law
⎟⎟⎟⎟⎟
⎠
⎞
⎜⎜⎜⎜⎜
⎝
⎛
−=
−
oo
HAA
gm
HAA
eToo
1.0
16000
( )Ψ−−= 05.01 eTT gm
Evaluation
• Use CIB temperature and burning rate data to evaluate methods
Cardington
23 m
Closed end
Cribs distributed on floor
Thermocouple locations
2.7 m
5.5 m
Findings – Law
0
200
400
600
800
1000
1200
1400
0 10 20 30 40 50
( ) )(m / -1/2oo HAA
Findings – Law
0
0.05
0.1
0.15
0.2
0.25
0 10 20 30 40 50 60
A/AoHo (m^-1/2)
R/A
oHo(
D/W
)^1/
2 (k
g/s-
m^5
/2)
121
221
211
441
Law X 1.4
Findings – Law
0200400600800
100012001400
0 0.5 1
Time (h)
Tem
pera
ture
(C)
Measured
Law withoutreduction factorLaw
Findings – Law
Cardington Test #1
0200400600800
100012001400
0 1 2
Time (h)
Tem
pera
ture
(C)
MeasuredLaw Adusted
21
18−
= mHA
A
oo
Findings – Magnusson and Thelandersson
0
200
400
600
800
1000
1200
1400
0 0.5 1 1.5 2 2.5 3 3.5 4
Time (h)
Tem
pera
ture
(C)
Measured
Magnusson (Type C)
21
45−
= mHA
A
oo
Findings - Lie
0
100
200
300
400
500
600
700
800
900
0 1 2 3 4 5 6 7 8
Time (h)
Tem
pera
ture
(C)
Measured
Lie
21
45−
= mHA
A
oo
Are Correlations Based on Burning Wood Cribs OK?
Limitations
• Uncertainty in model inputs, e.g., fire load• Intervention, e.g. sprinklers or fire brigade• Designing for extreme events
Localized Fires
• Heat transfer from fire plume in contact with a structural element
• May be more severe than hot gas layer exposure– Large enclosures– Open parking garages– Bridges and overpasses– Tunnels
Heat Flux Boundary Condition
( ) ( )44∞∞ −−−−′′=′′ TTTThqq ssshfgnet σε
Ts General boundary condition ( ) 44
sssfffsnet TTThTqdxdTk σεσεε −−+=′′=−h(Tf –Ts)
Determined from heat flux gaugeεf εsσTf4
q”net
εsσTs4
Fire Types
• Bounding fires– Items immersed in large fires
• Specific geometries– Fire against vertical walls– Fire in a corner with a ceiling– Fire impinging on unbounded flat ceiling– Fire impinging on I-beam mounted below ceiling– Others in SFPE Handbook of Fire Protection
Engineering, 3rd Edition
Immersed Objects
• Peak in most tests– 150-170 kW/m2
• Highest in tests– 220 kW/m2
– appears exceptional
TEST POOL SIZE FUEL peakq ′′
(kW/m2) AEA Winfrith [1] 1.6 ft x 31 ft Kerosene 150
US DOT [1] Not listed. Kerosene 138 USCG [1] Not listed. Kerosene 110-142
US DOT [1] Not listed. Kerosene 136-159 Sandia [1] Not listed. Kerosene 113-150
HSE Buxton [1] Not listed. Kerosene 130 Shell Research [1] 13 ft x 23 ft Kerosene 94-112 Large cylinder [2] 30 ft x 60 ft JP-4 100-150 Small cylinder [2] 30 ft x 60 ft JP-4 150-220
Ref. [3] 8 ft x 16 ft JP-5 144 1. Cowley (1991). 2. Gregory, Mata, and Keltner (1987). 3. Russel and Canfield (1973).
Specific Geometries
• Empirical correlations– Heat flux gauge measurements
• Required input data– Heat release rate– Fuel diameter– Location relative to top of fuel package
General Calculation Approach
• Calculate flame height• Calculate virtual source origin (if required)• Calculate location of element relative to fire
centerline and top surface of fuel• Use correlations to determine heat flux
Vertical Wall
Heat Release Rate [kW]
0 100 200 300 400 500 600
Peak
Hea
t Flu
x, q
" peak
[kW
/m2 ]
0
20
40
60
80
100
120
140
Aspect Ratio ~1Aspect Ratio ~2Aspect Ratio ~3
Vertical Wall
z/Lf
0.01 0.1 1 10
Cen
terli
ne H
eat F
lux,
q" c
l [kW
/m2 ]
1
10
100
1000
Q ≈ 59 kWQ ≈ 121 kWQ ≈ 212 kWQ = 313 kWQ = 523 kWCorrelation for Q=59 kWCorrelation for Q=523 kW
Vertical on Centerline Horizontally off Centerline
Vertical Wall - Limitations
• Wall is vertical• Flames are luminous• No heating from upper-layer of gases • Fire assumed in contact with wall• Data developed for specific size fires
– Heat release rate up to 520 kW– Diameter up to 0.70 m
Corner with Ceiling
Regions for Correlations
Corner with Ceiling
Length of Area Burner Side, D [m]0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
Pea
k H
eat F
lux,
q" p
eak
[kW
/m2 ]
0
10
20
30
40
50
60
70
80
90
100
110
120
z/Lf,tip
0.01 0.1 1 10
Max
imum
Hea
t Flu
x in
Cor
ner,
q"m
ax (k
W/m
2 )
1
10
100
1000
Along Height in CornerPeak in Corner
Corner with Ceiling
(x+H) / Lf,tip
0.1 1 10
Max
imum
Hea
t Flu
x, q
" max
[kW
/m2 ]
1
10
100
1000
(r+H)/Lf,tip
0.1 1 10
Hea
t Flu
x to
Cei
ling
[kW
/m2 ]
0.1
1
10
100
1000
Along Top of Walls Along Ceiling
Corner with Ceiling - Limitations
• Walls are vertical and at a 90o angle• Ceiling is horizontal and at a 90o angle with walls• Flames are luminous• No heating from upper-layer of gases• Fire assumed in contact with wall• Data developed for specific size fires
– Heat release rate up to 300 kW– Diameter up to 0.50 m
Unbounded Ceiling
Unbounded Ceiling
At Stagnation Point
Unbounded Ceiling
w = (r+H+z')/(LH+H+z')
0.1 1 10H
eat F
lux,
q" [
kW/m
2 ]1
10
100
1000
Along Ceiling Radially out from Impingment Point
Unbounded Ceiling - Limitations
• Ceiling is flat with no pockets or beams• Flames are luminous• No heating from upper-layer of gases• Data developed for specific size fires
– Heat release rate up to 400 kW– Diameter up to 1.0 m
I-Beam Beneath Ceiling
I-Beam Beneath Ceiling
• Fires <1,000 kW– Within band of
unbounded ceiling data
• Depends on location on I-beam– Highest on lower
flange face
I-Beam Beneath Ceiling
w (- -)
0.1 1 10
Hea
t Flu
x, q
", (k
W/m
2 )
0.1
1
10
100
1000• Fires 500-3,600 kW– Data close to bounding
fit
• Large fires >2,000 kW– All faces of I-beam
exposed to similar heat flux
– Close to bounding fit
I-Beam Beneath Ceiling -Limitations
• Only one I-beam tested– Web
• 150 mm high and 5mm thick– Flanges
• 75 mm wide and 6 mm thick• Fire impinges on I-beam lower flange face• Flames are luminous• No heating from upper-layer of gases• Data developed for specific size fires
– Heat release rate up to 3,600 kW– Diameter up to 1.6 m
Summary
• Performance-based design of structural fire resistance requires three steps– Estimation of thermal boundary conditions– Estimation of heat transfer– Estimation of structural response at elevated
temperatures• SFPE Guide provides information needed to
estimate thermal boundary conditions
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