Numerical Modelling of Large Deflection Behaviour of Restrained Reinforced Concrete Beams in Fire

Sherwan Albrifkani

Supervisors:

Professor Yong Wang

Dr Zhenjun Yang

sherwan.albrifkani@postgrad.manchester.ac.uk

The Steel in Fire Forum (StiFF) London, April 2015

Introduction

Methodology of ABAQUS modelling

Large deflection behaviour of restrained RC beams in fire

Summary

Questions

Outline

Introduction

Approaches of evaluating fire resistance of structural elements

Prescriptive-Based Approach

Standard fire resistance tests.

The provisions based on standard tests do not address the:

Effects of realistic fire conditions.

Interaction among structural members within a frame.

Global response of frames in fire.

Restraint conditions.

Performance-based approach

Fire severity.

Material properties at elevated temperatures.

Member interactions.

Load level.

Restraint conditions.

This approach considers the:

Introduction

Cardington full-scale fire tests on framed structures

Towards Performance-based approach

The Cardington full-scale fire tests demonstrated that the real behaviour of structural members within a frame can be very different from that indicated by standard fire tests.

Alternative load paths are likely to be available at lager deflections, such as membrane action in floor slabs and catenary action in beams that are not possible at small deflections.

Introduction

- The experiences from Cardington tests have pushed researchers to fill the knowledge gaps in understanding the fire performance of structures subject to lager deformations.

- Considerable survival of beams in fire may be ensured from catenary action.

w

w

Under flexural action

Under catenary action Fire tests on steel beam-column sub-assemblages

Recent studies on large deflection behaviour of restrained beams in fire

Introduction

Introduction

Fire safety research of restrained RC beams have been limited to the beam performance at small deflections.

Knowledge gap

- The current research work intents to address the knowledge gap in catenary action contribution to the fire safety improvement of RC beams.

Def

lect

ion

(m

m)

Fire exposure time

Axi

al f

orc

e

Fire exposure time

Compression

Tension

Under flexural action Under flexural action

Under catenary

action

Under

catenary

action

Methodology of ABAQUS modelling

Finite element modelling of RC structures using ABAQUS

BM

Failed column

P N

N

(b) catenary action for top bars in beam

BM

Failed column

P

N N BE BE

BM

(c) catenary action for top and bottom bars in beam

BE

Failed column

P

N N

(d) catenary action for bottom bars in beam

(a) compressive arch action

BE

BM

BE

BM

Failed column

N N

P

w

A typical beam under catenary action

Challenges of simulating large deflection behaviour of RC beams in fire subject to: - Extreme deformations. - Material and geometry non-linearity. - Material damage. - Temporary instability.

Finite element modelling of RC structures using ABAQUS

Solution Strategy

• Static, General

• Static, Riks

Static Analysis

Dynamic Analysis

• Dynamic, Implicit

• Dynamic, Explicit

Methodology of ABAQUS modelling

Producing a quasi-static response using Explicit dynamic analysis

Speeding up the simulation by artificially: - scaling the real time to a very small time period. - Increasing the material density (Mass scaling).

Introducing damping to the numerical model

Methodology of ABAQUS modelling

An example illustrating the selection of appropriate loading speed and

damping ratio

RC beam-column sub-ssemblage by Yu and Tan (2011)

Methodology of ABAQUS modelling

Displacement-controlled procedure Reduce the time period

Effect of rate of loading on the numerical behaviour of the sub-assemblage

Stable

Catenary action

capacity Flexural capacity

Load

Displacement

Applied

displacement

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

0 100 200 300 400 500 600 700

Ho

rizo

nta

l rea

ctio

n (

kN)

Middle joint displacement (mm)

(a) Load-middle joint displacement

(b) Horizontal reaction force-middle joint displacement

0

20

40

60

80

100

120

0 100 200 300 400 500 600 700

Ver

tica

l rea

ctio

n (

kN)

Middle joint displacement (mm)

Test (LS = 0.1 mm/s) LS= 100 mm/sLS = 150 mm/s LS = 200 mm/sLS = 250 mm/s LS = 300 mm/s

Methodology of ABAQUS modelling

LS: Loading speed

Load-controlled procedure

Effect of rate of loading on the numerical behaviour

of the sub-assemblage

Stable Stable Unstable

Static Dynamic Static

Flexural capacity Catenary

action

capacity

Applied

Load

Load

Displacement

0

20

40

60

80

100

120

0 100 200 300 400 500 600

Ve

rtic

al r

eac

tio

n (

kN)

Middle joint displacement (mm)

Test LS = 10 kN/s

LS = 15 kN/s LS = 20 kN/s

-300

-200

-100

0

100

200

300

400

0 100 200 300 400 500 600

Ho

rizo

nta

l re

acti

on

(kN

)

Middle joint displacement (mm)

Methodology of ABAQUS modelling

Reduce the time period

LS: Loading speed

𝐿𝑆1

𝜔𝑚𝑖𝑛,1=

𝐿𝑆2

𝜔𝑚𝑖𝑛,2

Lowest natural frequency (𝜔𝑚𝑖𝑛) of the model =89.5 rad/s

𝐿𝑆1

𝜔𝑚𝑖𝑛,1=

𝐿𝑆2

𝜔𝑚𝑖𝑛,2

∆𝑡≤ 𝑚𝑖𝑛 𝐿𝑒

𝜌

𝜆 + 2𝜇

𝜆 = 𝐸𝜐

1 + 𝜈 1 − 2𝜈

𝜇 =𝐸

2(1 + 𝜈)

∆𝑡≤2

𝜔𝑚𝑎𝑥1 + 𝜉𝑚𝑎𝑥

2 − 𝜉𝑚𝑎𝑥

Methodology of ABAQUS modelling

Mass scaling

0

20

40

60

80

100

120

0 100 200 300 400 500 600

Ve

rtic

al r

eac

tio

n (

kN)

Middle joint displacement (mm)

Test (LS =0.1 mm/s)

LS=150 mm/s, f=1, CPU time = 92 min

LS=8.66 mm/s, f=300, CPU time = 92 min

LS =4.74 mm/s, f=1000, CPU time = 92 min

LS=0.1mm/s, f=2250000, CPU time = 83 min

Displacement-controlled procedure LS: Loading speed f: Mass scaling factor

𝜔 = 𝑘𝑚

𝐿𝑆1

𝜔𝑚𝑖𝑛,1=

𝐿𝑆2

𝜔𝑚𝑖𝑛,2

∆𝑡≤ 𝑚𝑖𝑛 𝐿𝑒

𝜌

𝜆 + 2𝜇

𝜆 = 𝐸𝜐

1 + 𝜈 1 − 2𝜈

𝜇 =𝐸

2(1 + 𝜈)

∆𝑡≤2

𝜔𝑚𝑎𝑥1 + 𝜉𝑚𝑎𝑥

2 − 𝜉𝑚𝑎𝑥

Methodology of ABAQUS modelling

Mass scaling

Load-controlled procedure LS: Loading speed f: Mass scaling factor

𝜔 = 𝑘𝑚

0

20

40

60

80

100

120

0 100 200 300 400 500 600

Ve

rtic

al r

eac

tio

n (

kN)

Middle joint displacement (mm)

Test

LS=15kN/s, f=1, CPU time = 155 min

LS=0.866kN/s, f=300, CPU time = 163 min

LS=0.474kN/s, f=1000, CPU time = 160 min

LS=0.03 kN/s, f=250000, CPU time = 161 min

𝐶 = 𝛼 𝑀 + 𝛽 𝐾

Rayleigh damping in

ABAQUS is used

𝜉𝑖 =𝛼

2 𝜔𝑖+

𝛽𝜔𝑖

2

𝜉𝑖 : damping ratio

𝜔𝑖 : the natural frequency of the mode i.

𝛼 = 2 𝜔𝑖𝜉𝑖

𝛽=0

𝛼: Mass proportional damping factor

𝛽:Stiffness proportional damping factor

0

20

40

60

80

100

120

0 100 200 300 400 500 600 700

Ve

rtic

al r

eac

tio

n (

kN)

Middle joint dispalcement (mm)

Test 𝛼=0, 𝜉=0% 𝛼=15, 𝜉=8.4%

𝛼=25, 𝜉=14% 𝛼=50, 𝜉=28% 𝛼=75, 𝜉=42%

𝛼=125, 𝜉=70%

-700

-600

-500

-400

-300

-200

-100

0

0 1 2 3 4 5 6 7

Mid

dle

join

t d

isp

lace

me

nt

(mm

)

Step time (s)

Methodology of ABAQUS modelling

Damping ratio

-20

0

20

40

60

80

100

0 1 2 3 4 5 6 7

Load

(kN

)

Step time (s)

𝛼=0, 𝜉=0% 𝛼=15, 𝜉=8.4% 𝛼=25, 𝜉=14%

𝛼=50, 𝜉=28% 𝛼=75, 𝜉=42% 𝛼=125, 𝜉=70%

Applied Load

0

400

800

1200

1600

2000

0 1 2 3 4 5 6 7Kin

etic

en

erg

y (J

)

Step time (s)

Methodology of ABAQUS modelling

0

20

40

60

80

100

120

0 100 200 300 400 500 600

Ve

rtic

al r

eac

tio

n (

kN)

Middle joint displacement (mm)

Test

LS=15kN/s, f=1, 𝛼=50

LS=0.866kN/s, f=300, 𝛼=2.886

LS=0.474kN/s, f=1000, 𝛼=1.581

LS=0.03 kN/s, f=250000, 𝛼= 0.1

0

500

1000

1500

2000

0

20

40

60

80

100

120

0 2 4 6

Kin

etic

en

erg

y (J

)

Load

(kN

)

Step time

0

500

1000

1500

2000

0

20

40

60

80

100

120

0 1000 2000 3000

Kin

etic

en

erg

y (J

)

Load

(kN

)

Step time (s)

Vertical reaction

Applied load

Kinetic energy

Methodology of ABAQUS modelling

𝛼 = 2 𝜔𝑖𝜉𝑖

𝛼1

2 𝜔𝑚𝑖𝑛,1=

𝛼2

2 𝜔𝑚𝑖𝑛,2

Sequential coupled thermos-mechanical technique is adopted

Thermal boundary conditions: Eurocode EN 1991-1-2

Steel reinforcement is disregarded in the heat transfer analysis

Minor spalling of normal strength concrete is neglected

Stress-strain relationships with strength/deformation reduction factors at elevated temperatures : EN 1992-1-2. Creep and transient strains are not explicitly considered.

Methodology of ABAQUS modelling

Numerical modelling of RC beams in fire

Heat transfer analysis

Structural analysis

Speeding up the fire loading duration

Effect of speeding up real fire duration on the

numerical behaviour of the RC beam

Loading, heating and specimen details by Dotreppe and Franssen

0

500

1000

0 50 100 150

Tem

pe

ratu

re

(oC

)

Time (min)

Test Abaqus

Predicted and measured reinforcing bar temperature

Methodology of ABAQUS modelling

Lowest natural frequency (𝜔𝑚𝑖𝑛) of

the model =90.6 rad/s

-500

-450

-400

-350

-300

-250

-200

-150

-100

-50

0

0 20 40 60 80 100 120 140

Def

lect

ion

(m

m)

Time (min)

1.2 s / 3600 s

2 s / 3600 s

3s / 3600 s

4 s / 3600 s

Simulation (FRD) / Real

𝐹𝐿𝐷1 × 𝜔𝑚𝑖𝑛,1=𝐹𝐿𝐷2 × 𝜔𝑚𝑖𝑛,2

𝐹𝐿𝐷: fire loading duration

w

Description of the Analysed Beam

Large deflection behaviour of restrained RC beams in fire

Lowest natural frequency (𝜔𝑚𝑖𝑛)

of the model =119 rad/s

Restrained RC beams in fire

f ’c=30MPa

fy=453 MPa

-600

-400

-200

0

200

400

0 100 200 300 400

Axi

al f

orc

e (

kN)

Time (min)

-600

-500

-400

-300

-200

-100

0

0 100 200 300 400

Def

lect

ion

(m

m)

Time (min)

A

B

C

A

B

Large deflection behaviour of restrained RC beams in fire

C

Restrained RC beams in fire

-0.075

-0.05

-0.025

0

0.025

0.05

0.075

0 100 200 300 400

Stra

in (

mm

/mm

)

Time (min)

1324

1

2 3

4 Rupture strain

(tension)

Ultimate strain (compression)

Large deflection behaviour of restrained RC beams in fire

-600

-500

-400

-300

-200

-100

0

100

200

300

0 100 200 300 400

Axi

al f

orc

e (

kN)

Time (min)

-600

-500

-400

-300

-200

-100

0

0 100 200 300 400

Axi

al f

orc

e (

kN)

Time (min)

FLD= 1.5 s / 3600s (f=1, 𝛼=75, CPU time=463 min)

FLD= 3600 s / 3600s (f=5760000, 𝛼=0.03125, CPU time=394 min)

SLD: Fire loading duration f: Mass scaling factor 𝛼:Mass proportional damping factor

0

50

100

150

200

250

300

350

0

20

40

60

80

100

120

140

160

0 2 4 6 8 10

Kin

etic

en

erg

y (J

)

Load

(kN

)

Step time (s)

Vertical reaction forceApplied loadKinetic energy

f=1, 𝛼=75

0

50

100

150

200

250

300

350

0

20

40

60

80

100

120

140

160

0 5000 10000 15000 20000 25000

Kin

etic

en

erg

y (J

)

Load

(kN

)

Step time (s)

𝐹𝐿𝐷1 × 𝜔𝑚𝑖𝑛,1=𝐹𝐿𝐷2 × 𝜔𝑚𝑖𝑛,2

𝛼1

2 𝜔𝑚𝑖𝑛,1=

𝛼2

2 𝜔𝑚𝑖𝑛,2

f=5760000, 𝛼=0.03125

Summary

- ABAQUS/Explicit solver is efficient in solving RC problems that encounters large deformations, material and geometry nonlinearity and temporary instability.

- The simulation methodology is suitable to model RC structural

behaviour at ambient and elevated temperatures. - Speeding up the real loading duration is possible in explicit

solver providing that the inertia effects remain insignificant during the analysis.

- By adopting mass scaling to reduce the simulation time, the real

time scale can be preserved. - If a RC beam is provided with an adequate amount of restraint

at ends, catenary action could develop.

Thank You !

Any

Questions