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

Applicazioni strutturali con il Calcestruzzo Fibrorinforzato

Prof. Giovanni Plizzari

giovanni.plizzari@unibs.it

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.

Ftsf / F

Ftuf / F

softeninghardening

G. Plizzari

Bending in FRC beams

P/2 P/2

120 12012020 20

8/10 cm L=100cm

G. Plizzari

Load-Displacement Curve (2 16)

0 50 100 150 200

Displacement [mm]

Load [kN

PC 30 60

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 %

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

- 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

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 20 40 60 80Displacement [mm]

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

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

0 100 200 300 400Load [kN]

NSC1-PC

NSC1-FRC1

NSC1-FRC2V V

Average First

Cracking

30 kg/m3,

30/0.6

15 kg/m3,

12/0.18

30 kg/m3,

30/0.6

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 20 40 60 80Displacement [mm]

HSC-PC

HSC-FRC1

HSC-FRC2

50 kg/m3, 80/30

50 kg/m3, 45/30

High Strength Concrete

0 100 200 300 400 500Load [kN]

HSC-PC

HSC-FRC1

HSC-FRC2

Average First

Cracking

50 kg/m3,

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

Collapse

150 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

p = 35 kN/m

2Ø24 Deformed Bars

35 / ( )

500 ; 460

30 ; 500

1.5; 1.15

30 50020 ; 435

1.5 1.5

2 ( 2)

p kN m ULS

h mm d mm

f MPa f MPa

f MPa EC

1 135 6 157.5

1 135 6 105

9040.98%

200 460

M p l kN m

V p l kN

b d mm mm

M kN m

G. Plizzari

0.18(100 ) 0.15 49

WRd ct ck CP

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

2 8@300

swR ds yd Rd Rd ct

AV z f V V kN

0.75 345

0.08 0.0009

2 6 @300

s d mm

Minimum Shear Reinforcement:

G. Plizzari

15.0))5.71(100(

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

300 27

ff . MPa

, , 242 6@300

swR ds yd Rd Rd ct

AV z f V V kN

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

Design Shear Reinforcement

G. Plizzari

Example of optimized shear reinforcement

2Ø8@300mm 2Ø6@300mm

2Ø6@300mm

Plain concrete

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

Local rebars

G. Plizzari

Case study

Geometry

Elevated slab made with Steel Fiber Reinforced Concrete

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

617519

13%210GPa

G. Plizzari

Results of the parametric study

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

0 20 40 60 80 100 120

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)

B dr= ·100

B=400mm ; d=170mm

G. Plizzari

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

Overlo

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

0 500 1000 1500 2000 2500

Maximum Overload (Qmax) [kg/m2]

TRC30 - TRC50

TRC30 - TRC70

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

Overlo

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

500 1000 1500 2000

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

- 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

DiameterYield strength

Ultimate strength

Longitudinal

bars14mm 520 614

Stirrups 8mm 567 600

G. Plizzari

Tests for determining material properties

(UNI 11039)

0 500 1000 1500 2000

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 50 100 150 200 250

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%

0.14 0.140.16

TQ1_E ST1_E ST2_E POL1_E POL2_E

Crack width reduction of the FRC beams respect

to the plain beam (Dw /%).

steel polyester

G. Plizzari

Cracking behavior at SLS

(50kN)

ST1-2 35%

POL1-2 28%

SHORT TERM

LONG TERM

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

(100kN)

ST1-2_E 56%

POL1_E 25%

POL2_E 54%

(100kN)

ST1-2 41%

POL1-2 39%

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

SHORT TERM

LONG TERM

G. Plizzari

Carbonation depth

CARBONATION DEPTHCHLORIDE CONTENT

G. Plizzari

Carbonation depth between the cracks

G. Plizzari

Carbonation depth at cracks

(mm/anni

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

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

1 2 3 4 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

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]

G. Plizzari

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

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

(CQ40S)

Shell elements

(CQ40S)

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

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)

giovanni.plizzari@unibs.it

Giovanni Plizzari

University of Toronto - August 26th, 2015

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