Tools for Performance and/or

Objective Based Structural

Fire Design

ACI Convention

Kansas City, MO April 2015

Maged A. Youssef, P.Eng.Associate Professor

Associate Chair for Undergraduate Affairs

E-mail: youssef@uwo.ca

2

Design Codes and Structural Fire Engineering

• Architect and Structural Engineer

• EuroCode 2:

– estimate the fire resistance of structural elements.

– basis for advanced models at the structure level.

• 2005 NBCC:

– Objective-Based Design.

• US:

– ASCE 7 / Performance-Based Design.

3

RESEARCH OBJECTIVES

• Provide engineers with the ability to analyze structures exposed to fire

– Simple Methods (develop engineering sense).

• Develop design tools for different RC elements.

This presentation will cover the major challenges and the overall vision

4

(1) Thermal Strains

• Non-uniform distribution.

• Will the concrete section allow these strains to develop?

(Plane section!)

-600

-400

-200

0

200

400

600

800

1000

Tem

pe

ratu

re (

oC

)

305

mm

305 mmsteel bars

Fire (Bottom)

Fire (Upper)

Fire

(R

ight

)

Fire

(Lef

t)

5

(2) Temperature Distribution

Temperature o

C

200 400 600 800

He

igh

t (m

m)

-150

-75

0

75

150

T1

f ’cT1

T2

f ’cT2

T3

f ’cT3

Tav

f ’cTavT av

( t = 1 hr)

avg. Temp.

(temperature)

avg. Temp.

(strength)

Z

X

6

h

b

𝜓𝑐𝑇

-

+

z

equivalent

linear strain

nonlinear

thermal strain

thermalstrain in

top bars

thermalstrain in

bottom bars

𝜀𝑖

𝜓𝑖

- 𝜓

-

+

Fire Fire

Fire

x

y

b

h( Left ) ( Right )

( Bottom )

𝜀𝑖

𝜓𝑖

𝑀𝑎𝑝𝑝

𝜓𝑐𝑇

-

+

z

equivalent

linear strain

nonlinear

thermal strain

thermalstrain in

top bars

thermalstrain in

bottom bars

𝜀𝑖

𝜓𝑖

- 𝜓

-

+

Fire Fire

Fire

x

y

b

h( Left ) ( Right )

( Bottom )

𝜀𝑖

𝜓𝑖

𝑀𝑎𝑝𝑝

𝜀 = 𝜀𝑡ℎ + 𝜀𝑠𝑡 + 𝜀𝑐 + 𝜀𝑡𝑟 = 𝜀𝑡ℎ + 𝜀𝑐𝑇

𝜓𝑐𝑇

-

+

z

equivalent

linear strain

nonlinear

thermal strain

thermalstrain in

top bars

thermalstrain in

bottom bars

𝜀𝑖

𝜓𝑖

- 𝜓

- +

Fire Fire

Fire

x

y

b

h( Left ) ( Right )

( Bottom )

𝜀𝑖

𝜓𝑖

𝑀𝑎𝑝𝑝

𝜀𝑡ℎ

_

Thermal

Strain

Equivalent Thermal

Strain

Self-induced

Strain

𝜀 = 𝜀𝑡ℎ + 𝜀𝑠𝑡 + 𝜀𝑐 + 𝜀𝑡𝑟 = 𝜀𝑡ℎ + 𝜀𝑐𝑇

7

= f (ASTM-E119 Time, Width, Area of

Steel Bars in Tension and

Compression, Number of Layers of

Tension Steel Bars , Aggregate Size)

Fire duration (hr)

0.0 0.5 1.0 1.5 2.0 2.5

i x

10

-3 (

M+

ve)

0

2

4

6

8

i x

10

-3 (

M-v

e)

0

4

8

12

16

B7

I7

Eq. 5

Eq. 7

siliceous

(M+ve)

(M-ve)carbonate

carbonate

siliceous

Fire duration (hr)

0.0 0.5 1.0 1.5 2.0 2.5

i x 1

0-6

0

2

4

6

8

10

B7

I7

Eq. 6

Eq. 8siliceous

carbonate

siliceous

(M+ve)

(M-ve)

𝜀𝑖

(3) Unrestrained Thermal Strains= f (ASTM-E119 Time, Width, Height, Area

of Steel Bars in Tension and Compression,

Number of Layers of Tension Steel Bars ,

Aggregate Size)

M+ve: Lower tension steel properties,

need higher steel strain or lower curvature.

M-ve: Tension steel unaffected and

concrete in compression

h

b

equivalent

linear strain

nonlinear

thermal strain

thermal

strain in

top bars

thermal

strain in

bottom bars

+

+

_

𝜓 + =

_ =

𝜓𝑐𝑇

+

_

+ 𝜀𝑖

+ 𝜀𝑖

+

𝜓 𝑖

𝜓 𝑖

Fire Fire

Fire

mesh for

heat transfer

concrete and

steel layers for

x

y

b

h( Left ) ( Right )

( Bottom )

sectional analysisFire

( Top )

c) equivalent linear

thermal strain (𝜀𝑡ℎ )

b) total strain (𝜀) d) equivalent

mechanical strain (𝜀𝑐𝑇 )

f) nonlinear thermal

strain (𝜀𝑡ℎ )

a) fiber model

c) equivalent linear

thermal strain (𝜀𝑡ℎ )

e) self-induced

thermal strain (𝜀𝑠𝑡 )

𝜀 = 𝜀𝑡ℎ + 𝜀𝑠𝑡 + 𝜀𝑐 + 𝜀𝑡𝑟 = 𝜀𝑡ℎ + 𝜀𝑐𝑇

+

𝜓𝑐𝑇

- +

z

equivalent

linear strain

nonlinear

thermal strain

thermalstrain in

top bars

thermalstrain in

bottom bars

𝜀𝑖

𝜓𝑖

- 𝜓

-

+

Fire Fire

Fire

x

y

b

h( Left ) ( Right )

( Bottom )

𝜀𝑖

𝜓𝑖

𝑀𝑎𝑝𝑝

𝜓𝑐𝑇

-

+

z

equivalent

linear strain

nonlinear

thermal strain

thermalstrain in

top bars

thermalstrain in

bottom bars

𝜀𝑖

𝜓𝑖

- 𝜓

-

+

Fire Fire

Fire

x

y

b

h( Left ) ( Right )

( Bottom )

𝜀𝑖

𝜓𝑖

𝑀𝑎𝑝𝑝

Self-induced

StrainMech.

Strain

𝜀 = 𝜀𝑡ℎ + 𝜀𝑠𝑡 + 𝜀𝑐 + 𝜀𝑡𝑟 = 𝜀𝑡ℎ + 𝜀𝑐𝑇

(4) Sectional Analysis at Elevated Temperatures

Thermal Strains.

Transient Strains.

Temperature Distribution.

Temperature-dependent material properties.

9

(5)EA and EI for Fire-Exposed Elements

M nM

Fire

M+ve

M+ve

M+veP

appP nP

PP

Fire

𝜀𝑖 𝜀𝑐𝑇

𝐸𝐴𝑒𝑓𝑓

1

𝜀

𝜀𝑖 𝜀𝑐𝑇

𝐸𝐴𝑒𝑓𝑓

1

𝜀

Simplified Approach to Calculate EAeff and EIeff

10

(6) Solution Procedure for a Structure

1) Calculate primary moments & axial forces in different members.

2) Identify elements exposed to fire and use their section properties

and fire duration to evaluate , , EAeff and EIeff.

3) Convert and to elongations and rotations

4) Apply the elongations and rotations for fire-exposed elements and

calculate the secondary moments and associated axial forces.

5) Recalculate EAeff, Eieff, and the primary moments.

6) Repeat steps 4 and 5 until convergence is achieved.

𝜀𝑖

𝜀𝑖

11

The beam is divided

into segments

Eieff is calculated based

on the primary BMD

Thermal curvatures are

simulated by concentrated

rotations

Secondary moments are

generated

M1

M

S3S2S1 S1S2

S1 S2 S3

M2

M3

M1M

2

M1 M

2

M3

Fire Fire

+veM

+veM

-ve

S3S2S1 S1S2

a) beam loading and reinforcement configuration

b) primary BMD

(𝑡 = 0.0 ℎ𝑟)

c) 𝑀 − 𝜓 diagrams at fire duration ( 𝑡 )

d) 𝐸𝐼𝑒𝑓𝑓 and 𝜓𝑖

distributions at fire duration ( 𝑡 )

e) equivalent thermal moments 𝑀𝑡ℎ at 𝑡

f) secondary moments due to

thermal effect 𝑀𝑡ℎ at 𝑡

𝐸𝐼𝑒𝑓𝑓 3 𝜓𝑖 3 ×

𝑀𝑡ℎ 1 = 𝑀𝑡ℎ 3 =

𝜓𝑖 1 × 𝐸𝐼𝑒𝑓𝑓 1

𝑀𝑡ℎ 1 =

𝜓𝑖 1 × 𝐸𝐼𝑒𝑓𝑓 1

𝐸𝐼𝑒𝑓𝑓 2 𝜓𝑖 2 × 𝑀𝑡ℎ 2 = 𝐸𝐼𝑒𝑓𝑓 2 𝜓𝑖 2 × 𝑀𝑡ℎ 2 =

𝜓𝑖 2

𝜓𝑖 3

𝐸𝐼𝑒𝑓𝑓 2

1

𝐸𝐼𝑒𝑓𝑓 3

1

𝜓𝑖 1

𝐸𝐼𝑒𝑓𝑓 1

1

𝜓𝑖 1

𝜓𝑖 3

𝜓𝑖 1

𝜓𝑖 2

𝜓𝑖 2

𝐸𝐼𝑒𝑓𝑓 1 𝐸𝐼𝑒𝑓𝑓 1 𝐸𝐼𝑒𝑓𝑓 3 𝐸𝐼𝑒𝑓𝑓 2 𝐸𝐼𝑒𝑓𝑓 2

M1

M

S3S2S1 S1S2

S1 S2 S3

M2

M3

M1M

2

M1 M

2

M3

Fire Fire

+veM

+veM

-ve

S3S2S1 S1S2

a) beam loading and reinforcement configuration

b) primary BMD

(𝑡 = 0.0 ℎ𝑟)

c) 𝑀 − 𝜓 diagrams at fire duration ( 𝑡 )

d) 𝐸𝐼𝑒𝑓𝑓 and 𝜓𝑖

distributions at fire duration ( 𝑡 )

e) equivalent thermal moments 𝑀𝑡ℎ at 𝑡

f) secondary moments due to

thermal effect 𝑀𝑡ℎ at 𝑡

𝐸𝐼𝑒𝑓𝑓 3 𝜓𝑖 3 ×

𝑀𝑡ℎ 1 = 𝑀𝑡ℎ 3 =

𝜓𝑖 1 × 𝐸𝐼𝑒𝑓𝑓 1

𝑀𝑡ℎ 1 =

𝜓𝑖 1 × 𝐸𝐼𝑒𝑓𝑓 1

𝐸𝐼𝑒𝑓𝑓 2 𝜓𝑖 2 × 𝑀𝑡ℎ 2 = 𝐸𝐼𝑒𝑓𝑓 2 𝜓𝑖 2 × 𝑀𝑡ℎ 2 =

𝜓𝑖 2

𝜓𝑖 3

𝐸𝐼𝑒𝑓𝑓 2

1

𝐸𝐼𝑒𝑓𝑓 3

1

𝜓𝑖 1

𝐸𝐼𝑒𝑓𝑓 1

1

𝜓𝑖 1

𝜓𝑖 3

𝜓𝑖 1

𝜓𝑖 2

𝜓𝑖 2

𝐸𝐼𝑒𝑓𝑓 1 𝐸𝐼𝑒𝑓𝑓 1 𝐸𝐼𝑒𝑓𝑓 3 𝐸𝐼𝑒𝑓𝑓 2 𝐸𝐼𝑒𝑓𝑓 2

M1

M

S3S2S1 S1S2

S1 S2 S3

M2

M3

M1M

2

M1 M

2

M3

Fire Fire

+veM

+veM

-ve

S3S2S1 S1S2

a) beam loading and reinforcement configuration

b) primary BMD

(𝑡 = 0.0 ℎ𝑟)

c) 𝑀 − 𝜓 diagrams at fire duration ( 𝑡 )

d) 𝐸𝐼𝑒𝑓𝑓 and 𝜓𝑖

distributions at fire duration ( 𝑡 )

e) equivalent thermal moments 𝑀𝑡ℎ at 𝑡

f) secondary moments due to

thermal effect 𝑀𝑡ℎ at 𝑡

𝐸𝐼𝑒𝑓𝑓 3 𝜓𝑖 3 ×

𝑀𝑡ℎ 1 = 𝑀𝑡ℎ 3 =

𝜓𝑖 1 × 𝐸𝐼𝑒𝑓𝑓 1

𝑀𝑡ℎ 1 =

𝜓𝑖 1 × 𝐸𝐼𝑒𝑓𝑓 1

𝐸𝐼𝑒𝑓𝑓 2 𝜓𝑖 2 × 𝑀𝑡ℎ 2 = 𝐸𝐼𝑒𝑓𝑓 2 𝜓𝑖 2 × 𝑀𝑡ℎ 2 =

𝜓𝑖 2

𝜓𝑖 3

𝐸𝐼𝑒𝑓𝑓 2

1

𝐸𝐼𝑒𝑓𝑓 3

1

𝜓𝑖 1

𝐸𝐼𝑒𝑓𝑓 1

1

𝜓𝑖 1

𝜓𝑖 3

𝜓𝑖 1

𝜓𝑖 2

𝜓𝑖 2

𝐸𝐼𝑒𝑓𝑓 1 𝐸𝐼𝑒𝑓𝑓 1 𝐸𝐼𝑒𝑓𝑓 3 𝐸𝐼𝑒𝑓𝑓 2 𝐸𝐼𝑒𝑓𝑓 2

M1

M

S3S2S1 S1S2

S1 S2 S3

M2

M3

M1M

2

M1 M

2

M3

Fire Fire

+veM

+veM

-ve

S3S2S1 S1S2

a) beam loading and reinforcement configuration

b) primary BMD

(𝑡 = 0.0 ℎ𝑟)

c) 𝑀 − 𝜓 diagrams at fire duration ( 𝑡 )

d) 𝐸𝐼𝑒𝑓𝑓 and 𝜓𝑖

distributions at fire duration ( 𝑡 )

e) equivalent thermal moments 𝑀𝑡ℎ at 𝑡

f) secondary moments due to

thermal effect 𝑀𝑡ℎ at 𝑡

𝐸𝐼𝑒𝑓𝑓 3 𝜓𝑖 3 ×

𝑀𝑡ℎ 1 = 𝑀𝑡ℎ 3 =

𝜓𝑖 1 × 𝐸𝐼𝑒𝑓𝑓 1

𝑀𝑡ℎ 1 =

𝜓𝑖 1 × 𝐸𝐼𝑒𝑓𝑓 1

𝐸𝐼𝑒𝑓𝑓 2 𝜓𝑖 2 × 𝑀𝑡ℎ 2 = 𝐸𝐼𝑒𝑓𝑓 2 𝜓𝑖 2 × 𝑀𝑡ℎ 2 =

𝜓𝑖 2

𝜓𝑖 3

𝐸𝐼𝑒𝑓𝑓 2

1

𝐸𝐼𝑒𝑓𝑓 3

1

𝜓𝑖 1

𝐸𝐼𝑒𝑓𝑓 1

1

𝜓𝑖 1

𝜓𝑖 3

𝜓𝑖 1

𝜓𝑖 2

𝜓𝑖 2

𝐸𝐼𝑒𝑓𝑓 1 𝐸𝐼𝑒𝑓𝑓 1 𝐸𝐼𝑒𝑓𝑓 3 𝐸𝐼𝑒𝑓𝑓 2 𝐸𝐼𝑒𝑓𝑓 2

Application for a Continuous Beam

(7) Simplified Tools

• Stress-Block Parameters of RC Beams Exposed to Fire.

• Interaction Diagrams of RC Columns Exposed to Fire.

• Shear Capacity of RC Beams Exposed to Fire.

13

(8) Strain Defining Section Capacity

εc max : concrete

strain corresponds

to Moment of

Resistance Mr

A parametric study

is conducted to

evaluate εc max at

elevated temperatures

Reasonable

predictions are

obtained at r = 0.25

cT x 10-3

0 10 20 30 40

f cT

/ f

' c

0.00

0.25

0.50

0.75

1.00Tavg = 200

oC

400 oC

600 oC

= 0.02

r.

cT

ma

x

Mo

me

nt

(M)

= 0.3

Curvature ( )

= 0.0

= 0.9

= 0.6

concrete crushing

flexural capacity

i

M x 102 (kN.m)

0.0 0.5 1.0 1.5 2.0 2.5

P x 103 (kN)

0

1

2

3

4r = 1.0(peak points)

r = 0.0

r = 0.25

r = 0.50

r = 0.75

r = 1.0

Flexural capacity x 106 (kN.m)

0 300 600 900 1200 1500

Pre

dic

ted

ca

pa

city

x 1

06 (

kN

.m)

0

300

600

900

1200

1500

line of equality

Mean 0.985

SD 0.088

CV 0.089

b) ) 𝑟 = 0.25 Δ𝜀

M x 102 (kN.m)

0.0 0.5 1.0 1.5 2.0 2.5

P x 103 (kN)

0

1

2

3

4r = 1.0(peak points)

r = 0.0

r = 0.25

r = 0.50

r = 0.75

r = 1.0

14

Location of Critical Strain

x

y

h =

0.6 m

b = 0.6 m

Fire

( Left )

Fire

( Right )

Fire

( Top )

Fire

( Bottom )

c

cT x 10-3

-40 -30 -20 -10 0 10 20 30

y x 10-3

(m)

0

150

300

450

600

oT + tr cT max

x = 0.005

concrete crushing

z3 = 0.089 ,

z4 = -0.033

A

B

h

c = 0.226 m

b) 𝜀𝑐𝑇 dist. a) four-face heated

RC section c) concrete

forces

15

(9) Axial Capacity of Fire-Exposed RC Columns

x

y

h

b

Pr T

𝜀𝑐𝑇

y

𝑇𝑎𝑣𝑔 dist 𝑓𝑐𝑇 fcT

Cc

Temperature dependant

f ( Tavg )

100

200

300

400

500

600

700

800

900

305 mm3

05

mm

dy +

𝜀𝑠𝑡

16

Closed Form Solution for Standard Fire Exposure

Temperature Distribution

-600

-400

-200

0

200

400

600

800

1000

Tem

pe

ratu

re (

oC

)

305

mm

305 mmsteel bars

Fire (Bottom)

Fire (Upper)

Fire

(R

ight

)

Fire

(Lef

t)

Wickstrom’s Simple Method (1986)

Tavg 1Tavg 2

Tavg 1

x1

x2

Tavg 1Tavg 2

Tavg 1

x1

x2

x

y

z

zR 1L , B

R 20 , B

R 1R , B

R 1

L , 0

R 2

0 , 0

R 1

R , 0

R 1L , T

R 2

0 , T

R 1

R , T

z

T avg 1

Fire

( Left )

Fire

( Right )

Fire

( Top )

Fire

( Bottom )

area affectedby fire temp

area not affectedby fire temp

2

1

Line 1-1

Line 2-2

b

h

T avg 1T avg 2

T avg 1 T avg 1T avg 2

R 1L , B

R 20 , B

R 1R , B

R 1

L , 0

R 2

0 , 0

R 1

R , 0z

y

z

z

actual temp.

dist.

average

dist.

T avg

dist.

actual temp.

dist.

average

dist.

x

y

z

zR 1L , B

R 20 , B

R 1R , B

R 1

L , 0

R 2

0 , 0

R 1

R , 0

R 1L , T

R 2

0 , T

R 1

R , T

z

T avg 1

Fire

( Left )

Fire

( Right )

Fire

( Top )

Fire

( Bottom )

area affectedby fire temp

area not affectedby fire temp

2

1

Line 1-1

Line 2-2

b

h

T avg 1T avg 2

T avg 1 T avg 1T avg 2

R 1L , B

R 20 , B

R 1R , B

R 1

L , 0

R 2

0 , 0

R 1

R , 0z

y

z

z

actual temp.

dist.

average

dist.

T avg

dist.

actual temp.

dist.

average

dist.

Average Temperature

x

y

h

b

Pr T

𝜀𝑐𝑇

y

𝑇𝑎𝑣𝑔 dist

+

𝜀𝑠𝑡 𝑓𝑐𝑇 fcT

Cc

closed form solution

to evaluate fcT

Integration

Validation (33 columns)

Applied load x 103 (kN)

0 1 2 3 4

Pre

dic

ted

ca

pa

city x

10

3 (

kN

)

0

1

2

3

4

line of equality

Lie and Wollerton [15]

Mean 1.117

SD 0.294

COV 0.263

Applied load x 103 (kN)

0.0 0.2 0.4 0.6 0.8 1.0

Pre

dic

ted

ca

pa

city x

10

3 (

kN

)

0.0

0.2

0.4

0.6

0.8

1.0

Proposed method

line of equality

Hass [17]

Mean 0.877

SD 0.258

COV 0.295

Applied load x 103 (kN)

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

Pre

dic

ted

ca

pa

city x

10

3 (

kN

)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

line of equality

Dotreppe et al. [16]

Mean 0.782

SD 0.140

COV 0.179

a)

c)

b)

Applied load x 103 (kN)

0 1 2 3 4

Pre

dic

ted

ca

pa

city x

10

3 (

kN

)

0

1

2

3

4

line of equality

Lie and Wollerton [15]

Mean 1.117

SD 0.294

COV 0.263

Applied load x 103 (kN)

0.0 0.2 0.4 0.6 0.8 1.0

Pre

dic

ted

ca

pa

city x

10

3 (

kN

)

0.0

0.2

0.4

0.6

0.8

1.0

Proposed method

line of equality

Hass [17]

Mean 0.877

SD 0.258

COV 0.295

Applied load x 103 (kN)

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

Pre

dic

ted

ca

pa

city x

10

3 (

kN

)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

line of equality

Dotreppe et al. [16]

Mean 0.782

SD 0.140

COV 0.179

a)

c)

b)

Applied load x 103 (kN)

0 1 2 3 4

Pre

dic

ted

ca

pa

city x

10

3 (

kN

)

0

1

2

3

4

line of equality

Lie and Wollerton [15]

Mean 1.117

SD 0.294

COV 0.263

Applied load x 103 (kN)

0.0 0.2 0.4 0.6 0.8 1.0

Pre

dic

ted

ca

pa

city x

10

3 (

kN

)

0.0

0.2

0.4

0.6

0.8

1.0

Proposed method

line of equality

Hass [17]

Mean 0.877

SD 0.258

COV 0.295

Applied load x 103 (kN)

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

Pre

dic

ted

ca

pa

city x

10

3 (

kN

)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

line of equality

Dotreppe et al. [16]

Mean 0.782

SD 0.140

COV 0.179

a)

c)

b)

20

(10) Validation RC Beams

Fire duration (min)

0 30 60 90 120 150

w* (

cm)

-120

-80

-40

0

Test Lin et al.

FEM - Kodur et al.

Sectional Analysis

Curvature x 10-3

(1/in)

0 1 2 3 4 5 6

Mom

ent (f

t.Ib

) x

10

10

0

2

4

6

8

10

12

Curvature x 10-6

(1/mm)

0 50 100 150 200 250

Mom

ent (k

N.m

)

0

40

80

120

160

Prior to Fire

1 hr fire exposure

6.10 m [20.01 ft]

20 kN

*w

0.75 m 1.50 m 1.50 m 0.75 m1.50 m

2#19

4#19

[4496 Ib]20 kN[4496 Ib]

20 kN[4496 Ib]

20 kN[4496 Ib]

[4.9 ft] [4.9 ft] [4.9 ft][2.5 ft] [2.5 ft]

i

21

Validation for RC Walls

0

10

20

30

40

50

60

70

80

90

100

0 10 20 30 40 50 60 70

Mid

-sp

an D

efle

ctio

n (m

m)

Time (min.)

Experimental Results -

Crozier and Sanjayan 2000

Calculated Results -

Sectional Analysis

22

Validation Restrained Beam

1.8 m

6.1 m

1.8 m

P2

1. Loaded prior to Fire test

2. P1 and P2 were 59 kN prior to fire

test.

3. During fire test, P1 and P2 varied

such that the cantilever deflection

stays constant.

1.8 m

6.1 m

1.8 m

P1

Δ

23

Fire duration (min)

0 60 120 180 240

Mid

-sp

an

de

fle

ctio

n (

mm

)

-250

-200

-150

-100

-50

0

Mid

-sp

an

de

fle

ctio

n (

in)

-8

-6

-4

-2

0

Test Lin et al. 5

Sectional Analysis

(3 iterations)

Fire duration (min)

0 60 120 180 240

Ca

ntile

ve

r lo

ad

s (

kN

)

0

30

60

90

120

Ca

ntile

ve

r lo

ad

s (

kip

s)

0

5

10

15

20

25

Test - P1 and P2

Sectional Analysis

(3 iterations)

P1

P2

Validation for a Frame

Axial load on column

= 1727 kN

P1 & P2= 78 & 49 kN

Δ1 and Δ2 were

monitored during

the fire test

Δ2 Δ1

24

P1

P2

Ball Bearing

Hinge

Roller

Support

150 mm Ceramic

Fiber Shielding

1750 2600 1400 1025

6775

10

50

13

10

28

60

50

0

FireFire

Fire

SEC 2-2

400 x 500

2-22 MM +

2-25 MM

FireFire

Fire

SEC 3-3

400 x 500

2-22 MM

FireFire

Fire

SEC 4-4

400 x 500

2-22 MM

Fire

Fire

SEC 1-1

500 x 500

Fire

11

11

2

2

4-22 MM 4-22 MM 4-22 MM

2000 3750 825

3

3

4

4

12-22 MM

150

150

50

50

DEFLECTION

mm

mm

SAP2000

Fang et al.

SCALE

P1

P2

(2012)

Fig. Error! No text of specified style in document.-1-Beam-column subassemblage

deformation after 𝟑 𝐡𝐫𝐬 ISO-834 fire exposure

𝜃 ∆2

∆1 (23% error)

I II III IV

P1

P2

V

VI 278181

47

101

142

P1

P2

91 15

110

38

53

P1

P2

187 166 6363

89

a) Primary BMD

c) Total BMD (Stiffnesses in 𝑁.𝑚𝑚2 )

b) Secondary BMD

13.50× 1012

137.60× 1012

16.50× 1012

3.47 × 1012

10.30× 1012

𝐸𝐼𝑒𝑓𝑓 =

8.26× 1012

I II III IV

P1

P2

V

VI 278181

47

101

142

P1

P2

91 15

110

38

53

P1

P2

187 166 6363

89

a) Primary BMD

c) Total BMD (Stiffnesses in 𝑁.𝑚𝑚2 )

b) Secondary BMD

13.50× 1012

137.60× 1012

16.50× 1012

3.47 × 1012

10.30× 1012

𝐸𝐼𝑒𝑓𝑓 =

8.26× 1012

(5% error)

(10% error)

25

Shear Capacity Validation

26

For additional details, please refer to:• Youssef MA, Diab M, EL-Fitiany SF, in-press, “Prediction of the Shear Capacity of

Reinforced Concrete Beams at Elevated Temperatures”, Magazine of ConcreteResearch.

• El-Fitiany SF, Youssef MA, 2014, “Interaction Diagrams for Fire-Exposed ReinforcedConcrete Sections”, Engineering Structures, 70: 246-259.

• El-Fitiany SF, Youssef MA, 2014, “Simplified Method to Analyze ContinuousReinforced Concrete Beams during Fire Exposure”, ACI Structural Journal, 111(1):145-155.

• El-Fitiany SF, Youssef MA, 2011, “Stress-Block Parameters for Reinforced ConcreteBeams during Fire Events”, ACI SP-279: Innovations in Fire Design of ConcreteStructures, Paper No. 1, pp. 1-39.

• El-Fitiany SF, Youssef MA, 2009, “Assessing the Flexural and Axial Behaviour ofReinforced Concrete Members at Elevated Temperatures using Sectional Analysis”,Fire Safety Journal, 44(5): 691-703.

• Youssef MA, El-Fitiany SF, Elfeki M, 2008, “Flexural Behavior of Protected ConcreteSlabs after Fire Exposure”, ACI SP-255: Designing Concrete Structures for FireSafety, Paper No. 3, pp. 47-74.

• Youssef MA and Moftah M, 2007, “General Stress-Strain Relationship for Concreteat Elevated Temperatures”, Engineering Structures, 29 (10): 2618-2634.

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