Development of dimensionless P-I diagram for curved SCS sandwich shell subjected to uniformly distributed blast pressure

Abstract

The curved steel-concrete-steel (SCS) sandwich shell was recently proposed to resist blast loading and it showed better blast resistant performance as compared to flat SCS sandwich shell via developing compressive force along the shell. In this paper, a dimensionless Pressure-Impulse (P-I) diagram was constructed as a convenient tool to predict the damage level of curved SCS sandwich shell subjected to uniformly distributed blast loading. The curved SCS sandwich shell was equivalent to a single-degree-of-freedom (SDOF) system and the equation of motion was established by employing the Lagrange’s equation. To construct the dimensionless P-I diagram, the energy balance method was utilized to yield the pressure and impulse asymptotes and the responses in the dynamic response regime were obtained via employing the SDOF method. Then, the finite element method was employed to validate the developed dimensionless P-I diagram. Finally, the procedures of using the constructed dimensionless P-I diagram to quickly conduct the blast resistant design of curved SCS sandwich shell were presented.

Keywords

blast loading / curved steel-concrete-steel sandwich shell / Pressure-Impulse diagram / single-degree-of-freedom method / finite element analysis

References

[1] Oduyemi T O S, Wright H D. An experimental investigation into the behavior of double skin sandwich beams. Journal of Constructional Steel Research, 1989, 14(3): 197–220

[2] Malek N, Machida A, Mutsuyoshi H, Makabe T. Steel-concrete sandwich members without shear reinforcement. Transactions of the Japan Concrete Institute, 1993, 15(2): 1279–1284

[3] Foundoukos N. Behavior and design of steel-concrete-steel sandwich construction. Thesis for the Doctoral Degree. London: University of London, 2005

[4] Huang Z, Liew J Y R. Structural behaviour of steel-concrete-steel sandwich composite wall subjected to compression and end moment. Thin-walled Structures, 2016, 98: 592–606

[5] Yan J B, Liew J Y R, Zhang M H. Tensile resistance of J-hook connectors used in Steel-Concrete-Steel sandwich structure. Journal of Constructional Steel Research, 2014, 100: 146–162

[6] Liew J Y R, Sohel K M A, Koh C G. Impact tests on steel-concrete-steel sandwich beams with lightweight concrete core. Engineering Structures, 2009, 31(9): 2045–2059

[7] Remennikov A M, Kong S Y. Numerical simulation and validation of impact response of axially-restrained steel-concrete-steel sandwich panels. Composite Structures, 2012, 94(12): 3546–3555

[8] Anandavalli N, Lakshmanan N, Rajasankar J, Parkash A. Numerical studies on blast loaded steel-concrete composite panels. JCES, 2012, 1(3): 102–108

[9] Wang Y, Liew J Y R, Lee S C. Theoretical models for axially restrained steel-concrete-steel sandwich panels under blast loading. International Journal of Impact Engineering, 2015, 76: 221–231

[10] Crawford J E, Lan S. Blast barrier design and testing. In: Proceedings of the ASCE Structures Congress, St. Louis, Missour, 2006

[11] Liew J Y R, Wang T Y. Novel steel-concrete-steel sandwich composite plates subjected to impact and blast load. Advances in Structural Engineering, 2011, 14(4): 673–687

[12] Lan S, Lok T S, Heng L. Composite structural panels subjected to explosive loading. Construction & Building Materials, 2005, 19(5): 387–395

[13] Wang Y, Liew J Y R, Lee S C. Experimental and numerical studies of non-composite Steel-Concrete-Steel sandwich panels under impulsive loading. Materials & Design, 2015, 81: 104–112

[14] Wang Y, Zhai X, Lee S C, Wang W. Responses of curved steel-concrete-steel sandwich shells subjected to blast loading. Thin-walled Structures, 2016, 108: 185–192

[15] Yan J B, Liew J Y R, Zhang M H, Sohel K M A. Experimental and analytical study on ultimate strength behavior of steel-concrete-steel sandwich composite beam structures. Materials and Structures, 2015, 48(5): 1523–1544

[16] Yan J B, Liew J Y R, Zhang M H, Li Z X. Punching shear resistance of steel-concrete-steel sandwich composite shell structure. Engineering Structures, 2016, 117: 470–485

[17] Yan J B, Xiong M X, Qian X, Liew J Y R. Numerical and parametric study of curved steel-concrete-steel sandwich composite beams under concentrated loading. Materials and Structures, 2016, 49(10): 3981–4001

[18] Yan J B, Richard Liew J Y, Qian X, Wang J Y. Ultimate strength behavior of curved Steel-Concrete-Steel sandwich composite beams. Journal of Constructional Steel Research, 2015, 115: 316–328

[19] Huang Z, Liew J Y R. Nonlinear finite element modeling and parametric study of curved steel-concrete-steel double skin composite panels infilled with ultra-lightweight cement composite. Construction & Building Materials, 2015, 95: 922–938

[20] Huang Z Y, Wang J Y, Richard Liew J Y, William Marshall P. Lightweight steel-concrete-steel sandwich composite shell subject to punching shear. Ocean Engineering, 2015, 102: 146–161

[21] Biggs J M. Introduction to Structural Dynamics. New York: McGraw-Hill, 1964

[22] Wang Y, Xiong M X. Analysis of axially restrained water storage tank under blast loading. International Journal of Impact Engineering, 2015, 86: 167–178

[23] Rigby S E, Tyas A, Bennett T. Elastic-plastic response of plates subjected to cleared blast loads. International Journal of Impact Engineering, 2014, 66: 37–47

[24] Morison C M. Dynamic response of walls and slabs by single-degree-of-freedom analysis-a critical review and revision. International Journal of Impact Engineering, 2006, 32(8): 1214–1247

[25] Nassr A A, Razaqpur A G, Tait M J, Campidelli M, Foo S. Single and multi degree of freedom analysis of steel beams under blast loading. Nuclear Engineering and Design, 2012, 242(1): 63–77

[26] Carta G, Stochino F. Theoretical models to predict the flexural failure of reinforced concrete beams under blast loads. Engineering Structures, 2013, 49: 306–315

[27] Krauthammer T, Bazeos N, Holmquist T J. Modified SDOF analysis of box-type structures. Journal of Structural Engineering, 1986, 112(4): 726–744

[28] Astarlioglu S, Krauthammer T, Morency D, Tran T P. Behavior of reinforced concrete columns under combined effects of axial and blast-induced transverse loads. Engineering Structures, 2013, 55: 26–34

[29] UFC 3-340-02. Structures to Resist the Effects of Accidental Explosions. Washington, D.C.: US Department of Army, Navy and the Air Force, 2008

[30] ASCE. Design of Blast-Resistant Buildings in Petrochemical Facilities. American Society of Civil Engineers, 2010

[31] ASCE. Blast Protection of Buildings. ASCE/SEI 59-11. American Society of Civil Engineers, 2011

[32] Mays G, Smith P D. Blast Effects on Buildings: Design of Buildings to Optimize Resistance to Blast Loading. London: T. Telford, 1995

[33] Li Q M, Meng H. Pressure-impulse diagram for blast loads based on dimensional analysis and single-degree-of-freedom mode. Journal of Engineering Mechanics, 2002, 128(1): 87–92

[34] Li Q M, Meng H. Pulse loading shape effects on pressure-impulse diagram of an elastic-plastic, single-degree-of-freedom structural model. International Journal of Mechanical Sciences, 2002, 44(9): 1985–1998

[35] Fallah A S, Louca L A. Pressure-impulse diagrams for elastic-plastic-hardening and softening single-degree-of-freedom models subjected to blast loading. International Journal of Impact Engineering, 2007, 34(4): 823–842

[36] Krauthammer T, Astarlioglu S, Blasko J, Soh T B, Ng P H. Pressure-impulse diagrams for the behaviour assessment of structural components. International Journal of Impact Engineering, 2008, 35(8): 771–783

[37] Dragos J, Wu C. A new general approach to derive normalised pressure impulse curves. International Journal of Impact Engineering, 2013, 62: 1–12

[38] Shi Y, Hao H, Li Z X. Numerical derivation of pressure-impulse diagrams for prediction of RC column damage to blast loads. International Journal of Impact Engineering, 2008, 35(11): 1213–1227

[39] Mutalib A A, Hao H. Development of P-I diagrams for FRP strengthened RC columns. International Journal of Impact Engineering, 2011, 38(5): 290–304

[40] Rabczuk T, Areias P M A, Belytschko T. A meshfree thin shell method for non-linear dynamic fracture. International Journal for Numerical Methods in Engineering, 2007, 72(5): 524–548

[41] Nguyen-Thanh N, Zhou K, Zhuang X, Areias P, Nguyen-Xuan H, Bazilevs Y, Rabczuk T. Isogeometric analysis of large-deformation thin shells using RHT-splines for multiple-patch coupling. Computer Methods in Applied Mechanics and Engineering, 2017, 316: 1157–1178

[42] Rabczuk T, Kim J Y, Samaniego E, Belytschko T. Homogenization of sandwich structures. International Journal for Numerical Methods in Engineering, 2004, 61(7): 1009–1027

[43] Rabczuk T, Zi G, Bordas S, Nguyen-Xuan H. A geometrically non-linear three-dimensional cohesive crack method for reinforced concrete structures. Engineering Fracture Mechanics, 2008, 75(16): 4740–4758

[44] Rabczuk T, Zi G, Bordas S, Nguyen-Xuan H. A simple and robust three-dimensional cracking-particle method without enrichment. Computer Methods in Applied Mechanics and Engineering, 2010, 199(37–40): 2437–2455

[45] Rabczuk T, Belytschko T. A three-dimensional large deformation meshfree method for arbitrary evolving cracks. Computer Methods in Applied Mechanics and Engineering, 2007, 196(29–30): 2777–2799

[46] Hallquist J O. LS-DYNA Theory Manual. Livermore Software Technology Corporation (LSTC), 2006

[47] Foundoukos N, Chapman J C. Finite element analysis of steel-concrete-steel sandwich beams. Journal of Constructional Steel Research, 2008, 64(9): 947–961

[48] Clubley S K, Moy S S J, Xiao R Y. Shear strength of steel-concrete-steel composite panels. Part II—Detailed numerical modelling of performance. Journal of Constructional Steel Research, 2003, 59(6): 795–808

[49] Li X, Chen J F, Lu Y, Yang Z. Modelling static and dynamic FRP-concrete bond behaviour using a local concrete damage model. Advances in Structural Engineering, 2015, 18(1): 45–58

[50] Chen W, Hao H, Chen S. Numerical analysis of prestressed reinforced concrete beam subjected to blast loading. Materials & Design, 2015, 65: 662–674

[51] Federal Highway Administration. Users Manual for LS-DYNA Concrete Material Model 159. Publication No. FHWA-HRT-05-062, 2007

[52] Federal Highway Administration. Evaluation of LS-DYNA Concrete Material Model 159. Publication No. FHWA-HRT-05-063, 2007

[53] Cowper G R, Symonds P S. Strain Hardening and Strain Rate Effects in the Impact Loading of Cantilever Beams. Applied Mathematics Report. 1958

[54] Jones N. Structural Impact. Cambridge/New York: Cambridge University Press, 1988

[55] Kang W K, Lee S C, Liew J Y R. Analysis of steel-concrete composite column subject to blast. Proceedings of the Institution of Civil Engineers. Structures and Buildings, 2013, 166(1): 15–27

[56] Xie M, Foundoukos N, Chapman J C. Static tests on steel-concrete-steel sandwich beams. Journal of Constructional Steel Research, 2007, 63(6): 735–750

[57] Dym C L, Williams H E. Stress and displacement estimates for arches. Journal of Structural Engineering, 2011, 137(1): 49–58

[58] Baker W E, Cox P A, Westine P S, Kulesz J J, Strehlow R A. Explosion and Hazards and Evaluation. Amsterdam: Elsevier Scientific Publishing Compay, 1983

[59] Eurocode 2. Design of concrete structures—part 1-1: General rules and Rules for Buildings. EN 1992-1-1. London: British Standards Institution, 2004

RIGHTS & PERMISSIONS

Higher Education Press and Springer-Verlag GmbH Germany, part of Springer Nature