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Reinforcement optimization
for structural FRC elements
University of Brescia (Italy),
Department of Civil Engineering,
Architecture, Environment, Land
and of Mathematics (DICATAM)
Giovanni Plizzari
Madrid – October 13th, 2016
Reinforcement optimization for structural FRC elements 2/72Madrid, October 13th, 2016
G. Plizzari
fib Model Code 2010
Reinforcement optimization for structural FRC elements 3/72Madrid, October 13th, 2016
G. Plizzari
Place the best performing reinforcement
(fibers and/or rebars) where required by
tensile stresses in the structural elements
Optimized reinforcement: definition
Reinforcement optimization for structural FRC elements 4/72Madrid, October 13th, 2016
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
Reinforcement optimization for structural FRC elements 5/72Madrid, October 13th, 2016
G. Plizzari
FRC and degree of redundancy of structures
1- Structural elements with low degree of redundancy
Fibers can not generally replace the main flexural reinforcement but they can used to substitute the secondary reinforcement or the shear reinforcement
Conventional reinforcement
Example: Box culverts
Optimized reinforcement
Reinforcement optimization for structural FRC elements 6/72Madrid, October 13th, 2016
G. Plizzari
1- Structural elements with low degree of redundancy
Fibers can not generally replace the main flexural reinforcement but they can used to substitute the shear reinforcement
Example: Linear elements (beams)
RC spandrel
wide-shallow
beam
Lightweight ribbed
one-way reinforced
concrete slab
RC central
wide-shallow
beam
Topping concrete layerTypical Concrete Floor used in
Southern Europe
Conventional Reinforcement for Wide Shallow Beams
Floor section
Wide Shallow Beams with Optimized Reinforcement
FRC (Vf=25kg/m3)
FRC and degree of redundancy of structures
Reinforcement optimization for structural FRC elements 7/72Madrid, October 13th, 2016
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).
Reinforcement optimization for structural FRC elements 8/72Madrid, October 13th, 2016
G. Plizzari
W750 PC
Wide Shallow Beams with b=750 mm
W750 FRC25
Reinforcement optimization for structural FRC elements 9/72Madrid, October 13th, 2016
G. Plizzari
W1000 MSR
Wide Shallow Beams with b=1000 mm
W1000 FRC35
Reinforcement optimization for structural FRC elements 10/72Madrid, October 13th, 2016
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
Reinforcement optimization for structural FRC elements 11/72Madrid, October 13th, 2016
G. Plizzari
Example of Application for Shear
13
, 1
0.18(100 ) 0.15 49
WRd ct ck CP
c
V k f b d kN
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
Minimum Shear Reinforcement:
Reinforcement optimization for structural FRC elements 12/72Madrid, October 13th, 2016
G. Plizzari
Example of Application for Shear
dbff
fkV
WCPck
ctk
uFtk
c
FRd
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/f =67 and fFtk,u=0.90 MPa (tested at the
University of Brescia)
Minimum shear reinforcement
OK
Design Shear Reinforcement
Reinforcement optimization for structural FRC elements 13/72Madrid, October 13th, 2016
G. Plizzari
Example of optimized shear reinforcement
2Ø8@300mm 2Ø6@300mm
2Ø6@300mm
Plain concrete
FRC
Reinforcement optimization for structural FRC elements 14/72Madrid, October 13th, 2016
G. Plizzari
Salò, 15-16 October, 2010
Reinforcement optimization for structural FRC elements 15/72Madrid, October 13th, 2016
G. Plizzari
2- Structural elements with a high degree of redundancy
Fibers can partially replace the main flexural reinforcement. Conventional rebars are placed only in the areas of the structures with subjected to localized stresses.
Example: Elevated slabs Slab with Optimized Reinforcement
Loading set-up
FRC (Vf=30kg/m3)Localized
reinforcement
FRC and degree of redundancy of structures
Aim of the optimization: to find a best combination between rebar contend and FRC toughness (volume fraction of FRC)
Reinforcement optimization for structural FRC elements 16/72Madrid, October 13th, 2016
G. Plizzari
FRC slabs
Reinforcement optimization for structural FRC elements 17/72Madrid, October 13th, 2016
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
Reinforcement optimization for structural FRC elements 18/72Madrid, October 13th, 2016
G. Plizzari
Slab on grade: stresses along the borders
Slabs on grade can be made with FRC without conventional reinforcement. However, some areas of the structures can be subjected to high local stresses (borders, corners)
and thus fibers could not be enough.
High stresses due to concentrated loads
along the slab border
Reinforcement optimization for structural FRC elements 19/72Madrid, October 13th, 2016
G. Plizzari
Slab on grade: cracking at SLS
The optimized reinforcement may consist in a combination of fibers and conventional reinforcement placed only along the borders.
FRC
Conventional
reinforcement
(wire mesh)
Reinforcement optimization for structural FRC elements 20/72Madrid, October 13th, 2016
G. Plizzari
Case study
Geometry
Elevated slab made with Steel Fiber Reinforced Concrete
Loads
1. Dead weight (G1)
2. Overload (Q)Overload (Q)
Reinforcement optimization for structural FRC elements 21/72Madrid, October 13th, 2016
G. Plizzari
Reinforcement optimization
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
Reinforcement optimization for structural FRC elements 22/72Madrid, October 13th, 2016
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
Reinforcement optimization for structural FRC elements 23/72Madrid, October 13th, 2016
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
Reinforcement optimization for structural FRC elements 24/72Madrid, October 13th, 2016
G. Plizzari
Parametric study
Mechanical properties according MC2010
Compression properties of SFRC
fck=30MPafck
Tensile properties of conventional reinforcement
t
et
[MPa]
617519
13%210GPa
Reinforcement optimization for structural FRC elements 25/72Madrid, October 13th, 2016
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
Reinforcement optimization for structural FRC elements 26/72Madrid, October 13th, 2016
G. Plizzari
Results of the parametric study
Summary of the analysis program
Diagonal reinforcement ratio (d)
Longitudinal reinforcement ratio (l)
As
B d = ·100
B=400mm ; d=170mm
Reinforcement optimization for structural FRC elements 27/72Madrid, October 13th, 2016
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 = 50kg/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
Results of the parametric study
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
Reinforcement optimization for structural FRC elements 28/72Madrid, October 13th, 2016
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]
Fiber Content = 30kg/m^3
Fiber Content = 50kg/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
Results of the parametric study
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.
Reinforcement optimization for structural FRC elements 29/72Madrid, October 13th, 2016
G. Plizzari
Results of the parametric study
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]
Fiber Content = 30kg/m^3
Fiber Content = 50kg/m^3
Fiber Content =70kg/m^3
Qmax,1 Qmax,2
Optimal reinforcement
for the load level Qmax,1
Optimal reinforcement
for the load level Qmax,2
Reinforcement optimization for structural FRC elements 30/72Madrid, October 13th, 2016
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).
Reinforcement optimization for structural FRC elements 31/72Madrid, October 13th, 2016
G. Plizzari
Tunnel linings
Reinforcement optimization for structural FRC elements 32/72Madrid, October 13th, 2016
G. Plizzari
Segmental lining
Reinforcement optimization for structural FRC elements 33/72Madrid, October 13th, 2016
G. Plizzari
Design features in tunnel segments
Modelling the loading/boundary conditions generally adopted by designers
Ring joint
Longitudinal joint
Bearing pad
Ring joint
Longitudinal joint
Bearing pad
Modelling the loading/boundary conditions representing possible
irregularities
Irregular supportsOuter/Inner eccentricities
Eccentricity
Inside tunnel
Outside tunnel Outside tunnel
Inside tunnel
Outside tunnel
Inside tunnel
Eccentricity inside Eccentricity
outside
Design of an optimized reinforcement
50/1,0-Vf=0,57%45 kg/m3
50/0,75-Vf=0,32%25 kg/m3 RC97 kg/m3
350mm
350mm
2 chords
Stiirups6@200mm
14 =0,22%
350mm
350mm
2 chords
Stiirups6@200mm
14 =0,22%
RCO+50/0,75-Vf=0,32%71 kg/m3
RC+50/0,75-Vf=0,32%122 kg/m3
Reinforcement optimization for structural FRC elements 34/72Madrid, October 13th, 2016
G. Plizzari
Thrust jack actions
Spalling cracks
Splitting cracks
Relative displacement in the region between the thrust jacks [mm]
0
5
10
15
20
25
30
35
0,00 0,50 1,00 1,50 2,00 2,50
Normal loading condition
To
tal
Lo
ad
[M
N]
0
0,5
1
1,5
2
2,5
3
Lo
ad
/Se
rvic
e l
oa
d [
-]
50/1,0 - Vf=0,57%
50/0,75 - Vf=0,32%
RC
RC + 50/0,75 - Vf=0,32%
RCO + 50/0,75 - Vf=0,32%
Relative displacement in the region between the thrust jacks [mm]
0
5
10
15
20
25
30
35
0,00 0,50 1,00 1,50 2,00 2,50
Normal loading condition
To
tal
Lo
ad
[M
N]
0
0,5
1
1,5
2
2,5
3
Lo
ad
/Se
rvic
e l
oa
d [
-]
50/1,0 - Vf=0,57%
50/0,75 - Vf=0,32%
RC
RC + 50/0,75 - Vf=0,32%
RCO + 50/0,75 - Vf=0,32%
Relative displacement in radial direction under the thrust jacks [mm]
0
5
10
15
20
25
30
35
0,00 0,20 0,40 0,60 0,80 1,00 1,20
Normal loading condition
To
tal L
oad
[M
N]
0
0,5
1
1,5
2
2,5
3
Lo
ad
/Serv
ice lo
ad
[-]
50/1,0 - Vf=0,57% - Point 1
50/0,75 - Vf=0,32% - Point 1
RC - Point 1
RC + 50/0,75 - Vf=0,32% - Point 1
RCO + 50/0,75 - Vf=0,32% - Point 1
Relative displacement in radial direction under the thrust jacks [mm]
0
5
10
15
20
25
30
35
0,00 0,20 0,40 0,60 0,80 1,00 1,20
Normal loading condition
To
tal L
oad
[M
N]
0
0,5
1
1,5
2
2,5
3
Lo
ad
/Serv
ice lo
ad
[-]
50/1,0 - Vf=0,57% - Point 1
50/0,75 - Vf=0,32% - Point 1
RC - Point 1
RC + 50/0,75 - Vf=0,32% - Point 1
RCO + 50/0,75 - Vf=0,32% - Point 1
Splitting cracks Spalling cracks
Reinforcement optimization for structural FRC elements 35/72Madrid, October 13th, 2016
G. Plizzari
9,3MN
12,6MN
Outer eccentricity:
Relative displacement in the region between the thrust jacks [mm]
0
5
10
15
20
25
-1,00 0,00 1,00 2,00 3,00 4,00 5,00 6,00
Eccentricity outside
To
tal
Lo
ad
[M
N]
0
0,5
1
1,5
2
Lo
ad
/Se
rvic
e l
oa
d [
-]
50/1,0 - Vf=0,57%
50/0,75 - Vf=0,32%
RC
RC + 50/0,75 - Vf=0,32%
RCO + 50/1,0 - Vf=0,32%
Relative displacement in the region between the thrust jacks [mm]
0
5
10
15
20
25
-1,00 0,00 1,00 2,00 3,00 4,00 5,00 6,00
Eccentricity outside
To
tal
Lo
ad
[M
N]
0
0,5
1
1,5
2
Lo
ad
/Se
rvic
e l
oa
d [
-]
50/1,0 - Vf=0,57%
50/0,75 - Vf=0,32%
RC
RC + 50/0,75 - Vf=0,32%
RCO + 50/1,0 - Vf=0,32%
- Safety factor reduction
- Crack increase between loading areas;
Average displacement under the load surfaces [mm]
0
5
10
15
20
25
30
0,00 0,50 1,00 1,50 2,00 2,50 3,00
Eccentricity outside
Tu
nn
el
Lo
ad
[M
N]
0
0,5
1
1,5
2
2,5
Lo
ad
/Se
rvic
e l
oa
d [
-]
50/1,0 - Vf=0,57%
50/0,75 - Vf=0,32%
RC
RC + 50/0,75 - Vf=0,32%
RCO + 50/0,75 - Vf=0,32%
0
5
10
15
20
25
30
0,00 0,50 1,00 1,50 2,00 2,50 3,00
0
0,5
1
1,5
2
2,5
Normal l.condition
Additional moments due to outer eccentricity
Eccentricity
Inside tunnel
Outside tunnel Outside tunnel
Inside tunnel
Outside tunnel
Inside tunnel
Eccentricity inside Eccentricity
outside
Reinforcement optimization for structural FRC elements 36/72Madrid, October 13th, 2016
G. Plizzari
Precast structural elements
Reinforcement optimization for structural FRC elements 37/72Madrid, October 13th, 2016
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)
Reinforcement optimization for structural FRC elements 38/72Madrid, October 13th, 2016
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
Floor slab for Electrical Equipment Shelters
Geometry of the simply supported slab
Aim of the research:
Reinforcement optimization for structural FRC elements 39/72Madrid, October 13th, 2016
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
Floor slab for Electrical Equipment Shelters
Proposal of an optimized reinforcement for the tested slabs
Reinforcement optimization for structural FRC elements 40/72Madrid, October 13th, 2016
G. Plizzari
Conventional RC tank
Section B-B
Section A-A
Tank with optimized reinforcement
Numerical
simulation
Conventional
steel wire mesh
FRC (Vf=30Kg/m3)
Local rebars
Local rebars
Water tanks
Reinforcement optimization for structural FRC elements 41/72Madrid, October 13th, 2016
G. Plizzari
Properties of the tank
Typical loading conditions
Plan view (dimensions in mm)
Section Y-Y (dimensions in mm)
Ground pressure acting on the outer surface Water pressure acting on the inner surface
Water tanks
Reinforcement optimization for structural FRC elements 42/72Madrid, October 13th, 2016
G. Plizzari
ULS non-linear analysis for reinforcement optimization
Ground pressure acting on the outer surface Water pressure acting on the inner surface
Inner surface
Outer surfaceInner surface
Outer surface
Inner surfaceOuter surface
Localized stresses along the vertical corner Localized stresses along the vertical corner
Localized stresses along the long wall Localized stresses along long wall
Water tanks
Reinforcement optimization for structural FRC elements 43/72Madrid, October 13th, 2016
G. Plizzari
Optimized reinforcement and behavior at SLS
Ground pressure acting on the outer surface Water pressure acting on the inner surface
Optimized reinforcement:
- SFRC (V f=30kg/m3)
- 8/30cm steel rebars
Crack pattern at service loadCrack pattern at service load
Optimized reinforcement:
- SFRC (V f=30kg/m3)
-8/30cm steel rebars
-16 rebars
Water tanks
Reinforcement optimization for structural FRC elements 44/72Madrid, October 13th, 2016
G. Plizzari
Structural elements that transfer to the main structure:
Self weight Wind pressure
Geometrical classificazion:Panels with horizontal axis
Panels with vertical axis
Precast facade panels
Reinforcement optimization for structural FRC elements 45/72Madrid, October 13th, 2016
G. Plizzari2
00
200
20
0
200
Substitution of conventional reinforcement (welded mesh)
with fibers
Industrialisation of the production
process
Reduction of the structural thickness
Weight reduction of the elements
Enhanced thermal insulation
Lower transportation costs
Structural optimisation
Reinforcement optimization for structural FRC elements 46/72Madrid, October 13th, 2016
G. Plizzari
Moment vs. Displacement
Mid-Span Section - RC Panels
0
10
20
30
40
50
60
70
80
0 50 100 150 200 250 300
Displacement [mm]
Mo
me
nt
[kN
m]
Mes
PT1
PT2 5
Ø5/2
0/2
5
5 10
Ø5/2
0/2
5
125 3
Experimental results 1/2
RC Panels
SFRC Panels
(Vf=0.45%)
Moment vs. Displacement
Mid-Span Section - SFRC Panels (Vf=0.45%)
0
10
20
30
40
50
60
70
80
0 50 100 150 200 250 300 350
Displacement [mm]
Mo
men
t [k
Nm
]
Mes
PT1
PF3
PF4
PF1
PF2
PF5
2.54.5 13
5 12 3
3125
Reinforcement optimization for structural FRC elements 47/72Madrid, October 13th, 2016
G. Plizzari
Moment vs. Displacement
Mid-Span Section - SFRC Panels (Vf=0.38%)
0
15
30
45
60
75
90
0 50 100 150 200 250 300
Displacement [mm]
Mo
me
nt
[kN
m]
Mes
PT1
PF6
PF7
PF8Self weight reductions
~20%
Experimental results 2/2
Consistent experimental results
L/400
Reinforcement optimization for structural FRC elements 48/72Madrid, October 13th, 2016
G. Plizzari
Durability of FRCFibers for durability of RC beams
Reinforcement optimization for structural FRC elements 49/72Madrid, October 13th, 2016
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
Reinforcement optimization for structural FRC elements 50/72Madrid, October 13th, 2016
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Cracks in a beam
Reinforcement optimization for structural FRC elements 51/72Madrid, October 13th, 2016
G. Plizzari
Cracking and durability
Reinforcement optimization for structural FRC elements 52/72Madrid, October 13th, 2016
G. Plizzari
Durability of FRCCrack development in RC elements
Reinforcement optimization for structural FRC elements 53/72Madrid, October 13th, 2016
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Four point bending tests on a beam
Constant Moment:
reinforcement and
surrounding concrete like a
tension tie
Beam Cross-Section Sample
Experimental Program
Reinforcement optimization for structural FRC elements 54/72Madrid, October 13th, 2016
G. Plizzari
Experimental Program II
Two fiber typologies:
Macro (M): Hook ended, 30 mm long, 0.62 mm
diameter
Micro (m): Straight, 13 mm long, 0.2 mm
diameter mm
950
Reinforcement
b
LVDT
900
Base of measurement 4 LVDTs, one for each side
of the specimen
b
b
Reinforcement optimization for structural FRC elements 55/72Madrid, October 13th, 2016
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vIl
f Vf b
[mm]
As
[mm2]
Ac,eff
[mm2]
Reinf.
Ratio (%)
Clean
cover
[mm]
Denomination # of
specimens
f 10
0*
50 79 2421 3,24 20
N 50/10 - 0 3
0,5%* N 50/10 - 0,5/M 3
1,0 %* N 50/10 - 1/M 3
0,5%+0,5%* N 50/10 - 1/M+m 3
1%+1% N 50/10 - 2/M+m 3
f 10
0*
80 79 6321 1,24 35
N 80/10 - 0 2
0,5%* N 80/10 - 0,5/M 3
1,0 %* N 80/10 - 1/M 3
0,5%+0,5%* N 80/10 - 1/M+m 3
1%+1% N 80/10 - 2/M+m 3
f 20
0*
100 314 9686 3,24 40
N 100/20 - 0 3
0,5%* N 100/20 - 0,5/M 3
1,0 %* N 100/20 - 1/M 3
0,5%+0,5%* N 100/20 - 1/M+m 3
1%+1% N 100/20 - 2/M+m 3
f 20
0*
150 314 22186 1,41 65
N 150/20 - 0 3
0,5%* N 150/20 - 0,5/M 3
1,0 %* N 150/20 - 1/M 3
0,5%+0,5%* N 150/20 - 1/M+m 3
1%+1% N 150/20 - 2/M+m 3
f 30
0*
150 707 21793 3,24 60
N 150/30 - 0 3
0,5% N 150/30 - 0,5/M 3
1,0 % N 150/30 - 1/M 3
0,5%+0,5% N 150/30 - 1/M+m 3
1%+1% N 150/30 - 2/M+m 3
f 30
0*
200 707 39293 1,80 85
N 200/30 - 0 2
0,5% N 200/30 - 0,5/M 3
1,0 % N 200/30 - 1/M 3
0,5%+0,5% N 200/30 - 1/M+m 3
1%+1% N 200/30 - 2/M+m 3
Bar diameter f=10 mm
Bar diameter f=20 mm
Bar diameter f=30 mm
50
50
80
80
150
15
0
95
0
11
50
100
10
0
150 200
15
0
20
0
Reinforcement
b
Varia
tion o
f the re
bar d
iam
ete
rVariation of the specimen
size, b
Variation of the longitudinal
steel ratio, ρ=3,24% to 1,24%
Varia
tion o
f the re
bar d
iam
ete
r
Experimental Program III
Reinforcement optimization for structural FRC elements 56/72Madrid, October 13th, 2016
G. Plizzari
Experimental Results
Comparison specimens N 50/10 - 10 - =
3,24%
0
10
20
30
40
50
60
0 1 2 3 4 5
Average strain [‰]
Axia
l lo
ad
, N
[kN
]
Bare bar Ф 10
Average response plain
Average response Vf=0,5%
Average response Vf=0,5%+0,5%
Average response Vf=1%
ΔN Plain
ΔN SFRC Vf=0,5%
ΔN SFRC Vf=0,5%+0,5%
ΔN SFRC Vf=1%
Comparison specimens N 80/10 - 10 - =
1,24%
0
10
20
30
40
50
60
0 1 2 3 4 5
Average strain [‰]A
xia
l lo
ad
, N
[kN
] Bare bar Ф 10
Average response plain
Average response Vf=0,5%
Average response Vf=0,5%+0,5%
Average response Vf=1%
ΔN Plain
ΔN SFRC Vf=0,5%
ΔN SFRC Vf=0,5%+0,5%
ΔN SFRC Vf=1%
DN: combined effect of tension stiffening and
residual tensile stresses
Reinforcement optimization for structural FRC elements 57/72Madrid, October 13th, 2016
G. Plizzari
Plain Concrete FRC
Results
w
Reinforcement optimization for structural FRC elements 58/72Madrid, October 13th, 2016
G. Plizzari
Plain Concrete FRC
Tension stiffening in FRC
s c=fctm
t bm
concrete stress
bond stress
s c=0
lt lt
s c=fctm
t bm
s c= fFtsm
ltFRC lt
FRC
s c=0
s c=fctm
t bm
x s c=fFtsm
s c=fctm
t bm
x
s c=fctm
t bm
concrete stress
bond stress
s c=0
lt lt
s c=fctm
t bm
s c= fFtsm
ltFRC lt
FRC
s c=0
s c=fctm
t bm
x s c=fFtsm
s c=fctm
t bm
x
Average strain
Non-fibrous tie
Fibrous tie
N
esm esm Average strain
Non-fibrous tie
Fibrous tie
N
esm esm Average strain
Non-fibrous tie
Fibrous tie
N
esm esm
Reinforcement optimization for structural FRC elements 59/72Madrid, October 13th, 2016
G. Plizzari
Average crack spacing: comparison with
standard formulations
0
50
100
150
200
250
300
350
400
0 300 600 900 1200 1500 1800f/r eff [mm]
Ave
rag
e c
rack
sp
ac
ing
[m
m]
Plain
SFRC Vf=0,5%
SFRC Vf=0,5%+0,5%
SFRC Vf=1%
CEB - FIP Model Code, 1978
Eurocodice 2, 1991
CEB - FIP Model Code, 1993
Eurocodice 2, 2003
Comparison against code provisions
eff
21b
mρ
kk10
sc2s
f
CEB, FIP Model Code 1978:
eff
mρ3.63
2s
f
CEB, FIP Model Code 1993:
Reinforcement optimization for structural FRC elements 60/72Madrid, October 13th, 2016
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
Reinforcement optimization for structural FRC elements 61/72Madrid, October 13th, 2016
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
Reinforcement optimization for structural FRC elements 62/72Madrid, October 13th, 2016
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%
Reinforcement optimization for structural FRC elements 63/72Madrid, October 13th, 2016
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)
Reinforcement optimization for structural FRC elements 64/72Madrid, October 13th, 2016
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.
Reinforcement optimization for structural FRC elements 65/72Madrid, October 13th, 2016
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
Reinforcement optimization for structural FRC elements 66/72Madrid, October 13th, 2016
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.
Reinforcement optimization for structural FRC elements 67/72Madrid, October 13th, 2016
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
Reinforcement optimization for structural FRC elements 68/72Madrid, October 13th, 2016
G. Plizzari
Carbonation depth
CARBONATION DEPTHCHLORIDE CONTENT
Reinforcement optimization for structural FRC elements 69/72Madrid, October 13th, 2016
G. Plizzari
Carbonation depth between the cracks
Reinforcement optimization for structural FRC elements 70/72Madrid, October 13th, 2016
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
Reinforcement optimization for structural FRC elements 71/72Madrid, October 13th, 2016
G. Plizzari
Workshop proceedings
Reinforcement optimization for structural FRC elements 72/72Madrid, October 13th, 2016
G. Plizzari
Thank you for your kind attention!
University of Brescia, Italy
Reinforcement optimization for structural FRC elements 73/72Madrid, October 13th, 2016
G. Plizzari
FRC Roof ElementsFRC Roof Elements
Reinforcement optimization for structural FRC elements 74/72Madrid, October 13th, 2016
G. Plizzari
Tests on Full-Scale Roof Elements
F1
F2
F3
F4
F5
Reinforcement optimization for structural FRC elements 75/72Madrid, October 13th, 2016
G. Plizzari
Set up and Testing
HEB 550
HEB 260
UPN 300
HEB 160
Reinforcement optimization for structural FRC elements 76/72Madrid, October 13th, 2016
G. Plizzari
Experimental Results
Moment vs. Wing Displacement
0
100
200
300
400
500
600
0 50 100 150 200 250 300
Displacement [mm]
Mo
me
nt
[kN
m]
S45
S80
SWM
Elastic limit
SWM
S45
S80
Reinforcement optimization for structural FRC elements 77/72Madrid, October 13th, 2016
G. Plizzari
Transverse Flexure Failure
Longitudinal flexural failure at the two bottom chords
Experimental Results
Reinforcement optimization for structural FRC elements 78/72Madrid, October 13th, 2016
G. Plizzari
Comparison specimens : average crack spacing
0
25
50
75
100
125
150
175
200
225
250
275
300
Φ=10,
ρeff=3,24%
Φ=10,
ρeff=1,24%
Φ=20,
ρeff=3,24%
Φ=20,
ρeff=1,41%
Φ=30,
ρeff=3,24%
Φ=30,
ρeff=1,80%
Ave
rag
e c
rack
sp
ac
ing
[m
m]
Plain
SFRC Vf=0,5%
SFRC Vf=0,5%+0,5%
SFRC Vf=1%
SFRC Vf=1%+1%
ratiogreinforcin
diameterBar
ρeff
f
Crack Spacing Comparison
-51% -69%
-27% -45% -24%-46%
-51% -25%
Reinforcement optimization for structural FRC elements 79/72Madrid, October 13th, 2016
G. Plizzari
Crack Spacing and Experimental Residual Stress
Comparison specimens: average crack
spacing
050100150200250300
Φ=10, ρeff=3,24%
Φ=10, ρeff=1,24%
Φ=20, ρeff=3,24%
Φ=20, ρeff=1,41%
Average crack spacing [mm]
SFRC Vf=1%
SFRC Vf=0,5%+0,5%
SFRC Vf=0,5%
Plain
Comparison specimens: estimated residual
post-cracking strength fres
0,0 0,5 1,0 1,5 2,0 2,5
Φ=10, ρeff=3,24%
Φ=10, ρeff=1,24%
Φ=20, ρeff=3,24%
Φ=20, ρeff=1,41%
fres [MPa]
Comparison specimens: average crack spacing and
estimated residual post-cracking strength fres
Comparison specimens: average crack
spacing
050100150200250300
Φ=10, ρeff=3,24%
Φ=10, ρeff=1,24%
Φ=20, ρeff=3,24%
Φ=20, ρeff=1,41%
Average crack spacing [mm]
SFRC Vf=1%
SFRC Vf=0,5%+0,5%
SFRC Vf=0,5%
Plain
Comparison specimens: estimated residual
post-cracking strength fres
0,0 0,5 1,0 1,5 2,0 2,5
Φ=10, ρeff=3,24%
Φ=10, ρeff=1,24%
Φ=20, ρeff=3,24%
Φ=20, ρeff=1,41%
fres [MPa]
Comparison specimens: average crack spacing and
estimated residual post-cracking strength fres