Lecture 10 - Di Prisco

8/17/2019 Lecture 10 - Di Prisco

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Retaining structures

M. di PriscoDepartment of Civil and Environmental Engineering,Politecnico di Milano


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CONCRETE RETAINING (cantilever) WALL

Surcharge

Load condition

23SLS

SLU=

δ

δ

%15.0: =s

rebar ρ

MC (2010) classification of SFRC:

Class “2b” - Vf = 25kg/m3


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Advantages of R/C sheet piles over steel:


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Sheet piles

b Jansze et al. 2005


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V u

[ k N ]


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No splitting cracks

occurred!


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General framework

Ground slope

Varenna

Caslino


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General framework


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July 2003

Ground slope stabilization

The slope in Caslino d’Erba (Lecco, Italy)

Safety factor= 1.1


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General framework

CASLINO

Nailing

Anchored bulkhead

New design solution


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Sheltering Structures


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Description of the retaining structure


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2003 2004 2005 2006

2007 2008 2009 2010

Preliminary

investigations

Soil investigations

Element design Element

positioning

Plate

installation

monitoring (full equipment)

Chronology

Stability

checks

Design and casting elements

Monitoring (partial equipment )


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Construction phases: preliminary operations on site


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Construction phases: slope scaling


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Construction phases: safety operations


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Construction phases: drainage setting-up


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Construction phases: testing on plates

L t f

L t b L f r e e

L c o ns t r a i nt

L e


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Construction phases: relief, template positioning and anchor fixing


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Construction phases: template formwork


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Construction phases: ground anchor boring and grouting


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Construction phases: casting of bedding bottom layer

C i h l h dli


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Construction phases: panel handling

Construction phases: anchor plate positioning


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Construction phases: anchor plate positioning

Construction phases: final view


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Construction phases: final view


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New design aspects

Main Concepts

• to strenghten the structure “ground slope”• to use precast elements to accelerate the in-situ operations

• to apply FRC materials to benefit of local thoughness

• to use such construction as an environmental structurecarefully monitored to check the reliability of both the

structure and the monitoring exp. techniques• to calibrate NDT, by perfectly knowing the mechanical

characteristics of the materials

N d i t


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New design aspects

EDL

EUL

Ne design aspects


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2D Jambuapproach

New design aspects

0.5

0.75

1

1.25

1.5Safety

factor

0 1 2 3 4 5 6 7 8 9 10 11 12 13Step

Failure 1

Failure 2

Failure 2: 1.4Failure 1: 1.4

Actual anchor load values

after 10 days from post-tensioning

Anchor loads at the onset of post-tensioning


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constituent quantity [kg/ m3]

Cement (CEM I

52.5R)400

Coarse aggregate A 569 (da < )

Coarse aggregate B 403 (da < )

Sieved sand 676 (da

< )

Calcareous filler 96 (da < )

Steel fibres 60/0.8 50

Superplasticizer/

cement ratio 2.2 %

Water/binder ratio 0.39

Material characterization: mix design

or pane s: wor a ty


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p y

suitable tests

SFRC for panels: mechanical tests


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0 1000 2000 3000

COD [µm]

0

4

8

12

N

[ M P a ]

Mean

SFRC for panels: mechanical tests

fibre content

50 kg/m3

df = 0.8 mm

Lf = 60 mm


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SFRC Classification

C60–S5–12–XC4–F4–DH1–DS1

UNI 11039

4a

f R1k / f Lk ≈ 0,94 > 0.4

f R3k / f R1k ≈ 0,70 > 0.5

MC 2010 (EN14651)


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0 1000 2000 3000COD [µm]

0

4

8

12

N

[ M P a ]

Mean

0 1200 2400 3600COD [µm]

0

4

8

12

N

[ M P a ]

fctf = 6.09 MPa [s = 0.84]

f1tf = 6.10 MPa [s = 0.77]

fFtf* = 2.57 MPa [s = 0.79]

P P

l l l

L=3.5 l

h + a = l

a

h

Material characterization: workability suitable tests


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Material characterization: workability suitable tests

Test 1 Test 2 Test 3 Cast Slump T50Ratio Scatter Ratio Scatter Ratio Scatter [mm] [sec]

Sector [kg/m3] [%] [kg/m3] [%] [kg/m3] [%] 1 625 8.8

1 40.01 -20.24 60.33 -7.73 44.43 -25.3 2 618 10.6

2 54.48 8.61 63.36 -3.10 69.33 16.56 3 560 12.0

3 54.16 7.98 68.12 4.19 53.62 -9.85 4 666 5.4

4 47.25 -5.79 61.15 -6.48 64.66 8.71 5 580 12.6

5 45.34 -9.62 64.12 -1.93 57.69 -3.01 6 714 6.2

6 50.35 0.37 76.00 16.23 61.94 4.13 7 685 6.8

7 46.58 -7.13 70.63 8.02 62.41 4.93 8 686 6.2

8 57.56 14-76 66.95 2.39 62.87 5.69 9 658 8.1

9 55.71 11.06 57.82 -11.57 58.37 -1.87 10 641 10.5

Mean 50.16 65.39 59.48 Mean 643 8.7


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Structural designMain doubts

hardening

behaviour, lcs ?

which advantages

with respect to plainconcrete ?

adequate safety

coefficient ?

which ductility?

In favour of safety

no redundancy effect was taken into

account !

Experimental programme


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Not Post-tensioned beams

30

3 0

Total: 15 beams (6 typologies) 3 0

30

R0

2 x

S0

3 x

p p g

Post-tensioned beams

3 0

30

3 0

30

S1

3 x 3 x

3 0

30

P1

2 x 2 x

P2 3 0

30


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Material characterization: bending strength


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f If[MPa]

f peak[MPa]

f Ft[MPa]

f eq(0-0.6)[MPa]

f eq(0.6-3)[MPa]

σFt1[MPa]

σFt2[MPa]

D0 D1

R0A - 3.850 3.465 - - - - - -

R0B - 4.509 4.058 - - - - - -

P1A - 3.716 3.344 - - - - - -

Average - 4.025 3.622 - - - - - -Variation

Coefficient [%]- 10.56 10.55 - - - - - -

S0A 3.899 6.181 3.509 5.559 2.879 2.501 0.189 1.425 0.512

S0B 4.350 6.805 3.915 6.063 3.890 2.728 0.581 1.391 0.649

S0C 4.736 6.644 4.263 5.600 4.014 2.520 0.747 1.187 0.732

S1A 4.334 7.023 3.900 6.216 4.545 2.797 0.874 1.437 0.733

S1B 4.231 4.982 3.808 4.623 2.496 2.081 0.208 1.092 0.553

S1C 4.195 6.279 3.776 5.602 3.661 2.521 0.570 1.314 0.651

S2A 4.575 6.526 4.118 5.825 3.672 2.621 0.526 1.263 0.638

S2B 5.003 5.571 4.503 4.920 2.409 2.214 0.097 0.983 0.506S2C 4.131 5.269 3.718 4.650 2.809 2.092 0.358 1.120 0.604

Average 4.384 6.142 3.945 5.451 3.375 2.453 0.461 1.246 0.620

Variation

Coefficient [%]7.69 11.61 7.68 10.79 22.19 - - - -

Material characterization: elastic modulus and time hardening


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0 0.02 0.04 0.06 0.08 0.1

ε [%]

0

5

10

15

20

25σ [MPa]

cilindro S1C-5

4 cylinders

cylinder ∆σ [MPa] ∆ε [-] E [MPa]

R0A-3 11.87 4.044E-04 29350

S0A-1 13.75 4.573E-04 30069S1C-5 14.40 4.741E-04 30375

S2A-5 13.43 4.188E-04 32069

Mean value 13.36 4.386E-04 30466 (3.8 %)

0 7 14 21 28tempo [gg]

0

20

40

60

80

Rcm [MPa]

evoluzione resistenza a compressione

cls tradizionale

cls fibrorinforzato

Experimental tests: post-tensioning


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step(1) (2) (3) (4) (5)

1 -5.16 -1.02 3.03 -1.11 -3.13

2 -2.12 -2.12 -2.12 -2.12 -2.12

3 -3.23 0.91 -3.14 -7.28 -5.25

4 -4.24 -4.24 -4.24 -4.24 -4.24

5 -7.37 -3.23 -3.23 -7.37 -7.37

6 -12.53 -4.25 -0.20 -8.48 -10.50

7 -9.49 -5.35 -5.35 -9.49 -9.49

8 -10.60 -2.32 -6.37 -14.65 -12.62

9 -11.61 -7.47 -7.47 -11.61 -11.61

10 -14.74 -6.46 -6.46 -14.74 -14.74

σ [MPa]

B C

(2) (3)

A D

(1) (4)(5)

E

f cm 60 MPa

k 1.48 -

s 3.6 MPa

f ck 54.67 MPa

f ctk 4.34 MPa

Strength at 7 days

(control type B)

Experimental tests: demoulding and lifting


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k·g

F

Fv

Fh

α

x

kNm f W M ctm,fl R 3.17 =⋅=

kNm x M M S 9.1)(max ==

S R M M >

Experimental tests: demoulding and lifting

f cm,1 = 34 Mpa

β = β(h)= 1.23


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Experimental tests: test set-up


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Prova di flessione a quattro punti

P/2 P/2L/4 L L L L/4


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L 1 L 2 L 3

L 4

L 7L 6 L 8

Vert A1 Vert A2 Vert B1 Vert C1 Vert D1 Vert E2 Vert E1

A B C D E

lato 1

Experimental tests: test instrumental equipment



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L 1 L 2 L 3

L 4

L 7L 6 L 8


A B C D E

lato 1



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L 7

L 9

L 1

L 3

L 5

L 6

A B C D E

lato 1

Experimental tests: reference grid


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Digital Image Correlation

Experimental tests: reference grid

Experimental tests: post-tensioned beams


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0 30 60 90 120

δ [mm]

0

50

100

150

200

250

P [kN]

S1A

S1B

S1C

0 20 40 60 80 100δ [mm]

0

100

200

300P [kN]

P2A

P2B

0 20 40 60 80 100

δ [mm]

0

100

200

300

P [kN]

S2A

S2B

S2C

SFRC

P/C

0 30 60 90 120δ [mm]

0

50

100

150

200

250P [kN]

P1A

P1B

4 strands

5 strands

Experimental tests: not post-tensioned beams


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0 0.004 0.008 0.012 0.016 0.02

θ [1/m]

0

5

10

15

20

25M [kNm]

S0A

S0A sx

S0B

S0C

Carichi pre-esistenti (mezzeria):Momento da peso proprio: 2.46kNmMomento da ripartitore: 1.1kNm

0 4 8 12δ [mm]

0

10

20

30

40

50P [kN]

S0A

S0B

S0C

Carichi pre-esistenti (oltre al peso proprio)Carico del ripartitore: 2.2kN

0 0.04 0.08 0.12

θ [1/m]

0

40

80

120

160

200M [kNm]

R0A

R0B

R0B dx

0 40 80 120δ [mm]

0

100

200

300

400P [kN]

R0A

R0B

SFRC

R/C

Midspan loads MG

MQ

Load device = 2.2 kN

Experimental tests: comparisons


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Obseration!

-separated performance level

- different initial stiffnesses

- ductility

42

374

207

101

0 0.2 0.4 0.6 0.8δ [mm]

0

4

8

12

16P [kN]

R0B

S1C

S0A

0 30 60 90 120δ [mm]

0

100

200

300

400

P [kN]

R0B

S1C

S0A

Experimental tests: comparisons


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0 30 60 90 120

0

100

200

300

P [kN] P2

S2

0 30 60 90 120

stroke [mm]

0

100

200

300

P [kN] P1

S1

"ensioncontrib#tion

Com$ression

contrib#tion

P1B (4 strands - PC)

S1B (4 strands) S!C)

120 kN

100 kNdesig

n

Experimental results: observation


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" Contri#uto delle fi#re a tra$ione

" Buona ripeti#ilit% del comportamento degli elementi strutturali

No cracking of ducts!

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Concrete

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fIF 5.94 MPa

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fptk 1860 Mpa

Fpk 1650 MPa

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Monitoring of retaining structure


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Load vs. strand sliding Which load during

ground anchor post-

tensioning?

Meteo conditions


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Rainfall

Temperature

Temperature evolution


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winter summer

Long term monitoring of load cells


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EDL

EDR

EUL

EUR

Load cell single strand

Monitoring of retaining structure


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LEFE assessment

X

Y

Z

Concluding remarks


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• a new retaining structure continuously monitored via GPRS isnow also ready to be used as a lab for NDT

• a synergic action between University and local and regionaladministration gives rise to a new environmental lab on slope

stability used by Polo Regionale di Lecco

• new concept design and advanced materials have been used to

design a new retaining structure solution

• main aims: to check via GPRS the structure in the time, to investigateon the monitoring control of protection structure database, to validate

Eurocode 7 approach for special structures

Possible use combining plates and geomembranes for

deep strenghthening + skin retrofitting


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02

0GP&I,EC%IC *I MI%


M*E&& C',I,,I ,I&I#,M*E&& C',I,,I ,I&I#,M*E&& C',I,,I ,I&I#,M*E&& C',I,,I ,I&I#,


84/114

'oftareD ##' 6.10##' 6.10##' 6.10##' 6.10

Moello costitti;oD Concrete *amage Plasticit MoelConcrete *amage Plasticit MoelConcrete *amage Plasticit MoelConcrete *amage Plasticit Moel

Moello a anno 2asato slla plasticitaH

*e meccanismi i rottraD cracking a tra=ione e crs"ing a

compressione.

&egame non associatoD istin=ione tra sperficie i sner;amento @FFFFB e

poten=iale plastico @++++B.

Poten=iale plastico @fn=.

*rcker PragerB

'p. i sner;amento

&egge i scorrimento

Φ⋅−+Φ⋅⋅= tan)tan( pq G t

22

0σ ε

⋅

⋅∂

∂= λ

σ

Gδε

ij

pl

ij

03

1

1=−⋅−⋅+⋅⋅−⋅

−

= )())((maxmax plc pl

pq F ε σ σ γ σ ε β α

α

)/(

/

12

1

00

00

−⋅

−=

cb

cb

σ σ

σ σ α

( ) ( )α α ε σ

ε σ β +−−⋅= 11

)(

)( pl

tt

pl

cc

12

13

−⋅

−⋅=

c

c

K

K )(γ

QConcrete *amage Plasticit MoelR

02

#&I*#I%E *EI &E+#MI C',I,,II#&I*#I%E *EI &E+#MI C',I,,II#&I*#I%E *EI &E+#MI C',I,,II#&I*#I%E *EI &E+#MI C',I,,II

08P&I,EC%IC *I MI%



85/114

fIFm feN1m feN$m fcm Ecm

MPa MPa MPa MPa MPa

4.68 5.$0 3.G3 G498 $5094

Pro;a a tra=ione monoassiale s pro;ino intagliatoConfrontoConfrontoConfrontoConfronto sperimentalisperimentalisperimentalisperimentali - *o=io $008

#%+& i *I,#%##%+& i *I,#%##%+& i *I,#%##%+& i *I,#%# ME':ME':ME':ME': )E+)I#I%E)E+)I#I%E)E+)I#I%E)E+)I#I%E

I'C'#I'C'#I'C'#I'C'#

02

#&I*#I%E *EI &E+#MI C',I,,II#&I*#I%E *EI &E+#MI C',I,,II#&I*#I%E *EI &E+#MI C',I,,II#&I*#I%E *EI &E+#MI C',I,,II

09P&I,EC%IC *I MI%



86/114

fIFm feN1m feN$m fcm Ecm

MPa MPa MPa MPa MPa

5.94 8.39 4.8G 69.00 39$G0

Pro;a a tra=ione iniretta ? flessione s 4 pntiConfrontoConfrontoConfrontoConfronto sperimentalisperimentalisperimentalisperimentali - *o=io $008

ME':ME':ME':ME': E&EME%,IE&EME%,IE&EME%,IE&EME%,I

#*)#,ICI#*)#,ICI#*)#,ICI#*)#,ICI

)E+)I#I%E)E+)I#I%E)E+)I#I%E)E+)I#I%E

I'C'#I'C'#I'C'#I'C'#

13P&I,EC%IC *I MI%


,)'I%E,)'I%E,)'I%E,)'I%E

M*E&I%E P)# ,)'I%EM*E&I%E P)# ,)'I%EM*E&I%E P)# ,)'I%EM*E&I%E P)# ,)'I%E

M ll


87/114

Moello M*E&& +EME,)ICM*E&& +EME,)ICM*E&& +EME,)ICM*E&& +EME,)IC ???? Moello 4

#%E&& )I+I*

O

Cernieratorsionale

F)C:E,,# )I+I*#O

)itegno torsionale

I%C&I

C%,#,, D

ire=ione normale D istacco e assen=a i compenetra=ione

ire=ione tangen=iale D

anello → µO0.45 @acciaio - calcestr==oB

forc"etta → µO0.04 @calcestr==o - teflonB

14P&I,EC%IC *I MI%


,)'I%E,)'I%E,)'I%E,)'I%E


)i lt ti i i M ll


88/114

)isltati nmerici Moello

,ra;e ,picco

k%m S

'perim 31.03 -

33.39 G.6

5.0 e-03

2.0 e-03

8.0 e-04

)I'&,#,I %ME)ICI)I'&,#,I %ME)ICI)I'&,#,I %ME)ICI)I'&,#,I %ME)ICI ---- Moello 4

'P)#

, 'T

',,

PE M#T principali -

picco

aro fessrati;o

sperimentale

15P&I,EC%IC *I MI%

'& CMP),#ME%, # ,)'I%E *I ,)#I FI))I%F)#,E---- M*E&I%E *E&M*E&I%E *E&M*E&I%E *E&M*E&I%E *E&

P)ECMP)E''I%EP)ECMP)E''I%EP)ECMP)E''I%EP)ECMP)E''I%E

EFFE,, *E& P)ECMP)E''I%E '& C#P#CI,#H ,)'I%#&EEFFE,, *E& P)ECMP)E''I%E '& C#P#CI,#H ,)'I%#&EEFFE,, *E& P)ECMP)E''I%E '& C#P#CI,#H ,)'I%#&EEFFE,, *E& P)ECMP)E''I%E '& C#P#CI,#H ,)'I%#&E

Formla=ione teorica e risltati sperimentali


89/114

' $50 > 1850

mm

'c"ema 'tatico'c"ema 'tatico'c"ema 'tatico'c"ema 'tatico

16P&I,EC%IC *I MI%



EFFE,, *E& P)ECMP)E''I%E '& C#P#CI,#H ,)'I%#&EEFFE,, *E& P)ECMP)E''I%E '& C#P#CI,#H ,)'I%#&EEFFE,, *E& P)ECMP)E''I%E '& C#P#CI,#H ,)'I%#&EEFFE,, *E& P)ECMP)E''I%E '& C#P#CI,#H ,)'I%#&E

Moello C e ;alia=ione ei moelli 7C


90/114

Moello C e ;alia=ione ei moelli 7C

)I'&,#,I #&I*#I%E)I'&,#,I #&I*#I%E)I'&,#,I #&I*#I%E)I'&,#,I #&I*#I%E ???? Moello

M*E&& CM*E&& CM*E&& CM*E&& C

Moello %mericoMoello %mericoMoello %mericoMoello %merico'c"ema'c"ema'c"ema'c"ema

'tatico'tatico'tatico'tatico

----0.50.50.50.5----$ 0.9$ 0.9$ 0.9$ 0.9

ffff'P'P'P'P

----0.50.50.50.5----$Wf$Wf$Wf$Wf'P'P'P'P

#&I*#I%E#&I*#I%E#&I*#I%E#&I*#I%E ---- Moello

C

M*E&& CM*E&& CM*E&& CM*E&& C

)isltati nmerici per la ner;atra )I1

1GP&I,EC%IC *I MI%




91/114

M*E&& CM*E&& CM*E&& CM*E&& C ????

)I41

PEM#T principaliθO 9.5 mra

PEM#T principali

θO 15 mra

PEM#T principali

θO 30 mra

,%M 33.39 k%m

,pr %M 55.10 k%m

,pr ," 5G.90 k%m

Pra ,orsione @ris. nmericoB

,orsione LPrecompressione @ris.

nmericoB

5.0 e-03

2.0 e-03

8.0 e-04

1.4 e-02

8.3 e-03

2.4 e-03

1.6 e-03

8.2 e-04

2.7 e-04

amento capacitJ torsionale @60SB

per effetto

ella precompressione

M*E&I%E *EI C#I *I P',M*E&I%E *EI C#I *I P',M*E&I%E *EI C#I *I P',M*E&I%E *EI C#I *I P',----,E%'I%E,E%'I%E,E%'I%E,E%'I%E ---- M*E&& *M*E&& *M*E&& *M*E&& *

)isltati nmerici e confronto con il caso i pressione niforme

alle estremitJ

18P&I,EC%IC *I MI%




92/114

M*E&& *M*E&& *M*E&& *M*E&& * ???? )I41

ca;i i

post-

tensione

alle estremitJ

Moello CMoello CMoello CMoello C ???? %o%o%o%o

Ca;iCa;iCa;iCa;i

Moello *Moello *Moello *Moello * ---- Ca;iCa;iCa;iCa;i

Ca;i i post-

tensione

Elementi 3*

Precompressione ∆, s ca;o

Precompressione Pressione

niforme

M*E&& CM*E&& CM*E&& CM*E&& C ???? )I41

*MI%I *I I%,E)#I%E F&E''I%E*MI%I *I I%,E)#I%E F&E''I%E*MI%I *I I%,E)#I%E F&E''I%E*MI%I *I I%,E)#I%E F&E''I%E ---- ,)'I%E,)'I%E,)'I%E,)'I%E

*omini i intera=ione presenti in letteratra

19P&I,EC%IC *I MI%

'& CMP),#ME%, # ,)'I%E *I ,)#I FI))I%F)#,E---- I%,E)#I%E F&E''I%EI%,E)#I%E F&E''I%EI%,E)#I%E F&E''I%EI%,E)#I%E F&E''I%E----,)'I%E,)'I%E,)'I%E,)'I%E


93/114

C&' 2iancoC&' 2iancoC&' 2iancoC&' 2ianco @1B@1B@1B@1B 'F)C'F)C'F)C'F)C @$B@$B@$B@$B 'F)C'F)C'F)C'F)C

precompressoprecompressoprecompressoprecompresso @3B@3B@3B@3B

@1B )epot on torsion in strctral concrete. ,ec"nical report #CI Committee 4457#'CE.@$B M. #. Mansr. ening-torsion interaction for concrete 2eams reinforce it" steel fi2res.

Maga=ine of Concrete )esearc"198$.@3B ). %araanan an #. '.


94/114

*imensioniD 85 > 1G8 > $400 mm

Precompressione ca;o

Carico ;erticale applicato per raggingere il momento flettente ric"iesto

Ceimento rota=ionale anelli rigii

#&I*#I%E M*E&& *#&I*#I%E M*E&& *#&I*#I%E M*E&& *#&I*#I%E M*E&& * ? %araanan et al. @AB

@AB ). %araanan an #. '.


95/114

@AB ). %araanan an #. '.


96/114

#&I*#I%E M*E&& *#&I*#I%E M*E&& *#&I*#I%E M*E&& *#&I*#I%E M*E&& * ? eforma=ioni plastic"e massime principalieforma=ioni plastic"e massime principalieforma=ioni plastic"e massime principalieforma=ioni plastic"e massime principali alpicco elle cr;e

MO0 MO0.$5M

MO0.50M MO0.G5M

'P)#'P)#'P)#'P)#

,,,,

',,',,',,',,

'P)#'P)#'P)#'P)#

,,,,

',,',,',,',,

'P)#'P)#'P)#'P)#

,,,,

',,',,',,',,

'P)#'P)#'P)#'P)#

,,,,

',,',,',,',,

5.0 e-032.0 e-03

8.0 e-04

5.0 e-03

2.0 e-03

8.0 e-04

5.0 e-033.0 e-038.0 e-04

2.0 e-021.0 e-024.0 e-03

M*E&I%E *E& %E)#,)# )I1M*E&I%E *E& %E)#,)# )I1M*E&I%E *E& %E)#,)# )I1M*E&I%E *E& %E)#,)# )I1

Moelli geometrici e nomenclatre

$3P&I,EC%IC *I MI%

'& CMP),#ME%, # ,)'I%E *I ,)#I FI))I%F)#,E---- %E)#,)# )I1 %E)#,)# )I1 %E)#,)# )I1 %E)#,)# )I1


97/114

M*E&I%E *E& %E)#,)# )I1M*E&I%E *E& %E)#,)# )I1M*E&I%E *E& %E)#,)# )I1M*E&I%E *E& %E)#,)# )I1

+eometria ei e moelli *ettagli el moello

Mes" $5mm

*ettagli el moello

Mes" 50mm

M*E&& *.0 @1$00 mmB M*E&& *.1 @3000 mmB

%ME%C,)# e C#)#,,E)I',IC:E M*E&&I *.0. e *.1.%ME%C,)# e C#)#,,E)I',IC:E M*E&&I *.0. e *.1.%ME%C,)# e C#)#,,E)I',IC:E M*E&&I *.0. e *.1.%ME%C,)# e C#)#,,E)I',IC:E M*E&&I *.0. e *.1.

mesh cavi n°El.. tipo El. nodi

D.0.25U 25x25 non

aderenti 17168 C3D8 21057

D.0.50U 50x50 non


D.0.25B 25x25 aderenti 17168 C3D8 21057

mesh cavi n°El.. tipo El. nodi

D.1.25U 25x25 non


D.1.50U 50x50 non


D.1.25B 25x25 aderenti 67959 C3D8 71521

M*E&& *.0

M*E&& *.1

#%#&I'I '&,E PE) %E)#,)# )I1#%#&I'I '&,E PE) %E)#,)# )I1#%#&I'I '&,E PE) %E)#,)# )I1#%#&I'I '&,E PE) %E)#,)# )I1

P)# ,)'I%E ? F&E''I%E e ,)'I%E

$4P&I,EC%IC *I MI%



98/114

•Pra torsionePra torsionePra torsionePra torsione

•Intera=ione flessione e torsione per i;ersiIntera=ione flessione e torsione per i;ersiIntera=ione flessione e torsione per i;ersiIntera=ione flessione e torsione per i;ersili;elli i caricoDli;elli i caricoDli;elli i caricoDli;elli i caricoD

•MO0.$5MO0.$5MO0.$5MO0.$5 MMMM

•MO0.50MO0.50MO0.50MO0.50 MMMM

•MO0.G5MO0.G5MO0.G5MO0.G5 MMMM

#%#&I'I %ME)IC:E '&,ED#%#&I'I %ME)IC:E '&,ED#%#&I'I %ME)IC:E '&,ED#%#&I'I %ME)IC:E '&,ED

'c"ema statico'c"ema statico'c"ema statico'c"ema statico

fctm feN1m feN$m fcm Ecm

MPa MPa MPa MPa MPa

3.90 5.G4 3.59 G$.03 30466

ProprietJ meie el materialeProprietJ meie el materialeProprietJ meie el materialeProprietJ meie el materiale

)I'&,#,I %ME)ICI PE) %E)#,)# )I1)I'&,#,I %ME)ICI PE) %E)#,)# )I1)I'&,#,I %ME)ICI PE) %E)#,)# )I1)I'&,#,I %ME)ICI PE) %E)#,)# )I1 ???? M*E&& *.0M*E&& *.0M*E&& *.0M*E&& *.0

Moello *.0. ? Pra ,orsione

$5P&I,EC%IC *I MI%


,)#E 1$00 mm,)#E 1$00 mm,)#E 1$00 mm,)#E 1$00 mm


99/114

PE ma> principal -θO

8 mra


10 mra


14 mra

Tpicco[kNm]

%

D.0.25U 57.06 -

D.0.50U 58.75 2.9

D.0.25B 57.51 0.7

assi scarti S rispetto al moello corrett

****....0000....$5$5$5$5

risltati con ca;i aerenti atteni2ili

,)#E 1$00 mm,)#E 1$00 mm,)#E 1$00 mm,)#E 1$00 mm

3.0 e-031.5 e-034.0 e-04

1.2 e-026.0 e-032.0 e-03

4.0 e-042.0 e-048.0 e-05

)I'&,#,I %ME)ICI PE) %E)#,)# )I1)I'&,#,I %ME)ICI PE) %E)#,)# )I1)I'&,#,I %ME)ICI PE) %E)#,)# )I1)I'&,#,I %ME)ICI PE) %E)#,)# )I1 ???? M*E&& *.0.M*E&& *.0.M*E&& *.0.M*E&& *.0.

Moello *.0. ? F&E''I%E e ,)'I%E

$6P&I,EC%IC *I MI%



100/114

M O 0.50 M

M O 0.$5 M

*istri2=ione PE massime

principali

θ O 5 mra

MMMMffff,,,,piccopiccopiccopicco

----1.6S1.6S1.6S1.6S

----4.$S4.$S4.$S4.$S

3.0 e-031.5 e-038.0 e-04

3.0 e-03

1.5 e-038.0 e-04

)I'&,#,I %ME)ICI PE) %E)#,)# )I1)I'&,#,I %ME)ICI PE) %E)#,)# )I1)I'&,#,I %ME)ICI PE) %E)#,)# )I1)I'&,#,I %ME)ICI PE) %E)#,)# )I1 ???? M*E&& *.1M*E&& *.1M*E&& *.1M*E&& *.1

Moello *.1. ? Pra ,orsione

$GP&I,EC%IC *I MI%


,)#E 3000 mm,)#E 3000 mm,)#E 3000 mm,)#E 3000 mm


101/114

PE ma> principali - θO 8 mra



Tpicco[kNm]

%

D.1.25U 55.30 -

D.1.50U 56.53 2.2

D.1.25B 55.21 0.2

2.5 e-04

1.0 e-04

8.0 e-05

2.0 e-031.0 e-03

3.0 e-04

5.0 e-032.0 e-03

8.0 e-04

*eforma=ioni plastic"e PE massime

)I'&,#,I %ME)ICI PE) %E)#,)# )I1)I'&,#,I %ME)ICI PE) %E)#,)# )I1)I'&,#,I %ME)ICI PE) %E)#,)# )I1)I'&,#,I %ME)ICI PE) %E)#,)# )I1 ???? M*E&& *.1.M*E&& *.1.M*E&& *.1.M*E&& *.1.

Moello *.1. ? F&E''I%E e ,)'I%E

$8P&I,EC%IC *I MI%



102/114

M = 0.25 MU

M = 0.50 MU

M = 0.75 MU

p

principali

θ O 13 mra

MMMMffff,,,,piccopiccopiccopicco

----1.9S1.9S1.9S1.9S

----4.8S4.8S4.8S4.8S

----11.4S11.4S11.4S11.4S

1.0 e-02

5.0 e-031.0 e-03

5.0 e-032.0 e-038.0 e-04

5.0 e-032.0 e-038.0 e-04

I%,E)#I%E F&E''I%E ,)'I%EI%,E)#I%E F&E''I%E ,)'I%EI%,E)#I%E F&E''I%E ,)'I%EI%,E)#I%E F&E''I%E ,)'I%E

Effetto ella lng"e==a sllHintera=ione flesso-torsionale

$9P&I,EC%IC *I MI%



103/114

,ra;e Corta,ra;e Corta,ra;e Corta,ra;e Corta ???? 1$00 mm1$00 mm1$00 mm1$00 mm

,ra;e &nga,ra;e &nga,ra;e &nga,ra;e &nga ???? 3000 mm3000 mm3000 mm3000 mm

----4.0S4.0S4.0S4.0S----4.3S4.3S4.3S4.3S

----4.5S4.5S4.5S4.5S


)isltati nmerici e omini i intera=ione

30P&I,EC%IC *I MI%



104/114

,)#E & O 1$00,)#E & O 1$00,)#E & O 1$00,)#E & O 1$00

mmmmmmmm,)#E & O 3000,)#E & O 3000,)#E & O 3000,)#E & O 3000

mmmmmmmm

C%C&'I%IC%C&'I%IC%C&'I%IC%C&'I%I

31P&I,EC%IC *I MI%

'& CMP),#ME%, # ,)'I%E *I ,)#I FI))I%F)#,E---- C%C&'I%IC%C&'I%IC%C&'I%IC%C&'I%I

P)#P)#P)#P)# ,)'I%E,)'I%E,)'I%E,)'I%E DDDD


105/114

•Moello nmerico &imitata so;rastima ella capacitJ torsionale

sperimentale

•Corrisponen=a el Naro fessrati;o

•Moello nel complesso affia2ile.

,)'I%E,)'I%E,)'I%E,)'I%E eeee P)ECMP)E''I%EP)ECMP)E''I%EP)ECMP)E''I%EP)ECMP)E''I%E DDDD

•ona corrisponen=a con i ;alori teorici @'ke ening ,"eorB

•)isltati confronta2ili tra Moello C @assen=a i ca;iB e Moello* @ca;i 3*B.

I%,E)#I%EI%,E)#I%EI%,E)#I%EI%,E)#I%E F&E''I%EF&E''I%EF&E''I%EF&E''I%E ????,)'I%E,)'I%E,)'I%E,)'I%E conconconcon precompressioneprecompressioneprecompressioneprecompressioneDDDD

•Corrisponen=a el Naro fessrati;o sperimentale @aletteratraB

•*ecremento ella resisten=a torsionale per alti ;alori i momentoflettente

•)isltati nmerici confronta2ili tra moella=ione ca;i aerenti enon aerenti

•Inflen=a ella lng"e==a ella tra;e slla capacitJ torsionale

'I&PPI F,)I'I&PPI F,)I'I&PPI F,)I'I&PPI F,)I

3$P&I,EC%IC *I MI%

'& CMP),#ME%, # ,)'I%E *I ,)#I FI))I%F)#,E ---- 'I&PPI F,)I'I&PPI F,)I'I&PPI F,)I'I&PPI F,)I

,)'I%E,)'I%E,)'I%E,)'I%E EEEE P)ECMP)E''I%EP)ECMP)E''I%EP)ECMP)E''I%EP)ECMP)E''I%E


106/114

,)'I%E,)'I%E,)'I%E,)'I%E EEEE P)ECMP)E''I%EP)ECMP)E''I%EP)ECMP)E''I%EP)ECMP)E''I%EDDDD

•Campagna sperimentale s tra;i precompresse cosX a caratteri==arecompitamente il comportamento i na singola ner;atra el

graticcio

I%,E)#I%EI%,E)#I%EI%,E)#I%EI%,E)#I%E F&E''I%EF&E''I%EF&E''I%EF&E''I%E ????,)'I%E,)'I%E,)'I%E,)'I%E conconconcon precompressioneprecompressioneprecompressioneprecompressioneDDDD

•#nalisi nmerica a collasso consierano lHeffettoellHintera=ione flesso- torsionale

•Campagna sperimentale s tra;i precompresse soggette a flessionee torsione

•Pro;a sperimentale a collasso ella strttra graticcio.

+)#IE PE)+)#IE PE)+)#IE PE)+)#IE PE)

&H#,,E%I%E&H#,,E%I%E&H#,,E%I%E&H#,,E%I%E

P&I,EC%IC *I MI%


,)'I%E,)'I%E,)'I%E,)'I%E


Confronto Moello # e Moello

C%F)%, %ME)ICC%F)%, %ME)ICC%F)%, %ME)ICC%F)%, %ME)IC ---- Moell0 # e

Moello 4


107/114

Moello 4

M*E&& #M*E&& #M*E&& #M*E&& #

incolo i Copling

@#2aNsB

M*E&& M*E&& M*E&& M*E&&

incoli

moellati

,ra;e ,piccok%m

S

'perim 31.03 -

33.39 G.6

# 3$.69 5.3

incolo iincolo iincolo iincolo i #2aNs#2aNs#2aNs#2aNs

@#B@#B@#B@#B

incoli moellatiincoli moellatiincoli moellatiincoli moellati

@B@B@B@B

Incompati2ile conprecompressione

Maggiore controllo ei

;incoli

Moello piK realistico

P&I,EC%IC *I MI%


,)'I%E,)'I%E,)'I%E,)'I%E

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02

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'F)C @'teel fi2re reinforce concreteB'F)C @'teel fi2re reinforce concreteB'F)C @'teel fi2re reinforce concreteB'F)C @'teel fi2re reinforce concreteB


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02

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Poten=iale plastico @fn=.

* k P B

Φ⋅−+Φ⋅⋅= tan)tan( pq G t

22

0σ ε

M*E&& C',I,,I ,I&I#,M*E&& C',I,,I ,I&I#,M*E&& C',I,,I ,I&I#,M*E&& C',I,,I ,I&I#,

QConcrete *amage Plasticit MoelR


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*rcker PragerB

'p. i sner;amento @&ee Fen;esB

&egge i scorrimento⋅

⋅∂

∂= λ

σ

Gδε

ij

pl

ij

031

1=−⋅−⋅+⋅⋅−⋅

−= )())((

maxmax plc pl pq F ε σ σ γ σ ε β α

α

)/(

/

12

1

00

00

−⋅

−=

cb

cb

σ σ

σ σ α

( ) ( )α α ε σ

ε σ β +−−⋅= 11

)(

)( pl

tt

pl

cc

12

13

−⋅

−⋅=

c

c

K

K )(γ

Parametri i inptD

ElasticitJD

EEEE ν.

Plasticità:

Φ = angolo i ilatan=a


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,ra;e &O3000mm,ra;e &O3000mm,ra;e &O3000mm,ra;e &O3000mm

'for=i minimi principali in corrisponen=a i momento

flettente massimo


Effetto ella lng"e==a sllHintera=ione flesso-torsionale

P&I,EC%IC *I MI%



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,ra;e &O1$00mm,ra;e &O1$00mm,ra;e &O1$00mm,ra;e &O1$00mm


flettente massimo

,ra;e &O3000mm,ra;e &O3000mm,ra;e &O3000mm,ra;e &O3000mm


flettente massimo


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Lecture 10 - Di Prisco