Lecture 01 - Di Prisco

8/17/2019 Lecture 01 - Di Prisco

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DESIGN OF ENVIRONMENTAL AND PROTECTIVE

STRUCTURES

Prof. Marco di PriscoDepartment of Civil and Environmental Engineering,

Politecnico di Milano

Master Course in

Civil Engineering for Risk Mitigation

Academic year 2014-2015


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Constitutive and design laws of steel , concrete, fibre

reinforced concrete employed in steel, reinforced -

prestressed concrete structures (4h)


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13 October 2014 3

Model Code: design for

sustainabilityConcrete’s Level I Method

Comparison of green house gas emission:

material substitution: BREAM (UK), HQE

(France), LEED (USA), CASBEE (Japan), GreenStar (Netherlands)

Level II Method

Environmental Impact Calculation (EIC):

- Measure of Embodied Energy

- Measure of CO2- Calculation of Global Warming Potential

(GWP)

-Level III Method

Full life cycle assessment (LCA), including

durability and maintenance considerations, recyle

and reuse


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13 October 2014 4

EIC: Environmental Impact

Calculation

- CO2 Emission

- EE = Embodied Energy

Energy consumed in the production of Portland Cement is estimated to be 4.88

MJ/kg and the total energy in the production of steel 23.7 MJ/kg

(Struble and Godfrey (2004)

- GWP = Global Warning PotentialContribution of CO2 on global warming, calculated through the equivalence of the

effect of greenhouse gas (Elrod, 1999):for simplicity:

100 – year GWP = CO2 + 298 Nox + 25CH4

Courtesy Joost Walraven


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by fib Bulletin 67


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STEEL


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von Mises - Huber yield criterion


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STEEL FOR METALLIC STRUCTURES

For design, the following nominal values can be adopted for the material properties:

Elastic modulus

Transverse elasticity modulus

Poisson ratio

Thermal expansion coifficient

(T< 100°C)

density

Steels for flat and hot-rolled long products

The possible supply conditions are related to the manufacturing process used:

crude steel rolling "as rolled“

steel rolling normalized

steel thermomechanical rolling

steel with improved atmospheric corrosion resistance (ex Corten)

steel with high tensile strength reclaimed "Quench and tempered"


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Nominal thickness of the elementSteel standards

Hot rolled with open cross section profiles


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Hot rolled with hollow section profiles

Nominal thickness of the elementSteel standards


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P

δδy δu

µδ = δu / δy

Homogeneous

steel bar (Φ)

δ

P

σσσσ

εεεεεuεy

µε = εu / εy


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P

δ

Steel bar

δ

P

δy δu

µ = δu / δy

defect

σσσσ

εεεεεuεy

µε = εu / εy


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Steel for High Bond bars

s

sd yd

E

f =ε

L

susd ε ε


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B450C

Characteristic yielding strength

Characteristic failure strength

Characteristics Requirementsfractile

Max. elongation

Mandrel diameter for bend tests at 90° and

subsequent straightening without cracks


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B450A

Characteristics Requirements

fractile

Characteristic yielding strength

Characteristic failure strength

Max. elongation

Mandrel diameter for bend tests at 90° and

subsequent straightening without cracks


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Limits of acceptability

Nominal diameter

Tolerance % on cross section

admitted for the use

characteristic Limit value

for steel

minimum

maximum

minimum

minimumfailure/yielding

failure/yielding

bending / straightening lack of cracks for all


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(*)

(*) after the 90 ° bend keeps the bar for 30 minutes in boiling water and proceeding, after cooling in air,to the partial straightening for at least 20 °. After the test the specimen shall not exhibit cracks.

In Model Code 2010 :

duttilità mediante prova di piegamento

mandrino

Φ!mm" #eB$%k #eB&&k

≤ 12

12'1%

1%'2(

2( ' $0

$Φ

)Φ

%Φ

10Φ

&Φ

%Φ

10Φ

12Φ

*iegamento a 1%0+

*iegamento e raddri,,amento

a -0+ a./20+±(+

ductility measure by bending test

bending and straightening

mandrel

Bending at 180°


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steel in bars steel in roll

load load

displacement displacement


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CEB MC’90


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Prestressing steel

D.M. 2008 εuk ≥ 3.5% (MC90)

Control in plant

sn ≤ 0.03 f ptk e sn ≤ 0.04 f p..k

Control on site

at failure (f pt) gmn ≥ 1.03 f ptk ; sn ≤ 0.05 f ptk

at serv.ice (f py f p(0.2) f p1) gmn ≥ 1.04 f p..k ; sn ≤ 0.07 f p..k

Ep = 195 - 205 MPa


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REINFORCEDCONCRETE


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The uniaxial compression test

UNI EN12390-1

UNI EN12390-3:

• planarity error< 0.0006d mm

• size tolerance < ± 0.5%• tolerance shaven face and opposite < 1%d

• perpendicularity corners < 0.5mm

• tests at 24,72h;7,14,28,90,180,365d

• (tests for at least 48h in room at 20 ± 2 °C eRH 95% until 2h before)

• 0.2 < dσ /dt < 1MPa/s

max-. aggregate size (mm)

specimen side (mm)


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Cubic compression test


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YES

NO


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Resistance classes for normal concrete


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Conversion factors of compressive strengths for cubes

Conversion factors of compressive strengths for cylinders

For different slenderness h/d

Strength indexes

and cylinders


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Conversion factors for compressive strengths

measured on cubes of different sizes

Conversion factors for compressive strengths

measured on cylinders of different sizes and equal

slenderness h/d = 2.00

side

slenderness h/d

Proposed

index

Proposed

Index h/d


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Sargin urve

1

2

11

1

)2(1

)(

)(

1,1

c

cccc

c

k

k

f

fc

E k

ε

ε

ε ε

ε ε

ε σ

ε

−+

−⋅−=

−

⋅⋅=

y ax bx cx d

CC

x y

x y E

x y fc

x y

fc E fc E E

c

c

c

c c c c

= + + +

= =

= =

= =

= =

= + + −

− +

3 2

1

1

1

3

1

2

3

1

2

1

2

0 0

0

0

2 3 2

:'

'

( ) ( ) ( )

ε

ε

σ ε ε ε

ε ε ε

ε ε

Saen, urve

l d l f C


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niaial onstitutive model for Conrete

ε

σ

εcu1.5‰

ε

σ

εcu0.7‰

ε

σ

f c1

εcuεc1

arc

tg(1000f cd)

εc1=.002εcu=.0035f c1 = 0.85 f cd =

0.85f ck / γ c

Stress-strain relation for short-term loading – compression -


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Parameters of the strain relation:

( )

2

1 2

c

c

k

f k

σ η η

η

⋅ −= −

+ − ⋅ c c ,lim

ε ε <

1

cε η ε

=

with:

Stress-strain relation for short-term loading – compression -

MC2010

Bilinear stress-crack opening relation for short-term loading


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Bilinear stress crack opening relation for short term loading

1

1 0 80

= ⋅ − ⋅ ct ctm

w f .

wσ

1

0 25 0 05

= ⋅ − ⋅

ct ctm

w f . .

wσ

1 for w w≤

1 c for w w w< ≤

1

1 0 85

= ⋅ − ⋅

ct ctm

w f .

wσ

( )1

0 15= −

−ctm

ct c

c

. f w w

w wσ

1 for w w≤

1 c for w w w< ≤

= F c F

ctm

Gw

f α

1 2 0 15= −

F

cctm

G

w . w f ( )=

F max

f d α

Dependency on maximum aggregate size is not

significant

5= ⋅

F

cctm

G

w f 1 =

F

ctm

G

w f

MC 2010MC 90


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Kupfer et al.

1969

Biaxial failure domain for concrete

Strength under multiaxial states of stress


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g

no continuous transition

between triaxial and

biaxial states of stress

triaxial criteria does not

exactly describe the

uniaxial compressive

strength

Inconsistencies in MC 90:

New in MC 2010:

One failure

criteria for all

states of stress-1,6

-1,4

-1,2

-1,0

-0,8

-0,6

-0,4

-0,2

0,0

0,2

-1,6 -1,4 -1,2 -1,0 -0,8 -0,6 -0,4 -0,2 0,0 0,2

MC 90

C12

C20

C30

C40

C50C60

C70

C80

C90

C100

C110

C120

σ 2 f /f cm

σ 3 f /f cm

σ 3 f /f cm

σ 2 f /f cm

σ 1 f /f cm

σ 1 f /f cm

σ 1 f /f cm

σ 3 f /f cm

with f cm > 0 and

f cm = f ck + 8 N/mm²

triaxial criteria forbiaxial states of stress


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Nelissen, 1972

σ2 J2J33


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θθ = 60

θ = 0

modello a 5 parametri (Willam-Warnke,1975)

σ1

σ3

σ2P(σ1,σ2,σ3)

asse idrostatiooct3τ

oct3σ

( ) ( ) ( )[ ]2132

32

2

212oct

9

1J

3

2σ−σ+σ−σ+σ−σ==τ

σ+σ+σ==σ

3I

3

1 3211oct

rξ 2321

3

oct

3

2 / 3

2

3

J322cos

J2

J

J

2

333cos

σ−σ−σ=θ

τ==θ


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#I*3C4B

Bull5206

7oal strength


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Conr5

7oal strength

steel

ck ck

cd

ck 1

0

ck

cd

f

40

3

5.12

f

f

40

A

A

3

7.0

f

=σ

=σ

splittingA0 /A1≤ 320

A0 /A1≥ 320spalling

σu /f

c

γ m

splitting

spalling


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oppure

• In columns with steel liners [O.3274; 11.3.4.2] or in the main

columns [EC8; 5.4.3.2.2. (7)] the action of confinement onconcrete can be considered:


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8hih strength9


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Material strength potential strength / ompressive strength of onretefrom ubes or ;linders made and matured in thelaborator; aording to standard onditions !


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>ualit; variation due to: omponent materials

related mi design

environment onditions !thermo'higrometrial"

oasional ad?ustements !plant manteinane"

ast eeution !ompation= uring"

normal !or @aussian" log'normal


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5% 5%

x

0.05

0.95F(x)

f(x)

x1

x'k

k's k''s

x''k

0.50

x0

5% 5%

x

0.05

0.50

0.95F(x)

f(x)

x = x01x'k

ks ks

x''k

f (x) = 2

2

2s

)x-(x-

esπ 2

1

'kx = x – ks per F('kx ) = 0,05

"kx = x – ks per F("kx ) = 0.95

con k = 1,645 .

! " g

'kx = x – k's per F(

'kx ) = 0,05

"kx = x + k''s per F(

"kx ) = 0,95

δ = 0,05 k' = 1,578 k'' = 1,713 δ = 0,10 k' = 1,513 k'' = 1,783 δ = 0,15 k' = 1,450 k'' = 1,854

( )2s2

2

ex2

1)x(f

ξ−ξ−

σπ=

( )( )2f

xln

ξ−ξξ=σ

=ξ

∫

Aeliabilit; inde


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x

f(x)MODELLOANALITIC

xx'k

k's

MODELLO

AFFIDABILE

CODA DA

TRONCARE

VALORI

IMPOSSIBILI

SENZA SIGNIFICATO

FISICO

RANGO DEI VALORI POSSIBILI

βs

x'0

PROBABILITA'

FORMALE

Aeliabilit; inde

c1 =c

c

δ β

δ

β -1

k'-1

s-x

sk'-x

x

x

'

0

'

k ==

CONTROLLO DELLA PRODUZIONE CO NTINUA TIVA DEL CALCESTRUZZO (MOD. UNI 10025/98)


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CLASSE C55 MISCELA R2 LINEA:Planar STABILIMENTO: Larco Astori - Carvico (BG)

CEMENTO: TIPO I 52.5 R DOSE: 400 kg A/C = 0.45 SUPERFL. 3% INERTI ≤ 15 mm

MATURAZIONE: Forzata a vapore β = 0,08 anno : 97 mese : novembre

Data Data RESISTENZE PROVA UNIFORMAZ. VALORI VALORI LOTTO MOBILE (21gg)

Prelievo Prova R1 R2 fj= 0.83Rm ETA' g fj/f f n f m s f k

1

2

3 01.12 75,9 76,5 63,2 28 1 63,2 17 64,1 1,74 61,5

4 02.12 78,9 79,2 65,6 28 1 65,6 17 64,2 1,78 61,6

5 03.12 79,2 78,4 65,4 28 1 65,4 17 64,3 1,79 61,7

6 04.12 77,6 79,1 65,0 28 1 65,0 17 64,4 1,79 61,7

7 05.12 81,3 79,3 66,6 28 1 66,6 17 64,6 1,86 61,8

8 06.12 80,2 81,3 67,0 28 1 67,0 17 64,9 1,89 62,1

9

10 09.12 77,1 78,8 64,7 29 1,001 64,6 17 65,0 1,87 62,2

11 09.12 80,2 78,2 65,7 28 1 65,7 17 65,2 1,83 62,5

12 10.12 79,2 77,6 65,1 28 1 65,1 17 65,1 1,75 62,6

13 11.12 80,2 80,4 66,6 28 1 66,6 17 65,2 1,77 62,6

14 12.12 81,2 80,4 67,1 28 1 67,1 17 65,4 1,80 62,7


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PRESTRESSED

CONCRETE

Prestressed concrete


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constRHconstT ==compatibility

ε


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)(

const RH ,const T

cr ,csh ,crel , p0 pel , pel ,c

rel , p0 pel , pcr ,csh ,cel ,c

0 p pc

ε ε ε ε ε ε

ε ε ε ε ε ε

ε ε ε

−−−−=

+−=−−

−=

i

red

p

c

red

p

red

p p p pcc

i

lossi p p pelc p p

c

ccc

i

lossi pelc p pelccc

el p p pelccc

p

A

pc

A

c

A

N N

N N N A A A

N A E A E E

E A

N A E A E N A E A E

N dAdA

pc

+−=

+−=+−=+

+−−=+

=−++=+

=+

∑

∑

∫∫

0

00

,0,

,0,,

,,

)(

)(

)(

σ

σ α σ

ε ε ε σ

ε ε ε ε ε ε

σ σ

equilibrium

εP

εP0

εc


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Fibre Reinforced Concrete


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Equivalent

diameter

[mm]

Minimum tensile strength

[N/mm2]

Alternated

bending test

R1 R2 R3 All theclass1) 2) 1) 2) 1) 2)

Rm Rp0,2 Rm Rp0,2 Rm Rp0,2 Rm Rp0,2 Rm Rp0,2 Rm Rp0,2 Not failure

0.15≤ d f <

0.50

400 320 480 400 800 720 1080 900 1700 1360 2040 1700

0.50≤ d f <

0.80

350 280 450 350 800 640 1040 800 1550 1240 2015 1550

0.80≤ d f ≤

1.20

300 240 390 300 700 560 910 700 1400 1120 1820 1400

1) For straight fibres

2) For shaped fibres

Table 2-1 – Resistance classes for steel fibres.


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CNR DT 204

30 mm


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1 4 0 °

30 mm.

2 . 0 m m

2.0 mm.

l / df = 48

0 , 6

2

fiber ontent (0kg3m$

F

lb= βl ≅ l/4

τα=τππ

α=τπ=f

f f bf 2

f

f bf

dlVld

dV4ldNF

F = Fy lf =lcr

5.0zoom w = 0.20 mm

TRA0 med


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0.00 0.10 0.20displacement w (mm)

0.0

1.0

2.0

3.0

4.0

a v e r a g e t e n s i o n σ t

( M P a

)

TRA4 med

TRA8 med

0.00 2.50 5.00deflection f (mm)

0.0

4.0

8.0

12.0

l o a d P

( K N )

zoomw = 5.00 mm

FLE0 med

FLE4 med

FLE8 med

60

Redundant structure behaviour


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P

[kN]

0 5 1 0

60

440

60

30

0

w [mm]

P

w

by di Prisco & Felicetti, 1997

Vf = 0.8 [%]

Vf = 0 [%]

Redundant structure behaviour


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0 5 10 15 20

displacement wt (mm)

0

10

20

30

40

load(kN)

sandrubber

0.4%

Vf = 0.8%

0.4%

0.8%

plain concrete

Pusplain

23.4 kN

by di Prisco & Felicetti, 2004


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P

P P

PPcr crP

crack formationcrack

crack formation

localization

Softening material Hardening material

δu


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Behavior in compression Behavior in compression Behavior in compression Behavior in compression


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EN 14651

Reference testReference testReference testReference test


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2

sp

j

,

2

3

hb

lF f j R =

hsp = 125 mm

b = 150 mm

S.L.E.

f R,1

f R,3

S.L.U.

Which difference with plain concrete ?Which difference with plain concrete ?Which difference with plain concrete ?Which difference with plain concrete ?


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slump flow diameter: 690 mm

T50 2 seccement 425: 472 kg fine sand 0/4 850kg

d 4/8 886 k


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ClassificationClassificationClassificationClassification

T50 2 sec

V-funnel time (0 min) 3.5 secV-funnel time (5 min) 4 sec

L-box (standard) h2/h1 = 1

fly ash: 45 kg

water 200 l (w/b =0.39)superplast. 1.3%

coarse sand 4/8 886 kg

hooked-end fibres 65/35 50 kg

4,33

4,47

3,77

σNf

Performance based designPerformance based designPerformance based designPerformance based design


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(5) Fibre reinforcement can substitute (also partially)conventional reinforcement at ultimate limit state if the

following relationships are fulfilled:

f R1k /f Lk > 0.4 Eq. 5.X2

f R3k /f R1k > 0.5 Eq. 5.X3

CMOD (mm)

f LK

0.5 2.50

f R1k f R3k

f gf gf gf g

Which models?Which models?Which models?Which models?


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f Ftu = f R3 /30)2.05.0( 13

3

≥+−−= R RFtsu

FtsFtu f f f CMOD

w f f

145.0 RFts f f =

σ σ

FromFromFromFrom σσσσ----w tow tow tow to σσσσ----εεεε 17/32


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ε = w / lcs σ

ε ε Fu ε ε Fu

f Fts

σ

incrudente

degradante

rigido-plastico f Ftu

f Ftu

f Ftu

f Ftu

Elastic-linear Rigid-plastic

wu

σ hardening

softening

w

f Fts

f Ftu

f Ftu

w

rigid-plastic f Ftu

f Ftu

wu

The characteristic structural lengthThe characteristic structural lengthThe characteristic structural lengthThe characteristic structural length

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lcs = min{srm, y},

srm is the average crack spacing

In sections without traditional reinforcement under

bending or under combined tensile – flexural andcompressive – flexural forces with resulting force external to

the section, y = h is assumed. The same assumption can be

taken for slabs.

Influenza orientamento fibre (by Ferrara et al. 2008)

Orientation factorOrientation factorOrientation factorOrientation factor

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b e a m .

1

b e a m .

2

b e a m .

$

50mm

150 mm150 mm150 mm 500 mm

beam 7$

beam 72

beam 71 1 5 0 m

m

1 5 0 m m

1 5 0 m m 5 0

m m

castingdirection

supposed flow lines

0 2 & ) % 10

CB !mm"

0

2000

&000

)000

%000

10000

l o a d ! < "

beam 7$

beam 71

beam 72

beam .2

beam .1

beam .$

Orientation factor Orientation factor Orientation factor Orientation factor

by Ferrara et al., 2009

23/32


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5.6.7 Orientation factor

f Ftsd,mod=⋅f Ftsd / K f Ftud,mod=⋅f Ftud / K

Isotropic fibre distribution is assumed K = 1.0For favourable effects K < 1.0

For unfavourable effects K > 1.0

Special tests can be used to determine the effect of fibre

orientation due to casting and compaction in real structuralelements, by using structural specimens which better

reproduce the material in the structural elements.

Lecture 01 - Di Prisco

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Transcript of Lecture 01 - Di Prisco