Developing for Modelling Structures in Fire

Asif Usmani

School of Engineering, University of Edinburgh

with thanks to,Jian Zhang, Jian Jiang, Yaqiang Jiang and Panagiotis Kot sovinos

Steel in Fire forum, 12 April 2011

Why OpenSees?

♦ Difficult to continuously maintain, update and re-use research codes

♦ Commercial software expensive and restricted

♦ OpenSees is free, and

– a good platform to test ideas and make implementations available

– uses modern programming paradigms with greater granularity

– excellent structural/geotechnical analysis capabilities developing all the time

– HPC version

– excellent wiki with lots of help for users including many example scripts

OpenSees Abstractions

DomainModelBuilder Analysis

Recorder

Constructs the objects in the model and adds them to the domain.

Monitors user defined parameters in the model during the analysis

Moves the model from state at time tto state at time t + ∆∆∆∆t

Holds the state of the model at time t and (t + ∆∆∆∆t)i

Source: Frank McKenna (PEER/UC Berkeley)

Domain

Domain

Element Node TimeSeriesMP_Constraint SP_Constraint LoadPattern

ElementalLoad NodalLoad SP_ConstraintTrussZeroLengthElasticBeamColumnNonlinearBeamColumn(force, displacement)BeamWithHingesQuad(std, bbar, enhanced, u-p)ShellBrick(std, bbar, 20node, u-p, u-p-U)JointGenericClientExperimentalElement

ConstantLinearRectangularSinePath

Source: Frank McKenna (PEER/UC Berkeley)

Material

Source: Frank McKenna (PEER/UC Berkeley)

Material

UniaxialMaterial nDMaterial section

ElasticElasticPPHardeningConcreteSteelHystereticPY-TZ-QZParallelSeriesGapFatigueMaterial

ElasticJ2TemplateElasto-PlastoFluidSolidPorousPressureMultiYield(dependent, independent)

ElasticFiber

Addition of “SiF” capability

♦ Objectives– All development consistent with OpenSees OOP and modular structure

– Enable SiF analysis including fire and heat transfer calculations– Enable SiF analysis on “damaged” model after earthquake analysis

CFD dataLocal / movingZoneParametricStandardFiresFlux orTemp. q(t) q(t) q(z,t) q(x,y,z,t) q(x,y,z,t)

Hea

t Tra

nsfe

r Sla

bB

eam

Col

umn

T(z,t) T(z,t) T(z,t) T(x,y,z,t) T(x,y,z,t)

T(y,z,t)T(x,z,t)

T(y,z,t)T(x,z,t)

T(y,z,t)T(x,z,t) T(x,y,z,t)

T(x,y,z,t)

T(x,y,t) T(x,y,t) T(x,y,z,t) T(x,y,z,t) T(x,y,z,t)

New thermo-mechanical classes

New heat transfer classes

Thermal benchmarks

Phase change benchmark

0.00 0.02 0.04 0.06 0.08 0.100

10

20

30

40

50

60 Analytical Solution 4-noded, dt = 2s 8-noded, dt = 2s

T /

°C

x / m

T = 100 sinπt

40

◦CT = 100 sin

πt

40

◦C

T = 0◦CT = 0

◦C

x = 0.0mx = 0.0m x = 0.1mx = 0.1mx = 0.08mx = 0.08m

(a) geometry and boundary conditions

(b) FE discretised mesh

0 20 40 60 80-30

-20

-10

0

10

20

30

40

Analytical Solution 4-noded, dt =2s 8-noded, dt = 2s

T /

°C

t / s

Transient boundary condition benchmark

600

550

50045

0

400

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20

0.1

0.2

0.3

300

400

500

600

Testing local fire

Thermo-mechanical Benchmark 1

1 2 3

1 2

0T∆ ≠ 0T∆ =

1m 1m

0.1m

0.1m

1 2 3

1 2

0T∆ ≠ 0T∆ =

1m 1m

0.1m

0.1m

2.8e8

σ

ε

E0

Esh

T=400

2.8e8

σ

ε

E0

Esh

T=400

Left half of steel restrained beam subjected to a uniform temperature increment, ∆T = 1000oC

0 100 200 300 400 500 600 700 800 9000.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

2.2

2.4

2.6

Did

plac

emen

t (m

m)

Temperature (oC)

ABAQUS OpenSees

0 100 200 300 400 500 600 700 800 9000

20

40

60

80

100

120

140

160

180

200

220

240

260

280

300

Temperature (oC)

ABAQUS OpenSees

Str

ess

(MP

a)

1 2 3

1 2

0T∆ ≠ 0T∆ =1 2 3

1 2

0T∆ ≠ 0T∆ =

u

Benchmark 1 result

6m0.1m

0.2mKr Kr

Kt6m

0.1m

0.2mKr Kr

Kt

0 200 400 600 800 10000.0

5.0x104

1.0x105

1.5x105

2.0x105

Mod

ulus

of e

last

icity

(M

Pa)

Temperature (oC)

Ttop=0

Tbot=100oC-1000oC

Single beam subjected to uniformly distributed load and thermal gradient

Height of section

Temperature distribution

UDL=1kN/m

Thermo-mechanical Benchmark 2

Free end Spring end Pin end

0 200 400 600 800 10000

2

4

6

8

10

12

Hor

izon

tal d

ispl

acem

ent (

mm

)

Temperature at the bottom of the beam (oC)

ABAQUS-Free end ABAQUS-Spring end OpenSees-Free end OpenSees-Spring end

0 200 400 600 800 10000

50

100

150

200

250

300

350

Temperature at the bottom of the beam (oC)

Def

lect

ion

at m

id-s

pan(

mm

)

ABAQUS - free end ABAQUS - Spring end ABAQUS - Pin end OpenSees - free end OpenSees - Spring end OpenSees - Pin end

Benchmark 2 results

0 200 400 600 800 1000

-1800

-1600

-1400

-1200

-1000

-800

-600

-400

-200

0

ABAQUS - Spring end ABAQUS - Pin end OpenSees - Spring end OpenSees - Pin end

Temperature at the bottom of the beam (oC)

Axi

al fo

rce

(KN

)

0 200 400 600 800 10000

50

100

150

200

250

Temperature at the bottom of the beam (oC)

ABAQUS - free end ABAQUS - Spring end ABAQUS - Pin end OpenSees - free end OpenSees - Spring end OpenSees - Pin end

Mom

ent a

t mid

-spa

n (K

N.m

)

Benchmark 2 results

0 200 400 600 800 1000 1200

0

50

100

150

200

250

300

Temperature at the bottom of the beam ( oC)

Def

lect

ion

at m

id-s

pan(

mm

)

ABAQUS - Pin end ABAQUS - Spring end ABAQUS - Fix end OpenSees - Pin end OpenSees - Spring end OpenSees - Fix end

0 200 400 600 800 10000

20

40

60

80

100

120

140

160

180

200

Temperature at the bottom of the beam (oC)

Rot

atio

n of

the

end

(10-

3 rad

)

ABAQUS - Pin end ABAQUS - Spring end OpenSees - Pin end OpenSees - Spring end

Pin end Spring end Fix end

Benchmark 2 results

0 200 400 600 800 1000

-10000

-8000

-6000

-4000

-2000

0

ABAQUS - Pin end ABAQUS - Spring end ABAQUS - Fix end OpenSees - Pin end OpenSees - Spring end OpenSees - Fix end

Temperature at the bottom of the beam (oC)

Axi

al fo

rce

(KN

)

0 200 400 600 800 1000 1200

-300

-200

-100

0

100

200

300

Temperature at the bottom of the beam (oC)

ABAQUS - Pin end

ABAQUS - Spring end

ABAQUS - Fix end

OpenSees - Pin end

OpenSees - Spring end

OpenSees - Fix endM

omen

t at m

id-s

pan

(KN

.m)

Benchmark 2 results

0 200 400 600 800 1000 1200

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

Mom

ent o

f bea

m a

t mid

-spa

n (K

N.m

)

Temperature at the bottom of the beam (oC)

Kr=0 Kr=3e6 Kr=1.5e7 Kr=3e7 Kr=3e8 Kr=3e9 Kr=Infinite

Kr KrKr Kr

Benchmark 2 results

F1 F2

1240

1170

v4

u2

F1=112kN

F2=28kN

F1 F2

1240

1170

v4

u2

F1=112kN

F2=28kN

0 100 200 300 400 500 600

0

5

10

15

20

25

30

35

40

45

Dis

plac

emen

t (m

m)

Temperature (oC)

EHR Frame u2: Test v4: Test u2: OpenSees v4: OpenSees

0 100 200 300 400 500 600

5

10

15

20

25

30

35

40

45

Temperature (oC)

Dis

plac

emen

t (m

m)

ZSR Frame u1: Test u2: Test u1: OpenSees u2: OpenSees

EHR Frame ZSR Frame

Rubert and Schaumann, Fire Safety Journal, 10, 173-184, 1986

Validation problem 1

3000

1500

1300

Raft top Raft top

500

Ventilationopening

Fire level/Topof beam

Typical column,300 x 300

Plinth beam,230 x 230

Footing,1100 x 1100 x 500

Bricked box container filledwith sand with fuel tray on top

(level with the top of beam)

Roof slab120 thk

Roof beam230 x 230

Steel framingsystem

Simulated gravityloading of 2nd and 3rdabove floor

Superimposed live loadon floor 1

Extendedcolumn

Reactionwall

4300

5000

Hydraulicjack

Thermocouples at fivedifferent elevation levelsin three plan locations offire compartment

Validation problem 2

Full scale test of damagedRC frame subjected to fireIIT Roorkee, India (UKIERI funding)

2D frame model & cyclic loading

Response over 13 cycles

-200 -100 0 100 200

-300

-200

-100

0

100

200

300

Horizontal dsiplacement (mm)

Tot

al R

eact

ion

For

ce (

kN)

node1

1 23

displacement – force curve of control node 1

-80 -60 -40 -20 0 20 40 60 80-300

-200

-100

0

100

200

300

App

lied

For

ce (

kN)

Horizontal Dsiplacement (mm)

node 1

1 2

3

Comparison with test (5 cycles)

-350

-250

-150

-50

50

150

250

350

-100 -80 -60 -40 -20 0 20 40 60 80 100

Load

(KN

)

Displacement (mm)

Load-Displacement Plot for Roorkee Frame

Fire loading

0 200 400 600 800 1000

-140

-130

-120

-110

-100

-90

-80

-70

-60

Hor

izon

tal d

ispl

acem

ent (

mm

)

Temperature at the edge of the beam toward fire (C)

node1 node2

1 23

0 200 400 600 800 1000

-30

-25

-20

-15

-10

-5

0

5

Mid

-spa

n de

flect

ion

(mm

)

Temperature at the edge of the beam toward fire (C)

node 3

1 23

Residual strength testing

Final remarks

♦ 2D-3D truss and 2D beam-column element completed and tested

♦ New C++ OOP heat transfer code completed and tested

♦ Work progressing on 3D beam-column, shell and 3D heat transfer

♦ Interfacing fire-heat transfer-structural analysis should begin soon

♦ Fully functional capability expected by summer 2012

♦ All code (after exhaustive testing and benchmarking) will be offered to be included in OpenSees official release for free open-source access

♦ OpenSees is becoming a “community code” for the earthquake engineering, it makes sense for it to be adopted by the SiF community as well

0 200 400 600 800 1000

0

50

100

150

200

250

300

Def

lect

ion

at m

id-s

pan

(mm

)

Temperature at the bottom of beam (oC)

Theory - UDL only OpenSees - UDL only Theory - UDL+T,y OpenSees - UDL+T,y

0 200 400 600 800 1000

0

5

10

15

20

Def

lect

ion

at m

id-s

pan

(mm

)

Temperature at the bottom of beam (oC)

Theory - UDL only OpenSees - UDL only

Benchmark 2 results