performance based methodology for tracing the response of
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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
Beams Exposed to FireBeams Exposed to Fire
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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
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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
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4Source: Fire Loss in the United States During 2008, by Michael J. Karter, Jr., NFPA, Quincy, MA, August 2009
Fire Problem in the US.
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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
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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
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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
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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
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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
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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
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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
Beams Exposed to FireBeams Exposed to Fire
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
Beams Exposed to FireBeams Exposed to Fire
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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.
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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
Axial force / Moment
Pmax
FR2
Pmax
FR2
Axial force / Moment
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
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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
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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
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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
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• 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
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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.
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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.
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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.
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Validation:Validation:Li and Li and Guo’sGuo’s Restrained Beam Test (2008) 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.
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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.
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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)
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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
Kodur V.K.R. and Dwaikat M.M.S. (2009), “Response of Steel Beam–Columns Exposed to Fire”, Engineering Structures, (31), pp. 369-379.
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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
Kodur V.K.R. and Dwaikat M.M.S. (2009), “Response of Steel Beam–Columns Exposed to Fire”, Engineering Structures, (31), pp. 369-379.
-1200
-1000
-800
-600
-400
-200
00 200 400 600 800 1000
Steel temperature, °C
Mid
span
def
lect
ion,
mm
.
AR = 0AR = 10%AR = 30%AR = ∞
Section W24x76, L = 9 m, RR = 0, LR = 50%
Local buckling(web)
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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
Kodur V.K.R. and Dwaikat M.M.S. (2009), “Response of Steel Beam–Columns Exposed to Fire”, Engineering Structures, (31), pp. 369-379.
-1200
-1000
-800
-600
-400
-200
00 200 400 600 800 1000
Steel temperature, °C
Mid
span
def
lect
ion,
mm
.
RR = 0RR = 10%RR = 30%RR = ∞
Section W24x76, L = 9 m, AR = 10%, LR = 50%
Local buckling
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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
Kodur V.K.R. and Dwaikat M.M.S. (2009), “Response of Steel Beam–Columns Exposed to Fire”, Engineering Structures, (31), pp. 369-379.
-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
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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
Kodur V.K.R. and Dwaikat M.M.S. (2009), “Response of Steel Beam–Columns Exposed to Fire”, Engineering Structures, (31), pp. 369-379.
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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
Kodur V.K.R. and Dwaikat M.M.S. (2009), “Response of Steel Beam–Columns Exposed to Fire”, Engineering Structures, (31), pp. 369-379.
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
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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
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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)
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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
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.
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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
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.
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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
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.
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
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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.
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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
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Deflection of Restrained Steel BeamsComparison to Test Data { Li and Guo Test (2008) }Li and Guo 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.
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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.
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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
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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
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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
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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.
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Acknowledgments
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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.
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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
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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
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Performance Problems – Concrete
Fire Resistance Strategy
• 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
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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
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Performance Problems – Wood
Fire Resistance Strategy
• 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
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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
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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
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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)
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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
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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,
,