numerical study on load distribution in hc floors

Aix-en-Provence, May 29 - June 1

NUMERICAL STUDY ON LOAD NUMERICAL STUDY ON LOAD DISTRIBUTION IN HC FLOORSDISTRIBUTION IN HC FLOORS

P. Bernardi, R. Cerioni, N. Garutti & E. Michelini

DISTRIBUTION IN HC FLOORSDISTRIBUTION IN HC FLOORS

Dept. of Civil and Environmental Engineering and Architecture, University of Parma, Parma, Italy

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LOAD DISTRIBUTION IN HC FLOORSLOAD DISTRIBUTION IN HC FLOORS

REQUIREMENTS OF

HC FLOORS• Vertical load bearing capacity

• Transverse load distribution � longitudinal joints

Load

INTRODUCTION NLFE ANALYSES NUMERICAL RESULTS CONCLUSIONS

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MAIN EFFECTS DUE TO CONCENTRATED LOADS:

• additional shear stresses due to torsion

• transverse bending moments � two-way slab behavior of the floor

Load

1/17

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• transverse bending moments � two-way slab behavior of the floor

Transverse distribution of shear forces and of bending and torsional moments:

- SIMPLIFIED CURVES (DESIGN STANDARDS)

- NUMERICAL APPROACHES

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SIMPLIFIED CURVES (UNI EN 1168)SIMPLIFIED CURVES (UNI EN 1168)

Main simplified assumptions:

• Theory of elasticity

• Simply supported floor


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� Not clear if they are referred to:

• bending moment distribution at midspan


• Five 1200mm wide units

• Line or point loads applied in the

centre or along the edge of the floor

MAY BE VERY

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• bending moment distribution at midspan

• shear force distribution at supports

MAY BE VERY

DIFFERENT FROM

EACH OTHERS

� Not dependent on the ratio EI/GJt of the HC cross section

NUMERICAL APPROACHES required

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SIMPLIFIED LINEAR ELASTIC FE MODELSSIMPLIFIED LINEAR ELASTIC FE MODELS


• Five units, 1200mm wide and 300mm thick

• Variable net spans (4 - 14m)

Definition of the case studies and adopted FE mesh

INTRODUCTION NLFE ANALYSES (1) NUMERICAL RESULTS CONCLUSIONS

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in • Variable net spans (4 - 14m)

• Floor FE mesh, with four-node, one-layered shell elements:

3/17

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• Floor FE mesh, with four-node, one-layered shell elements:

- presence of webs neglected

- same bending stiffness as the real units in the main direction

- overestimation of torsional stiffness

EI/GJt = 0.73 (effective value 1.06)

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SIMPLIFIED LINEAR ELASTIC FE MODELSSIMPLIFIED LINEAR ELASTIC FE MODELS

Joint modelling

Two adopted approaches:

1

2


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“Model S1”: spring elements

connected to shell elements

modelling the units

Spring stiffness/Shell thickness evaluated

so to simulate an hinge behaviour

1

2

3

4/17

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“Model S2”: horizontal shell

elements with variable thickness,


modelling the units

1

2

3

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SIMPLIFIED FE MODELS: NUMERICAL RESULTSSIMPLIFIED FE MODELS: NUMERICAL RESULTS

Bending moment,

slab j: βj·qL2/8

Load on slab j:

αj·qL

-]

theoretical [9]

EI/GJt = 0.73line load on panel 3

INTRODUCTION NLFE ANALYSES NUMERICAL RESULTS (1) CONCLUSIONS

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0.00

0.10

0.20

0.30

0.40

0.50

lenght [m]

ββββ1 ≡ ββββ5


ββββ3

fra

ctio

n o

f b

end

ing

mo

men

t [

-

UNI EN 1168theoretical [9]numerical, S1 model

numerical, S2 model

0.00

0.10

0.20

0.30

0.40

0.50

lenght [m]

αααα1 ≡ αααα5


αααα3

fra

ctio

n o

f to

tal lo

ad

[ -

]

theoretical [9]numerical, S1 modelnumerical, S2 model

([9] Lindström 2010) ([9] Lindström 2010)

5/17

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0.00

2 4 6 8 10 12 14

0.00

2 4 6 8 10 12 14a) b)

• Shear at support less distributed with respect to bending effects.

• Similar numerical curves (S1, S2).

Better agreement with theoretical provisions in terms of bending effects.

bending moment at midspan total load at support

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Bending moment,

slab j: βj·qL2/8

Load on slab j:

αj·qL

0.50

0.60

0.70

ββββ1

fract

ion

of

ben

din

g m

om

ent

[ -

]


0.50

0.60

0.70

αααα1

fract

ion

of

tota

l lo

ad

[ -

]

theoretical [9]numerical, S1 modelnumerical, S2 model line load on panel 1

SIMPLIFIED FE MODELS: NUMERICAL RESULTSSIMPLIFIED FE MODELS: NUMERICAL RESULTS

EI/GJt = 0.73


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Bending moment,

slab j: βj·PL/4

Load on slab j:

αj·P

0.70

ββββ

fract

ion

of

ben

din

g m

om

ent

[ -

]

theoretical [9]

0.70

]

theoretical [9]numerical, S1 model

0.00

0.10

0.20

0.30

0.40

2 4 6 8 10 12 14

lenght [m]

fract

ion

of

ben

din

g m

om

ent

[

ββββ2

ββββ3

ββββ4 ββββ5

0.00

0.10

0.20

0.30

0.40

2 4 6 8 10 12 14

lenght [m]

fract

ion

of

tota

l lo

ad

[

αααα2

αααα3

αααα4 αααα5

a) b)

point load on panel 1

Shear effects less distributed than

bending ones.

6/17

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0.00

0.10

0.20

0.30

0.40

0.50

0.60

2 4 6 8 10 12 14

lenght [m]

ββββ1

fract

ion

of

ben

din

g m

om

ent

[


ββββ2

ββββ3

ββββ4 ββββ5

0.00

0.10

0.20

0.30

0.40

0.50

0.60

2 4 6 8 10 12 14

lenght [m]

αααα1

fract

ion

of

tota

l lo

ad

[ -

] numerical, S1 modelnumerical, S2 model

αααα2

αααα3

αααα4 αααα5

a) b)

point load on panel 1

Bending effects

less distributed than shear ones.

([9] Lindström 2010)bending moment at midspan total load at support

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MORE COMPLEX FE MODELSMORE COMPLEX FE MODELS

Simplified models not able to represent the effective behaviour of HC floors

For a correct description of shear and torsion transferring mechanisms it is

necessary to model each web with solid or shell elements


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in necessary to model each web with solid or shell elements

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FE mesh, with four-node, one-layered shell elements representing the middle

plane of the webs and of the bottom and top slabs for HC units

EI/GJt = 1.06 (effective value)

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MORE COMPLEX FE MODELSMORE COMPLEX FE MODELS

Joint modelling1

2


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“Model C1”: spring elements


nodes, in the external webs of

the units

“Model C2”: horizontal shell

elements connected to shell

element nodes, in the external

same as

“Model S1”

same as

“Model S2”

8/17

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webs of the units

“Model C3”: vertical shell

elements connected to shell


webs of the units

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COMPARISONS BETWEEN SIMPLIFIED AND COMPARISONS BETWEEN SIMPLIFIED AND COMPLEX MODELSCOMPLEX MODELS

• Same modelling technique for joints but different schematization for units

e.g.:


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Bending moment,

slab j: βj·qL2/8

Load on slab j:

αj·qL

0.70

0.80

0.90

ββββ

fra

ctio

n o

f b

end

ing m

om

ent

[ -

]

numerical, C2 modelnumerical, S2 model

0.70

0.80

0.90

αααα1

numerical, C2 modelnumerical, S2 model

fra

ctio

n o

f to

tal lo

ad

[ -

]

e.g.:

S2

When considering the real floor

geometry

C2

line load on panel 1

9/17

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0.00

0.10

0.20

0.30

0.40

0.50

0.60

2 4 6 8 10 12 14

lenght [m]

ββββ1

fra

ctio

n o

f b

end

ing m

om

ent

[

ββββ2

ββββ3

ββββ4 ββββ5

0.00

0.10

0.20

0.30

0.40

0.50

0.60

2 4 6 8 10 12 14

lenght [m]

fra

ctio

n o

f to

tal lo

ad

[

αααα3

αααα2

αααα4 αααα5

a) b)

greater concentration

of loading

effects

bending moment at midspan total load at support

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COMPARISONS AMONG COMPLEX MODELSCOMPARISONS AMONG COMPLEX MODELS• Same modelling technique for units but different schematization for joints

Bending moment,

slab j: βj·qL2/8

Load on slab j:

αj·qL

EI/GJt = 1.06line load on panel 3


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in j

j

0.00

0.10

0.20

0.30

0.40

0.50

0.60

lenght [m]



ββββ3

fract

ion

of

ben

din

g m

om

ent

[ -

]

theoretical [9]numerical, C1 modelnumerical, C2 model

numerical, C3 model

0.00

0.10

0.20

0.30

0.40

0.50

0.60

lenght [m]αααα1 ≡ αααα5


αααα3


numerical, C3 model

fra

ctio

n o

f to

tal lo

ad

[ -

]

10/17

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0.00

2 4 6 8 10 12 14

lenght [m]

0.00

2 4 6 8 10 12 14

lenght [m]

a) b)

� Models C1, C2, C3 predict the different behaviour in shear and bending

� Overestimation of load effects with respect to theoretical solutions

bending moment at midspan total load at support([9] Lindström 2010)

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� Different

Bending moment,

slab j: βj·qL2/8

Load on slab j:

αj·qL

0.80

0.90

fra

ctio

n o

f b

end

ing

mom

ent

[ -

]


0.80

0.90

αααα1

theoretical [9]numerical, C1 model

-]

COMPARISONS AMONG COMPLEX MODELSCOMPARISONS AMONG COMPLEX MODELSline load on panel 1

EI/GJt = 1.06


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Different behaviour in shear and bending

� Overestimation of load effects with respect to theoretical

solutions

especially for shear

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

2 4 6 8 10 12 14

lenght [m]

ββββ1

fra

ctio

n o

f b

end

ing

mom

ent

[

numerical, C2 model

ββββ2

ββββ3

ββββ4 ββββ5

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

2 4 6 8 10 12 14

lenght [m]

αααα1

numerical, C2 model

fra

ctio

n o

f to

tal lo

ad

[ -

αααα2

αααα3

αααα4

αααα5

0.75

0.85

0.95

fra

ctio

n o

f b

end

ing

mom

ent

[ -

]


0.75

0.85

0.95

αααα1


fract

ion

of

tota

l lo

ad

[ -

]

a) b)

11/17

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especially for shear distribution

-0.05

0.05

0.15

0.25

0.35

0.45

0.55

0.65

0.75

2 4 6 8 10 12 14

lenght [m]

ββββ1

fra

ctio

n o

f b

end

ing

mom

ent

[

ββββ2

ββββ3

ββββ4 ββββ5

-0.05

0.05

0.15

0.25

0.35

0.45

0.55

0.65

0.75

2 4 6 8 10 12 14

lenght [m]

1

fract

ion

of

tota

l lo

ad

[

αααα2

αααα3

αααα4

αααα5

a) b)

bending moment at midspan total load at support ([9] Lindström 2010)

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� Different

Bending moment,

slab j: βj·PL/4

Load on slab j:

αj·P

0.60

0.70 ββββ1

fract

ion

of

ben

din

g m

om

ent

[ -

]

theoretical [9]numerical, C1 modelnumerical, C2 model 0.60

0.70

αααα1


-]

COMPARISONS AMONG COMPLEX MODELSCOMPARISONS AMONG COMPLEX MODELSpoint load on panel 1

EI/GJt = 1.06


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� Different behaviour in shear and bending

� Overestimation of total load with respect to theoretical

solutions

� Greater load effects redistribution

0.00

0.10

0.20

0.30

0.40

0.50

0.60

2 4 6 8 10 12 14

lenght [m]

fract

ion

of

ben

din

g m

om

ent

[

numerical, C2 model

ββββ2

ββββ3

ββββ4 ββββ5

0.00

0.10

0.20

0.30

0.40

0.50

0.60

2 4 6 8 10 12 14

lenght [m]

1

numerical, C2 model

fract

ion

of

tota

l lo

ad

[ -

αααα2

αααα4 αααα5

αααα3

0.65

0.75

0.85

ββββ1

fract

ion

of

ben

din

g m

om

ent

[ -

]


0.65

0.75

0.85

αααα1


fract

ion

of

tota

l lo

ad

[ -

]

c) d)

12/17

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effects redistribution

in bending with respect to shear, differently from

theoretical solutions

-0.05

0.05

0.15

0.25

0.35

0.45

0.55

0.65

2 4 6 8 10 12 14

lenght [m]

fract

ion

of

ben

din

g m

om

ent

[

ββββ2

ββββ3

ββββ4 ββββ5

-0.05

0.05

0.15

0.25

0.35

0.45

0.55

0.65

2 4 6 8 10 12 14

lenght [m]

1

fract

ion

of

tota

l lo

ad

[

αααα2

αααα3

αααα4

αααα5

c) d)

bending moment at midspan total load at support ([9] Lindström 2010)

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FE MODEL VALIDATION FE MODEL VALIDATION –– COMPARISONS COMPARISONS WITH EXPERIMENTAL RESULTSWITH EXPERIMENTAL RESULTS

Simulation of a full-scale test on a HC floor (Suikka et al., VTT, 1991)

through the complex models

Geometry of the specimen:


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in Geometry of the specimen:

• Six 400 mm thick panels

• Simply supported floor (net span = 12.1 m)

Loading arrangement:

Point load positions:

• P1

• P2

• P3

floor edge, L/6 from one support

floor edge, midspan

centre of panel 3, L/6 from one support

4 loading cases

(service

13/17

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• P3

• P4

centre of panel 3, L/6 from one support

centre of panel 3, midspan

(service

loads)

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Flexural behaviour

Numerical values of

midspan deflections are:



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Torsional behaviour

midspan deflections are:

• similar to experimental

ones • not influenced by joint

modelling technique

Theoretical provisions (for

5 units) suggest a lower redistribution

0

5

10

15

20

25

30

35

40

45

0 1.2 2.4 3.6 4.8 6 7.2

x [m]

numerical, C2 model

numerical, C3 model

experimental

theoretical [9]

1 2 3 4 5 6panel n°

mid

spa

n d

efle

ctio

n d

istr

ibu

tion

[%

]

0

5

10

15

20

25

30

35

40

0 1.2 2.4 3.6 4.8 6 7.2

x [m]

numerical, C2 model

numerical, C3 model

experimental

theoretical [9]

1 2 3 4 5 6panel n°

mid

spa

n d

efle

ctio

n d

istr

ibu

tion

[%

]

1 2 3 4 5 6panel n° 1 2 3 4 5 6panel n°

14/17

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Torsional behaviour

Numerical values of

torsional moments are

affected by joint modelling

model C3 better fits experimental data

([9] Lindström 2010)

-2

0

2

4

6

8

10

12

0.0 1.2 2.4 3.6 4.8 6.0 7.2

x [m]

numerical, C2 model

numerical, C3 model

experimental

1 2 3 4 5 6panel n°

tors

ion

al m

om

ent

at

sup

po

rt [k

Nm

]

-10

-8

-6

-4

-2

0

2

4

6

8

10

0.0 1.2 2.4 3.6 4.8 6.0 7.2

x [m]

numerical, C2 model

numerical, C3 model

experimental

1 2 3 4 5 6panel n°

tors

ion

al m

om

ent

at

sup

po

rt [k

Nm

]

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Shear behaviour

Numerical values of

support reactions are



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support reactions are

affected by joint modelling

Theoretical provisions (for

5 units) suggest a greater

redistribution


-20

0

20

40

60

80

100

0.0 1.2 2.4 3.6 4.8 6.0 7.2

x [m]

numerical, C2 model

numerical, C3 model

experimental

theoretical [9]

1 2 3 4 5 6panel n°

sup

po

rt r

eact

ion

dis

trib

uti

on

[%

]

0

5

10

15

20

25

30

35

40

45

0.0 1.2 2.4 3.6 4.8 6.0 7.2

x [m]

numerical, C2 model

numerical, C3 model

experimental

theoretical [9]

1 2 3 4 5 6panel n°

sup

po

rt r

eact

ion

dis

trib

uti

on

[%

]

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� Load case P2: similar response of models C2 and C3, close to experimental data in

the central part of the floor.

� Load case P4: trend of models C2 and C3 consistent with theoretical provisions

even if it seems not to be confirmed by experimental data.

Higher concentration of loading effects for model C2 with respect to model C3.


, E

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inH

Cfl

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CONCLUSIONSCONCLUSIONS

• FE procedures represent a useful tool for analyzing the distribution of

loading effects in HC floors. Different modelling techniques have been

applied both for panels and for longitudinal joints, with an increasing

degree of complexity.


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rna

rdi,

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in degree of complexity.

• When a simplified approach is used for panel discretization, the

global behaviour is very close to theoretical one both in flexure and in

shear, independently of joint modelling.

• When a schematization more close to effective panel geometry is

adopted, a larger gap between numerical and theoretical provisions can

be observed (especially for shear distribution), since FE models

suggest a minor redistribution of load effects among panels. This trend

16/17

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suggest a minor redistribution of load effects among panels. This trend

seems to be confirmed also by experimental data, which are quite

correctly predicted by complex approaches.

• In this last case, joint modelling exerts a major influence on structural

response.

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FURTHER DEVELOPMENTSFURTHER DEVELOPMENTS

Further developments will be relative to the extension of this model to

nonlinear FE analysis, able to describe global HC floor behaviour up

to failure


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R. C

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ACKNOWLEDGEMENTSACKNOWLEDGEMENTS

This research work is part of a larger study funded by the ASSAP

Association (Prestressed HC floor Producers Association).

Authors gratefully acknowledge Dr Gösta Lindström at Strängbetong

(Sweden), for allowing the use of his load distribution curves and for

his valuable suggestions on FE modelling.

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his valuable suggestions on FE modelling.

The Authors would also like to thank Dr Tony Crane at IPHA, as well

as Dr Olli Korander and Dr Erkki Kaivola at Consolis Technology Oy

(Finland), for having provided the technical reports containing the

experimental data.

numerical study on load distribution in hc floors

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