Behaviour of Cellular beams and composite floors

in

ambient and elevated temperatures

Contents:

• Literature review

• Work done so far on:

� Cellular beam

� Cellular composite Floor

� Ambient and elevated temps

• Future work

Cellular beams in comparison

� aesthetically

� Generally lighter

� Having a far more flexible geometry

1) solid-webbed beams

2) castellated beams

� Remarkable increase in vertical bending stiffness

� holes as a passage for services and ducts

Advantages:

Disadvantage:

� Wasting amount of material in Double cut fabrication process

1. Finished depth

2. Opening diameter

3. Opening spacing

Major modes of failure

• Vierendeel Mechanism

• Web-post Buckling

• Rupture of web-post weld

• Pure Bending

• Lateral-torsional buckling

• Local failures

FEA of cellular beam (CB)

Single beams modelled

• Natal Beam No.4• Leeds Beam No.2

• Leeds Beam No.3

• Leeds Beam No.5

Cellular composite floor:• University of Kaiserslautern (2002)

• Ulster Beam A1 (2005)

• Ulster Beam B1 (2005)

1. Ambient Temp.s

2. Elevated TempsSingle Solid beams

Cellular composite floor• Ulster Beam A• Ulster Beam B

• Ulster Beam E

• Ulster Beam F

Modelling Natal Beam No.4

Shell elements:

� Large deformation

� Large strains� Plasticity

Material property:

� Bilinear kinematic

Software: ABAQUS , ANSYS

Load-Deflection comparison

LOAD-DEFLECTION CURVES

0.0

20.0

40.0

60.0

80.0

100.0

120.0

140.0

160.0

0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 10.00

Lo

ad

(K

N)

Def. (Cm)

ANSYS

ABAQUS

Exp.

Vierendeel Mechanism (P=108 KN )

Web Buckling (P=114 KN)

Vierendeel Mechanism (P~125 KN)

About 16% discrepancy

Main reasons causing difference between FEA and experiment results

• Residual stresses

• Imperfections

• Nominal dimensions

• Boundary conditions

• FE and Instrumental errors

Modelling Leeds Beam No. 2

Flange lateral support at 1m intervals

• Role of B.C.s

Load-Deflection

E= 190 KN, eeeeu = 10*eeeey and Fu= 1.1Fy

0

50

100

150

200

250

300

0 10 20 30 40 50 60

Def. (mm)

Lo

ad

(K

N)

BEAM 1

BEAM 2

Experiment

Buckling starts

Vierendeel+Plastic Def.s

Role of B.C.

Role of Lateral Support on the Behaviour of CBs

Cellular composite Floor:

Ulster Beam B1 (2005):

� High density of shear connector: Full interaction (Tied)� Symmetry (Half of the structure is modelled)

� Composite shell with Smeared cracking approach for concrete

Material Property• Steel

Stress strain curve for steel EC2-1-2

0

50

100

150

200

250

300

350

400

450

500

0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20

Total strain [%]

Str

es

s [

N/m

m2]

20o C 100o C 200o C 300o C 400o C 500o C 600o C

700o C 800o C 900o C 1000o C 1100o C 1200o C

Stress strain curve for siliceous concrete under compression (EN1992-1-2)

0

5

10

15

20

25

30

35

0.00 0.01 0.01 0.02 0.02 0.03 0.03 0.04 0.04 0.05 0.05

Total strain [%]

Str

es

s [

N/m

m2]

20o C 100o C 200o C 300o C 400o C 500o C

600o C 700o C 800o C 900o C 1000o C 1100o C

• Concrete

Tension Compression

Imperfection

• Trigger Load

Imp = aM1+bM2+cM3+…

• Imperfection amplitude

Load-Deflection Comparison

Riks Analysis- Test B1

0

100

200

300

400

500

600

0 5 10 15 20 25 30 35 40 45 50

Def. (Cm)

Lo

ad

(K

N)

Experiment

ABAQUS

Web post Buckling (P=474 KN)

Web post Buckling (P=430 KN)

10% Difference

Results (Ulster Beam B1)

Solid Beams in Elevated temps

Time-Deflection Comparison for solid beam 1A

0

20

40

60

80

100

120

140

160

0 5 10 15 20 25 30 35Time (Min)

De

f (C

m)

Experiment

ABAQUS

Beam 1A :

• Beams 1A, 9A, 14A, …

Elevated temperatures

Concrete temps

0

50

100

150

200

250

300

350

400

450

0 10 20 30 40 50 60 70 80 90

Time (mins)

tem

pera

ture

mid-depth of the slab

Interface beam/slab

free slab surface

Beam 1A:

• Slow rate heating

• Load Factor 50%

Results:

Load-Deflection Curves for Modelling and Experiment

TEST A1

0.00

50.00

100.00

150.00

200.00

250.00

0 10 20 30 40 50 60 70 80 90

Time (Min)

Def.

(m

m)

Experiment

Recorded Temps

Extrapolated Temps

TEST 1A

0

100

200

300

400

500

600

700

800

0 20 40 60 80 100

Time

Te

mp

Top Flange

Bot Flange

Web

Conc

Modified Web

• Recorded Temps

• Modified temps

Failed Beam 1A

Beam 1B:

• Slow rate heating

• Load Factor 50%

Results:

Load- Deflection Curves for modelling and experiment

Test B1

0.00

50.00

100.00

150.00

200.00

250.00

300.00

350.00

60 65 70 75 80 85 90 95 100 105 110 115 120 125 130 135 140 145 150 155 160

Time(mins)

Defl

ecti

on

(m

m)

Experiment

ABAQUS

Proposed Targets

� Understand stress distribution leading to

proposal of a simple web post buckling model

for ambient and elevated temperatures.

� Investigating the role of factors like BCs,

Residual stresses and Imperfections in CBs in

ambient and elevated temperatures.

� Parametric studies on the role of different load

heating rates on different geometries of CBs and

Composite slabs.

Thanks for your attention