applicazioni strutturali con il calcestruzzo fibrorinforzato€¦ · g. plizzari applicazioni del...

Applicazioni strutturali con il Calcestruzzo Fibrorinforzato

Prof. Giovanni Plizzari

[email protected]

Collegio dei tecnici dell’Industrializzazione edilizia

G. Plizzari

Applicazioni del FRC – Lecce, 9 Febbraio, 2017 2/72

Place the best performing reinforcement

(fibers and/or rebars) where required by

tensile stresses in the structural elements

Optimized reinforcement: definition

G. Plizzari


• In structural elements both distributed and localized

stresses are generally present

• Conventional rebars represent the best

reinforcement for localized stresses

• Fibers represent the best reinforcement for diffused

stresses

• Structural optimization generally requires the use of

a combination of rebars and fibers

• Structural ductility is generally enhanced

Reinforcement use in structural elements

G. Plizzari


Workshop proceedings

G. Plizzari


Flessione in elementi in FRC

G. Plizzari


Ultimate Limit States (ULS) Verification

The bending failure is considered to occur when one of the following conditions arises:

• attainment of the maximum compressive strength, cu, in the FRC;

• attainment of the maximum tensile strength su, in the steel (if present);

• attainment of the maximum tensile strength, Fu, in the FRC.

M

Fu

su

cu

Asl

cdf

Ftsf / F

Rd

NSd

cd·f

Ftuf / F

·xx

y

softeninghardening

G. Plizzari


Bending in FRC beams

P/2 P/2

120 12012020 20

8/10 cm L=100cm

10

10

15

25

216

210

20

30

G. Plizzari


Load-Displacement Curve (2 16)

0

20

40

60

80

100

120

0 50 100 150 200

Displacement [mm]

Load [kN

]

PC 30 60

Trave

Py Pmax Pu dy du

md[KN] [KN] [KN] [mm] [mm]

216-PC 81,48 89,82 84,84 20,54 110,50 5,38

216-30 88,20 96,24 75,48 20.30 182,01 8,97

216-60 85,86 95,70 80,64 18,16 113,72 6,26

Failure

P/2 P/2

Failure

P/2 P/2

Failure

P/2 P/2

216-PC

216-30

216-60

Flexural behavior of FRC beams

G. Plizzari


216 - rs = 0,67 % 416 - rs = 1,34 %

30

kg

/m3

60

kg

/m3

PC

For bonded beams

rs = 0,67 %: concrete crushing → steel rupture

rs = 1,34 %: concrete crushing → concrete crushing more ductile

Fibers do influence ductility and rupture mode under flexure

FRC:

- Increase in concrete compressive toughness;

- Optimization steel-to-concrete bond;

- Tension Softening at crack;

- More chance to stress concentration.

G. Plizzari


Taglio in travi in FRC

G. Plizzari


Shear in beams without stirrups

V = Vc + Vf

In FRC elements there is an additional contribution to shear resistance provided by fiber reinforcement:

Vc represents the concrete contribution.Vf represents the fiber contribution (post cracking strength).

G. Plizzari


FRC for Shear-Critical Beams I

2Ø24 Bars, L=4550 mm

480 m

m

V Va

d

200

45

480

45

2Ø24 Deformed Bars

4350 mm

Steel Plate 200x90x30 mm

a/d=2.5Reinforcement Ratio of 1%

Several experimental results are available for beams with longitudinal rebars without stirrups.More results are needed for prestressed beams

G. Plizzari


Normal Strength Concrete, f'c = 24.8 MPa

0

100

200

300

400

0 20 40 60 80Displacement [mm]

Load

[k

N]

NSC1-PC

NSC1-FRC1

NSC1-FRC2

30 kg/m3, 30/0.6 + 15 kg/m

3, 12/0.18

30 kg/m3,

30/0.6

V V

d

Typical experimental results from NSC beams

f’c = 24.8 MPa.

Fibers:

0,38% of macro-fibers, 30 mm longwith aspect ratio = 50

0,19% of micro-fibers,

12 mm long with aspect ratio = 66.7

Normal Strength Concrete, f'c = 24.8 MPa

0

1

2

3

0 100 200 300 400Load [kN]

Cra

ck W

idth

[m

m]

NSC1-PC

NSC1-FRC1

NSC1-FRC2V V

d

V

V

CPT

TPT

Average First

Cracking

30 kg/m3,

30/0.6

+

15 kg/m3,

12/0.18

30 kg/m3,

30/0.6

Ø 0

.38

Ø 0

.62

30

30

Ø 0

.6

30

50

Ø 1

.0

Ø 0

.18

12

Ø 0

.38

Ø 0

.62

30

30

Ø 0

.6

30

50

Ø 1

.0

Ø 0

.18

12

G. Plizzari


Typical experimental results from HSC beams

f’c = 60 MPa.

Fibers:

0,6% of macro-fibers,

Low carbon (45/30) or

High carbon (80/30)

Reinforcement optimizationrequires that fiber tensilestrength must be related toconcrete compressive strength

High Strength Concrete

0

100

200

300

400

500

0 20 40 60 80Displacement [mm]

Load

[k

N]

HSC-PC

HSC-FRC1

HSC-FRC2

50 kg/m3, 80/30

50 kg/m3, 45/30

V V

d

Ø 0

.38

Ø 0

.62

30

30

Ø 0

.6

30

50

Ø 1

.0

Ø 0

.18

12

Ø 0

.38

Ø 0

.62

30

30

Ø 0

.6

30

50

Ø 1

.0

Ø 0

.18

12

High Strength Concrete

0

0.5

1

1.5

2

2.5

0 100 200 300 400 500Load [kN]

Cra

ck

Wid

th [

mm

]

HSC-PC

HSC-FRC1

HSC-FRC2

V V

d

V

V

CPT

TPT

Average First

Cracking

50 kg/m3,

45/30

50 kg/m3,

80/30

G. Plizzari


Shear-Critical Beams VI, series HSC

Fibers are highly effective in controlling development and propagation of cracking. The

combination of short and long fibers proved to be

particularly efficient at the beginning of cracking.

Plain Concrete 45/30 Fibers

80/30 Fibers

90 kN

Collapse

150 kN

90 kN

Collapse

150 kN

G. Plizzari


W750 PC

Wide Shallow Beams with b=750 mm

W750 FRC25

G. Plizzari


W1000 MSR

Wide Shallow Beams with b=1000 mm

W1000 FRC35

G. Plizzari


Example of Application for Shear

2Ø24 Bars

500

mm

p = 35 kN/m

d

6 m

2Ø24 Deformed Bars

500

200

35 / ( )

500 ; 460

30 ; 500

1.5; 1.15

30 50020 ; 435

1.5 1.5

2 ( 2)

u

ck yk

c s

cd yk

ctk

p kN m ULS

h mm d mm

f MPa f MPa

f MPa f MPa

f MPa EC

2 2

max

max

2

1 135 6 157.5

8 8

1 135 6 105

2 2

9040.98%

200 460

161

sl

w

u

M p l kN m

V p l kN

A mm

b d mm mm

M kN m

r

G. Plizzari



13

, 1

0.18(100 ) 0.15 49

WRd ct ck CP

c

V k f b d kNr

1.6 1.4

Minimum Shear Reinforcement

3.2 meters requiring design shear reinforcement; 2.8 meters requiring

minimum shear reinforcement.

Design Shear Reinforcement:

, , 56

321

2 8@300

swR ds yd Rd Rd ct

AV z f V V kN

s

s mm

mm

,min

0.75 345

0.08 0.0009

2 6 @300

ck

w

yk

s d mm

f

f

mm

r

Minimum Shear Reinforcement:

G. Plizzari



dbff

fkV

WCPck

ctk

uFtk

c

FRd

r

15.0))5.71(100(

18.03

1,

1,

13

,

0.18 200 0.901 (100 0.0098 (1 7.5 ) 20) 200 460 81

1.5 460 2Rd FV kN

Minimum Shear Reinforcement

2.30.7

ck

Ftuk

300 27

20 20

ff . MPa

, , 242 6@300

420

swR ds yd Rd Rd ct

AV z f V V kN

mms

s mm

Assume 30 kg/m3 of steel fibers having l/ =67 and fFtk,u=0.90 MPa (tested at the

University of Brescia)

Minimum shear reinforcement

OK

Design Shear Reinforcement

G. Plizzari


Example of optimized shear reinforcement

2Ø8@300mm 2Ø6@300mm

2Ø6@300mm

Plain concrete

FRC

G. Plizzari


Piastre in FRC

G. Plizzari


Slab on piles

Example: Slab on piles

Pressure

Maximum principal stresses acting on the top surface

Minimum principal stresses acting on the top surfaceOptimized reinforcement

FRC

Local rebars

G. Plizzari


Case study

Geometry

Elevated slab made with Steel Fiber Reinforced Concrete

Loads

1. Dead weight (G1)

2. Overload (Q)Overload (Q)

G. Plizzari


Reinforcement optimization

Contour of the principal tensile stresses detected in the elastic stage

Top view Bottom view

[MPa] [MPa]

Most stressed lines

G. Plizzari



Optimized reinforcement: combination of steel fibers and rebars placed in the

most stressed areas of the slab

Proposal of an optimal reinforcement layout

Hypothesis: top and bottom

reinforcement have the

same effective area

Reinforcement placed within

diagonal and longitudinal chords

G. Plizzari


Parametric study

Parameters investigated by numerical simulations:

1. longitudinal reinforcement ratio;

2. diagonal reinforcement ratio;

3. steel fiber content.

3D f.e. model implemented in the program Diana 9.6

1/4 of the whole slab Rebars layout

G. Plizzari


Parametric study

Mechanical properties according MC2010

Tensile properties of SFRC

fct =2MPa

Fiber content fR1,k fR3,k

[kg/m3] [MPa] [MPa]

30 2.3 2.6

50 3.0 2.8

70 3.7 3.1

G. Plizzari


Parametric study

Mechanical properties according MC2010

Compression properties of SFRC

fck=30MPafck

Tensile properties of conventional reinforcement

t

t

[MPa]

617519

13%210GPa

G. Plizzari


Results of the parametric study

Typical Overload (Q) – Deflection (d) curve obtained from the simulations

0

200

400

600

800

1000

1200

0 20 40 60 80 100 120

Overl

oad

(Q

) [k

g/m

2]

Maximum deflection (d) [mm]

Maximum deflection (d)

Qmax = maximum overload

G. Plizzari



Summary of the analysis program

Diagonal reinforcement ratio (rd)

Longitudinal reinforcement ratio (rl)

As

B dr= ·100

B=400mm ; d=170mm

G. Plizzari


0

400

800

1200

1600

2000

2400

2800

0 20 40 60 80 100 120 140 160 180 200 220

Maxim

um

Overlo

ad

(Q

max)

[kg/m

2]

Total Rebars Content (TRC) [kg/m3]

Fiber Content = 30kg/m^3


Fiber Content =70kg/m^3

Q = 606+(5965·TRC)0.53

R2 = 0.97

Q = 330+(5965·TRC)0.53

R2 = 0.98

Q = 850+(5965·TRC)0.53

R2 = 0.94


Effect of the total rebars content (longitudinal+diagonal) on the slab capacity (Qmax)

The diagram may be used to

design the optimal Hybrid

Reinforcement for the slab

G. Plizzari


0

10

20

30

40

50

60

70

80

90

100

110

0 500 1000 1500 2000 2500

To

tal

Reb

ars

Co

nte

nt

red

ucti

on

(D

TR

C)

[kg

/m3]

Maximum Overload (Qmax) [kg/m2]

TRC30 - TRC50

TRC30 - TRC70

0

400

800

1200

1600

2000

2400

2800

0 20 40 60 80 100 120 140 160 180 200 220

Maxim

um

Overlo

ad

(Q

max)

[kg/m

2]

Total Rebars Content (TRC) [kg/m3]




Q = 606+(5965·TRC)0.53

R2 = 0.97

Q = 330+(5965·TRC)0.53

R2 = 0.98

Q = 850+(5965·TRC)0.53

R2 = 0.94


Increment of the Total Rebars Content (TRC) at a fixed loading level

The diagram highlights the

additional rebars content (DTRC)

that has to be employed with respect

to the slab with 30kg/m3 of fibres to

ensure the same maximum overload

level.

G. Plizzari



Total reinforcement (fibres + rebars) vs. Maximum overload

30

50

70

90

110

130

150

170

190

210

230

250

500 1000 1500 2000

Tota

l R

ebars

Con

ten

t (T

RC

) +

Fib

re c

on

ten

t

[kg/m

3]

Maximum Overload (Qmax) [kg/m2]




Qmax,1 Qmax,2

Optimal reinforcement

for the load level Qmax,1

Optimal reinforcement

for the load level Qmax,2

G. Plizzari



DTRC [%] = +10% DQ [%] = +36%

Effectiveness of the diagonal reinforcement on the slab response

Comparison of the slab reinforced only with fibres

DQ [%] = +83%

G. Plizzari


Elementi con fibre e armatura convenzionale

La verifica di elementi di calcestruzzo fibrorinforzato con armatura

convenzionale può essere eseguita con i metodi tradizionalmente

adottati per il calcestruzzo armato; il contributo delle fibre può essere

considerato adottando metodi di analisi non lineare (analisi limite,

analisi non lineare evolutiva).

G. Plizzari


Strutture prefabbricate

G. Plizzari


Floor slab for Electrical Equipment Shelters

Typical modular Self Compacting Concrete (SCC) Electrical Equipment Shelter reinforced with conventional steel bars

Properties of a typical the precast reinforced concrete floor:

- Reinforcing steel weight-to-concrete

volume ratio (RR) :

Steel Weight / Concrete Volume = 77kg/m3

- Dimensions: 2.5x4.2x0.08m

Typical rebars

layout for a

r.c. floor slab

- SCC class: C40/50 (EC2)

- Reinforcing steel: B450C (NTC2008)

G. Plizzari


The research aim at testing full scale Steel Fiber Reinforced Self Compacting Concrete

(SFRSCC) slabs under Four Point Loads. No conventional reinforcement is used.

Conventional reinforced SCC Optimized reinforcement (SFRSCC+rebars)

Optimize the reinforcement typically used in the conventionally reinforced concrete slab


Geometry of the simply supported slab

Aim of the research:

G. Plizzari


FE program: Diana 9.4

Fracture behavior of

SFRSCC modeled by

the “total strain

rotating crack model”

(smeared crack

approach)

No-tension spring

elements for

modeling the slab

supports

Behavior of concrete in compression: stress-

strain parabola according Eurocode2

Behavior of concrete in tension: stress-strain law

obtained from back-analysis of 3PBTs

Characteristic length lc=30mm


Non-linear finite element simulation: properties of the 3D model

G. Plizzari


Optimized reinforcement (fibers + localized bars)

SFRSCC (Vf =0.32%)

Reinforced concrete

Conventional bar reinforcement layout

Reinforcing steel weight-to-concrete volume ratio (RR)

Total rebars weight (SW) = 65kg

Slab volume (V) = 0.84m3

RR=SW/V= 77 kg/m3

Total rebars weight (SW) = 15 kg

Slab volume (V) = 0.84 m3

RR=(SW+FW)/V= 47kg/m3

Total Steel Fiber weight (FW) = 25 kg/m3


Proposal of an optimized reinforcement for the tested slabs

G. Plizzari


- The optimized reinforcement is designed to allow the slab to achieve the maximum capacity of the

conventional reinforced concrete slab


Results of the numerical simulation: conventional r.c. slab vs. slab with optimized reinforcement

G. Plizzari


Durabilità in elementi di FRC

G. Plizzari


Classi di esposizione Corrosione da cloruri Nessun

rischio di corrosione o attacco

Corrosione da carbonatazione Acqua marina

Altri cloruri (diversi dall’acqua

di mare)

Attacco gelo/disgelo Ambienti chimici

aggressivi

X0 XC1 XC2 XC3 XC4 XS1 XS2 XS3 XD1 XD2 XD3 XF1 XF2 XF3 XF4 XA1 XA2 XA3 Rapporto massimo a/c

- 0.65 0.60 0.55 0.50 0.50 0.45 0.45 0.55 0.55 0.45 0.55 0.55 0.50 0.45 0.55 0.50 0.45

Classe di resistenza minima

C12/15 C20/25 C25/30 C30/37 C30/37 C30/37 C35/45 C35/45 C30/37 C30/37 C35/45 C30/37 C25/30 C30/37 C30/37 C30/37 C30/37 C35/45

Contenuto minimo di cemento [kg/m

3]

- 260 280 280 300 300 320 340 300 300 320 300 300 320 340 300 320 360

Contenuto minimo di aria [%]

- - - - - - - - - - - - 4.0a) 4.0a) 4.0a) - - -

Altri requisiti

Aggregati conformi al prEN12620:2000 con

sufficiente resistenza al gelo/disgelo

Cemento

resistente ai solfati b)

a) Quando il calcestruzzo non contiene aria aggiunta, le sue prestazioni dovrebbero essere verificate conformemente ad un metodo di prova appropriato rispetto ad un calcestruzzo per il quale è provata la resistenza al gelo/disgelo per la relativa classe di esposizione.

b) Qualora la presenza di SO42- comporti le classi di esposizione XA2 e XA3, è essenziale utilizzare un cemento resistente ai solfati.

Se il cemento è classificato a moderata o ad alta resistenza ai solfati, il cemento dovrebbe essere utilizzato in classe di esposizione XA2 (e in classe di esposizione XA1 se applicabile) e il cemento ad alta resistenza ai solfati dovrebbe essere utilizzato in classe di esposizione XA3.

Durability in EN 206

I valori si riferiscono all’uso di cemento CEM I 32.5 R e aggregato con 20 < Dmax < 32 mm

G. Plizzari


Cracks in a beam

G. Plizzari


Cracking and durability

G. Plizzari


Exposure in aggressive (marine) environment

10 beams has been exposed for more than 2 years in a coastal zone,

under a load equal to 50% of the ultimate load

Aim of the research: evaluate the influence of fibers on mechanical

behaviour of FRC in short and long term bending test

G. Plizzari


Materials

(UNI 11039)

3Ø14 18

2 Ø14

18

300

25

294

25

25

7 7

10

14 14

10

294

3

3

52

DiameterYield strength

(MPa)

Ultimate strength

(MPa)

Longitudinal

bars14mm 520 614

Stirrups 8mm 567 600

G. Plizzari


Tests for determining material properties

(UNI 11039)

0 500 1000 1500 2000

0

2

4

6

8

10

12

06S

09P

TQ065

LO

AD

(kN

)

CTOD (microns)

0.6% steel

0.9% polyester

Vf=0,6%

Vf=0,9%

G. Plizzari


Crack monitoring

Crack width, crack length and

crack position have been

measured during the exposure

period. The crack width has been

measured with a digital

microscope (200x magnification)

G. Plizzari


Cracking monitoring

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0 50 100 150 200 250

pp1

pp2

st1

st2

tq

In FRC beams the crack widths were in the range of 0.1 to 0.2 mm, without overcome the

threshold of 0.2 mm. In plain beam the 93.3% of cracks had a crack width over 0.1 mm, while

the 60% over 0.2 mm.

G. Plizzari


Cracking monitoring

Average of crack widths between the loading points

Beams Dw /%

ST1-2_E 54%

POL1-2_E 53%

0.31

0.14 0.140.16

0.13

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

TQ1_E ST1_E ST2_E POL1_E POL2_E

Cra

ck w

idth

(m

m)

Crack width reduction of the FRC beams respect

to the plain beam (Dw /%).

steel polyester

PC

G. Plizzari


Cracking behavior at SLS

SLE

(50kN)

ST1-2 35%

POL1-2 28%

SHORT TERM

BEAMS

LONG TERM

BEAMS

SLE (50kN)

ST1-2_E 43%

POL1_E 37%

POL2_E 43%

Crack width reduction of the FRC beams respect to the plain beam.

G. Plizzari


Cracking behavior at ULS

SLU

(100kN)

ST1-2_E 56%

POL1_E 25%

POL2_E 54%

SLU

(100kN)

ST1-2 41%

POL1-2 39%

Crack width reduction of the FRC beams respect to the plain beam.

SHORT TERM

BEAMS

LONG TERM

BEAMS

G. Plizzari


Carbonation depth

CARBONATION DEPTHCHLORIDE CONTENT

G. Plizzari


Carbonation depth between the cracks

G. Plizzari


Carbonation depth at cracks

K

(mm/anni

^0.5)

t

armature

(anni)

TQ_E 19.4 2.4

ST1_E 12.7 5.6

ST2_E 13.4 5.0

POL1_E 12.5 5.8

POL2_E 14.7 4.2

G. Plizzari


Onna, April 6th, 2009

G. Plizzari


Earthquake effects

G. Plizzari


Masonry buildings reinforced with FRC mortar

Ground acceleration

G. Plizzari


Ground acceleration

Diagonal cracks in

bearing walls

Strengthening with Fiber Reinforced

Mortar

Strengthening with Fiber Reinforced Mortar

G. Plizzari


Section view of a typical 2-storey URM building

Ground acceleration

Thin SFRM

overlays

To use thin overlays made of an innovative steel fiber reinforced mortar for:

• improving the out-of-plane resistance of masonry walls (future step of the research);

• enhancing the in-plane shear capacity of the masonry walls

Experimental tests on walls: aim of the research

3x2x0.23m3 cantilever URM wall used in the tests

Floor loads Lateral (seismic) load

G. Plizzari


Material properties: solid clay brick masonry

(3)

(

4)(

5)

(

2)

(1)

Flexural strength (according EN 1015-11, 2007) 1.5MPa(1)

(size:23x11x5cm3)

Mortar for masonry joints (M2.5 – according Eurocode 6)

Solid clay bricks

Compressive strength (according EN 1015-11, 2007) (2)4.2MPa

Flexural strength (3)1.72MPa

Copressive strength (EN 772-1, 2002) (4)12.4MPa

Tensile strength (5)0.9MPa

Composite solid clay MASONRY (Masonry specimens : 71x48x23cm3)

Compressive strength (EN 1052-1, 2001)

fm,90°=5.7MPa

Different bed joint orientations (0°,22.5°,45°,90°)

fm,0°=6.1MPa fm,45°=4.0MPa

fm,22.5°=2.6MPa

0° 90° 22.5° 45°

Elastic modulus (EN 1052-1, 2001) Em=4200MPa

G. Plizzari


321 4

1 2 3 4 5

4

1

2

3

5

Lateral displacement = difference between F1 and B

Wall height = 2070 mm

Test instrumentation

DRIFT (%) = LATERAL DISPLACEMENT

WALL HEIGHT

Horizontal load

Vertical loadDisplacement

G. Plizzari


TESTING FRAME

32 41

Experimental set-up

250 kN

G. Plizzari


Experimental results

INCREMENT OF THE FIRST CRACKING LOAD WITH RESPECT TO MW1

LATERAL STRENGTH INCREMENT WITH RESPECT TO MW6

Displacement [mm]

Load

[kN

]

G. Plizzari


Simulation of a full-scale masonry building: shaking table test results

d

Base shear vs. top lateral displacement Envelope of the cyclic curve

Damage pattern at failure

G. Plizzari


Numerical modelling of full-scale building

Shell elements

FLOOR

(CQ40S)

Shell elements

ROOF

(CQ40S)

Shell

elements

MASONRY

WALL +

MORTAR

(CQ40L)

FV3 = 20,55 N/mm

FH2 = 3183,5 N

FH1 = 1582,35 N

FH3 = 468,3 N

FV1 = 4,49 N/mm

FV2 = 2,39 N/mm

FV3 = 20,55 N/mm

Smeared Crack Model

(Total Strain Rotating Crack Model)

Curved Shell Layered Element

BUILDING 2

STONE MASONRY

BIOGLOB® MORTAR

Compression

Nonlinear tension softening Parabolic compression curve

Traction

&

G. Plizzari


Numerical simulation of the masonry building without coating

Numerical – URM

Experimental – URM

positive

direction

negative

direction

Numerical and experimental damage

patterns comparison

G. Plizzari


Numerical simulation of the masonry building strengthened with 1 layer of SFRM

No coating 1 layer of SFRM

North

side

East

side

South

side

Numerical - unstrengthened

Numerical – 1 layer coating

G. Plizzari


Damage pattern after the

experimental test

Numerical crack pattern of the

unstrengthened specimen

Numerical crack pattern of

the specimen strengthened

with 1 layer of SFRM

Results of the finite element analyses

G. Plizzari


Thank you for your kind attention!

University of Brescia, Italy


for structural FRC elements

University of Brescia (Italy),

Department of Civil Engineering,

Architecture, Environment, Land

and of Mathematics (DICATAM)

[email protected]

Giovanni Plizzari

University of Toronto - August 26th, 2015

applicazioni strutturali con il calcestruzzo fibrorinforzato€¦ · g. plizzari applicazioni del...

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