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