Finite element and analytical approaches for predicting the structural response of reinforced concrete slabs under blast loading

Transcription

1 Section: Blast Blind Predict of Response of Concrete Slabs Subjected to Blast Loading (Contest Winners) - October, :00 PM - 6:00 PM, C- B Chair: Prof. Ganesh Thiagarajan Finite element and analytical approaches for predicting the structural response of reinforced concrete slabs under blast loading Olmati P (), Trasborg P (), Sgambi L (), Naito CJ (), Bontempi F () () Ph.D. Candidate, P.E., Sapienza University of Rome, pierluigi.olmati@uniroma.it () Ph.D. Candidate, Lehigh University, pat0@lehigh.edu () Associate Researcher, Ph.D., P.E., Politecnico di Milano, sgambi@stru.polimi.it () Associate Professor and Associate Chair, Ph.D., P.E., Lehigh University, cjn@lehigh.edu () Professor, Ph.D., P.E., Sapienza University of Rome, franco.bontempi@uniroma.it cjn@lehigh.edu

2 Presentation outline Introduction Finite Element Model Analytical Model Conclusions Questions/References

3 The team - Short bio 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 0 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. cjn@lehigh.edu

4 The team - Short bio Patrick Trasborg, Ph.D. Candidate Patrick Trasborg is in his th 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. cjn@lehigh.edu

5 The team - Short bio Luca Sgambi, Associate Researcher, Ph.D., P.E. He studied Structural Engineering (998) and took a nd level Master degree in R.C. Structures (00) at Politecnico di Milano. He pursued his studies with a Ph.D. at La Sapienza University of Rome (00). At present, he holds the position of Assistant Professor at Politecnico di Milano and teaches Structural Analysis (since 00) at School of Civil Architecture, Politecnico di Milano. He is author of 7 papers on international journals and 7 paper on national and international conference proceedings; his research fields concerning the non linear structural analyses, soft computing techniques, durability of structural systems. cjn@lehigh.edu

6 6 The team - Short bio 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. cjn@lehigh.edu

7 7 The team - Short bio Franco Bontempi, Professor, Ph.D., P.E. Prof. Bontempi, born 96, obtained a Degree in Civil Engineering in 988 and a Ph.D. in Structural Engineering in 99, 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 000. 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 0 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. cjn@lehigh.edu

8 8 Presentation outline Introduction Finite Element Model Analytical Model Conclusions Questions/References

9 9 Finite element for modeling the concrete part of the slab 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 0,0. [image from ANSYS] Image provided by: Lawrence Software Technology Corporation (LSTC). LS-DYNA theory manual. California (US), Livermore Software Technology Corporation.

10 0 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. Image provided by: Lawrence Software Technology Corporation (LSTC). LS-DYNA theory manual. California (US), Livermore Software Technology Corporation.

11 The finite element mesh Solid elements: 70,960 Beam elements: 0 Total nodes: 90,68 Upper support Down support cjn@lehigh.edu

12 Pressure [psi] Demand PH-Set a PH-Set b Load Load Time [msec] cjn@lehigh.edu

13 Material model for the concrete The Continuous Surface Cap Model Material Model 9 LS-Dyna The cap retract in function of the equation of state. The dynamic increasing factor affects the failure surface. U.S. Department of Transportation, Federal Highway Administration. Users Manual for LS-DYNA Concrete, Material Model 9. cjn@lehigh.edu

14 DIF [-] Material model for the concrete The Continuous Surface Cap Model Material Model 9 LS-Dyna Density.8 lb f /in s.*0 kg/m 8 6 Compressive Tensile f c Cap retraction Rate effect Erosion 00 psi 7 N/mm active active none Strain-rate [/sec] U.S. Department of Transportation, Federal Highway Administration. Users Manual for LS-DYNA Concrete, Material Model 9. cjn@lehigh.edu

15 Material model for the rebar Piecewise Linear Plasticity Model Material Model LS-Dyna

16 Stress [kpsi] 6 Material model for the rebar Piecewise Linear Plasticity Model Material Model LS-Dyna ε: engineering strain σ: engineering stress ε T : true strain σ T : true stress σ y : engineering yield stress ε T = ln + ε σ T = σ e ε T True Stress Stress Plastic strain [-] ε T p = ε T σ T E σ T p = σ eε T σ y cjn@lehigh.edu

17 DIF [-] 7 Material model for the rebar Piecewise Linear Plasticity Model Cowper and Symonds model for the Material Model LS-Dyna DIF = + ε C q C= 00 [/s] q= Strain-rate [/sec] US Army Corps of Engineers, 008.Methodology Manual for the Single-Degree-of- Freedom Blast Effects Design Spreadsheets (SBEDS). cjn@lehigh.edu

18 8 Boundary conditions

19 9 Boundary conditions Shock load Upper support Gap 0. Contact surfaces Contact surfaces Down support

20 0 Boundary conditions

21 Results Deflection

22 Results Deflection

23 6 in. (6 mm) 6 in. (6 mm) Results Crack patterns.7 in. (87 mm).7 in. (87 mm) cjn@lehigh.edu

24 Presentation outline Introduction Finite Element Model Analytical Model Conclusions Questions/References

25 Concrete Stress [psi] Steel Stress [psi] Cross Section of Slab Analytical Model Fiber Analysis Cross section approximated by dividing into discrete fibers [Kaba, Mahin 98] Fiber Analysis of Section 6000 Steel Strain i number of layers A =d *b i i Conc Data Mod Popovics DIF Conc Steel Data 0000 DIF Steel Concrete Strain 0.0 Normal Strength Panel Strengths d d/i Concrete material model approximated with Popovic s model DIF models same as numerical model Correct DIF required iterative process b cjn@lehigh.edu

26 Moment [kip-in] 6 Analytical Model Moment Curvature & Boundary Conditions Curvature [/in] Normal Strength Panel Boundary conditions change as panel deflects due to support gap and panel yielding Normal Strength Panel Obtained through fiber-analysis Independent of boundary conditions SEC A-A " 0." BLAST LOAD High strength panel: hinging occurs " at ends before center SEC A-A " BLAST LOAD SEC A-A Deformed Simple-Simple KLM=0.78 Fixed-Fixed KLM=0.77 Hinge Center KLM=0.78 KLM=0.6 Mechanism KLM=0.66 cjn@lehigh.edu

27 Resistance [psi] 7 Analytical Model SDOF Approach & Results Normal Strength Panel Resistance Function Fixed-Fixed Simp-Simp Switches to Fixed Hinge Center to Fixed Center Ends Deflection [in]. Simple-Simple KLM=0.78 Fixed-Fixed KLM=0.77 Center KLM=0.6 Mechanism KLM=0.66 cjn@lehigh.edu

28 Deflection [in] Deflection [mm] Deflection [in] Deflection [mm] Resistance [psi] Resistance [psi] 8 Analytical Model SDOF Approach & Results Fixed-Fixed Switches to Fixed Center Ends Simp-Simp Deflection [in] Normal Strength Panel Load Load Avg Residual Avg Residual Time [ms] Results Switches to Fixed Ends Center Fixed-Fixed Deflection [in] High Strength Panel Load Avg Residual Load Avg Residual Time [ms] 0 cjn@lehigh.edu Simp-Simp

29 9 Analytical versus Experimental

30 0 Presentation outline Introduction Finite Element Model Analytical Model Conclusions Questions/References

31 Conclusions () - Use the symmetry when possible in order to reduce the computational cost and to improve the quality of the mesh. - The CSCM (mat 9 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 Down support cjn@lehigh.edu

32 Conclusions () - Analytical methods proved accurate when compared to numerical methods - Increasing the material strengths of the panel affected the progression of hinge formation Cross Section of Slab Fiber Analysis of Section Simple-Simple KLM=0.78 Fixed-Fixed KLM=0.77 Center KLM=0.6 Mechanism KLM=0.66 Simple-Simple KLM=0.78 Fixed-Fixed KLM=0.77 Simple-Simple KLM=0.78 Mechanism KLM=0.66 cjn@lehigh.edu

33 Deflection [in] Deflection [mm] 6 in. (6 mm) - 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.7 in. (87 mm) Conclusions () Analytical Numerical Time [ms] cjn@lehigh.edu

34 Presentation outline Introduction Finite Element Model Analytical Model Conclusions Questions/References

35 Questions Placement Normal Strength Numerical Prediction (LS-Dyna) st place Normal Strength Analytical Prediction (SDOF) nd place High Strength Analytical Prediction (SDOF) rd place (unofficial) High Strength Numerical Prediction (LS-Dyna) Not released References Kaba, S., Mahin, S., Refined Modeling of Reinforced Concrete Columns for Seismic Analysis, Nisee e-library, UCB/EERC-8/0, 98, 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 9. Olmati P, Trasborg P, Naito CJ, Bontempi F. Blast resistance of reinforced precast concrete walls under uncertainty. International Journal of Critical Infrastructures 0; accepted