Lecture 06 - Di Prisco

Prefabricated tunnel segments

SFRC solution

M. di Prisco

2

Outline

transient phases during segment production

bending resistance in FRC structures

shear resistance in FRC structures

KRd factor

TBM jack pushing: strut and tie model with and

without fibres, 2D and 3 D conditions

Considering additional loads due to:

Adhesion: 2 kN/m2

Humidity: 0.5 kN/m3

Dynamic increasing factor: 20% Wc

DEMOULDING AND FIRST HANDLING

ACCIDENTAL SETTINGS

STOCKPILING

Considering additional load:

Dynamic increasing factor:

60% Wc

Considering both:

External

Internal

Disalignment

Structural design models for transient stages

Scheme 1 Scheme 2

ACCIDENTAL SETTINGS

7.7.3 Verification of safety (ULS)

7.7.3.1 Bending and/or axial compression in linear members

(1) The bending failure is considered when one of the following

conditions is obtained (see Fig.XX.7):

• attainment of the maximum compressive strain in the FRC, ecu;

• attainment of the maximum tensile strain in the steel (if present), esu;

• attainment of the maximum tensile strain in the FRC, eFu.

M

Fue

sue

cue

Asl

cdf

Ftsf / F

Rd

NSd

cd·f

Ftuf / F

·xx

y

hardening softening

Bending of FRC structures

For FRC structures without the minimum reinforcement

du(wu) ≥ 20 dSLS

dpeak ≥ 5 dSLS

Du ultimate displacement

dpeak displacement at the maximum load

dSLS displacement at service load computed by performing a

linear elastic analysis with the assumptions of uncracked

condition and initial elastic Young’s modulus.

P

PU

UPEAKSLS

Displacement

SLSP

Load

MAX

P

crack formationP

CRPu > Pcr

or

Structural constraints to remove bars

Not Post-tensioned beams

30

30 30

30

R0

2 x

S0

3 x

Experimental programme

Post-tensioned beams

30

30

30

30

S1

3 x 3 x

30

30

P1

2 x 2 x

P2 30

30

Total: 15 beams (6 typologies)

M2

fck [MPa] 60

Cement CEM I 52.5R

[kg/m3]

400

Agg. < 12mm

[kg/m3]

569

Agg. < 8mm [kg/m3] 403

Agg. < 4mm [kg/m3] 676

Filler [kg/m3] 96

Plasticizer/cement 2.2%

Water /binder 0.39

F4

Df [mm] 0.8

Lf [mm] 60

Aspect ratio 75

Tensile Strength [Mpa] 1192

Type hooked

end

Class 4a

Fibre dispersion

Mechanical properties

Test modelling: uniaxial constitutive relationships

0 0.02 0.04 0.06

0

400

800

1200

1600

2000

[MPa]

e

steel

Model Code 90

a = 0.83

Test modelling: FE approach

S2C

Reliability of the model

Reliability of the models

peak

m =1

SLE

507.43.1/3.5

SLS

peak

d

d

0 30 60 90 120

d [ m m ]

0

100

200

300

400

P [ k N ]

R0B

S1C

S0A

R0

30

30

30

30

S1

Constraint check

Example: beam in FRC 300x300x3000 mm

MPa2.15.1/)f45.0(f k,1Rd,Fts

MPa13.05.1/)f2.0f5.0(f k,1Rk,3Rd,Ftu

02.0Fu e

mm5.2)l02.0;mm5.2min(w csu

kNm57.66

hhb)ff(

2

hhbfM FtudFtsdFtudRd

kN08,17KM2P RdRdu

Class 4a:

Rigid-plastic method

MPa44.0)5.1*3/()f(f k,3Rd,Fu Linear softening method

mm300lcs

0083.0300/5.2h/wuu

mm25.6)2/(1500 uu d

fR1k= 4 MPa; fR3k= 2 MPa

kNmh

bhfM FtudRd 62

kNm6.153.1*12K*2*MP RdRdu

k mf f ks

0

1

2

3

4

5

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

CTODm [mm]

No

min

al S

tre

ss

s

N [

MP

a]

Load vs. Central deflection

0

50

100

150

200

250

300

350

0 1 2 3 4 5 6

Central deflection [mm]

Lo

ad

[k

N]

Slab P22 50/0,75 Vf=0,38 %

Slab P21 50/0,75 Vf=0,38 %

Slab P20 50/0,75 Vf=0,38 %

di Prisco, M., Failla, C., Plizzari, G.A., Toniolo, G

(2004).

P = P (fm)

P = P (fk)

the key role of the scattering

the key role of the scattering

4.1max,

max,

k

m

m

k

f

f

P

PPRd = KRd P(fFd)

2 5

V V0

KRd = KRd (V/V0 , Pmax/Pcr) =

tests

CONCRETE RETAINING (cantilever) WALL

Surcharge

Load condition

35

SLS

SLU

d

d

%15.0: srebar

MC (2010) classification of SFRC:

Class “2b” - Vf = 25kg/m3

SLS

SLU

Material design values

Courtesy by Giovanni Plizzari

Models for members without shear reinforcement:

MC 90 and EC2 approach

Zsutty, T. C., 1968, Beam shear strength prediction by analysis

of existing data, ACI Journal, November 1968, Vol. 65, No. 11,

pp. 943-951

13

W

FtukRd,F 1 ck cp

c ctk

0 18100 1 7 5 0 15 [tensioni in MPa]

f.V k . f . b d

f

Shear resistance without shear

reinforcement

w = 1.5

MC 90 and EC2 approach

Prestressing (EC2)

Concrete strength

Reinforcement ratio

Size effect

Area of cross section

VR,c = C∙b∙d∙k∙1/3∙fck1/3+ Cp∙b∙d∙cp

21

Muttoni, A., 2003, : Introduction to SIA 262 code,

Documentation SIA, D 0182, Zürich, Switzerland, pp.

5–9.

Preliminary design, non

governing failure modes

Typical design

Assessment of critical existing

structures, design of special

cases

Multi level approach to shear

Models for members with shear reinforcement (girders):

compression strut strength

Brittleness

effect

Strain

effect 1f

303/1

ckcf

fck in MPa

Girders (crushing of compression struts)

Vecchio, F. J. and Collins, M. P., 1986, The

modified compression field theory for reinforced

concrete elements subjected to shear, ACI

Journal, 83, March-April, pp. 219-231

Strain

effect

ke

Sigrist V., 2011, Generalized Stress Field

Approach for Analysis of Beams in Shear, ACI

Structural Journal, V. 108 (4), pp. 479-487.

ke

Brittleness

effect

The levels-of-approximation approach:

shear in girders with transverse reinforcement

Level I

Level II

Level III

Level IV

(7.7-7))

(7.7-8))

1d16

32k75.0

g

dg

mm125.010002.0w

700029

45

xu

xmin

min

e

e

26

Shear resistance : validation

Verification at SLS

esh

Crack width limitations at SLS

31 ENGINEERING FRAMEWORK

Tunnel Boaring Machine – TBM -

Structural problems

Advancing direction

Hydraulic jack

Shield

Cutter head

Tunnel Ring

splitting

hydraulic

jacks

hydraulic

jacks

in-plane actions

(placing situation)

spalling

hydrauli

c jacks

Schnütgen 2000

- general assumptions and

strut and tie models

- diffusion effects associated

to local pressures

- validity limits of FRC ties in

Strut and Tie Models

D-REGIONS

Strut and tie model

D-regions for geometrical

discontinuities

Strut and tie model

D-regions for statical and/or

geometrical discontinuities

Strut and tie model

Strut and tie model

Strut and Tie model

Strut and tie model

Basic concepts

Strut and tie model

Strut and tie model

Superposition of two models

Strut and tie model

Strut and tie model

Minimum complementar energy with Su 0

Strut and tie model

Strut and tie model

Strut and tie model

By J. Schlaich and K. Schäfer, 1991: “Design and detailing of

structural concrete using strut and tie models

Strut and tie model

check lb

Strut and tie model

Strut and tie model

90

Courtesy by J. Walraven

The case of a deep beam

Strut and tie model

Engineering problem

Model Code ‘90 Approach

12

2

111

* 6.013.0 hbfb

bhbf ctcc

cc

yk

21

sxx

f

f

b6.0h

A

ccx2

2

11

*cc fb6.0

b

b1bf3.0

x

cc

cc

bb

bb

f

f

12

12

2

12

*

Materials

Plain concrete

(PC)

SFRC

Cement Type: CEM I 42.5 (300

Kg/m3)

Aggregates 8/16: 1035 kg/m3



w/c ratio: 0.6

Dmax aggregates : 16 mm

Super-plasticizer: 1%

Rcm=34.64 MPa

Fiber length (l): 60 mm

Fiber diameter (d): 0.8 mm

Aspect ratio (l/d): 75

Fiber content: 25 kg/m3

SFRC shape bottle strut

Mechanical characterization of SFRC

150

150

600

150 96 96150

1 221

Provini sui quali viene effettuata la prova di compressione

Provini sui quali viene effettuata la prova di trazione indiretta

Specimen for compression tests

Specimen for splitting tests

Test number Average value

MPa Standard dev.

MPa

Uniaxial compression tests (Rc)

Uniaxial compression tests

reduced friction (fc)

Splitting tests (fct,sp)

12

12

12

40.97

32.23

2.98

2.368

3.319

0.215

Uniaxial

compression tests

reduced friction (fc)

Splitting

tests (fct,sp)

Mechanical characterization of SFRC

a

P/2 P/2

CTOD

b

hN

0.6mm 2.4mmCTOD

N=b·hN

2

feq0.6-3

feq0-0.6

fIf

b = 150 mm

hN = 105 mm

a = 150 mm

fIf=4.30 MPa

feq0-0.6=3.45 MPa

feq0.6-3=3.31 MPa D0= feq0-0.6 / fIf =0.81

D1= feq0.6-3 / feq0-0.6 =0.97

Experimental set-up

a

b

b

t

b = 270 mm

t = 60 mm

=b/a

-250 -200 -150 -100 -50 0 50

x (N/mm2)

0

100

200

300

z (m

m)

b/c=1

b/c=1.5

b/c=2

b/c=2.5

b/c=3

30

13

5/1

60

30

27

0

LVDT

LVDT

LVDT

a

d d

4.0

60

dd

LV

DT

LV

DT

LV

DT

27

0

270

135

30 30

(a) (b)

dd

30

13

5/1

60

30

27

0

LVDT

LVDT

LVDT

a

d d

4.0

60

dd

LV

DT

LV

DT

LV

DT

27

0

270

135

30 30

(a) (b)

dd

1

1.5

2

2.5

3

Z

(mm)

Experimental tests

PC =b/a=1-1.5-2-3 SFRC =b/a=1-1.5-2-2.5-3

3 nominally identical tests

2 standard tests 1 moirè test

Front Front Rear Rear +

Test results

0 1 2 3

D [mm]

0

100

200

300

400

500

P [

KN

]

FRC1_media

PC1_media

0 0.5 1 1.5 2

D [mm]

0

100

200

300

400

P [K

N] FRC1.5_media

PC1.5_media

0 1 2 3

D [mm]

0

100

200

300

P [K

N]

FRC2_media

PC2_media

0 1 2 3

D [mm]

0

50

100

150

200

250

P [

KN

]

C3_ media

P3 _media

SFRC

PC = 1 = 1.5

= 2 = 3

P

d P

d

d

d

P

P

[kN, mm]

P

P

d

Crack Patterns

PC SFRC

=1

=2

=3

Test results - COD

0 0.4 0.8 1.2 1.6 2

0

0.4

0.8

1.2

1.6

top

middle

bottom

D [mm]

COD[mm] PC

= 1

0 0.4 0.8 1.2

0

1

2

3

top

middle

bottom

D [mm]

COD[mm]

PC

= 2

0 0.4 0.8 1.2

0

1

2

3

top

middle

bottom

D [mm]

COD[mm] PC

= 3

0 0.4 0.8 1.2 1.6 2

0

1

2

3

top

middle

bottom

D [mm]

COD[mm] SFRC

= 1

0 0.4 0.8 1.2 1.6 2

0

1

2

3

top

middle

bottom

D [mm]

COD[mm] SFRC

= 2

0 0.4 0.8 1.2 1.6 2

0

1

2

3

top

middle

bottom

D [mm]

COD[mm] SFRC

= 3

D

Concentrated pression

1 1.5 2 2.5 3

0

0.4

0.8

1.2

SFRC w=1.5mm

SFRC w=0.3mm

PC w=1.5mm

PC w=0.3mm

pa/fcm

1 1.5 2 2.5 3

0.4

0.8

1.2

SFRC load peak

SFRC first cracking

PC load peak

PC first cracking

pa/fcm

Pre-peak Post-peak

pa/fcm

Concentrated pression

1 1.5 2 2.5 3

0.4

0.8

1.2

1.6

Load peak

First cracking

w=1.5mm

Model Code

pa/peak(=1)

PC

1 1.5 2 2.5 3

0

0.4

0.8

1.2

1.6

2

Load peak

w=0.3mm

w=1.5mm

Model Code =3.42%

pa/peak(=1)

SFRCpa/ppeak (β=1)

no valley

Design prediction models

b/2

f Tt

a/4

a/2

b/4

b/2

b

pat/2

fcm

xx

T=As fy

fcm

pat/2

b

b/2

b/4

a/2

a/4pa*a*t/2 pa*a*t/2

Reinforced

concrete SFRC

fFtu

Design prediction (t=60mm)

1 1.5 2 2.5 3

0

0.4

0.8

1.2

1.6

2

1

1+1

exp SFRC w=1.5mm

SFRC design

pa/fcm

18

1+16

HPFRC

Fiber length (l): 13 mm

Fiber diameter (d): 0.16 mm

Aspect ratio (l/d): 80

Fiber content: 1.28% by volume

Component Conetnt

Cement Type I 52.5 600 kg/m3

Water 200 l/m3

Sand 0-2mm 983 kg/m3

Slag 500 kg/m3

Superplasticizer 33 l/m3

Fibres 100 kg/m3

Mechanical characterization of HPFRC

Uniaxial compression strength (fcc)

First cracking strength (fIf)

110 N/mm2

11.05 N/mm2

SLS residual strength (feq1) 14.09 N/mm2

ULS residual strength (feq2) 14.00 N/mm2

Italian Standard CNR DT 204

Experimental set-up

a

b

b

t

b = 270 mm

t = 60 mm

=b/a = 1 / 1.5 / 2 / 3

-250 -200 -150 -100 -50 0 50

x (N/mm2)

0

100

200

300

z (m

m)

b/c=1

b/c=1.5

b/c=2

b/c=2.5

b/c=3

30

13

5/1

60

30

27

0

LVDT

LVDT

LVDT

a

d d

4.0

60

dd

LV

DT

LV

DT

LV

DT

27

0

270

135

30 30

(a) (b)

dd

30

13

5/1

60

30

27

0

LVDT

LVDT

LVDT

a

d d

4.0

60

dd

LV

DT

LV

DT

LV

DT

27

0

270

135

30 30

(a) (b)

dd

1

1.5

2

2.5

3

Z

(mm)

3 Nominally identical tests

x (MPa)

Test results

= 1 P

P

d

Test results

= 1.5 P

P

d

Test results

= 2 P

P

d

Test results

= 3 P

P

d

Test results

P

P

d

Comparison with SFRC

b/a c,max/fc

NSC HSC UHSC UHPC-1-HT UHPC-2-HT

2.3 0.89 0.6 0.41 0.87 0.96

4.7 1.18 0.59 0.38 1.04 1.44

6.9 1.75 0.73 0.56 1.28 1.66

10.7 2.48 1.15 0.81 1.73 2.22

by T. Leutbecher, E. Fehling, 2012

Bottle shaped strut

Size effect

Stati tensionali diffusivi

2.3

0

1.5

0

0

0

15 0.07

1 1.3 0.1

e

sp

i bp

e

e

P

b e l

e

e k

h

a

a

a

1.2

1.0

Stati tensionali diffusivi

Basic anchorage length

Trasmission length

Design anch. length

Development length

Development length

1 2 2 1 1

1

1

2

2 /

bs sd

bs

bs bs bs bs

n n t n t

N Fz

N b l

bs bursting

Fsd = design force for each

tendon

1= 1.1 safety factor

(overstressing by

overpumping)

bpt2

bptbsbs

bsbs

ll6.0hl

hl

Bursting

(indirect anchorage)

(direct anchorage)

131

D-region stresses

132

Structural design for damage mechanisms

TBM MAX THRUST ACTION

MEAN COMPRESSION ON THE RING

LOCAL COMPRESSION UNDER THE JACK PLATE

BURSTING STRESS IN RADIAL AND CIRCUMFERENTIAL DIRECTION

Concrete check under compression:

c.m = 11.29 MPa < 42 MPa = fcd,sfrc

c = 33.26 MPa < 94 MPa = fcd,hpfrcc

c = 73.20 MPa < 94 MPa = fcd,hpfrcc

QuickTime™ e undecompressore

sono necessari per visualizzare quest'immagine.

cr = 1.77 MPa

ct = 1.16 MPa

fctk = 2.87 MPa

<

0

50

100

150

200

0 1 2 3 4 5 6 7 8 9 10

Displacement (mm)

Lo

ad

(kN

)

Type B

Type B

Type A

Type C

A

courtesy by Meda, 2012

PANAMA tunnel 133

134

Structural design for damage mechanisms

GASKETS

SHEAR-OFF OF THE MOUNTING GROOVE EDGES

Shear action:

Shear bearing capacity of unreinforced concrete:

Vsc 12.0 kN m1

Vsc 1.35 p 0.0085 m

Vrdct

fctk0.05

c

0.04 m

Vrdct 56kN m1

TENSILE SPLITTING STRESSES

Design max tensile splitting stress:

Tensile strength of un-reinforced concrete:

ct,d Zsd

0.5 0.8ds

ct,d 0.46 MPa

Rd ,ct fctk ,0.05

c

Rd,ct 1.39 MPa

<

lcg= 0.0085 m

il = 0.04 m

< Zsd = Design transverse tensile force

2.80

Selection of the Concrete Composition

(by R. Gettu et al. – BEFIB 2004)

Requirements

• 28-day characteristic compressive strength of at least 40 MPa.

• Early-age (4-6 hours) mean compressive strength of at least 25 MPa.

• 28-day mean equivalent flexural strength of at least 2.9 MPa.

Practical Considerations

• Adequate “placeability” with 30 kg/m3 of steel fibers.

• Maximum cement content of 400 kg/m3.

• Cement and aggregates should be those normally used in the

prefabrication plant.

135

Composition and Properties


Component kg/m3

Cement CEM I 52.5R 400

Sand 0/5 mm 745

Gravel 5/14 mm 558

Grava 12/22 mm 559

Water 132.2

Superplasticizer 4.8

Property Test result

Slump after 20 minutes from casting

3 cm

Density of fresh concrete 2430 kg/m3

28-day cylinder strength 62,8 MPa (±2,4%)

at 4+0,5 hours

18,7 MPa (±3,7%)

at 5+0,5 hours

25,0 MPa (±3,1%)

Compressive strength with accelerated curing

at 6+0,5 hours

28,2 MPa (±2,4%)

136

Selection of Fiber Type


Toughness Characterization

Belgian standard was

chosen for determining the

equivalent flexural strength

(deflection limit of 1.5 mm).

• Toughness evaluated with

different fibers.

• Fibers had lengths of 50-60

mm and diameters of 0.75-

1.0 mm.

0 1 2 3 4

Flecha (mm)

0

10

20

30

40

50

Carga (

kN

)

Dramix 80/60

Dramix 65/60

Wirand 1.0/50

Novocon 1060

Duoloc 47×1.0

Tests with 45 kg/m3 of fibres

Midspan deflection (mm)

Load (

kN

)

137

Evaluation of Possible Use of Fibers

as the only reinforcement (by R. Gettu et al. 2004)

• More than 3 km of tunnel lining has been constructed with rebar + fibre reinforcement. • Is the total substitution of bar reinforcement with fibers cost-effective, in this project? • Yes, if the required performance can be obtained with a dosage of about 60 kg/m3. Duration of study ≤ 4 months

138

Performance of the Tunnel Lining


Requirements

• Adequate flexural strength during demolding and

storage in order to avoid cracking.

• Resistance against cracking or crushing due to the

reactions of the actuators of the tunnelling machine

during the boring operation.

• Ability to resist the soil pressure during service.

139

Tunnel Lining of Section 4


Numerical Analysis: Level of stresses

High tensile stresses can occur when the supports are eccentric during storage by piling.

Posibles eccentricidades respecto el eje de apoyoPossible eccentricities between supports

140

Eccentricities in the reaction of the actuators of the tunelling machine, especially in the radial direction, can generate high localized tensile

stresses.




141

The low tensile stresses obtained in the analyses motivated further study of the possibility of using steel fibres as the only reinforcement of the concrete in the segments.




During service, the soil pressure can generate compressive stresses of up to 17 MPa. The maximum values of tensile stress are less than 1 MPa.

142



Material

Characterization

• Comparison of the

performance of

different fibres.

• Evaluation of

reference

compressive and

flexural strengths,

and toughness.

• Accelerated curing

was simulated in a

environmental

chamber.

0 0.25 0.5 0.75 1 1.25 1.5

Flecha (mm)

0

10

20

30

40

Ca

rga

(k

N)

Dramix 80/60 BN

Dramix 65/60 BN

Wirand 50x1 mm

Novocon HE 1060

Duoloc 47×1.0

Dramix 80/60

Dramix 65/60

WirandDuoloc Novocon

Deflection (mm)

Loa

d (

kN

)

143



Material

Characterization

• Comparison of the

performance of

different fibres.

• Evaluation of

reference

compressive and

flexural strengths,

and toughness.

• Accelerated curing

was simulated in a

environmental

chamber.

0 0.5 1 1.5 2 2.5 3

Flecha (mm)

0

20

40

60

Ca

rga

(k

N)

60 kg/m3

45 kg/m3

30 kg/m3

Deflection (mm)

Loa

d (

kN

)

144



Real-Scale Structural Testing: Stacking

No cracking occurs in the SFRC segments when the eccentricity of the supports is equal to or less than 50 cm, even when all the segments of a ring are piled at the age of 4 days.

145



Real-Scale Structural Testing:

Flexure

146



Real-Scale Structural Testing: Flexure

For small crack openings (less than 0.2 mm), the segment with 60 kg/m3 of fibres has similar load-carrying capacity as the segment with conventional rebars.

147



Real-Scale Structural Testing: Flexure

For small crack openings (less than 0.2 mm), the segment with 60 kg/m3 of fibres has similar load-carrying capacity as the segment with conventional rebars.

Tensile displacement or crack opening (mm)

Load (

kN

)

Load (

kN

)

Tensile displacement or crack opening (mm)

148



Real-Scale Structural Testing: In-Plane Compression

Some local cracking appears. The behaviour is similar for the SFRC and reference panels.

LVDT cara

encofrada

LVDT cara

regleada

LVDT lateral 1

LVDT lateral 2

Plato de carga (excéntrica) 540 x 120 x 10 mm

Plato de carga continuo 540 x 180 x 10 mm

149



Real-Scale Structural Testing: Contact at Joints

Splitting cracks occur at high loads. Slightly more cracking is seen in SFRC specimens.

150



Quality Assurance Requirements:

• Fibre quality (dimensions, hooks, tensile strength and elastic

modulus, surface quality)

• Batching and Mixing (homogeneity, slump/workability)

• Fibre content in fresh concrete

• Toughness requirement of SFRC

• Placing should not affect the homogeneity of the concrete

• Vibration should be regulated to avoid preferential orientation and

segregation of fibers

151



Quality Check of Cast Segment

4 cores extracted perpendicular to the curved surface (radial direction) and

4 cores extracted from the flat edges, one from the middle of each side

Radial core

Core extracted from flat face

10 cm 20 c

m

To check preferential

orientation:

Fibre count made on

halved core. Differences

should not be more than

10% of the lower value. To check segregation:

Cores are crushed, fibres

are separated and

weighed. The fibre

content should not vary

by more than 5% from

the specified value.

152

Tunnel Segments: Non Linear Analyses, Fiber FF1-45

0

5000

10000

15000

20000

25000

0 0,5 1 1,5 2 2,5 3 3,5

Displacement [mm]

Lo

ad

[kN

]

Service Load

Max.

Load

Service Load =3000x4=12000 kN Segment is already cracked

Splitting cracks in radial and tangential direction in the loaded zones

Barcelona Metro: further structural analyses

(by Plizzari et al. Università di Brescia, 2005) 153

Staffe 8/200 mm

Aree di carico

dei martinetti

4 Staffe sotto

le zone di carico

31

5

4

Sezione longitudinale

23

4

Sezione trasversale

50Pilastrino

10 14

450

100 100

500

35

0

Original Design

Proposal

Vantages: 1) smaller encumbrance

2) simpler construction

3) simpler casting

Barcelona Metro: further structural analyses (by

Plizzari et al. Università di Brescia, 2005) 154

0

1

2

3

4

5

6

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

CMOD [mm]

No

min

al

str

ess [

MP

a]

CM

OD

1

CM

OD

2

CM

OD

3

CM

OD

4

fR1fR2

fR3

fR4

Type A

Type C

Type B

PANAMA tunnel


155

0

50

100

150

200

250

-1000 0 1000 2000 3000 4000 5000 6000 7000 8000

N [kN]

M [

kN

m]

Serviceability conditions


PANAMA tunnel 156

0

50

100

150

200

0 1 2 3 4 5 6 7 8 9 10

Displacement (mm)

Lo

ad

(kN

)

Type B

Type B

Type A

Type C

A


PANAMA tunnel 157

Lecture 06 - Di Prisco

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Transcript of Lecture 06 - Di Prisco