The Influence of HEMC on Cement and Cement-Lime Composites ...
BSE Public CPD Lecture – Textile-Cement Composites from ... · Textile-Cement Composites from...
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BSE Public CPD Lecture – Textile-Cement Composites from baskets to sustainable homes and jet engines on 24 November 2009 Organized by the Department of Building Services Engineering, a public CPD lecture delivered by Professor Barzin Mobasher on Textile-Cement Composites from baskets to sustainable homes and jet engines was held on 24 November 2009 (Tuesday).
Power Point file of the CPD lecture – Part I
Power Point file of the CPD lecture – Part II Professor Barzin Mobasher is Professor of Structural Materials at the Department of Civil and Environmental Engineering at Arizona State University. He has more than twenty five years of research experience in construction materials and experimental mechanics, and has published more than 100 papers in various journals and conference publications. He obtained his Ph.D. in 1990 from Northwestern University and joined Arizona State in 1991. His research interests include modeling the mechanical properties of cement based composite materials, structural testing, experimental mechanics, and durability of construction materials. He is a member of American Ceramics Society, American Concrete Institute, and American Society of Civil Engineers.
Souvenir presentation to Professor Barzin Mobasher by Professor W.K. Chow
Textiles are among the first products of human engineering endeavor and have been used for at least the past 8000 years. We have used textiles for clothing, storage, shelter, transportation, and composite materials, and are still dependant on them for many new and innovative functions. As we continuously struggle to develop more sustainable systems and control available resources, economical considerations for use of construction materials becomes of paramount importance. Concrete materials global production and use has surpassed the 6 billion tons per year mark, a consumption rate that is not sustainable in consideration to green house gas generation due to cement production. In this lecture, Professor Mobasher presented an overview of the recent developments in cement based textile composites as sustainable materials for construction industry.
The lecture concluded with an overview of recent experimental and modeling work in the application of textile materials to Jet engine containment systems.
CPD public lecture by Professor Mobasher
23-Dec-09
1
Textile-Cement Composites:From jugs and baskets to sustainable homes and jet
engines
Barzin Mobasher, PhD, PEDepartment of Civil and Environmental Engineering
Arizona State University
Invited Talk, Hong Kong Polytechnic University, Nov. 23, 2009
Temporal, Spatial, and Scientific Span of Cement & Concrete Technology
DisciplinesMaterials ScienceEngineeringChemistryMechanics Computational TechniquesManufacturing products and systemsSustainable developmentTechnical & non-technical labor pool
Space
Time
Seconds to Centuries
1 to 3x1010 Seconds
hydration Early age Long termPerformance
Service life
nanometers to kilometers
1x10-9 to 1x103 meters
Sustainability: Concrete Consumption in US Concrete Specified vs. Delivered
6000
8000
10000
engt
h, p
si
All concrete classes28 day strength
Each data point = 100 cubic yardsOver-strength
Level
2000 4000 6000Specified f'c, psi
2000
4000
6000
Del
iver
ed S
tre
Source: ADOT Database for One ready mix supplier over a course of two years
Our Generation’s Challenge
The need for a safe and secure shelter is an inherent global problem.
Approximately 924 million people worldwide, (31.6 percent of the global urban population) lived in slums in 2001 [UN-Habitat]Habitat].
This figure will double to almost 2 billion In the next thirty years, unless substantial policy changes are put in place.
Historical Perspectives
Throughout centuries technology has supported human development
Water – Collection, transportation, storage
– liquids, oils q ,– Jugs and Ceramic materials,
Food– agricultural products, food storage, transportation– Baskets, Textiles, woven fabrics
Shelter– Construction, building materials , cements
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Woven Fabrics are among the first engineered materials
A funerary model of a weaver's workshop found in an Egyptian tomb. This model contains a horizontal loom, warping devices and other tools, and weavers in action.
History of weaving
•20K – 30K BC First string by twisting of plant fibers. •7000-8000 BC Cloth making in Mesopotamia and in Turkey. •1766-1122 BC Shang Period in China- treadle and frame loom system•700-1000 Cotton fiber to Anasazi land via trade routes to Mesoamerica. •11th century Invention of weaving patterns used today•1760-1815 Industrial Revolution, Mechanization of cloth weaving
Pottery, Ceramics, cements
10,000 BC - 6,000 BC The earliest known pot making in parts of Asia and middle east. 9,000 BC The first use of functional pottery vessels. 8,000 BC Ancient glass manufacture flourished in Upper Egypt 2,350 BC Ancient Egyptian pottery Fourth, Fifth, and Sixth Dynasties, 1,500 BC Glass was produced independently of ceramics.
Ben Sham Culture China: 2 00 C
Greek Hydra: 533 B.C. Earthenware with slip decoration2500 B.C. Earthenware
with slip decoration.
Earthenware with slip decoration. Courtesy of IMA Pantheon, Rome
Bam Citadel, 2500 year old archeological site in Iran, Dec 2003
23-Dec-09
3
Long Beach, Mississippi- Reinforced Concrete House
Hurricane Katrina, August, 2005
Long Beach, Mississippi, October 30, 2005 -- A lone, mitigated home stands alone in Hurricane Katrina FEMA/Mark Wolfe
Construction systems based on empirical approaches – Hurricane Katrina
Natural disasters are a "growth" industry
•Since the 1960s, economic losses from natural disasters on a global scale have tripled.
•In the same period insured losses have quintupledlosses have quintupled.
•Berz, 1992, Natural Hazards, 5, 95-102
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Population GrowthRethink Engineering of Construction Materials : Focus on Fundamentals of Mechanics, Materials Science
Structure
Performance
Mechanical properties,fracture and FEM modeling onToughening Mechanisms
Full scale testsOptimizationCode development Long term PerformanceDurability
Processing & ManufacturingProperty
Composites processing Lab,extrusion, pultrusion, computer assistedmanufacturing.
materials characterization,SEM facility, XRD, Interfaces and matrix modifications. New fibers& composites.
Toughening Mechanisms
Multi-scale and multi-discipline Approach: Cradle-Grave-Cradle
Sustainable Materials- Sustainable Design Guides
Strengthening approaches
Fabric Reinforced Cement Composites
Sandwich composites
Experimental Characterization Experimental Characterization
Theoretical Modeling
Design Guides
Repair and Retrofit
Toughening Due to Interlock Mechanisms
Mechanisms:– Debonding and pullout, bridging, closing pressure,
crack face stiffness, stress intensity reduction. Three Main interdependent Variables: Bridging Stress, Crack length, Crack opening profile
Variables: Stress crack-width relationship *(u) Stress distribution along crack length Crack opening (width) profile
c
0
af
I
a
K = *(u) g(1, ) da
0 f
a aIF
f IP
a a
2 KCOD = *(u) K d d
E' F
*(x)u(x)
PP FRC Composites Carbon Fiber Composites
R + n Rm 1
R + Rm n2
Rm
Toughness Enhancements in Brittle Matrix Composites: R-Curves
Green’s function Approach:
G(a,x) = green’s functiona = crack lengthlb = bridging zone length
0
bl
b b bK ( l ) G( a,x ) ( x )dx
R + Rm n2
R + Rm n2
Rm
R
R + n Rm 1
R + Rm n2
a
Potential Energy Approach:
u(x) = crack opening profile
lb bridging zone lengthb = bridging stress
0
2bl
b b
duR ( u ) dx
dx
Pullout Modeling of Fabrics
1
Crack DeflectionCrack Deflection
2
Yarn Debonding
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FEM Simulation: Coupled problem of matrix and interface crack growth
Fiber Pullout
Closing Pressure Formulation
Toughening of Matrix
Ph
Pv
Mobasher, B., and, Li, C. Y., "Modeling of Stiffness Degradation of the Interfacial Zone During Fiber Debonding," Journal of Composites Engineering, Vol. 5, N0. 10-11, pp. 1349-1365, 1995.
fiberSliding contact
Interface
Substrate
Matrix Toughening model-FEM
due to applied load
60
80
100
-mm
1/2
due to fibers
composite
19 21 23 25Crack Length, mm
0
20
40
60
KI, M
Pa-
FEMR-Curve Model
P
Mobasher, B., and, Li, C. Y., "Effect of Interfacial Properties on the Crack Propagation in Cementitious Composites," Journal of Advanced Cement Based Materials, Vol. 4. No. 3, Nov. Dec. 1996, pp. 93-106.
Pultruded Cement composites
Tensile Strength = 50 MPa, strain Capacity = 1%
30
40
50
MPa
Unidirectional
0/90/0
0.000 0.004 0.008 0.012 0.016Strain, mm/mm
0
10
20Stre
ss,
Mortar
GFRC
Fabrics in Paste
Polyethylene (PE) Woven Fabric
E=2 GPa
AR GlassBonded Fabric
E= 78 GPa
Polypropylene (PP)Knitted Fabric
E=6 GPa
Slurry Infiltrated Fabric Pultrusion based approaches
Mobasher, B., and Pivacek, A.,”A Filament Winding Technique for Manufacturing Cement Based Cross-Ply Laminates,” Journal of Cement and ConcreteComposites,20 (1998) 405-415.
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New composites with fabrics
Multi Layer
Sandwich layers
Tension, Compression,and beam members
High pressure pipes
Effect of Processing- Fabrics vs. Conventional GFRC
12
16
20
MPa
AR Glass Fabric
GFRC Vf =5%
E-GlassFabric
0 0.01 0.02 0.03 0.04Strain, mm/mm
0
4
8Stre
ss,
PE Fabric
Mortar
ECC
Various stages of cracking Crack Spacing measurement
Damage evolution measurement using image analysis. Crack spacing and
15
20
25
MP
a60
80
cing
, mm
BT-GNSP21
Crack spacing and the stress-strain response of AR Glass fiber composites
0 0.01 0.02 0.03 0.04Strain, mm/mm
0
5
10Str
ess,
0
20
40
Cra
ck S
pac
Homogenization of Crack spacing
0.6
0.8
1
utio
n Fu
ncti
on
Zone 1= 0 015
Zone 2.0273
Zone 3 = 0.0387
15
20
25
MP
a
Zone 3
Zone 2
Zone 1
0 10 20 30 40Crack Spacing, mm
0
0.2
0.4
Cum
ulat
ive
Dis
trib = 0.015
AR-Glass Fabric
0 0.02 0.04 0.06Strain, mm/mm
0
5
10Str
ess,
Zone 1
AR-Glass Fabric
Tensile ResponseGlass
12
16
20
ess,
MP
a
12
16
20
ess,
MP
a
PultrudedCast
0 0.02 0.04 0.06 0.08Strain, mm/mm
0
4
8
Ten
sile
Str
e
0 0.02 0.04 0.06 0.08Strain, mm/mm
0
4
8
12
Ten
sile
Str
e
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7
Crack SpacingEffect of Processing
12
16
20
s, M
Pa
40
60
acin
g, m
m
Stress-StrainCrack Spacing
12
16
20
, MPa
40
60
acin
g, m
m
Stress-StrainCrack Spacing
0 0.02 0.04 0.06Strain, mm/mm
0
4
8Stre
ss
0
20
Cra
ck S
pa
p g
Pultrusion
0 0.02 0.04 0.06Strain, mm/mm
0
4
8Stre
ss,
0
20
Cra
ck s
pa
Cast
Stiffness degradation & Crack Spacing
100
1000
ffne
ss, M
Pa
Glass Fabrics
80 60 40 20 0Crack Spacing, mm
1
10
Tan
gent
Stif
Polyethylene Fabric
Mobasher B, Peled A, Pahilajani J. Distributed cracking and stiffness degradation in fabric-cement composites. Materials and Structures 2006; 39(287):317–331.
CastPultrudedPP
SEM observations
Reinforcing direction
non-coated yarns
Load Transfer Mechanism Attributed to the Failure of Junctions
Failure of Junctions High efficiency factor obtained by anchorage of polymeric & fracture of brittle fibers
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8
Anchorage due to interlock Effects of Matrix formulation on the pullout response
40
60
d (l
bf)
ControlWith Flyash
AR-glass + Pultrusion Process
0 0.1 0.2 0.3 0.4 0.5Deformation (inch)
0
20
Loa
d
Open net mesh allows penetration between the fabric openings and results in mechanical anchoring
Enable to control: orientation, distribution and volume content of the reinforcement
Different geometries of fabrics - wide variety of properties
Easy to handle and place in precast products
Cheap polymeric fabrics, PP, PVA, PE
Anchorage of polymeric based fabrics is the primary advantage for fabrics as reinforcement
Bonded Fabrics- Alkali Resistant Glass
500 m
Flexural Response of Cement Composites
300
400
500
N
0 0.4 0.8 1.2Displacement, in
80
lbs
0 10 20 30Displacement, mm
0
100
200Loa
d,
0
40
Loa
d, l
Actuator DisplacementLVDT Displacement
Aldea C. M., Mobasher, B., Jain, N., “Cement-Based Matrix-Grid System For Masonry Rehabilitation,” Textile Reinforced Concrete (TRC) - German/ International Experience symposium ACI SP-244-9, pp. 141-156, 2007.
23-Dec-09
9
Microstructural Evaluation
Crack DistributionCrack Bridging results insignificant energy dissipation
Composite Laminate Theory for Continuous Fiber/Textile Systems
Unidirectional approach for each layer
or in matrix form:
11
ik
ij
ijk
ik
kijk
ij
S
Sm=n, n
112
2
1
12
2
1
1
66
2221
1211
12
2
1
00
0
0
iii
k
S
SS
SS
)()()()( GSESESES
12
662
221
1212
111
111
m=1, 1
hmhm-1
Mobasher, B., Pivacek A., and Haupt, G. J. ” Cement Based Cross-Ply Laminates,” Journal of Advanced Cement Based Materials, 1997, 6, pp. 144-152.
Response of a 6 stack 0/90/0 lamina
8
-6
-4
-2
0
2
4
6
8
10Strain Distribution
z,m
m
50
100
150
Nom
inal
Str
ess,
MP
a
0 0.5 1 1.5 2 2.5 3 3.5
x 10-3
-10
-8
mm/mm
0 2 4 6 8 10 12-10
-8
-6
-4
-2
0
2
4
6
8
10Stress Distribution
x
MPa
z,m
m
0 0.5 1 1.5 2 2.5 3 3.5 4-10
-8
-6
-4
-2
0
2
4
6
8
10
Transverse Stress
MPa
z,m
m
0 0.5 1 1.5 2 2.5 3 3.5
x 10-3
0
Comparison With Experimental Results of unidirectional and 0/90/0 composites
40
50
60
Stress
Unidirectional
Theory
Experiment
t1
= 10 MPa
t2
= 5 MPa
c1
= 40 MPa
c2
= 40 MPa
12
= 5 MPa
23
= 5 MPa
0.000 0.005 0.010Strain, mm/mm
0
10
20
30Stress, MPa
[0/90]s
Experiment
Theory
Em = 30000
Ef = 70000
Vf = 5%
m = 0.18
Comparison of PPFRC with Experiments
ModelSimulation
Experiments,Pivacek, Haupt, and St
ress
, MP
a 15
10
t/2
t/2
k = 1K=4
k = 2
hn
h1
h2
h3
k = 3
k = n-2k = n-1k= n
21
Mid-Plane
hn-2
PositivDirecti
8.0.,5.,0
)(
0
10
umki
Damage Evolution Law0.000 0.005 0.010 0.015Strain, mm/mm
Polypropylene Fiber Composites
Vf = 6% Em= 30000 MPa Ef = 8000 MPam = 0.18 f = 0.25t1= 5 MPa w0= 3.5e-4 Softening Coefficient
Mobasher, 1998S
5hn-1
k n n 2
Modeling of a Single Crack Bridging
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10
Modeling of Fabric Pullout
Loa
d, N
AR Glass, Expt.AR Glass, Simul.PE, Expt.PE, Simul.
50
100
150
200
ad, N
Expt. Math. YarnMath. Woven
100
150
200
Slip, mm
00 2 4 6 8
P
DebondedLength
U
Anchorage
L
Elastic Foundation, K0
Fill Yarn
Deformation, mm
Loa
0
50
0 0.5 1 1.5 2 2.5
AR Glass Fabric
Modeling of Multiple Cracking
I II III IVCrack Spacing, SDamage,
C
S=S + S e1 0
- ( i- mu)
A
0 Strain
DamageCrack Spacing
mut1
Damage,
Crack Spacing, S
B
C
= + ( - )1 i t1
Modeling of Tensile Response
Stress
BOP
I II IIIIV
B
A
0 Strain
BOPMatrix
CompositeFabric
mut1
mu
t1
C
Modeling of Composite Tensile Response
0
20
40
60
Cra
ck s
paci
ng, m
m
0
1000
2000
3000
4000S
tiff
ness
, MPa CS, Expt.
CS, Simul.Stiffness, Expt. Stiffness, Simul.
0 0.01 0.02 0.03
Strain, mm/mm
0
4
8
12
16
Str
ess,
MP
a
Expt.Simulation
Modeling of Fabric Composites in Tension
10
20
30
40
50
Cra
ck S
paci
ng, m
m
Expt. 40% flyashExpt. Control
0 0.02 0.04 0.06Strain, mm/mm
0
10
20
30
Stre
ss, M
Pa
0 C
Expt. 40% flyashExpt. ControlSimulation 40% FA
Control
Typical Uniaxial Tension Test
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11
Unified material laws and cracking criteria Finite difference model
One way pullout segment
One way pullout segment
Two way pullout segment
Free body diagram at each node
Middle segment
Left end segment
n1 n2 n4n3
Right end segment
n6
n5
Equilibrium equations at typical nodes
1 2 1 22
1 1 2
10
2 2 2
y y y y
y y
E E E EA k h s A s
1 1 1 12
1 1
20
2 2 2i i ii i i i
y i y i i i y i
y y y y y y y
i
E E E E E E EA s A k h g h s A s
1 1 1 12
1 1
20
2 2 2i i ii i i i
y i y i y i
y y y y y y y
i
E E E E E E EA s A k h s A s
n1
n2
n3
1 1 2
1
10
2 2 2n n n ny y y y
y n y n n
E E E EA s A k h s
1 1 2
1
10
2 2 2n n n ny y y y
y n y n n
E E E EA s A k h s Ph
1 2 1 22
1 1 2
10
2 2 2
y y y y
y y
E E E EA k h s A s Ph
1 12 2 2y i y i y ii
n6
n5
n4 Move to the right -- > driving force
Parametric Study
Bond slip model
1
2
3
4
She
ar S
tres
s (M
Pa)
max=4 MPa
max=3 MPa
max=2 MPa
(a)
Matrix Strength
2.5
5
7.5
10
Spr
ing
For
ce (
N)
SFmax=10 N
SFmax=7.5 N
SFmax=5 N
(d)
0 0.25 0.5 0.75 1 1.25Slip (mm)
0
Yarn stress strain model
Matrix Grade
0
1
2
3
Mat
rix
Str
engt
h (M
Pa)
fcr=2.0 MPa
fcr=2.5 MPa
fcr=3.0 MPa(b)
Spring force slip model
0 0.005 0.01 0.015 0.02 0.025Strain (mm/mm)
0
250
500
750
1000
1250
Str
ess
(MP
a)
slack=0.006
slack=0.004
slack=0.002
slack=0.000
(c)
0 0.25 0.5 0.75 1 1.25Slip (mm)
0
Composite tensile stress strain response
Bond strength
5
10
15
Com
posi
te S
tres
s (M
Pa)
BND_4.0BND_3.0BND 2.0
(a)
Matrix strength
5
10
15
Com
posi
te S
tres
s (M
Pa)
MTX_3.0MTX_2.5MTX 2.0
(b)
0 0.005 0.01 0.015 0.02 0.025Strain (mm/mm)
0
BND_2.0
0 0.005 0.01 0.015 0.02 0.025Strain (mm/mm)
0
MTX_2.0
Slack level
0 0.005 0.01 0.015 0.02 0.025Strain (mm/mm)
0
5
10
15
Com
posi
te S
tres
s (M
Pa)
SLK_0.006SLK_0.004SLK_0.002SLK_0.000
(c)
Strength of spring
0 0.005 0.01 0.015 0.02 0.025Strain (mm/mm)
0
5
10
15
Com
posi
te S
tres
s (M
Pa)
SPR_10.0SPR_7.5SPR_5.0SPR_0.0
(d)
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12
Nominal stress strain response in matrix
Bond strength
1
2
3
Con
cret
e T
ensi
le S
tres
s (M
Pa)
BND_4.0BND_3.0BND_2.0
(a)
Matrix strength
1
2
3
Con
cret
e T
ensi
le S
tres
s (M
Pa) MTX_3.0
MTX_2.5MTX_2.0
(b)
0 0.005 0.01 0.015 0.02 0.025Strain (mm/mm)
00 0.005 0.01 0.015 0.02 0.025
Strain (mm/mm)
0
Slack level
0 0.005 0.01 0.015 0.02 0.025Strain (mm/mm)
0
1
2
3
Con
cret
e T
ensi
le S
tres
s (M
Pa)
slack=0.006
slack=0.004
slack=0.002
slack=0.000
(c)
Strength of spring
0 0.005 0.01 0.015 0.02 0.025Strain (mm/mm)
0
1
2
3
Con
cret
e T
ensi
le S
tres
s (M
Pa)
SPR_10.0SPR_7.5SPR_5.0SPR_0.0
(d)
Crack spacing – composite strain
Bond strength
25
50
75
100
Ave
rage
Cra
ck S
paci
ng (
mm
) BND_4.0BND_3.0BND_2.0
(a)
Matrix strength
25
50
75
100
Ave
rage
Cra
ck S
paci
ng (
mm
) MTX_3.0MTX_2.5MTX_2.0
(b)
0 0.005 0.01 0.015 0.02 0.025Strain (mm/mm)
0
Strength of spring
0 0.005 0.01 0.015 0.02 0.025Strain (mm/mm)
0
25
50
75
100
Ave
rage
Cra
ck S
paci
ng (
mm
) SPR_10.0SPR_7.5SPR_5.0SPR_0.0
(d)
Slack level
0 0.005 0.01 0.015 0.02 0.025Strain (mm/mm)
0
25
50
75
100
Ave
rage
Cra
ck S
paci
ng (
mm
) slack=0.006
slack=0.004
slack=0.002
slack=0.000
(c)
0 0.005 0.01 0.015 0.02 0.025Strain (mm/mm)
0
Final crack spacing
Use basic model
Deterministic crack 1 run for each Vf
– Mean fcr = 2 MPa
– Stdev = 0.0 MPa16
20
24
28
Spa
cing
(m
m)
Deterministic Crack 1 Sample
Stochastic Crack (5 Samples)
Stochastic crack 5 runs for each Vf
– Mean fcr = 2 MPa
– Stdev = 0.001 MPa
1 2 3 4 5Volume Fraction (%)
4
8
12
16
Fin
al C
rack
S
Simulation of AR-glass fabric tension specimen
Dimension
8x100x500, clear length 300 mm
Yarn
dy = 0.374 mm, Ay= 0.11 mm2
Ey = 76 GPa
tu = 1,300 MPa
Vf = 1.4% (3 layers)
Matrix
Fine mix concrete
fcr = 7 MPa, Ec = 30 GPa
Deterministic Crack, 2501 nodes0 0.1 0.2 0.3
Slip (mm)
0
2
4
6
She
ar S
tres
s (M
Pa)
Bond slip
Stress in matrix and Fiber as a function of applied strain
Stress in matrixStress in Fiber
Tensile and Flexural Responses Do not Correlate Directly
15
20
25
xura
l Str
ess,
MPa
0 0.02 0.04 0.06 0.08 0.1
Tensile Strain, mm/mm
15
20
25
MPa
MOR
0 10 20 30 40 50Flexural Deflection, mm
0
5
10
15
Ela
stic
ally
Equ
ival
ent F
lex
FlexureTension
0
5
10
15
Ten
sile
Str
ess,
LOP
BOP
UTS
23-Dec-09
13
Cumulative tensile and Flexural Strength Distribution
0.6
0.8
1
babi
lity
, p
BOPUTS
0 4 8 12 16Tensile or Flexural Strength, MPa
0
0.2
0.4
Fail
ure
Prob LOP
MOR
Simplified Tensile and Compressive stress strain model
c cy= cr E t
cr=crEE
E
cr =
p crE=
strain-hardening
c cy cr= cu cu cr=
E = Ec
Compression Elastic Plastic model Tension Strain Hardening-Softening model
cr trn cr= tu tu cr=
Et
Soranakom C, Mobasher B. Correlation of tensile and flexural response of strain softening and strain hardening cement composites. J. Cement & Concrete Composites, 2008;30:465-477.
Closed Form Moment-Curvature Formulation
Incrementally impose 0 < t < tu (or 0 < < tu)
Strain Distribution
Stress Distribution
F = 0, determine Neutral axis, k
M = Ciyci+ Tiyti and =c/kd
Normalization M’=M/M0 and ’=/cr
1 10
kd
c cF b f y dy
1 101
kd
c cc
by f y ydy
F
c
0 < t < tu
k
h
C2
T1
T2
T3
C1 M
Moment curvature
Zone 2.1 Tension Hardening-Compression Elastic
1 < < , 0 < <
c cr=
1hc1 kh
1yc1
Fc1
fc1
t cr=
1 ht1h
1yt1
yt2ft1
2 ht2
cr
Ft22
ft2
Ft1
Soranakom C, Mobasher B. Correlation of tensile and flexural response of strain softening and strain hardening cement composites. Cem Concr Compos, 2008;30:465-477.
Zone 3.1 Tension Softening-Compression Elastic
< < tu 0 < <
ctop cr=
1hc1 kd
1yc1
Fc1
fc1
tbot cr=
1 ht1 d 1yt1 yt2ft1
2 ht2
crFt22ft2
Ft1
3 ht3 3 Ft3
yt3
ft3
trn
Soranakom C, Mobasher B. Correlation of tensile and flexural response of strain softening and strain hardening cement composites. Cem Concr Compos, 2008;30:465-477.
Closed Form Solutions for Strain Hardening/Softening material
216
cr
cr cr
M =M' M
M bd E
'2
cr
cr
cr d
23-Dec-09
14
Model for strain Hardening-softening
Range k
1
0 < < 1 1
1 for =1
2
1 for 1
1
k
3 2
1 1 11
1
2 1 3 3 1'
1
k k kM
k
2.1 221 21D D 3 3 2
21 21 21 21 21 21 212 3 3'
C k C k C k CM
2cr cr
1M M M '= bd E M '
6
2 1cr
cr cr
2 = '
k d
1 < <
0 < <
21 2121 2
21
D Dk
D
221 2 1 2 1D
21211
Mk
3 2 2
21 2
(2 3 1) 3 1C
3.1
< < tu
0 < <
231 31
31 231
D Dk
D
231 2 1 2 2 1D
3 3 231 31 31 31 31 31 31
3131
2 3 3'
1
C k C k C k CM
k
3 2 2 2 2
31 2
(2 3 1) 3 3 1C
Range 2.1Compression Elastic - Tension Hardening
2A ( 1 2 )k 2
A
A1
2 1
2 1
kSpecial Case: Ec =Et (=1 ) , Elastic perfectly plastic tension (=0 )
A (
Ak )
)'(M k )'(M A, ( k
A
)
0.5 20.5( 1 - 2 ) 2 - 1 1 60.773 0.108 10 x k 0.507 0.686
0.2 20.2( 1 - 2 ) 2 - 1 2 60.654 0.516 10 x k 1.105 0.383
0.1 20.1( 1 - 2 ) 2 - 1 2 61.276 0.289 10 x k 1.461 .234
0.05 20.05( 1 - 2 ) 2 - 1 2 61.645 .1632 10 x k 1.720 .1401
0.01 20.01( 1 - 2 ) 2 - 1 10.852 0.456 k 1.342 0.371
Range 2.1Compression Elastic - Tension Hardening
Elastic perfectly plastic tension (=0 )Elastic (=1 )
=ratio of Slopes
Range 3.1 Compression Elastic Tension-Softening
Effect of Ultimate Strain Capacity,
=ratio of ultimate strain capacity to first crack strain
Range 3.1 Compression Elastic Tension-Softening
Effect of Post peak Stress level,
Post peak Stress level,
Strain Softening Materials (=0, =1)
Effect of post-peak tensile strength,
0.3
0.4
0.5
xis
dept
h ra
tio, k
= 10
cu = 0.004
tu = 0.0152
3
zed
Mom
ent,
M'
0 35
=0.68
=1.00
M’= 1.910
M’=1 0145
M’=2.727
0 4 8 12 16Normalized top compressive strain,
0
0.1
0.2
Neu
tral
ax
=0.01=0.35
=0.68
=1.00
=0.18
0 20 40 60Normalized Cuvature, '
0
1
Nor
mal
iz
=0.01
=0.35
=0.18
crcr
2 =
d
2cr cr
1M = bd E
6M '( ) = 3
+
M’=1.0145
M’= 0.530
M’=0.03
Soranakom, C., and Mobasher, B., “Closed-Form Solutions for Flexural Response of Fiber-Reinforced Concrete Beams,” Journal of Engineering Mechanics, Vol. 133, No. 8, August 2007, pp. 933-941
23-Dec-09
15
Interaction of Failure Zones Load Deflection Response
Moment area method
Crack localization rules
Moment
Mmax Non-Localized Zone
Localized Zone
P/2
S S S
P/2
Curvature
M0 Mfail j,Mj)
j-1,Mj-1)
Loading Unloading
S S/2
cS
P Localized Zone
Non-Localized Zone
Axis of Symmetry
M
M0
L
0
Tensile Stress-strain and Crack Spacing
Polyethylene (PE) Woven Fabric
E=2 GPa
AR GlassBonded Fabric
E= 78 GPa
Polyethylene Fabric composites
Alkali Resistant Glass Fabric Repair of Unreinforced Masonry Walls
MD
XMD
23-Dec-09
16
In-plane shear tests to simulate seismic action.
Full coverage, on one side of the wall only.
Three walls tested varying the reinforcement layout:
Wall 1 – 2 plies 0-90
Wall 2 – 2 plies 0-90, +/-45
Wall 3 – 3 plies 0-90, 2 x +/-45
Wall Retrofit: Fabric Cement, USACOE-CERL
300
-10 0 10 20 30Displacement, mm
-300
-200
-100
0
100
200
Cyc
lic
Hor
izon
tal L
oad,
kN
Load-Displ loops(-) Negative backbone(+) Positive backbone
2 Plies, 0/90°
The Beam-Column Joint Retrofit
0 20 40 60 80 100Time, sec
-60
-40
-20
0
20
40
60
Bea
m ti
p di
spla
cem
ent,
mm
-60 -40 -20 0 20 40 60Beam tip displacement, mm
-30
-20
-10
0
10
20
30
Bea
m C
ycli
c L
oad,
kN
CFRP 1 layer(L) loopsEnvelope of CFRP1
Beam Displacement-Cyclic Load
Drop Weight Impact
Hammer SpecimenLever arm LVDT
Impact response of 6 layer glass fabric composite
Impact response of 6 layer glass fabric composite Impact Event Characteristics
2000
2500
3000
orce
, N
20
30
40
eler
atio
n, g
4
6
8
n, m
m 200
400
cele
rati
on, g
ARGh= 101 6 mm
0.03 0.04 0.05 0.06 0.07 0.08Time, sec
0
500
1000
1500
Impa
ct F
o
Impact loadHammer AccelerationDeflectionSpecimen Acceleration
-10
0
10
Ham
mer
Acc
e
-2
0
2
Def
lect
ion
-200
0
Spe
cim
en A
cc
h= 101.6 mm
23-Dec-09
17
Safety aspects of Jet Engine casing Containment system FBO event- Fan Blade out
US Airways- Landing on the Hudson, Jan 2009 High Speed Testing of Kevlar 49 Fabric
Data Acquisition System
Signal Conditioners and Controllers
Laser Extensometer
Table
Grip
Grip
Load Cell
Stroke
Piezoelectric Force Transducer
Personal Computer
Command SignalsLVDT & Servo-Valve
Personal Computer
FAA Sponsored Program: LS-DYNA Implemented Fabric Material Model Development for Engine Fragment Mitigation
Test Setup Tensile Properties under static and high speed conditions
23-Dec-09
18
Test Response at Different Strain Rate
300
400
ess,
ksi
Strain Rate, s-1
212230686897101
300
400
ess,
ksi
Strain Rate, s-1
212230686897101
Stress vs. Time Stress vs. Strain
0 0.0004 0.0008 0.0012 0.0016 0.002Time, sec
0
100
200
Tru
e S
tre 101
92166167167166
0 0.02 0.04 0.06True Strain, in/in
0
100
200
Tru
e St
re 10192166167167166
Kevlar Fill and Warp Cross-sections under load
104
=1.0 %
=0.0 %
=1 5 %=1.5 %
=2.0 %
Warp Cross-sectionFill Cross-section
Constitutive Relation of Yarn105
• Kevlar Yarns are assumed to be transversely isotropic
• Constitutive relation can be defined in terms of five material constants
• UMAT for solid elements
1113121111
000
000
SSS
SSS
3
2
1
Yarn Model
80000
23
31
12
33
22
1211
44
44
331313
131112
23
31
12
33
22
00000
05.00000
005.0000
000
000
SS
S
S
SSS
SSS
111
1
ES
1
1212 E
vS
1
1313 E
vS
333
1
ES
1344
1
GS
0 0.01 0.02 0.03 0.04 0.05
Strain, in/in
0
10000
20000
30000
40000
50000
60000
70000
Stre
ss,
psi Elastic
Region
Warp Direction (11)
E11
1
CrimpRegion
E11crp
Micromechanical model of Kevlar fabric 106
•modeling fill and warp yarns and capturing yarn to yarn interaction.•modeling of contact surfaces as well as mass scaling.•BCs: Left end of the fabric is fixed and velocity is applied on right end.• Both contact types (SOFT = 1 & 2) were used
LG610 Results107
LG610 Experimental (16.9%)
Single Layer
(20.7%)
Multi Layer
(18.3%)
LG689 Results108
LG689 Experimental (47%) Single Layer
(37%)
Multi Layer
(31%)
23-Dec-09
19
LG657 Results109
LG657 Experimental (100%) Single Layer
(100%)
Multi Layer
(100%)
LG657 Results110
LG657 Experimental (100%) Single Layer
(100%)
Multi Layer
(100%)
LG657 Results111
Conclusions
Our generational challenge is to meet the demand through sustainability, intelligent construction practices, novel product manufacturing, in addition to promotion and use of alternate, and economical sources for construction materials.
The processing method has a significant influence on the mechanical behavior of fabric-cement composites.
The pultrusion process significantly improves the tensile behavior of fabric-cement composites compared with cast composites, mainly for fabrics made from multifilaments.
Strain hardening behavior even when the modulus of elasticity of the yarn is relatively low.
A range of sustainable products can be developed. Integration of mechanics, materials, and manufacturing techniques
allows development of new applications for structural engineering
Acknowledgements
National Science Foundation, Binational US Israel Science Foundation, SRP, Salt River Project, St. Gobain Technical Fabrics
Colleagues, former and current students: Calvin Young, Cheng Yu Li, Joanne Situ, Rajashekar Vodela, Andrew Pivacek, Garrett Haupt, Jitendra Pahilajani , Nora Singla, Sachiko Sueki, Alva Peled, Dnyanesh Naik Chote Soranakom Juan Erni Mustafa GencogluDnyanesh Naik, Chote Soranakom, Juan Erni, Mustafa Gencoglu, Chote Soranakom, Della Roy, Sandwip Dey, Subramaniam Rajan
23-Dec-09
1
Sustainable Homes- Application of Steel ppFiber Reinforced Concrete for
Elevated Slabs & Low Cost housing
Barzin Mobasher, Arizona State University, Tempe, AZXavier Destrée,Belgium
Chote Soranakom, IMMS, Thailand
Invited Talk, Hong Kong Polytechnic University, Nov. 23, 2009
Research and discovery lags when the societal need embraces worthy ideas
Quite often, research is used to validate ideas that are borne out of the need. (Science of Thermodynamics was developed long after the steam engine’s adoption)
For ideas to become tangible and acceptable, one has to g p ,establish their truth value.
Truth however is first ridiculed, then opposed, and finally evident.
Applications of SFRC in Elevated Slabs
Construction Methodology
Full scale testing of elevated slab
Round panel Testing
Inverse analysis to obtain material parametersparameters
Proposed Design Methods
Conclusions
Applications of Fiber Reinforced Concrete
Fiber reinforced concrete are primarily used for applications that toughness of materials are of concern
First floor, elevated slab Elevated slabs
Advantages of SFRSS systemsPumping Reinforcement -I
– Eliminate double layers of rebars and stirrups fabrication, installation.
– Removal of congestion
– Time savings of several weeks for projects larger than 10,000 m2
– No Cranes for lifting rebars
– Installation using laser screed machines
Si lifi ti t j b it d h i l d l b i t i t k– Simplification at jobsite reduces physical and labor intensive tasks
– Eliminate or reduce drop panels
– Safety improvement
Advantages of using SFRSS systemsPumping Reinforcement- II
– Reduction in labor force and finishing personnel
– 30% cost saving vs. traditional methods
– Shrinkage cracking control
– Bay areas larger than traditional areas
– Detailing cost reduction
23-Dec-09
2
Steel Fiber Reinforced Concrete
Composition Amount
Cement Type I 350 kg
Fly ash 60 kg
Aggregate (1 1:1) 1800 kg
Two volume fractions
– Vf = 80 kg/m3
– Vf = 100 kg/m3
Aggregate (1.1:1) 1800 kg
W/C < 0.5
Supper plasticizer 1.25 % by Vol.
BEMAT 400mm raft 50kg SF08, 2006
DittonNams-Superstore elevated slab Daugavspils, Latvia25 ft span, 10inches slab,200psf UDL
165lbs/cu.yd Tabix 1.3/50 140ksi Steelfibers
LKS struct.engineers headoffices, 5 floors 50000 sq.ft total ,Mondragon, Spain,
27ft span, 11 inches thickness, 140psf UDL165lbs/cy.yd Tabix 1.3/50 140ksi steelfibers
Veterinary hospital, Hannut Belgium17ft span, 7 inches slab
100lbs/cu.yd 1/60 210ksi steelfibers
Pumping SCC with 165lbs/cu.ydTabix 1.3/50 140ksi steelfibers
23-Dec-09
3
Full Scale Tests up to date
# Year Location # x & y spans # of columns
span length,
mm
Thickness mm
column size
mm x mm
dosage rate
of steel fibers, kg/m³
span/depth ratio
1 `94 Ternat,Belgium
3 / 3 / 16 3100 160 210 x 210 45 19
2 `00 Townsville,Australia
3 / 3 / 16 3100 160 210 x 210 45 19
3 `04 Bissen,Luxembourg
3 / 3 / 16 6000 200 300 x 300 100 30
4 `07 Tallinn,Estonia
3 / 3 / 16 5000 180 300 x 300 100 28
Full Scale Elevated Slab
Square grid floor 18.3 m x 18.3 m (3 bays each direction)
mix Vf=100 kg/m3
Slab thickness of 0.2 m
Column size of 0.3 m x 0.3 m
Bissen site Construction and Field Testing
Cast in place SFRC
Use minimum reinforcement along the column lines to prevent progressive collapse
Test rig centre span
Bissen test rig underneath Tallinn, Estonia , Test site Service Load, 4kNm² udl, (83 psf)
23-Dec-09
4
Center Point loading Bissen Test Corner span center point loading Test
120kN minute cracking at Tallinn test 320kN 0.55 mm crack opening more than 3 x the first crack load!
500kN negative moment cracking 595 kN edge cracking
23-Dec-09
5
Full scale Test Results Problem Statement
There is no standard analytical model to evaluate material properties
Practicing engineers rely on yield line theory or plastic analysis to evaluate strength– This method assumes a constant plastic strength and ductile
deformation, which may be suitable for ductile RC structures but may not for low-medium discrete fiber reinforced concrete
The objective of this study is to evaluate the existing analysis and design approach (yield line method) with a more advance nonlinear finite element analysis – use concrete damaged plasticity model that capable of simulating
cracking in brittle material
Round Panel Test
A round panel test is used to evaluate SFRC
Test setup– displacement control
– continuous support
– center point load
– measure load vs. mid span deflection
Dimensions– clear diameter 1500 mm
– thickness = 150 mm
– stoke diameter = 150 mm
Round Panel Tests
Deflection measuringdevice
Plastert
S
D
F
S
D= S=t = 150, 200 mmr=150
1660, 2100 mm1500, 2000 mm
r
Crack patterns in the Round Panel Specimen- 100 Kg/m3 steel fibers Typical Crack Patterns
Vf = 80 kg/m3
Sample 8-02Vf = 100 kg/m3
Sample 1-07
The test reveals unsymmetrical multiple radial crack patterns
23-Dec-09
6
FEM Response of a Full Model
In elastic range, the deformation is symmetrical such that symmetric criteria can be imposed as boundary conditions to improve the efficiency of the model
In plastic stage, strain energy density localizes in crack band regions
Moment distribution at various stages
40
50
m/m
m)
M (Vf 100 kg/m3)
M(Vf 80 kg/m3)
before cracking, the radial and circumferential response are almost the same.
After specimens crack, they continue to increase and reach the peak capacity.
Then the strength of the radial
0 0.0001 0.0002 0.0003
Curvature (mm-1)
0
10
20
30
40
Mo
me
nt p
er
Len
gth
(kN
-mm
Mr (Vf 100 kg/m3)
Mr (Vf 80 kg/m3)
Then the strength of the radialmoment decreases abruptly while the circumferential moment decreases gradually.
Test Results and Averaged Response
Load deflection responses of two mixes
160
200
Vf = 80 kg/m3 Vf = 100 kg/m3
200
0 10 20 30Deflection (mm)
0
40
80
120
160
Load
(kN
)
Samples 1-6Average
0 10 20 30Deflection (mm)
0
40
80
120
160
Load
(kN
)
Samples 1-9Average
Material Properties from Calibration
The first cracking tensile strength from -w are compared well with the plastic strength ftu from yield line theory
2
2.5
)
ftu = 2.11 MPa(yield line prediction)
2
2.5
)
ftu = 2.37 MPa(yield line prediction)
0 0.5 1 1.5 2Crack Width (mm)
0
0.5
1
1.5
2
Te
nsi
le S
tre
ss
(MP
a)
-w relationship,E = 20 GPa, = 0.15 (inverse analysis FEM)
0 0.5 1 1.5 2Crack Width (mm)
0
0.5
1
1.5
2
Te
nsi
le S
tre
ss
(MP
a)
-w relationshipE = 24 GPa, = 0.15 (inverse analysis FEM)
(y p )
Vf = 80 kg/m3 Vf = 100 kg/m3
Finite Element Simulation (1/4 Model)
Use symmetry condition and model only the upper left of the flat slab for efficiency reason
Use shell element S4R for plate bending problem
Use calibrated material parameters of mix Vf=100 kg/m3
Assume self weight of concrete = 2400 kg/m3
23-Dec-09
7
Major crack at Bottom Surface
FEM shows symmetrical cracks in x and y directions
Experiment shows major cracks propagate in y-direction more than the x-direction– Material placed in y–direction may be weaker than the x-directions
Major crack at Top Surface
FEM shows symmetrical cracks along the column lines in both x and y directions
Experiment shows major cracks propagate along the column line in y-direction– Material placed in column line y–direction may be weaker than the
x-directions
Load Deflection Response
600
mulation Response Experiment FEM Yield line
FEM predicts stiffer response and higher capacity than the experiment
Yield line predicts the strength between the experiment’s and the FEM prediction’s
0 50 100 150Mid-Span Deflection (mm)
0
200
400
Lo
ad
(kN
)
Simul
Experiment
line
Pcr 230 kN 401.2 kN -
cr 7 mm 3.0 mm -
Pult 470 kN 542.8 kN 536.1 kN
Material model Strain softening
Compression model Tension model
Stress and Strain Distribution
c=cr
kd
d
kd
d
c=c
r
cr
d
kd
cr
cr
c=cr
t c
1Fc1
yc1
t1Ft1
yt1
t c1
Fc1
yc1
Ft1
yt1
Ft2
yt2
t1
t2
t c1
Fc1
Fc2
Ft1yt1
Ft2
yt2
yc1yc2
t1
t2
0 < < 1 1 < < <
Moment Curvature Diagram
Incrementally impose 0 < t < tu
Strain Distribution
Stress Distribution
F = 0, determine k
M = Ciyci+ Tiyti and =c/kd
1 10
kd
c cF b f y dy
1 101
kd
c cc
by f y ydy
F
stress
k
d
0 < t < tu
strainc
C1
C2
T1
T2
T3
M M
Moment curvature diagram
23-Dec-09
8
Model for strain softening
Stage k M’=M/Mcr ’=/cr
1
0 < < 1
1
2
2k
2 2
2
2 ( 1) 1
23 2
2
(2 3 3 2)3 (2 1)
kk
2k
Stage k M’=M/Mcr ’=/cr
1
0 < < 1
1
2
2k
2 2
2
2 ( 1) 1
23 2
2
(2 3 3 2)3 (2 1)
kk
2k
crcr
2 =
d
1 < < 2 ( 1) 1 2
< cu 2
22 ( ) 2 1
22 3 2
2
(3 3 3 2)3 (2 1)
kk
2k
Soranakom, C., and Mobasher, B., “Closed Form Solutions for Flexural Response of Fiber Reinforced Concrete Beams,” ASCE, Journal of Engineering Mechanics, August- 2007
2cr cr
1M = bd E
6
1 < < 2 ( 1) 1 2
< cu 2
22 ( ) 2 1
22 3 2
2
(3 3 3 2)3 (2 1)
kk
2k
2cr cr
1M M M ' = bd E M '
6
Softening Region- Residual tensile strength,
0.3
0.4
0.5
xis
dept
h ra
tio, k
= 10
cu = 0.004
tu = 0.0152
3
zed
Mom
ent,
M'
0 35
=0.68
=1.00
M’= 1.910
M’=1 0145
M’=2.727
0 4 8 12 16Normalized top compressive strain,
0
0.1
0.2
Neu
tral
ax
=0.01=0.35
=0.68
=1.00
=0.18
0 20 40 60Normalized Cuvature, '
0
1
Nor
mal
iz
=0.01
=0.35
=0.18
crcr
2 =
d
2cr cr
1M = bd E
6
M '( ) = 3 +
M’=1.0145
M’= 0.530
M’=0.03
Calculation Example
What is the moment capacity of a fiber reinforced concrete beam? Given that:– b=4 in, d=4 in
E = 3x106 psi = 300 psi = 150 psi
2ult cr
1M 3 bd E
+ 6
– E = 3x106 psi, cr = 300 psi, p = 150 psi– fc’ = 4500 psi, cy ~ 0.8fc’
Calculations– = p/cr = 0.50– = cy/cr = 12– M’∞ = 3/(+) = 1.44 (no unit)– Mcr = 1/6bd2cr = 3,200 lb-in– M∞ = M’∞Mcr = 4,600 lb-in– Mu = 0.90M∞ = 4,150 lb-in Moment capacity
Development of Design Guides
Deflection Softening-Hardening Transition
Min Fiber loading:
crit ( = 10) = 0.355
0 5
110
150
1
2
3
Normalized Moment at Infinity
Min
f/Mcr
3 1crit
Typical SFRC: = 0 – 1 and = 5 – 15
Required Residual strength for a given moment
M’∞ = 0.1 – 2.5 and = 5 - 15
0
0.5
5 muomega
' 3M
'
'3
M
M
0
12
3
5
10
150
0.5
1
Minf/Mcr
Normalized Post Crack Tensile Strength
omega
mu
(req
uire
d)
2cr cr
1M = bd E
6
Theoretical Flexural Strength for strain softening FRC
2n cr
1M 3 bd E
3n n p cr uM M M
'f
''
'
0.850.126866
6.7
cy cc
cr c
ff
f
n cr+ 6
15 55
2cult cr'
c
fM bd E
. +2 f
Plastic analysis, Round Panel- Fixed or Free
D
max
D
max
Fixed edges
Free edges
max
max
int extW W
4ult PP M 2ult PP M
24
2 3ult
Pq RR
M
2
12ult
Pq R
M
Concentrated Load
Distributed Load
23-Dec-09
9
Example Application for Three point bending Beams Plastic analysis Beam and Panel Flexure
q
LNNN
L
L/2L/2
L/2
L
int extW W
max
q
22 2 2
2 2P P
LM M [ q ]
L
2
8ult
Pq L
M
L/2
max
max
Modes of Failure
max
w
M p
M 0
M >0p
M <0p
Precast panels
Panels are made of plain concrete and steel rebar to be installed on site
Installation of pre-cast water tank
Panels are assembled on site
The wall joints are connected using bolts and epoxy
The base slab is connected to the periphery walls by friction through slots
23-Dec-09
10
Analysis of Wall Panels
Assume continuous wall, pin connection at the bottom and free at the top
Lateral water pressure in ultimate andultimate and serviceability limit states
Critical Internal Forces
Critical moment, shear, and axial forces– Horizontal
– Vertical
Design thickness and reinforcement for both– Ultimate
– Serviceability
Cast in Place Water Tank
For small dimension, the cast in place water tank is usually used.
Finite Element Analysis
Lateral loading– Water– Earth pressure– Surcharge
Finite element model– Shell elements
Analysis Results
Load Case1:– 1.4 Self weight +
1.4 Water pressure
– Moment in short span direction SM1
Load Case2:– 1.4 Self weight +
1.7 Earth pressure + 1.7 Uniform pressure due to surcharge
– Moment in short span direction SM1
Septic Tanks- 4 cm thickness with FRC vs. 12 cm with WWF
23-Dec-09
11
Lightweight, Durable, and economical Low income housing
Interior and exterior Wall panels plus roof are formed as one system Full frame & Roof form set up
Subdivision development Rebar Set up
23-Dec-09
12
1 house per day with a crew of 8
Conclusions
The tensile crack width relationship obtained from the inverse analysis correlates well with the yield line prediction
Plastic analysis design methodologies which were developed more than 5 years ago can be applied to fiber reinforced concrete structures built with Steel fibers.
Finite element method, when used in conjunction with simplified material models can be effectively used to verify the design geometry for a variety of structural applications.
Acknowledgements
US National Science Foundation, NSF, Award # 032466903, Program Manager, P. Balaguru.
Prof. Dr.-Ing. U. Gossla, Aachen University of Applied Sciences.
Gossla, U., Development of SFRC Free Suspended , , p pElevated Flat Slabs – Analysis and Design Recommendations. Research Report, Aachen University of Applied Sciences, 2005.