Olmati P(1), Trasborg P(2), Sgambi L(3), Naito CJ(4), Bontempi F(5)
Olmati, Trasborg, Sgambi, Naito, Bontempi Sapienza University of Rome & Lehigh University
(3) Associate Researcher, Ph.D., P.E., Politecnico di Milano, Email: [email protected]
(1) Ph.D. Candidate, P.E., Sapienza University of Rome, Email: [email protected]
(4) Associate Professor and Associate Chair, Ph.D., P.E., Lehigh University, Email: [email protected] (5) Professor, Ph.D., P.E., Sapienza University of Rome, Email: [email protected]
(2) Ph.D. Candidate, Lehigh University, Email: [email protected]
Finite element and analytical approaches for predicting the structural response of reinforced
concrete slabs under blast loading
Section: Blast Blind Predict of Response of Concrete Slabs Subjected to Blast Loading (Contest Winners) - October 22, 4:00 PM - 6:00 PM, C-212 B
Chair: Prof. Ganesh Thiagarajan
Presentation outline
Introduction 1
Finite Element Model 2
Analytical Model 3
Conclusions 4
Questions/References 5
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Olmati, Trasborg, Sgambi, Naito, Bontempi Sapienza University of Rome & Lehigh University
The team - Short bio
3 Olmati, Trasborg, Sgambi, Naito, Bontempi Sapienza University of Rome & Lehigh University
Pierluigi Olmati is in the last year of his Ph.D. in
Structural Engineering at the Sapienza
University of Rome (Italy), with advisor Prof.
Franco Bontempi from the same University and
co-advisor Prof. Clay J. Naito from the Lehigh
University (Bethlehem, PA, USA).
The principal research topic of Mr. Olmati is blast engineering, addressed from
the point of view of FE modeling and probabilistic design. Mr. Olmati spent six
months at the Lehigh University in 2012 studying the performance of insulated
panels subjected to close-in detonations. Recently he was visiting Prof. Charis
Gantes and Prof. Dimitrios Vamvatsikos at the Department of Structural
Engineering of the National Technical University of Athens (Greece), performing
research on the probabilistic aspects of the blast design, and in particular,
developing fragility curves and a safety for built-up blast doors.
Pierluigi Olmati, Ph.D. Candidate, P.E. 1
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The team - Short bio 4
Olmati, Trasborg, Sgambi, Naito, Bontempi Sapienza University of Rome & Lehigh University
Patrick Trasborg, Ph.D. Candidate
Patrick Trasborg is in his 4th year of his
Ph.D. in Structural Engineering at Lehigh
University (Bethlehem, PA, USA), with
advisor Professor Clay Naito from the
same University.
The principal research topic of Mr. Trasborg is blast engineering, addressed from
the point of view of analytical modeling with experimental validation. Mr.
Trasborg’s dissertation is on the development of a blast and ballistic resistant
insulated precast concrete wall panel. Currently he is characterizing the
performance of insulated panels with various shear ties subjected to uniform
loading.
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The team - Short bio 5
Olmati, Trasborg, Sgambi, Naito, Bontempi Sapienza University of Rome & Lehigh University
Luca Sgambi, Associate Researcher,
Ph.D., P.E.
He studied Structural Engineering (1998) and took a 2nd
level Master degree in R.C. Structures (2001) at
Politecnico di Milano. He pursued his studies with a Ph.D.
at “La Sapienza” University of Rome (2005).
At present, he holds the position of Assistant Professor at Politecnico di Milano
and teaches “Structural Analysis” (since 2003) at School of Civil Architecture,
Politecnico di Milano. He is author of 7 papers on international journals and 57
paper on national and international conference proceedings; his research fields
concerning the non linear structural analyses, soft computing techniques,
durability of structural systems.
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The team - Short bio 6
Olmati, Trasborg, Sgambi, Naito, Bontempi Sapienza University of Rome & Lehigh University
Clay Naito, Associate Professor and
Associate Chair, Ph.D., P.E.
Clay J. Naito is an associate professor of Structural Engineering and associate chair at Lehigh University Department of Civil and Environmental Engineering. He received his undergraduate degree from the University of Hawaii and his graduate degrees from the University of California Berkeley.
He is a licensed professional engineer in Pennsylvania and California. His research interests include experimental and analytical evaluation of reinforced and prestressed concrete structures subjected to extreme events including earthquakes, intentional blast demands, and tsunamis. Professor Naito is Chair of the PCI Blast Resistance and Structural Integrity Committee and an Associate Editor of the ASCE Bridge Journal.
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The team - Short bio 7
Olmati, Trasborg, Sgambi, Naito, Bontempi Sapienza University of Rome & Lehigh University
Franco Bontempi, Professor, Ph.D., P.E.
Prof. Bontempi, born 1963, obtained a Degree in Civil
Engineering in 1988 and a Ph.D. in Structural Engineering in
1993, from the Politecnico di Milano. He is a Professor of
Structural Analysis and Design at the School of Engineering of
the Sapienza University of Rome since 2000.
He spent research periods at the Harbin Institute of Technology, the Univ. of Illinois
Urbana-Champaign, the TU of Karlsruhe and the TU of Munich. He has a wide activity
as a consultant for special structures and as forensic engineering expert.
Prof. Bontempi has a deep research activity on numerous themes related to
Structural Engineering, having developed approximately 250 scientific and technical
publications on the topics: Structural Analysis and Design, System Engineering,
Performance-based Design, Hazard and Risk Analysis, Safety and Reliability
Engineering, Dependability, Structural Integrity, Structural Dynamics and Interaction
Phenomena, Identification, Optimization and Control of Structures, Bridges and
Viaducts, High-rise Buildings, Special Structures, Offshore Wind Turbines.
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Presentation outline
Introduction 1
Finite Element Model 2
Analytical Model 3
Conclusions 4
Questions/References 5
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Olmati, Trasborg, Sgambi, Naito, Bontempi Sapienza University of Rome & Lehigh University
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Finite element for modeling the concrete part of the slab 9
Olmati, Trasborg, Sgambi, Naito, Bontempi Sapienza University of Rome & Lehigh University
Image provided by: Lawrence Software Technology Corporation (LSTC). LS-DYNA theory manual. California (US), Livermore Software Technology Corporation.
Eight-node solid hexahedron element (constant stress solid element) with reduced integration. Default in LS-Dyna®. Other choices were prohibitive because computationally expensive.
Hourglass: Flanagan-Belytschko stiffness form with hourglass coefficient equal to 0,05.
1
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5 [image from ANSYS]
Finite element for modeling the reinforcements of the slab 10
Olmati, Trasborg, Sgambi, Naito, Bontempi Sapienza University of Rome & Lehigh University
The Hughes-Liu beam element with cross section integration. Tubular cross section with internal diameter much smaller than the external diameter.
Image provided by: Lawrence Software Technology Corporation (LSTC). LS-DYNA theory manual. California (US), Livermore Software Technology Corporation.
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The finite element mesh 11
Olmati, Trasborg, Sgambi, Naito, Bontempi Sapienza University of Rome & Lehigh University
Upper support
Down support
Solid elements: 270,960 Beam elements: 130 Total nodes: 290,628 1
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5
Demand 12
Olmati, Trasborg, Sgambi, Naito, Bontempi Sapienza University of Rome & Lehigh University
0
10
20
30
40
50
60
0 20 40 60 80 100
Pre
ssure
[psi
]
Time [msec]
PH-Set 1a
PH-Set 1b
Load 1
Load 2
1
2
3
4
5
Material model for the concrete – The Continuous Surface Cap Model 13
Olmati, Trasborg, Sgambi, Naito, Bontempi Sapienza University of Rome & Lehigh University
U.S. Department of Transportation, Federal Highway Administration. Users Manual for LS-DYNA Concrete, Material Model 159.
The cap retract in function of the equation of state.
Material Model 159 – LS-Dyna®
The dynamic increasing factor affects the failure surface.
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Material model for the concrete – The Continuous Surface Cap Model 14
Olmati, Trasborg, Sgambi, Naito, Bontempi Sapienza University of Rome & Lehigh University
U.S. Department of Transportation, Federal Highway Administration. Users Manual for LS-DYNA Concrete, Material Model 159.
Material Model 159 – LS-Dyna®
Density 2.248 lbf/in
4 s
2
2.4*103 kg/m
3
fc 5400 psi
37 N/mm2
Cap
retraction active
Rate
effect active
Erosion none
0
2
4
6
8
0.001 0.1 10 1000D
IF [
-]Strain-rate [1/sec]
CompressiveTensile
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2
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4
5
Material model for the rebar– Piecewise Linear Plasticity Model 15
Olmati, Trasborg, Sgambi, Naito, Bontempi Sapienza University of Rome & Lehigh University
Material Model 24 – LS-Dyna®
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Material model for the rebar– Piecewise Linear Plasticity Model 16
Olmati, Trasborg, Sgambi, Naito, Bontempi Sapienza University of Rome & Lehigh University
Material Model 24 – LS-Dyna®
0
20
40
60
80
100
120
140
0 0.05 0.1 0.15 0.2
Str
ess
[kpsi
]
Plastic strain [-]
True Stress
Stress
εT= ln 1 + ε
σT= σ eεT
εTp= εT −σT
E
ε: engineering strain σ: engineering stress εT: true strain σT: true stress σy: engineering yield stress
σTp= σ eεT − σy
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2
3
4
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Material model for the rebar– Piecewise Linear Plasticity Model 17
Olmati, Trasborg, Sgambi, Naito, Bontempi Sapienza University of Rome & Lehigh University
1
1.2
1.4
1.6
1.8
2
0.001 0.01 0.1 1 10 100
DIF
[-]
Strain-rate [1/sec]
US Army Corps of Engineers, 2008.Methodology Manual for the Single-Degree-of-Freedom Blast Effects Design Spreadsheets (SBEDS).
Cowper and Symonds model for the Material Model 24 – LS-Dyna®
DIF = 1 +ε
C
1q
C= 500 [1/s] q=6 1
2
3
4
5
Boundary conditions 18
Olmati, Trasborg, Sgambi, Naito, Bontempi Sapienza University of Rome & Lehigh University
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Boundary conditions 19
Olmati, Trasborg, Sgambi, Naito, Bontempi Sapienza University of Rome & Lehigh University
Down support
Upper support
Contact surfaces
Contact
surfaces
Shock load
Gap 0.25”
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Boundary conditions 20
Olmati, Trasborg, Sgambi, Naito, Bontempi Sapienza University of Rome & Lehigh University
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Results – Deflection 21
Olmati, Trasborg, Sgambi, Naito, Bontempi Sapienza University of Rome & Lehigh University
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Results – Deflection 22
Olmati, Trasborg, Sgambi, Naito, Bontempi Sapienza University of Rome & Lehigh University
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Results – Crack patterns 23
Olmati, Trasborg, Sgambi, Naito, Bontempi Sapienza University of Rome & Lehigh University
33.75 in. (857 mm)
64
in. (
16
25
mm
)
33.75 in. (857 mm)
64
in. (
16
25
mm
)
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Presentation outline
Introduction 1
Finite Element Model 2
Analytical Model 3
Conclusions 4
Questions/References 5
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Olmati, Trasborg, Sgambi, Naito, Bontempi Sapienza University of Rome & Lehigh University
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Analytical Model – Fiber Analysis 25
Olmati, Trasborg, Sgambi, Naito, Bontempi Sapienza University of Rome & Lehigh University
Cross Section of Slab
Fiber Analysis of Section
Cross section approximated by dividing into discrete fibers [Kaba, Mahin 1983]
0 0.05 0.1 0.15 0.2
0
50000
100000
150000
200000
0
1500
3000
4500
6000
0 0.01 0.02 0.03
Steel Strain
Ste
el S
tres
s [p
si]
Co
ncr
ete
Str
ess
[psi
]
Concrete Strain
Conc DataMod PopovicsDIF ConcSteel DataDIF Steel
A =d *bi
dd/i
i number of layers
i
b
• Concrete material model approximated with Popovic’s model
• DIF models same as numerical model • Correct DIF required iterative process Normal Strength Panel Strengths
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Analytical Model – Moment Curvature & Boundary Conditions 26
Olmati, Trasborg, Sgambi, Naito, Bontempi Sapienza University of Rome & Lehigh University
-100
0
100
200
300
400
-0.02 -0.01 0 0.01 0.02 0.03
Mo
men
t [k
ip-i
n]
Curvature [1/in]
• Obtained through fiber-analysis • Independent of boundary
conditions
Simple-Simple
KLM=0.78
Fixed-Fixed
KLM=0.77
Hinge @ Center
KLM=0.64Mechanism
KLM=0.66
Boundary conditions change as panel deflects due to support gap and panel yielding
3"
4"
BLAST LOAD0.25"
BLAST LOAD
SEC A-A
SEC A-A
52"
SEC A-A Deformed
Simple-Simple
KLM=0.78
Fixed-Fixed
KLM=0.77
Simple-Simple
KLM=0.78Mechanism
KLM=0.66
Normal Strength Panel
High strength panel:
hinging occurs at ends
before center
Normal Strength Panel
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Analytical Model – SDOF Approach & Results 27
Olmati, Trasborg, Sgambi, Naito, Bontempi Sapienza University of Rome & Lehigh University
Normal Strength Panel Resistance Function
Simple-Simple
KLM=0.78
Fixed-Fixed
KLM=0.77
Hinge @ Center
KLM=0.64Mechanism
KLM=0.66
0
5
10
15
20
25
30
35
40
0 0.5 1 1.5 2 2.5 3
Res
ista
nce
[p
si]
Deflection [in]
Simp-Simp
0
5
10
15
20
25
30
35
40
0 0.5 1 1.5 2 2.5 3
Res
ista
nce
[p
si]
Deflection [in]
Simp-Simp
Fixed-Fixed
0
5
10
15
20
25
30
35
40
0 0.5 1 1.5 2 2.5 3
Res
ista
nce
[p
si]
Deflection [in]
Simp-Simp
Fixed-Fixed
0
5
10
15
20
25
30
35
40
0 0.5 1 1.5 2 2.5 3
Res
ista
nce
[p
si]
Deflection [in]
Switches to Fixed
Simp-Simp
Fixed-Fixed
0
5
10
15
20
25
30
35
40
0 0.5 1 1.5 2 2.5 3
Res
ista
nce
[p
si]
Deflection [in]
Switches to Fixed
Hinge @ Center
Simp-Simp
Fixed-Fixed
0
5
10
15
20
25
30
35
40
0 0.5 1 1.5 2 2.5 3
Res
ista
nce
[p
si]
Deflection [in]
Switches to FixedHinge @ CenterHinges @ Ends
Simp-Simp
Fixed-Fixed
0
5
10
15
20
25
30
35
40
0 0.5 1 1.5 2 2.5 3
Res
ista
nce
[p
si]
Deflection [in]
Switches to FixedHinge @ CenterHinges @ Ends
Simp-Simp
Fixed-Fixed
Simple-Simple
KLM=0.78
Fixed-Fixed
KLM=0.77
Hinge @ Center
KLM=0.64Mechanism
KLM=0.66
Simple-Simple
KLM=0.78
Fixed-Fixed
KLM=0.77
Hinge @ Center
KLM=0.64Mechanism
KLM=0.66
Simple-Simple
KLM=0.78
Fixed-Fixed
KLM=0.77
Hinge @ Center
KLM=0.64Mechanism
KLM=0.66
1
2
3
4
5
Analytical Model – SDOF Approach & Results 28
Olmati, Trasborg, Sgambi, Naito, Bontempi Sapienza University of Rome & Lehigh University
0
5
10
15
20
25
30
35
40
0 0.5 1 1.5 2 2.5 3
Res
ista
nce
[p
si]
Deflection [in]
Switches to FixedHinge @ CenterHinges @ Ends
Simp-Simp
Fixed-Fixed
Normal Strength Panel High Strength Panel
0
20
40
60
80
100
120
0
1
2
3
4
5
0 25 50 75 100 125 150
Def
lect
ion
[m
m]
Def
lect
ion
[in
]
Time [ms]
Load 1 Avg Residual
Load 2 Avg Residual
0
10
20
30
40
50
60
70
0
0.5
1
1.5
2
2.5
3
0 25 50 75 100 125 150
Def
lect
ion
[m
m]
Def
lect
ion
[in
]
Time [ms]
Load 1 Avg ResidualLoad 2 Avg Residual
Results
0
10
20
30
40
50
60
70
0 0.5 1 1.5 2 2.5 3 3.5 4
Res
ista
nce
[p
si]
Deflection [in]
Switches to FixedHinges @ EndsHinge @ Center
Simp-Simp
Fixed-Fixed
1
2
3
4
5
Analytical versus Experimental 29
Olmati, Trasborg, Sgambi, Naito, Bontempi Sapienza University of Rome & Lehigh University
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Presentation outline
Introduction 1
Finite Element Model 2
Analytical Model 3
Conclusions 4
Questions/References 5
30
Olmati, Trasborg, Sgambi, Naito, Bontempi Sapienza University of Rome & Lehigh University
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Upper support
Down support
Conclusions (1) 31
Olmati, Trasborg, Sgambi, Naito, Bontempi Sapienza University of Rome & Lehigh University
- Use the symmetry when possible in order to reduce the
computational cost and to improve the quality of the mesh.
- The CSCM (mat 159 LS-Dyna®) for concrete is appropriate for
modeling component responding with flexural mechanism.
- The reinforcements should be modeled by beam elements in order
to be able to carry shear stresses; this is crucial for component with
thin cross section.
- In this case the boundary conditions have a crucial importance.
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Conclusions (2) 32
Olmati, Trasborg, Sgambi, Naito, Bontempi Sapienza University of Rome & Lehigh University
Simple-Simple
KLM=0.78
Fixed-Fixed
KLM=0.77
Hinge @ Center
KLM=0.64Mechanism
KLM=0.66
Simple-Simple
KLM=0.78
Fixed-Fixed
KLM=0.77
Simple-Simple
KLM=0.78Mechanism
KLM=0.66
Cross Section of Slab
Fiber Analysis of Section
- Analytical methods proved accurate when
compared to numerical methods
- Increasing the material strengths of the panel
affected the progression of hinge formation
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Conclusions (3) 33
Olmati, Trasborg, Sgambi, Naito, Bontempi Sapienza University of Rome & Lehigh University
0
20
40
60
80
100
120
0
1
2
3
4
5
0 25 50 75 100 125
Def
lect
ion
[m
m]
Def
lect
ion
[in
]
Time [ms]
Analytical Numerical
- Analytical methods provide close results to numerical methods. This
is useful for a quick check of results before performing a detailed
design.
- For more detailed analysis, such as crack patterns, numerical
methods are required 33.75 in. (857 mm)
64
in. (
16
25
mm
)
33.75 in. (857 mm)
64
in. (
16
25
mm
)
1
2
3
4
5
Presentation outline
Introduction 1
Finite Element Model 2
Analytical Model 3
Conclusions 4
Questions/References 5
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Olmati, Trasborg, Sgambi, Naito, Bontempi Sapienza University of Rome & Lehigh University
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Questions 35
Olmati, Trasborg, Sgambi, Naito, Bontempi Sapienza University of Rome & Lehigh University
• Kaba, S., Mahin, S., “Refined Modeling of Reinforced Concrete Columns for Seismic Analysis,” Nisee e-library, UCB/EERC-84/03, 1984, http://nisee.berkeley.edu/elibrary/Text/141375
• Lawrence Software Technology Corporation (LSTC). LS-DYNA theory manual. California (US), Livermore Software Technology Corporation.
• U.S. Department of Transportation, Federal Highway Administration. Users Manual for LS-DYNA Concrete, Material Model 159.
• Olmati P, Trasborg P, Naito CJ, Bontempi F. Blast resistance of reinforced precast concrete walls under uncertainty. International Journal of Critical Infrastructures 2013; accepted
References
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2
3
4
5
Placement
• Normal Strength – Numerical Prediction (LS-Dyna) – 1st place
• Normal Strength – Analytical Prediction (SDOF) – 2nd place
• High Strength – Analytical Prediction (SDOF) – 3rd place (unofficial)
• High Strength – Numerical Prediction (LS-Dyna) – Not released
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