Performance Bas Performance Bas Performance Bas Performance Bas - - PowerPoint PPT Presentation

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Performance Bas ed Performance Bas ed Methodology for Tracing the Methodology for Tracing the Res pons e of Res trained S teel Res pons e of Res trained S teel Beams Expos ed to Fire Beams Expos ed to Fire Performance Bas ed Performance Bas ed Methodology for Tracing the Methodology for Tracing the Res pons e of Res trained S teel Res pons e of Res trained S teel Beams Expos ed to Fire Beams Expos ed to Fire

SLIDE 2

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Outline

• Fire Hazard
• Need for S

tructural Fire S afety

• Fire Res

is tance As s es s ment

• PBD Methodologies
• Res

pons e of Beam-Columns

• Experimental S

tudies

• Numerical Models
• PBD Approach
• Des

ign Applications

SLIDE 3

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Fire Problem Fire Problem – – S evere Hazard & Threat S evere 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

SLIDE 4

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

Fire Problem in the US .

SLIDE 5

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Fire – S evere 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

SLIDE 6

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Recent Fire Dis as ters 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 bridge

Gasoline tanker crashed into the bridge

– Collapse by fire (22

Collapse by fire (22 mins mins)

– Traffic disruption

Traffic disruption

• CA Tunnel – October 12, 2007

– 550 ft long tunnel

550 ft long tunnel

– Burned for 7 hrs

Burned for 7 hrs – 1400C 1400C

– Severe damage

Severe damage – Spalling Spalling of concrete

• f concrete
• MI I96 Bridge – July, 2008

– Gasoline tanker crashed into the bridge

Gasoline tanker crashed into the bridge

– Significant damage by fire

Significant damage by fire

– Traffic disruption

Traffic disruption

Oakland Bridge Collapse Euro Tunnel

SLIDE 7

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

SLIDE 8

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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 Dis as ters

Fire in Technical University of Delft, Architecture Building

SLIDE 9

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S tructural Fire S afety

• 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
• Prescriptive

Prescriptive-Based Approach Based Approach

• Performance

Performance-Based Approach Based Approach – Performance of structural systems under fire conditions

• Fire severity
• Material properties
• Structural parameters and member interactions
• Load, restraint, member interactions

200 400 600 800 1000 1200 1400 30 60 90 120 150 180 Time (min) Temperature, °C

ASTM E119 fire Hydrocarbon fire Severe fire Moderate Fire

Fire scenarios for compartment fires

SLIDE 10

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Fire Res is tance Analys is

• 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

SLIDE 11

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Fire Res is tance Analys is S tructural Parameters & Interactions

Time minute

10 20 30 40 50 400 300 200 100

Deflection mm

60

Fire response Fire response

Performance

Structural model Thermal model High Temperature High Temperature Material Properties Material Properties

Complex problem:

• Advanced thermo-mechanical analysis

– Loading, Restraint – Member interaction – Failure criteria – 3D modeling – Spalling, Charring, Local buckling – System level analysis

SLIDE 12

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MS U Res earch Project: MS U Res earch Project: Performance Bas ed Performance Bas ed Methodology for Tracing the Methodology for Tracing the Res pons e of Res trained S teel Res pons e of Res trained S teel Beams Expos ed to Fire Beams Expos ed to Fire MS U Res earch Project: MS U Res earch Project: Performance Bas ed Performance Bas ed Methodology for Tracing the Methodology for Tracing the Res pons e of Res trained S teel Res pons e of Res trained S teel Beams Expos ed to Fire Beams Expos ed to Fire

SLIDE 13

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S teel Framed Buildings S teel 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

• f practice.

Fire in Windsor Tower in Madrid, Feb. 2005

SLIDE 14

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Beam-Column – Res pons e 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, but

like a beam-column:



u u n n

M P + 1.0 Φ 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.

SLIDE 15

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Layout of typical Steel frame Deflected shapes Mr = Kr×θ M = wL2/8 + P×Δ – Mr P P Kr Ka, Kr Po L M = wL2/8 Δ θ Δ θ w Ka, Kr L Ka, Kr Restrained beam Bending moment and axial force Perimeter column Simply supported beam w L Δ

Beam-Columns in Fire

M = P×Δ + Mr P P

Thermal gradient

SLIDE 16

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

• Prescriptive

Prescriptive-Based Approach Based 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)
• Performance

Performance-Based Approach Based 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 Res is tance

w Ka, Kr L Ka, Kr Restrained beam Time

Temperature

Fire scenario

w Ka, Kr L Ka, Kr Restrained beam w Ka, Kr L Ka, Kr w Ka, Kr L Ka, Kr Restrained beam Time

Temperature

Fire scenario

Time

Temperature

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 Temperature

Standard fire

Tcr

FR

Exposure Time Temperature

Standard fire

Tcr

FR

Exposure Time Temperature

Standard fire

Tcr

FR 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

SLIDE 17

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Fire Res is tance Provis ions in Codes and S tandards

• 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-empirical formulas for computing Tcr

482 1 r 0.967 1 39.19ln T

3.833 EC3 cr

         

r 690 905 T SNZ

cr

  

r 375 700 T J

BC cr

  

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

Eurocode 3 New Zealand Standards Japanese Building Code

SLIDE 18

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Fire Res pons e of Res trained S teel Beams Fire Res pons e of Res trained S teel Beams

Fire induced Axial force Time Time

Temperature Compress Tension

Time

Deflection

Temperature Midspan Deflection

Catenary Action Stage

• Tensile force
• Improved response

2nd plastic hinge

1.0 (T)M k M (T)P k P

y y y y

 

Yield

Elastic Stage

• Expansion
• Fire induced axial force

Fire

Steel 1st plastic hinge

u y

• (T)M

k M



Elasto-plastic Stage

• Spread of plasticity, P-Δ effect
• Softening, Reduction in P

P = 0

Plastic mechanism

Failure Stage

• Reaching tensile capacity
• Connections

Dwaikat, 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

w Ka, Kr L Ka, Kr

SLIDE 19

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Development of Des ign 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

SLIDE 20

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Preparation of S pecimens Preparation of S pecimens

610 2385 305

2.5 2.5

Average insulation thickness: 44 mm Columns C1-W and C1-S

WSG1 WSG2 WSG3 WSG4 WSG5 25 90 65 25 25 50 STC3 STC2 STC1 SSG5 SSG4 SSG3 SSG1 SSG2 103 54 54 54 50 WTC2 WTC4 WTC3 WTC1 108 50 50 103

D D C C B B A A

380

P

2385 610 305

SFRM

(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 mm Columns C2-W and C2-S

W8x48 W8x48

SLIDE 21

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Experimental S tudies Experimental S tudies Tes t S etup Tes t S etup

1775 mm 2440 mm 3300 mm FURNACE FURNACE

Fixed end

610 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

SLIDE 22

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Tes t Res ults Tes t Res ults

D D C C B B A A

380

P

2385 610 305

SFRM

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

SLIDE 23

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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 Analys is Finite Element Analys is

SLIDE 24

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10 20 30 40 50 60

Thermal conductivity W/mK

Temperature ˚C

1 2 3 4 5 6 200 400 600 800 1000

Specific heat kJ/kgK

0.3 0.6 0.9 1.2 1.5 1.8 Thermal strain % Steel Temperature-stress-strain curves: Poh model (2001)

Physical properties of structural steel (EC3)

Specific heat Thermal strain Thermal conductivity

High High-temp. Material Properties

• temp. Material Properties

0.2 0.4 0.6 0.8 1 1.2 1.4 5 10 15 20 25 30 200 ˚C 20 ˚C 400 ˚C 600 ˚C 800 ˚C

F s,T / F y,20°C

 

C s C y T s

E F

 

20 , 20 , ,



0.0 0.2 0.4 0.6 0.8 1.0 200 400 600 800 1000 Temperature, ˚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.

SLIDE 25

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High-Temp. Creep

Time Creep strain ( )

Primary creep Secondary creep Tertiary creep

2 2

 dt d

cr

 2 2

 dt d

cr



cr



Fracture points

1

T

2

T

3

T

Increase in temperature

2 2

 dt d

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 (dσ

σs/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.

• AN

ANSYS SYS Creep Model “11” was calibrated using two independent material tests.

SLIDE 26

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Validation: Validation: Li and Guo’s Res trained Beam Tes t (2008) Li and Guo’s Res trained Beam Tes t (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.

SLIDE 27

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Validation: Validation: Li and Li and Guo’s Guo’sRes trained Beam Tes t (2008) Res trained Beam Tes t (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.

SLIDE 28

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Validation: Validation: MS U Beam MS U Beam-Column Tes ts (2009) Column Tes ts (2009)

• Partial S

imulation: Temperature from tes t Partial S imulation: Temperature from tes t

• Full s

imulation: Temperature from thermal analys is Full s imulation: Temperature from thermal analys is

• Us

ing Es timated res traint s tiffnes s es Us ing Es timated res traint s tiffnes s es Ka = 25000 kN/m, = 25000 kN/m, Kr = 2500 kN = 2500 kN-m/rad m/rad

• Load his

tory applied from tes t Load his tory applied from tes t

• For partial s

imulation: Temperature zones For partial s imulation: Temperature zones

380

F U R N A C E

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.

SLIDE 29

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380

F U R N A C E

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: MS U Beam MS U Beam-Column Tes ts (2009) Column Tes ts (2009)

SLIDE 30

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Parametric S tudies Effect of Load Ratio (LR)

• 800
• 600
• 400
• 200

150 300 450 600 750 900 Steel temperature, °C Midspan deflection, mm. LR = 30% LR = 50% LR = 70% Section W24x76, L = 9 m RR = AR = 10%

Local Buckling

• Higher load ratio leads

to higher mids pan deflection

• Load ratio reduces

fire res is tance under deflection or s trength limit s tates

• 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.

SLIDE 31

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Parametric S tudies Effect of Axial Res traint (AR)

• Higher axial res

train leads to higher initial mids pan deflection

• Axial res

traint improves fire res is tance bas ed on s trength limit s tate

• 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

200 400 600 800 1000 Steel temperature, °C M id s p a n d e fle c tio n , m m . AR = 0 AR = 10% AR = 30% AR = ∞ Section W24x76, L = 9 m, RR = 0, LR = 50%

Local buckling (web)

SLIDE 32

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Parametric S tudies Effect of Rotational Res traint (RR)

• Higher rotational res

train leads to les s er mids pan deflection

• Rotational res

traint improves fire res is tance

• 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

200 400 600 800 1000 Steel temperature, °C Midspan deflection, mm. RR = 0 RR = 10% RR = 30% RR = ∞ Section W24x76, L = 9 m, AR = 10%, LR = 50% Local buckling

SLIDE 33

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Parametric S tudies Effect of Location of Res traint

• Moving res

traint to the bottom flange improves

• verall res

pons e

• This

is due to the counter-acting moment that develops at s upport

• Local buckling has

minor influence on deflection s ince 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

200 400 600 800 1000 Steel temperature, °C M id sp an d eflectio n , m m .

y = d /2

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

y

y = 0

Uniform temperature

SLIDE 34

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Parametric S tudies Effect of Thermal Gradient

• Thermal gradient increas

es elas tic deflection due to thermal bowing

• Thermal gradient has

minor effect on the res pons e in the catenary phas e due to change in load bearing mechanis m

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

SLIDE 35

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Parametric S tudies Effect of Fire S cenario

• Three fire s

cenarios (including EC1 des ign fires ) were s elected

• Res

pons e is better under des ign fires due to the cooling phas e

• Failure occurs

under s tandard fire

• Partial recovery of deflection under

des ign 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.

200 400 600 800 1000 30 60 90 120 150 180 Time, min. Tem perature, °C Fire curve Bottom flange Middle of web Top flange 200 400 600 800 1000 1200 30 60 90 120 150 180 Time, min. Temperature, °C 15 mm insulation W24x76 1 m 0.61m 0.23 m 0.1m

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

150 300 450 600 750 900 30 60 90 120 150 180 Time, min. Tem perature, °C

(c) Design fire II

• 900
• 750
• 600
• 450
• 300
• 150

20 40 60 80 100 120 140 160 180 Fire exposure time, min. Midspan deflection, mm. Design fire I Design fire II W24x76, L = 9m, LR = 50% AR = RR = 10% ASTM E119 fire

SLIDE 36

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Development of Performance Development of Performance-Bas ed Bas ed Engineering Approach Engineering Approach

Thermal gradient

Use realistic “design” fire scenario

Time Temperature

Fire Scenario

Steel temperature

Restrained beam exposed to fire Predict steel temperature “with thermal gradient” Predict the response

• f restrained beam during fire

Predict the fire-induced forces and deflection of restrained beam

Summary of proposed approach

• Compute steel temperature and

thermal gradient

• Compute restraint forces
• Compute deflection

ΔT

Time Temperature

Ts

Time Axial Force Deflection Time Axial Force Deflection

P Δ

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

SLIDE 37

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S tep 1 : S teel temperature S tandard Fire

m T T T

f s p

 

 

F F w F F CF s p

B t t B t 2 / A F

    

     

f w w f web s p

2t d t t 2

• 2t

d 2 / A F

     

t T

ρc

Q T 2 k

    

General Heat Trans fer Equation

T(x,y,z,t) Tf(t)                  

4 f T 4 T 4eσ f T T con h rad Q con Q Q

• As

s umptions Uniform s teel temperature Radiation  Equivalent convection Thin ins ulation Fire temperature: Fire temperature: Tf = = a t a t n



Tf Ts Tp

        

st e 1 f T (t) s T

dt f dT 2 F s T f T 1 F dt s dT

          

1 n m p t s A p F s

ρ

s c p

ρ

p c 1 p / k p t 1/ h s

ρ

s c s / A p F 1 n 1 F s

                         

 

F F w F F BF s p

B t t B 2 t 2 / A F

     

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

Temperature

Tf(t)

SLIDE 38

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Time Temperature

T f,max t 1 t 2

Design fire curve Average steel temp. 20 °C

T s,max T s,1 t 3

decay rate of fire "r"

Time Temperature

T f,max t 1 t s,max

Design fire curve Average steel temp.

T s,max T s,1 A B

r

t 2

γ βt

2

αt

s T

  

At point A (t = t1): Ts= Ts

1(us

ing previous

• Eq. at t = t1), and

dTs/dt = s lope from previous

• Eq. at t = t1,

At point B (t = ts

,max):

Ts= Tf , and dTs/dt = 0.

             

1 rt s,1 T 2 1 s,1 T max f, T 1 1 t max s, t

s,1 r/ T 1 2t 1 r 1 2t max f, T max s, T

  

S tep 1 : S teel temperature Des ign 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.

SLIDE 39

39

S teel Temperature Comparis

• n to F.E.A.

100 300 500 700 900 100 300 500 700 900

Ts,max (oC) From proposed approach T s,m ax (oC) From finite elem ent analysis +10% margin

• 10% margin

50 100 150 200 250 50 100 150 200 250 ts,max (min.) From proposed approach ts,max (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.

SLIDE 40

40

S tep 2: Plas tic P S tep 2: Plas tic P-M Interaction under Thermal M Interaction under Thermal Gradient Gradient

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



u u n n

M P + 1.0 Φ 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) t t )(2B (T k ) (T dk t ) (T k t 2B 2 d e

w F F Ave s, E Ave s, E w CF s, E F F

2 d ) (T k A y ) (T k A Y Y e

i E i i i E i CG CS

      

 

e× P u = M TG M TG A A' B B' C C' M / M u P / Pu

T = T ave ΔT

1.0 F A P F Z M M

ave Ts, u, s ave Ts, u, x TG

  

1.0 F A P F Z M M

ave Ts, u, s Tave u, x TG

  

) (T P ) e(T M

ave u ave TG

 

SLIDE 41

41

Plas tic P Plas tic P-M Interaciton Diagrams M Interaciton Diagrams Comparis

• n to Tes

ts and F.E.

D D C C B B A A

P

2385 610 305 1930

hottest region 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.

SLIDE 42

42

S tep 3: Fire Induced Deflection in Res trained S tep 3: Fire Induced Deflection in Res trained Beams Beams

Fire induced Axial force Time Time

Temperature Compress Tension

Time

Deflection

Temperature Midspan Deflection

• Deflection Limit State

Tx

Temperature at yield Fire

Steel

Catenary temperature P = 0

• Design Fire Scenarios

 

2 x s A R y

• y

a / S YA 1 F

ΔT

0.5F / M M 1 T

    

          

2

ΔT

F M M M M 1 a 1 T

R u y u 2 c

20) (T 2α 2 L

Δ

c c

  

ky(Tx)AsFu

 

c F y c y DLS

Δ

L T T T T

  

F

L

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

SLIDE 43

43

Deflection of Res trained S teel Beams Comparis

• n to Tes

t Data { Li and Guo Tes

t (2008) } Li and Guo Tes t (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.

SLIDE 44

44

Deflection of Res trained S teel Beams Comparis

• n to Finite Element Analys

is Comparis

• n to Finite Element Analys

is

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

DLS (°C) From F.E.A

• 10%

margin +10% margin

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

D L S (°C

) F ro m F .E .A

• 10%

margin +10% margin

a) Deflection limit state (LF) = L/20 L/20 b) Deflection limit state (LF) = L/30 L/30

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.

SLIDE 45

45

Des ign 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

SLIDE 46

46

Des ign Applicability Res trained S teel 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

200 400 600 800 1000 1200 50 100 150 200 250 Time, min. Temperature, °C

Standard fire Design fire Steel temperature T DLS = 605°C

SLIDE 47

47

    

    

C 605 15 542 411 8 . 878 15 30 / 7000 411



             

y c y c y F y DLS

T T L T T

mm 542 ) 20 8 . 878 ( 10 14 2 2 7000 ) 20 ( 2 2

6

        

 c c

T L 

C 8 . 878 2 150 0032 . 9 . 1308 8 . 1023 9 . 1308 8 . 285 1 0008 . 1 2 1 1

2  

                        T F M M M M a T

R u y u c

C 411 0008 . 00037 . 150 0032 . 5 . 8 . 1023 / 8 . 285 1 5 . / 1

2 

            a F T F M M T

A R y

• y
• 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 TDLS

Check using temperature equations developed earlier Ts,max = 597°C < TDLS = 605°C (at 90 min. of fire exposure)

Des ign Applicability Deflection Limit S tate Temperature

mm 15 1 8 384 5

1 2 4

                     

s y R s E y

E F a F d T L I E k wL  

Fire resistance (minutes) Deflection limit state (L/ 30) Strength limit state Proposed approach 120 218 J apanese Building Code 132 132 Eurocode 3 160 160 New Zealand Standard 170 170 Finite element analysis 128 202

200 400 600 800 1000 1200 50 100 150 200 250 Time, min. Tem perature, °C

Standard fire Design fire Steel temperature T DLS = 605°C

SLIDE 48

48

Conclus ions Conclus ions

• 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.

SLIDE 49

49

Acknowledgments

SLIDE 50

50

SLIDE 51

51

Res earch Impact Res earch 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
• btaining 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.

SLIDE 52

52

Performance Problems

• S

teel

Fire Resistance Strategy

• Steel Structures

– 1-4 hours – Stability, no collapse

• Steel Columns, Decks

 Applied 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

SLIDE 53

53 Yield s trength

Variation in Properties

• Carbon S

teel

0.2 0.4 0.6 0.8 1 1.2 200 400 600 800 1000 Temperature, ˚C

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

Proportionality limit "EC3" Yield point "EC3"

y T y

F F /

,

10 20 30 40 50 60 200 400 600 800 1000 Temperature, ˚C Therm al Conductivity, W/m .˚C Rempe & Knudson 2008 Dale & Prasad 2007 Touloukain 1972 Yawata 1969 Powel 1956 EC3 model ASCE model

Thermal conductivity

SLIDE 54

54

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

SLIDE 55

55

0.50 0.75 1.00 1.25 1.50 1.75 2.00 2.25 2.50 2.75 3.00 200 400 600 800 Temperature °C Thermal Conductivity - W/m°C 0.29 0.43 0.58 0.72 0.86 1.01 1.15 1.30 1.44 1.58 1.73 32 212 392 572 752 932 1112 1292 1472 Temperature °F Thermal Conductivity Btu/hr.ft.°F

ASCE model (Siliceous) ASCE model (Carbonate) EC2 model (Upper limit) EC2 model (Lower limit) Test data- Carbonate Test data- Siliceous

0.2 0.4 0.6 0.8 1 1.2 200 400 600 800 1000 Temperature °C F'c (T) / F'c (20°C) 32 212 392 572 752 932 1112 1292 1472 1652 Temperature °F EC2 model- Siliceous EC2 model- Calcareous ASCE model- NSC Test data- Siliceous Test data- Carbonate

Variation in Properties

• Concrete

Compres s ive s trength Thermal conductivity

SLIDE 56

56

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

SLIDE 57

57

Variation in Properties

• Wood

Tens ile s trength Thermal diffus ivity

0.1 0.2 0.3 0.4 0.5 0.6 50 100 150 200 250 300 Temperature (°C) Thermal diffusivity(mm2/sec) Conventional wood Engineered lumber T&G wood OSB

0.2 0.4 0.6 0.8 1 1.2 100 200 300 400 Temperature (°C) Tensile strength ratio Lie Schaffer Thomas Knudson Best fit

SLIDE 58

58

Fire Res is tance - 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

SLIDE 59

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)

SLIDE 60

60

20 40 60 80 100 120 100 200 300 400 500 600 700 800 900

Temperature (°C) Strength (% of Initial)

FRP Wood S tructural S teel HS C NS C

• 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. s trength with T for materials

SLIDE 61

61

SLIDE 62

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) 0.2 0.4 0.6 0.8 1 1.2 1.4 5 10 15 20 25 30 200 ˚C 20 ˚C 400 ˚C 600 ˚C 800 ˚C

F s,T / F y,20°C

 

C s C y T s

E F

 

20 , 20 , ,

