Diapositiva 1 - Lehigh University

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

Finite element and analytical approaches for predicting the structural response of reinforced concrete slabs under blast loading Olmati P(1), Trasborg P(2), Sgambi L(3), Naito CJ(4), Bontempi F(5) (1)

Ph.D. Candidate, P.E., Sapienza University of Rome, Email: [email protected] (2) Ph.D. Candidate, Lehigh University, Email: [email protected] (3) Associate Researcher, Ph.D., P.E., Politecnico di Milano, 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] Olmati, Trasborg, Sgambi, Naito, Bontempi Sapienza University of Rome & Lehigh University

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Presentation outline

2

1

1

Introduction

2

2

Finite Element Model

3

3

Analytical Model

4

4

Conclusions

5

5

Questions/References

Olmati, Trasborg, Sgambi, Naito, Bontempi Sapienza University of Rome & Lehigh University

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The team - Short bio

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Pierluigi Olmati, Ph.D. Candidate, P.E. 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. Olmati, Trasborg, Sgambi, Naito, Bontempi Sapienza University of Rome & Lehigh University

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4

Patrick Trasborg, Ph.D. Candidate

1 2

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.

3 4 5

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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1 2 3 4

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.

5 Olmati, Trasborg, Sgambi, Naito, Bontempi Sapienza University of Rome & Lehigh University

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1 2 3 4

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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Franco Bontempi, Professor, Ph.D., P.E.

1 2 3 4 5

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. Olmati, Trasborg, Sgambi, Naito, Bontempi Sapienza University of Rome & Lehigh University

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1

1

Introduction

2

2


3

3

Analytical Model

4

4

Conclusions

5

5



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Finite element for modeling the concrete part of the slab

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1 2 3

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.

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[image from ANSYS]

Image provided by: Lawrence Software Technology Corporation (LSTC). LS-DYNA theory manual. California (US), Livermore Software Technology Corporation. Olmati, Trasborg, Sgambi, Naito, Bontempi Sapienza University of Rome & Lehigh University

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1

Finite element for modeling the reinforcements of the slab The Hughes-Liu beam element with cross section integration. Tubular cross section with internal diameter much smaller than the external diameter.

2 3 4 5

Image provided by: Lawrence Software Technology Corporation (LSTC). LS-DYNA theory manual. California (US), Livermore Software Technology Corporation. Olmati, Trasborg, Sgambi, Naito, Bontempi Sapienza University of Rome & Lehigh University

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The finite element mesh

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1

Solid elements: 270,960 Beam elements: 130 Total nodes: 290,628

Upper support

2 3 4

Down support


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Demand

12

60

2 3 4

Pressure [psi]

1

50

PH-Set 1a

40

PH-Set 1b

30

Load 1 Load 2

20 10 0

5

0

20

40 60 Time [msec]


80

100

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Material model for the concrete – The Continuous Surface Cap Model Material Model 159 – LS-Dyna®

1 The cap retract in function of the equation of state.

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The dynamic increasing factor affects the failure surface. U.S. Department of Transportation, Federal Highway Administration. Users Manual for LS-DYNA Concrete, Material Model 159. Olmati, Trasborg, Sgambi, Naito, Bontempi Sapienza University of Rome & Lehigh University

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Material model for the concrete – The Continuous Surface Cap Model Material Model 159 – LS-Dyna®

1 8

3 4

Density fc

5400 psi 37 N/mm2

Cap retraction Rate effect Erosion

active active none

6 DIF [-]

2

2.248 lbf/in4 s2 2.4*103 kg/m3

Compressive Tensile

4 2

0 0.001

0.1 10 Strain-rate [1/sec]

1000

5 U.S. Department of Transportation, Federal Highway Administration. Users Manual for LS-DYNA Concrete, Material Model 159. Olmati, Trasborg, Sgambi, Naito, Bontempi Sapienza University of Rome & Lehigh University

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15

Material model for the rebar– Piecewise Linear Plasticity Model Material Model 24 – LS-Dyna®

1 2 3 4 5 Olmati, Trasborg, Sgambi, Naito, Bontempi Sapienza University of Rome & Lehigh University

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1 2

Material model for the rebar– Piecewise Linear Plasticity Model Material Model 24 – LS-Dyna® ε: engineering strain σ: engineering stress εT = ln 1 + εT: true strain σT: true stress σT = σ eεT σy: engineering yield stress 140

ε

σT εT p = εT − E σT p = σ eεT −

3 4

Stress [kpsi]

120 100 80

60

True Stress Stress

40 20

5

0 0

0.05 0.1 0.15 Plastic strain [-]


0.2 [email protected]

σy

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Material model for the rebar– Piecewise Linear Plasticity Model Cowper and Symonds model for the Material Model 24 – LS-Dyna®

1

DIF = 1 +

ε C

1 q

2

C= 500 [1/s] q=6

2

US Army Corps of Engineers, 2008.Methodology Manual for the Single-Degree-ofFreedom Blast Effects Design Spreadsheets (SBEDS).

3

DIF [-]

1.8 1.6 1.4

4 1.2

5

1 0.001 0.01

0.1 1 10 Strain-rate [1/sec]


100

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Boundary conditions

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Boundary conditions

19

Shock load

1 Upper support

2

Gap 0.25”

Contact surfaces

3 4 Contact surfaces

5

Down support


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Boundary conditions

20


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Results – Deflection

21


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Results – Deflection

22


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Results – Crack patterns

23 33.75 in. (857 mm)

33.75 in. (857 mm)

1

64 in. (1625 mm)

3

64 in. (1625 mm)

2

4 5 Olmati, Trasborg, Sgambi, Naito, Bontempi Sapienza University of Rome & Lehigh University

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24

1

1

Introduction

2

2


3

3

Analytical Model

4

4

Conclusions

5

5



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Analytical Model – Fiber Analysis

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Cross section approximated by dividing into discrete fibers [Kaba, Mahin 1983] Cross Section of Slab

1 2

Fiber Analysis of Section

3 0

0.05

Steel Strain 0.1

0.15

200000

4500

150000

4

3000

Conc Data Mod Popovics DIF Conc Steel Data DIF Steel

1500

5

0 0

0.01 0.02 Concrete Strain

100000 50000 0 0.03

Normal Strength Panel Strengths

i number of layers

Steel Stress [psi]

Concrete Stress [psi]

6000

A i =di *b

0.2

d

d/i

b

• Concrete material model approximated with Popovic’s model • DIF models same as numerical model • Correct DIF required iterative process


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Analytical Model – Moment Curvature & Boundary Conditions

26

1 2 3

Moment [kip-in]

400 300

• Obtained through fiber-analysis • Independent of boundary conditions

200

100 0

-100 -0.02

-0.01

0 0.01 Curvature [1/in]

0.02

0.03

52"

BLAST LOAD

Normal Strength Panel

SEC A-A

3"

High strength0.25" panel: Boundary conditions change as panel deflects hinging occurs 4" at ends due to support gap and panel yielding

BLAST LOAD

before center

4

SEC A-A

SEC A-A Deformed

Normal Strength Panel

5

Simple-Simple Simple-Simple KLM=0.78 KLM=0.78

Fixed-Fixed Fixed-Fixed KLM=0.77 KLM=0.77


Hinge @ Center Simple-Simple KLM=0.64 KLM=0.78

Mechanism Mechanism KLM=0.66 KLM=0.66

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Analytical Model – SDOF Approach & Results

27

Normal Strength Panel Resistance Function

2

Resistance [psi]

1

3

40 35 30 25 20 15 10 5 0

Fixed-Fixed

Simp-Simp Switches Switches to to Fixed Fixed Hinge Switches @ Center to Fixed Hinge Hinges@ @Center Ends 0

0.5

1 1.5 2 Deflection [in]

2.5

3

4 5

Simple-Simple KLM=0.78

Fixed-Fixed KLM=0.77


Hinge @ Center KLM=0.64

Mechanism KLM=0.66

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Analytical Model – SDOF Approach & Results

Simp-Simp Switches to Fixed Hinge @ Center Hinges @ Ends 0

3

0.5

1 1.5 2 Deflection [in]

2.5

Normal Strength Panel Load 1 Load 2

5

Avg Residual Avg Residual

4

100

2.5

3

80

60 40

1

20

0

0 25

50

75 100 Time [ms]

125

Deflection [in]

3

0

Fixed-Fixed 0

120

2

5

3

Simp-Simp

0.5

150


1

1.5 2 2.5 Deflection [in]

3

3.5

4

High Strength Panel

Results

Deflection [in]

4

Resistance [psi]

Fixed-Fixed

Switches to Fixed Hinges @ Ends Hinge @ Center

70 60 50 40 30 20 10 0

Load 1 Load 2

Avg Residual Avg Residual

2

1.5 1

0.5 0 0

25

50

75 100 Time [ms]

125

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150

70 60 50 40 30 20 10 0

Deflection [mm]

2

40 35 30 25 20 15 10 5 0

Deflection [mm]

1

Resistance [psi]

28

Analytical versus Experimental

29


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30

1

1

Introduction

2

2


3

3

Analytical Model

4

4

Conclusions

5

5



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Conclusions (1)

31

- Use the symmetry when possible in order to reduce the computational cost and to improve the quality of the mesh.

1 2 3

- 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. Upper support

4 5

Down support


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Conclusions (2)

32

- Analytical methods proved accurate when compared to numerical methods

1 2

- Increasing the material strengths of the panel affected the progression of hinge formation Cross Section of Slab

Fiber Analysis of Section

3 4



Hinge @ Center KLM=0.64

Mechanism KLM=0.66




Mechanism KLM=0.66


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Conclusions (3)

33

5

4 5

Numerical

120

4

100

3

80

Deflection [in]

3

Analytical

60

2

40

1

20

0

0 0

25

50 75 Time [ms]

100


64 in. (1625 mm)

2

- For more detailed analysis, such as crack patterns, numerical 33.75 in. (857 mm) methods are required

Deflection [mm]

1

- Analytical methods provide close results to numerical methods. This is useful for a quick check of results before performing a detailed design.

125

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34

1

1

Introduction

2

2


3

3

Analytical Model

4

4

Conclusions

5

5



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Questions

35

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

1 2 3

References

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4

• •

5

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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 LSDYNA 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


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