Performance Based Methodology for Tracing the Response of

1

Performance Based Performance Based Methodology for Tracing the Methodology for Tracing the Response of Restrained Steel Response of Restrained Steel

Beams Exposed to FireBeams Exposed to Fire

Performance Based Performance Based Methodology for Tracing the Methodology for Tracing the Response of Restrained Steel Response of Restrained Steel


2

Outline

• Fire Hazard

• Need for Structural Fire Safety

• Fire Resistance Assessment

• PBD Methodologies

• Response of Beam-Columns

• Experimental Studies

• Numerical Models

• PBD Approach

• Design Applications

3

Fire Problem Fire Problem –– Severe Hazard & ThreatSevere Hazard & Threat

• Fires cause thousands of deaths & billions of $$ of damage each year

• Fires pose major security & economic threat– Home land security– Economic activity

• Fire risk can be mitigated through conscientious design and maintenance

– It is impossible to prevent ALL major fires

• Fire safety depends on numerous factors:– Fire prevention, suppression and extinction– Successful evacuation of occupants– Structural fire safety

4Source: Fire Loss in the United States During 2008, by Michael J. Karter, Jr., NFPA, Quincy, MA, August 2009

Fire Problem in the US.

5

Fire – Severe Hazard & Threat

• 2008 Data– 1.45 million fire incidents– 3320 fire deaths, 16,705 injuries– $15.7 billion property losses– Total cost > $70 billion

• Residential fires are the most significant- 83% of fire deaths, 27% of fires, 60% of the total $ loss

• Fire can be– Primary event – natural origin (e.g., lightning, accidental)– Secondary event - Post EQ, blast, explosion, impact

• Fire represents most severe condition– Buildings, Transit systems, Tunnels

• Structural elements – Fire resistance– Safe evacuation of occupants & fire personnel– Minimize property damage– Control spread of fire

• Structural fire safety – Least developed area– Important for Homeland Security, economic activity

6

Recent Fire Disasters in US

• WTC Disaster – Sept. 11, 2001– Fires - crucial to collapse

– 2850 deaths ( > 450 ER)– Damage ( $10’s B)– Collapsed/damaged buildings - 40

– Towers standing today! (if no fires)

• Oakland Bridge - April 29, 2007 –– Gasoline tanker crashed into the bridgeGasoline tanker crashed into the bridge–– Collapse by fire (22 Collapse by fire (22 minsmins))–– Traffic disruptionTraffic disruption

• CA Tunnel – October 12, 2007 –– 550 ft long tunnel 550 ft long tunnel –– Burned for 7 hrs Burned for 7 hrs –– 1400C1400C–– Severe damage Severe damage –– SpallingSpalling of concreteof concrete

• MI I96 Bridge – July, 2008 –– Gasoline tanker crashed into the bridgeGasoline tanker crashed into the bridge–– Significant damage by fireSignificant damage by fire–– Traffic disruptionTraffic disruption

Oakland Bridge Collapse

Euro Tunnel

Fire Incidents in Europe• April 13, 2009: Hostel fire, Kamień Pomorski, Poland,

21 ppl died.

• Aug. 18, 2007: Newquay, UK, Penhallow Hotel Fire, 3 deaths. Hotel collapsed.

• Apr. 15. 2005: Paris Opera Hotel , France, 24 deaths

• February 12, 2005: Windsor Tower Fire, Madrid, Spain. Partial collapse - Demolished

• Nov. 24, 2003: Fire in Student Hostel due to Electrical Fault, Moscow, Russia. 36 deaths.

• May 15, 2003: Hotel in La Plaine district, Marseilles, France, 10 deaths

• April 18, 2002: A plane crashed into the upper floors of the 30-story Pirelli Tower in Milan, Italy, 3 deaths.

• December 2001: Home for elderly people, Buccino, South Italy, 21 deaths.

• Euro Tunnel Fire – Nov. 18, 96– Severe damage, spalling of concrete

• Major repairs – damages (£ 50 M)The Pirelli Tower in Milan

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• DELFT Faculty of Architecture Bldg -May 13, 2008

– 13 storey RC building – Cause – Short circuit in coffee machine

at 6th floor– Huge amount of fire load

• Wood (Formwork, Arch. Studios)

• Sprinklers Ineffective

due to water damage• Fire Fighting Called off

– Bldg collapsed - 7 hrs– Fire extinguished - 21 hrs– Losses – 100’s of millions of Euros

Recent Fire Disasters

Fire in Technical University of Delft, Architecture Building

9

Structural Fire Safety

• Fire resistance• Measure of the ability of a building element to resist a fire

– Usually expressed in time as the duration during which a building element exhibits resistance with respect to:

• Structural integrity • Stability• Temp transmission during a fire-resistance test

- Methods of Evaluating Fire resistance•• PrescriptivePrescriptive--Based ApproachBased Approach•• PerformancePerformance--Based ApproachBased Approach

– Performance of structural systems under fire conditions• Fire severity• Material properties• Structural parameters and member interactions

- Load, restraint, member interactions

0

200

400

600

800

1000

1200

1400

0 30 60 90 120 150 180Time (min)

Tem

pera

ture

, °C

ASTM E119 fireHydrocarbon fireSevere fireModerate Fire

Fire scenarios for compartment fires

10

Fire Resistance Analysis - Materials

Fire resistance depends on

• Properties of constituent materials• Reliable high temperature properties are critical

for realistic analysis• No matter how complex numerical model is,

improper material properties can give misleading answers

• Conventional construction materials– Concrete, steel (protected), masonry, GWB– Good FR properties– Limited Performance problems– Large Variation in H.T. properties

11

Fire Resistance Analysis Structural Parameters & Interactions

Time minute

10 20 30 40 50

400

300

200

100

0

Def

lect

ion

mm

60

Fire responseFire response

Performance

Structural model

Thermal modelHigh Temperature High Temperature Material PropertiesMaterial Properties

Complex problem: Advanced thermo-mechanical analysis – Loading, Restraint– Member interaction– Failure criteria– 3D modeling– Spalling, Charring, Local buckling– System level analysis

12

MSU Research Project:MSU Research Project:Performance Based Performance Based

Methodology for Tracing the Methodology for Tracing the Response of Restrained Steel Response of Restrained Steel


MSU Research Project:MSU Research Project:Performance Based Performance Based

Methodology for Tracing the Methodology for Tracing the Response of Restrained Steel Response of Restrained Steel


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Steel Framed BuildingsSteel Framed Buildings

• Steel framed buildings are vulnerable to fire attack

• Fires can cause severe strength and stiffness degradation in steel structures

• Steel members in framed buildings are typically restrained, and thus axial force and bending moments develop due to restraint under fire exposure

• The fire induced forces can change the fire response and fire resistance

• The continuity/restraint effects are not accounted for in current codes of practice.

Fire in Windsor Tower in Madrid, Feb. 2005

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Beam-Column – Response under Fire

L Beams and columns in buildings:- Primary load bearing elements- Stability under fire- External fire insulation

At room temperature steel beams are designed for flexure

Under fire, steel expands non-uniformly due to thermal expansion

Restrained beams develop significant axial force & bending moment due to restraining of expansion

Beam will no longer behave like a beam, butlike a beam-column:

u u

n n

M P+ 1.0Φ M Φ P

Axial force

Pu

Bending moment

Mu

Beam-column

Expansion = Δℓ

Axial Restraint

Kodur V.K.R. and Dwaikat M.M.S. (2009), “Response of Steel Beam–Columns Exposed to Fire”, Engineering Structures, (31), pp. 369-379.

15

Layout of typical Steel frame

Deflected shapes

Mr = Kr×θ

M = wL2/8 + P×Δ – Mr

PP

Kr

Ka, Kr

Po L

M = wL2/8

Δ θΔ

θ

wKa, Kr

L

Ka, Kr

Restrained beam

Bending moment and axial force

Perimeter columnSimply supported beam

w

L

Δ

Beam-Columns in Fire

M = P×Δ + Mr

P

P

Thermal gradient

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The current methods for evaluating FR can be categorized under two broad approaches

--PrescriptivePrescriptive--Based ApproachBased Approach- Based on thermal criterion (critical temp. Tcr)- Tcr is the temperature at which steel loses 50% of its yield strength

- Standard fire exposure, no consideration to: loading, end-restraint, design fire exposure, or beam geometry.

- Still used in the U.S. (For structural steel : Tcr = 538°C)

-- PerformancePerformance--Based ApproachBased Approach- Based on realistic conditions- Failure based on thermal as well as strength, stability, deflection, and rate of deflection limit states

- Design fire exposures, member continuity, material and geometric nonlinearities and effect of end-restraint are considered

Current Approaches for Evaluating Fire Resistance

wKa, Kr

L

Ka, Kr

Restrained beam Time

Tem

pera

ture

Fire scenario

wKa, Kr

L

Ka, Kr

Restrained beam

wKa, Kr

L

Ka, KrwKa, Kr

L

Ka, Kr

Restrained beam Time

Tem

pera

ture

Fire scenario

Time

Tem

pera

ture

Fire scenario

Pmax

FR2

Axial force / Moment

Fire exposure time

5%L

Deflection

FR1

Pmax

FR2


Pmax

FR2

Pmax

FR2


Fire exposure time

5%L

Deflection

FR1

Fire exposure time

5%L

Deflection

FR1

Tcr

0.5Fy

Steel Yield Strength

Steel Temperature, °C

50%

300 600 900

1.0Fy

Tcr

0.5Fy

Steel Yield Strength

Steel Temperature, °C

50%

300 600 900

1.0Fy

FR : Fire Resistance

Exposure Time

Tem

pera

ture

Standard fire

TcrFR

Exposure Time

Tem

pera

ture

Standard fire

TcrFR

Exposure Time

Tem

pera

ture

Standard fire

TcrFR

Sectional capacity 50%

300 600 900

1.0 Mp

0.5Mp

Average Steel Temperature, °C

Tcr

Sectional capacity 50%

300 600 900

1.0 Mp

0.5Mp

Average Steel Temperature, °C

Tcr

17

Fire Resistance Provisions in Codes and Standards

• Steel members as treated as simply supported members(beams/columns), and use sectional analysis to compute capacity.

• Failure criterion is based on critical temperature Tcr• Eurocode 3 (EC3 2005), New Zealand Standards (SNZ 1997), and

Japanese Building Code (Harada et al. 2004) provide semi-empiricalformulas for computing Tcr

4821r0.967

139.19lnT

3.833EC3

cr

r690905T SNZcr

r375700T JBCcr

r is load ratio defined as the ratio between the bending moment (Mo)resulting from reduced load during fire to the room-temperature plasticmoment capacity of the steel beam (Mp).

Eurocode 3

New Zealand Standards

Japanese Building Code

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Fire Response of Restrained Steel BeamsFire Response of Restrained Steel Beams

Fire induced Axial force

Time

Time

Tem

pera

ture

Com

pres

sTe

nsio

n

Time

Def

lect

ion

Temperature

Midspan DeflectionCatenary Action Stage

- Tensile force- Improved response

2nd plastic hinge

1.0(T)MkM

(T)PkP

yyyy

Yield

Elastic Stage- Expansion- Fire induced axial force

Fire

Steel

1st plastic hinge

uyo (T)MkM

Elasto-plastic Stage- Spread of plasticity, P-Δ effect- Softening, Reduction in P

P = 0

Plastic mechanismFailure Stage- Reaching tensile capacity- ConnectionsDwaikat, M.M.S and Kodur, V.K.R. (2009) “An Engineering Approach for Predicting Fire Response of Restrained Steel Beams.” Submitted, Journal of Engineering Mechanics, ASCE

Simply Supported

wKa, Kr

L

Ka, Kr

19

Development of Design Approach

• Experimental studies – Beam-columns – Standard and design fires– Thermal gradients in different orientations– Different load scenarios

• Finite element analysis– Material nonlinearities

• Nonlinear temperature-dependent stress-strain curves• High-temperature creep

– Geometrical nonlinearities• Local and global instabilities

– Validated using MSU tests and tests from literature• Design approach

– Simplified equations suitable for office design• Computation of thermal gradient• Design equations based on strength criteria• Design equation based on deflection criteria under fire

• Applications– Design of beam-columns under strength and deflection limit states

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Preparation of SpecimensPreparation of Specimens

610

2385

305

2.5

2.5

Average insulation thickness: 44 mmColumns C1-W and C1-S

WSG1WSG2

WSG3

WSG4 WSG5

25

9065

25

2550

STC3

STC2

STC1

SSG5SSG4SSG3

SSG1SSG2

103

5454

54

50

WTC2

WTC4WTC3

WTC1

108

50

50

103

D D

C C

B B

A A

380

P

2385

610

305SFRM

(d) Strain gauges at D-D for C1-W and C2-W

(b) Thermocouple locations for C1-W and C2-W at A-A,

B-B, C-C and D-D

(a) Thermocouple locations for C1-S and C2-S at A-A,

B-B, C-C and D-D

(c) Strain gauges at D-D for C1-S and C2-S

C1: 740 C2: 990

C1: 460 C2: 430

C1: 460 C2: 430

bare steel

bare steel

Average insulation thickness: 38 mmColumns C2-W and C2-S

W8x48 W8x48

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Experimental StudiesExperimental StudiesTest SetupTest Setup

1775

mm

2440 mm

3300

mm

FURNACEFURNACE

Fixed end610 mm

600kips total per column

305 mm

Pinned end

Dwaikat, M.M.S., Kodur, V.K.R., Quiel, S.E., Garlock, M.E.M., (2011) “Experimental Behaviour of Steel Beam-Columns Subjected to Fire-Induced Thermal Gradients”, Journal of Constructional Steel Research, 67, 30-38

22

Test ResultsTest Results

D D

C C

B B

A A

380

P

2385

610

305SFRM

C1: 740 C2: 990

C1: 460 C2: 430

C1: 460 C2: 430

Dwaikat, M.M.S., Kodur, V.K.R., Quiel, S.E., Garlock, M.E.M., (2011) “Experimental Behaviour of Steel Beam-Columns Subjected to Fire-Induced Thermal Gradients”, Journal of Constructional Steel Research, 67, 30-38

23

• ANSYS finite element software:– SUR151 and PLANE55 elements for

thermal analysis– SHELL93 element for structural

analysis• Temperature obtained from thermal

analysis is applied on the structural mesh.

• Non-uniform temperature over the cross-section, and uniform along the heated length.

• Kinematic restraint is imposed on top by applying measured rotations

• High-temp. steel properties as a function of steel temperature

• ANSYS Creep Model 11: Generalized high-temperature creep, including primary and secondary creep strains

• Transient non-linear analysis

Finite Element AnalysisFinite Element Analysis

24

10

20

30

40

5060

Ther

mal

con

duct

ivity

W

/mK

Temperature ˚C

1

2

3

4

56

200 400 600 800 1000

Spec

ific

heat

kJ/

kgK

0.3

0.6

0.9

1.2

1.51.8

Ther

mal

str

ain

%

Steel Temperature-stress-strain curves: Poh model (2001)

Physical properties of structural steel (EC3)

Specific heat

Thermal strain

Thermal conductivity

HighHigh--temp. Material Propertiestemp. Material Properties

00.20.40.60.8

11.21.4

0 5 10 15 20 25 30

200 ˚C 20 ˚C 400 ˚C

600 ˚C

800 ˚CFs,T

/ Fy,

20°C

CsCy

TsEF 20,20,

,

0.0

0.2

0.4

0.6

0.8

1.0

0 200 400 600 800 1000Temperature, ˚C

E s,T /E s,20 °C

F y,T /F y,20 °C

F u,T /F u,20 °C

Thermal properties used for the insulation material “CAFCO 300”

Temp.(°C)

Thermal Conductivity (W/m-K)

Specific Heat

(J/kg-K)

Density (kg/m3)

20 0.078 900 310

1200* 0.3* 1400* 310*

*Assumed values based on previous experimental data (NIST 2005)

Kodur, V.K.R., Dwaikat, M.M.S, and Fike R., (2009) “High-Temperature Properties of Steel for Fire Resistance Modeling of Structures”, In Press, Journal of Materials in Civil Engineering- ASCE.

25

High-Temp. Creep

Time C

reep

str

ain

(

)

Primary creep

Secondary creep

Tertiary creep

02

2

dtd cr

02

2

dtd cr

cr

Fracture points

1T

2T3T

Increase in temperature

02

2

dtd cr

Creep: Time-dependent plastic strain under constant stress and temperature.

Three phases of creep strain: Primary, secondary, and tertiary creep At elevated temperature creep strain rate becomes very high, leading to

very significant creep deformations • Creep material tests and models: constant stress with time (ddσσss/dt/dt = 0)= 0)

Kodur, V.K.R., and Dwaikat, M.M.S, (2009) “Effect of High Temperature Creep on the Fire Response of Restrained Steel Beams”. In Press, Materials & Structures Journal.

•• ANANSYSSYS Creep Model “11” was calibrated using two independent material tests.

26

Validation:Validation:Li and Guo’s Restrained Beam Test (2008) Li and Guo’s Restrained Beam Test (2008)

Dwaikat, M.M.S and Kodur, V.K.R. (2009) “An Engineering Approach for Predicting Fire Response of Restrained Steel Beams.” Accepted, Journal of Engineering Mechanics, ASCE.

27

Validation:Validation:Li and Li and Guo’sGuo’s Restrained Beam Test (2008) Restrained Beam Test (2008)


28

Validation: Validation: MSU BeamMSU Beam--Column Tests (2009) Column Tests (2009)

-- Partial Simulation: Temperature from testPartial Simulation: Temperature from test-- Full simulation: Temperature from thermal analysisFull simulation: Temperature from thermal analysis-- Using Estimated restraint stiffnesses Using Estimated restraint stiffnesses KKaa = 25000 kN/m, = 25000 kN/m, KKrr = 2500 kN= 2500 kN--m/radm/rad-- Load history applied from testLoad history applied from test-- For partial simulation: Temperature zonesFor partial simulation: Temperature zones

380

FUR

NA

CE

Transition

305 Transition

305

305

610

A-A

B-B

C-C

D-D

A-A

B-B

C-C

460

460

855

C1 460

660

655

C2

Quiel, S.E., Garlock M.E.M., Dwaikat, M.M.S., Kodur, V.K.R., (2009) “Computational Studies of Steel Beam-Columns with Thermal Gradients.” Submitted, Fire Safety Journal.

29

380

FUR

NA

CE

Transition

305 Transition

305

305

610

A-A

B-B

C-C

D-D

A-A

B-B

C-C

460

460

855

C1 460

660

655

C2

Validation: Validation: MSU BeamMSU Beam--Column Tests (2009) Column Tests (2009)

30

Parametric StudiesEffect of Load Ratio (LR)

-800

-600

-400

-200

00 150 300 450 600 750 900

Steel temperature, °C

Mid

span

def

lect

ion,

mm

.

LR = 30%LR = 50%LR = 70%

Section W24x76, L = 9 m RR = AR = 10%

Local Buckling

- Higher load ratio leads to higher midspan deflection- Load ratio reduces fire resistance under deflection or strength limit states- Local buckling has minor influence on deflection due to catenary action


31

Parametric StudiesEffect of Axial Restraint (AR)

- Higher axial restrain leads to higher initial midspan deflection- Axial restraint improves fire resistance based on strength limit state- Local buckling has minor influence on deflection due to catenary action


-1200

-1000

-800

-600

-400

-200

00 200 400 600 800 1000


Mid

span

def

lect

ion,

mm

.

AR = 0AR = 10%AR = 30%AR = ∞

Section W24x76, L = 9 m, RR = 0, LR = 50%

Local buckling(web)

32

Parametric StudiesEffect of Rotational Restraint (RR)

- Higher rotational restrain leads to lesser midspan deflection- Rotational restraint improves fire resistance - Local buckling has minor influence on deflection due to catenary action


-1200

-1000

-800

-600

-400

-200

00 200 400 600 800 1000


Mid

span

def

lect

ion,

mm

.

RR = 0RR = 10%RR = 30%RR = ∞

Section W24x76, L = 9 m, AR = 10%, LR = 50%

Local buckling

33

Parametric StudiesEffect of Location of Restraint

- Moving restraint to the bottom flange improves overall response- This is due to the counter-acting moment that develops at support- Local buckling has minor influence on deflection since it is followed by catenary action


-1000

-850

-700

-550

-400

-250

-100

0 200 400 600 800 1000Steel temperature, °C

Mid

span

def

lect

ion,

mm

.

y = d /2

Section W24x76 , L = 9 m, LR = 50%RR = AR = 10%

y

y = 0

Uniform temperature

34

Parametric StudiesEffect of Thermal Gradient

- Thermal gradient increases elastic deflection due to thermal bowing- Thermal gradient has minor effect on the response in the catenary phase due to change in load bearing mechanism


35

Parametric StudiesEffect of Fire Scenario

- Three fire scenarios (including EC1 design fires) were selected- Response is better under design fires due to the cooling phase- Failure occurs under standard fire - Partial recovery of deflection under design fire


0

200

400

600

800

1000

0 30 60 90 120 150 180Time, min.

Tem

pera

ture

, °C

Fire curveBottom flangeMiddle of webTop flange

0

200

400

600

800

1000

1200

0 30 60 90 120 150 180Time, min.

Tem

pera

ture

, °C

15 mm insulation W24x76

1 m

0.61m

0.23 m

0.1m

(a) ASTM E119 standard fire (b) Design fire I

0

150

300

450

600

750

900

0 30 60 90 120 150 180Time, min.

Tem

pera

ture

, °C

(c) Design fire II

-900

-750

-600

-450

-300

-150

00 20 40 60 80 100 120 140 160 180

Fire exposure time, min.

Mid

span

def

lect

ion,

mm

.

Design fire IDesign fire II

W24x76, L = 9m, LR = 50% AR = RR = 10%

ASTM E119 fire

36

Development of PerformanceDevelopment of Performance--Based Based Engineering ApproachEngineering Approach

Thermal gradient

Use realistic “design”fire scenario

Time

Tem

pera

ture

Fire Scenario

Steel temperature

Restrained beam exposed to fire

Predict steel temperature “with thermal gradient”

Predict the response of restrained beam during fire

Predict the fire-induced forcesand deflection of restrained beam

Summary of proposed approach Compute steel temperature and

thermal gradient Compute restraint forces Compute deflection

ΔT Time

Tem

pera

ture

Ts

Time

Axi

al F

orce

Def

lect

ion

Time

Axi

al F

orce

Def

lect

ion

P

ΔStrength/Deflection/Thermal criteria can be applied at any step

37

Step 1: Steel temperature Standard Fire

m

TTT fs

p

FF

wFFCFsp Bt

tBt2/AF

fw

wfwebsp 2tdt

t2-2td2/AF

tT

ρcQT2k

General Heat Transfer Equation

T(x,y,z,t)

Tf(t)

4

fT4T4eσfTTconhradQconQQ

-AssumptionsUniform steel temperatureRadiation Equivalent convectionThin insulationFire temperature: Fire temperature: TTff = = a ta t nn

Tf

Ts

Tp

ste1fT(t)sT

dtfdT

2FsTfT1Fdt

sdT

1nmpt

sApF

sρscpρpc

1p/kpt1/hsρsc

s/ApF

1n1F

s

FF

wFFBFsp Bt

tB2t2/AF

Dwaikat, M.M.S and Kodur, V.K.R. (2009) “A Simplified Approach for Evaluating Plastic Axial and Moment Capacity Curves for Beam-Columns with Non-uniform Thermal Gradients”, In Press, Engineering Structures.

Time

Tem

pera

ture

Tf(t)

38

Time

Tem

pera

ture

T f,max

t 1 t 2

Design fire curveAverage steel temp.

20 °C

T s,max

T s,1

t 3

decay rate of fire "r"

Time

Tem

pera

ture

T f,max

t 1 t s,max

Design fire curveAverage steel temp.

T s,max

T s,1 A

B

r

t 2

γβt2αtsT At point A (t = t1):Ts = Ts1 (using previous Eq. at t = t1), and dTs/dt = slope from previous Eq. at t = t1,At point B (t = ts,max):Ts = Tf , and dTs/dt = 0.

1rts,1T21

s,1Tmaxf,T11tmaxs,t

s,1r/T12t1

r12tmaxf,T

maxs,T

Step 1: Steel temperature Design Fire


39

Steel TemperatureComparison to F.E.A.

100 300 500 700 900100

300

500

700

900

Ts,max (oC) From proposed approach

T s,m

ax (o C

) Fro

m fi

nite

ele

men

t ana

lysi

s

+10% margin

-10% margin

0 50 100 150 200 2500

50

100

150

200

250

ts,max (min.) From proposed approach

t s,m

ax (m

in.)

From

F.E

.A. +10% margin

- 10% margin


40

Step 2: Plastic PStep 2: Plastic P--M Interaction under Thermal M Interaction under Thermal GradientGradient

The P-M diagrams are the main tool to check capacity of beam-columns Provisions in codes and standards Provisions in codes and standards

provide plastic Pprovide plastic P--M relationships for M relationships for uniform temperature conditions:uniform temperature conditions:

u u

n n

M P+ 1.0Φ M Φ P

However, under thermal gradient, the shape of plastic P-M diagrams changes


1

d)tt)(2B(Tk

)(Tdkt)(Tkt2B

2d

ewFFAves,E

Aves,EwCFs,EFF

2d

)(TkA

y)(TkAYYe

iEi

iiEiCGCS

e × P u = M TG

M TG

A A'

B

B' C

C'

M / M u

P / P

u

T = T ave

ΔT

1.0FA

PFZ

MM

aveTs,u,saveTs,u,x

TG 1.0

FAP

FZ

MM

aveTs,u,sTaveu,x

TG

)(TP)e(TM aveuaveTG

41

Plastic PPlastic P--M Interaciton Diagrams M Interaciton Diagrams Comparison to Tests and F.E.

D D

C C

B B

A A

P

2385

610

305

1930

hotte

st re

gion

location of failure

base moment

Kodur, V.R, Garlock, M.E, Dwaikat, M.S, Quiel, S.,(2009) “Collaborative Research: Fire Engineering Guidelines for the Design of Steel Beam-Columns”, Proceedings of 2009 NSF Engineering Research and Innovation Conference, Honolulu, Hawaii.

42

Step 3: Fire Induced Deflection in Restrained Step 3: Fire Induced Deflection in Restrained BeamsBeams

Fire induced Axial force

Time

Time

Tem

pera

ture

Com

pres

sTe

nsio

n

Time

Def

lect

ion

Temperature

Midspan Deflection

Deflection Limit State

Tx

Temperature at yield

Fire

Steel

Catenary temperature

P = 0

Design Fire Scenarios

2xsA

Ryoy a/SYA1F

ΔT0.5F/MM1T

2

ΔTF

M

M

MM

1a1

T R

u

y

u2c

20)(T2α2L

Δ cc

ky(Tx)AsFu

c

FycyDLS Δ

LTTTT

FL Ty

Tc

Δ(T)

Interpolate

Δy

Dwaikat, M.M.S and Kodur, V.K.R. (2009) “A performance-based methodology for fire design of restrained steel beams”, Accepted, Journal of Constructional Steel Research.

Assume full recovery of elastic deflection Δy after Ts,max (Maximum steel temperature) is conservative measure

where:

Deflection at Tc

Deflection Criteria Either L/20 or L/30

Buckling (local and global) limit states are not considered since it is generally followed by tensile catenary action

43

Deflection of Restrained Steel BeamsComparison to Test Data { Li and Guo Test (2008) }Li and Guo Test (2008) }


44

Deflection of Restrained Steel BeamsComparison to Finite Element AnalysisComparison to Finite Element Analysis

400

500

600

700

800

900

1000

400 500 600 700 800 900 1000T DLS (°C) From simplified approach

T DLS

(°C

) Fro

m F

.E.A

-10% margin

+10% margin

400

500

600

700

800

900

1000

400 500 600 700 800 900 1000T DLS (°C) From simplified approach

T DLS

(°C

) Fro

m F

.E.A

-10% margin

+10% margin

a) Deflection limit state (LF) = L/20L/20 b) Deflection limit state (LF) = L/30L/30Dwaikat, M.M.S and Kodur, V.K.R. (2009) “An Engineering Approach for Predicting Fire Response of Restrained Steel Beams.” Accepted, Journal of Engineering Mechanics, ASCE.

45

Design Applicability

• Problem:Compute the maximum compressive force (P) attained in the beam-column with the following characteristics

• Given:– A beam-column is exposed to ASTM E119 standard fire (ASTM

2008)– Beam-column section W14x176 (Fy = 345 MPa.) – Effective and unbraced length of the beam-column is = 4.5 m – Average section temperature Tave = 500ºC, thermal gradient ΔT

= 200ºC – Initial bending moment Mo = 320 kN.m

Mo = 320 kN.m

P

L = 4.5m

Mo = 320 kN.m

Critical Capacities AISC 2005 EC 3 2005 T&D 2007

Mcr kN.m 1329 985 1131.5

Pcr kN 7150 5690 4812

Max. P kN (Eq. 1)using current provisions 3707 1530.4 2090

Max. P kN (Eq. 7)using proposed approach 1935.5 1273 1783

Max. P kN (ANSYS)Finite element solution 1660

46

Design ApplicabilityRestrained Steel Beam

• Problem:Design the beam for 2 hours of fire exposure under ASTM E119 standard and specified design fire. Use deflection limit state of LF = L/30.

• Given:– Beam length and section: 7000 mm, W24x76.– Loading: uniformly distributed dead and live service loads: wD = 35 kN/m, wL = 70

kN/m. – Axial restraint stiffness (Ka): 41.3 kN/mm (≈ 0.1EsAs/L). – Rotational restraint stiffness (Kr): 50 kN.m/milirad (≈ 2.0EsI/L ) – Initial thermal gradient (ΔT) = 150°C.– Steel properties: Grade 50 steel; Fy = 355 MPa and Fu = 445 MPa. – High temperature properties: as per ASCE specified temperature-dependent

reduction factors (ASCE 1992). wL = 70 kN/m, wD = 35 kN/m

L = 7 m

W24 ×76

Mm = 285.8 kN.m

Ms = 143 kN.m

a) Beam loading and properties

b) Bending moment diagram under fire load

0

200

400

600

800

1000

1200

0 50 100 150 200 250Time, min.

Tem

pera

ture

, °C

Standard fire

Design fire

Steel temperature

T DLS = 605°C

47

C605

155424118.8781530/7000411

yc

ycyFyDLS

TTLTT

mm 542)208.878(101422

7000)20(22

6 cc TL

C8.8782

1500032.09.13088.1023

9.13088.2851

0008.01

211

2

TFMM

MM

aT R

u

y

uc

C4110008.000037.0

1500032.05.08.1023/8.28515.0/1

2

aFTFMM

TA

Ryoy

Under standard fire: TDLS needs to be delayed for 2 hours. Based on thermal analysis: Supply 25 mm thickness spray-applied insulation(thermal conductivity of 0.1 W/m.°C and heat capacity of 375 kJ/m3.°C. )

Under design fire: The maximum a steel temperature must not exceed TDLSCheck using temperature equations developed earlierTs,max = 597°C < TDLS = 605°C (at 90 min. of fire exposure)

Design ApplicabilityDeflection Limit State Temperature

mm1518 384

5

1

24

s

yR

sEy E

FaF

dTL

IEkwL

Fire resistance (minutes) Deflection limit state

(L/30) Strength limit state

Proposed approach 120 218 Japanese Building Code 132 132

Eurocode 3 160 160 New Zealand Standard 170 170 Finite element analysis 128 202

0

200

400

600

800

1000

1200

0 50 100 150 200 250Time, min.

Tem

pera

ture

, °C

Standard fire

Design fire

Steel temperature

T DLS = 605°C

48

ConclusionsConclusions

Provisions of appropriate fire resistance measures are critical for minimizing fire induced damage/collapse in steel framed buildings.

For evaluating realistic fire response of structural systems, factors such as end restraints, thermal gradient, fire scenario and failure criteria need to be properly accounted.

Restrained beams and columns can develop significant fire induced forces and these forces transform their response to that of beam-columns.

Current design methods do not fully account for the influence of thermal gradient and end restraint conditions on the fire response of beam-columns.

The proposed approach accounts for the effect of end restraints, thermal gradient, fire scenario and failure criteria, and can be applied in design situations.

49

Acknowledgments

51

Research ImpactResearch Impact

The current design approaches may not be fully applicable for undertaking performance-based design which provides rational and cost-effective fire safety solutions.

The proposed design approach provides a convenient way of obtaining fire response and fire resistance of restrained steel beams, and thus can be used for estimating fire resistance in lieu of full-scale standard fire resistance tests.

The proposed approach will facilitate a rational fire design under a performance-based code environment. Such a rational design approach will contribute to reduced loss of life and property damage in fire incidents.

52

Performance Problems - Steel

Fire Resistance Strategy

• Steel Structures– 1-4 hours– Stability, no collapse

• Steel Columns, DecksApplied protection Limiting temperature

– Problems-Insulation• Critical for fire performance• Problems – stickability

(adhesion/cohesion) Ex: WTC 5

• LG Steel – local buckling• ICC – New provisions

WTC 5

53

Yield strength

Variation in Properties - Carbon Steel

0

0.2

0.4

0.6

0.8

1

1.2

0 200 400 600 800 1000Temperature, ˚C

Outinen & Mäkeläinen 2004Outinen et al. 1997Mäkeläinen et al.1998Chen et al. 2006Li et al. 2003 EC3 model ASCE model Poh model

Proportionality limit "EC3"

Yield point "EC3"

yT

yF

F/

,

0

10

20

30

40

50

60

0 200 400 600 800 1000Temperature, ˚C

Ther

mal

Con

duct

ivity

, W/m

.˚C

Rempe & Knudson 2008Dale & Prasad 2007Touloukain 1972Yawata 1969Powel 1956EC3 modelASCE model

Thermal conductivity

54

Performance Problems – Concrete


• Concrete Structures– 45 min to 4 hours– Stability, Integrity

• RC columns, slabs Cover to rebar Limiting temp. in rebar

• Problems• Spalling under fire exposure• Bond between concrete &

rebar• New type of concrete

H.T. properties

55

0.50

0.75

1.00

1.25

1.50

1.75

2.00

2.25

2.50

2.75

3.00

0 200 400 600 800Temperature °C

Ther

mal

Con

duct

ivity

- W

/m°C

0.29

0.43

0.58

0.72

0.86

1.01

1.15

1.30

1.44

1.58

1.7332 212 392 572 752 932 1112 1292 1472

Temperature °F

Ther

mal

Con

duct

ivity

Btu

/hr.f

t.°F

ASCE model (Siliceous)

ASCE model (Carbonate)

EC2 model (Upper lim it)

EC2 model (Lower lim it)

Test data- Carbonate Test data- Siliceous

0

0.2

0.4

0.6

0.8

1

1.2

0 200 400 600 800 1000

Temperature °C

F'c

(T) /

F'c

(20°

C)

32 212 392 572 752 932 1112 1292 1472 1652

Temperature °F

EC2 model- SiliceousEC2 model- CalcareousASCE model- NSC

Test data- SiliceousTest data- Carbonate

Variation in Properties - Concrete

Compressive strength Thermal conductivity

56

Performance Problems – Wood


• Wood Structures– 30 minutes to 2 hours

• Columns/beam– Insulation– Limit temp rise

• Walls/floor– GWB/insulation protection– Limit temp. rise

• Problems– Wide range of timber– Charring– Glue (Parallam)– Insulation/protection materials

57

Variation in Properties - Wood

Tensile strength Thermal diffusivity

0

0.1

0.2

0.3

0.4

0.5

0.6

0 50 100 150 200 250 300Temperature (°C)

Ther

mal

diff

usiv

ity(m

m2/

sec)

Conventional woodEngineered lumberT&G woodOSB

0

0.2

0.4

0.6

0.8

1

1.2

0 100 200 300 400Temperature (°C)

Tens

ile s

tren

gth

ratio

LieSchafferThomasKnudsonBest fit

58

Fire Resistance - High Performing Materials

• HPM - HSC, FRP, HPS– Benefits

• Superior performance Strength, Durability Corrosion resistance

– Applications• Bridges, Infrastructure projects• Buildings, Parking garages

FRP- Internal & External reinforcement• Retrofitting – columns, beams• Rebars and prestressing rods

HSC - replacing NSC• Major Concern – Fire Performance

– FR properties - not good

• Serious performance problems

• New design approaches needed

59

Performance Problems - FRP

• Design Considerations– Smaller c/s size– Min. cover - Corrosion free– Directly exposed to fire

• Complexities - FRP– Various types, Resin-matrix composite– Lower critical Temp– Combustible– Material properties - high temp.

• Failure criterion– Tg, FRP burning, Debonding– Conventional failure criteria may not apply

• Need innovative solutions

GFRP bar at 450oC

Sprayed insulation

1220mm

150mm

250mm 1-layer CFRP

Tyfo or MBrace

EI-R coating (Fyfe only)

60

0

20

40

60

80

100

120

0 100 200 300 400 500 600 700 800 900

Temperature (°C)

Stre

ngth

(% o

f Ini

tial)

FRP WoodStructural Steel HSC

NSC

• New types of concrete – HSC, HPC, FRC, FAC• Advantages

– Superior strength– Higher stiffness– More durable

• Characteristics– Low w/c– Admixtures– Silica Fume– Dense/compact– Low permeability– Brittle

• Problems– Fire behavior is different– Faster degradation of strength & stiffness– Fire induced spalling

• Current FR provisions may not be applicable

New Concretes:Performance Problems

Variation of comp. strength with T for materials

Material Nonlinearities

• Strain hardening at 400C• Strength increases from

0.6Fy to 1.0Fy due to strain hardening effect.

• This increases improves fire resistance of steel members, and needs to be account for.

• In the approach, it is account for in computing Tc(the catenary temperature)

00.20.40.60.8

11.21.4

0 5 10 15 20 25 30

200 ˚C 20 ˚C 400 ˚C

600 ˚C

800 ˚CFs,T

/ Fy,

20°C

CsCy

TsEF 20,20,

,

Performance Based Methodology for Tracing the Response of

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