Preparing the Pressure-Impulse Diagrams for Reinforced Concrete Columns with Axial Load using Single Degree of Freedom Approach

Document Type : Research Note

Authors

• Mohammad Esmaeil Nia Omran
• Somayeh Mollaei

Kurdistan University

10.22067/civil.v32i1.57788

Abstract

In this paper, moment-curvature behavior of reinforced concrete column with constant axial load is determined by finite element method and then it is introduced to a single degree of freedom (SDOF) model based on Euler-Bernoulli theory. Using this SDOF model, dynamic response of the RC column under the blast loading is estimated. The introduced SDOF includes secondary moments (P-δ) effects, nonlinear behavior of the material and effects of strain rate on concrete and steel materials through the calculation steps of the model. In order to validation, results obtained from SDOF model for transverse displacement  of  RC column under blast  loading is compared to finite element analysis results (OPENSEES) and real-scale explosion test results on RC columns. Then, introduced SDOF method is used to draw Pressure-Impulse (P-I) diagram of the column with considering the presence of axial compressive load. According to the results, introduced SDOF approach, under the far field explosion conditions (Z>1 kg/m1/3), has acceptable accuracy. As well, the effect of axial load on P-I diagram of the RC column is very important.
 

Keywords

• Blast Loading
• Equivalent Single Degree of Freedom Model
• Pressure-Impulse diagram
• RC column

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References

1. U.S. Dept. of Army, the Navy and Air Force, "The Design of Structures to Resist the Effects of Accidental Explosions", TM 5-1300, Technical Manual, Washington DC, (1990).

2. U.S. Department of Defense (DOD), "Structures to Resist the Effects of Accidental Explosions", UFC 3-340-02, Washington DC, (2008).

3. ASCE, "Design of Blast Resistant bBuildings in Petrochemical Facilities", Reston VA, (1997).

4. Nassr, A.A., Razaqpur, A.G., Tait, M.J., Campidelli, M. and Foo, S., "Single and Multi Degree of Freedom Analysis of Steel Beams under Blast Loading", Nuclear Engineering Design, Vol. 242, pp. 63-77, (2012).

5. Dragos, J. and Wu, C., "Single-Degree-of-Freedom Approach to Incorporate Axial Load Effects on Pressure Impulse Curves for Steel Columns", Journal of Engineering Mechanics, 10.1061/ (ASCE) EM.1943-7889.0000818, 04014098, (2014).

6. 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, Vol. 32, pp. 1214–1247, (2006).

7. Oswald, C.J., "Comparison of Response from Combined Axial and Blast Loads Calculated with SDOF and Finite Element Methods", In: DDESB Explosive Safety Seminar, Portland, Oregon, (2010).

8. Stochino, F. and Carta, G., "SDOF Models for Reinforced Concrete Beams under Impulsive Loads Accounting for Strain Rate Effects", Nuclear Engineering Design, Vol. 276, pp. 74–86, (2014).

9. Andersson, S. and Karlsson, H., "Structural Response of Reinforced Concrete Beams Subjected to Explosions", Master Thesis, Chalmers University of Technology, Goteborg, Sweden, (2012).

10. Wu, C., Wu, W. and Chen, D.J., "Analysis of Retrofitted RC Beam with Fixed End Supports against Blast Loads", Key Engineering Materials, Vol. 400-402, pp. 795-800, (2009).

11. PDC-TR 06-01 Rev 1. Methodology Manual for the Single-Degree-of-Freedom Blast Effects Design Spreadsheets (SBEDS). US Army Corps of Engineers, Protective Design Center (PDC) Technical Report, (2008).

12. Dragos, J. and Wu, C., "A New General Approach to Derive Normalized Pressure-Impulse Curves", International Journal of Impact Engineering, Vol. 62, pp. 1-12, (2013).

13. Florek, J.R. and Benaroya, H., "Pulse–pressure Loading Effects on Aviation and General Engineering Structures—review", Journal of Sound and Vibration, Vol. 284, pp. 421–453, (2005).

14. Krauthammer, T., Astarlioglu, S., Blasko, J., Soh, T.B. and Ng, P.H., "Pressure–Impulse Diagrams for the Behavior Assessment of Structural Components", International Journal of Impact Engineering, Vol. 35, pp. 771–783, (2008).

15. Mutalib, A.A., Abedini, M., Baharom, S. and Hao, H., "Derivation of Empirical Formulae to Predict Pressure and Impulsive Asymptotes for P-I Diagrams of One-way RC Panels", Journal of Civil, Enviroment, Structural, Construction and Architecture Engineering, Vol. 7, pp. 585-588. (2013).

16. Mutalib, A.A. and Hao, H, "Development of P-I Diagrams for FRP Strengthened RC Columns", International Journal of Impact Engineering, Vol. 38, pp. 290–304, (2011).

17. Biggs, J.M., Introduction to Structural Dynamics, New York: McGraw-Hill, (1964).

18. Stochino, F. and Tattoni, S., "Exceptional Actions: Blast Loads on Reinforced Concrete Structures", In: Proceedings of CIAS (Cornell International Affairs Society) Conference, Cornell University, (2013).

19. Chopra, A.K., "Dynamics of Structures: Theory and Applications to Earthquake Engineering", New Jersey: Prentice Hall, (1995).

20. Timoshenko, S.P. and Gere, J.M., "Theory of Elastic Stability", 2nd ed. New York: McGraw-Hill, (1963).

21. Paulay, T. and Priestley, M.J.N., "Seismic Design of Reinforced Concrete and Masonry Buildings", John Wiley and Sons, New York, (1992).

22. Brode, H.L., "Numerical Solutions of Spherical Blast Waves", Journal of Applied Physics, Vol. 26, pp. 766-775, (1955).

23. Cormie, D., Mays, G. and Smith, P.D., "Blast Effects on Buildings", 2nd ed, London: Thomas Telford, (2009).

24. Mazzoni, S., McKenna, F., et al., "OpenSees Command Language Manual", University of California, Berkeley, (2006).

25. Mazzoni, S. and Frank M.K., "Example 9. Moment-Curvature Analysis of Section", (2006) http://opensees.berkeley.edu/OpenSees/manuals/ExamplesManual/HTML/3909.htm.

26. Mazzoni, S. and Frank M.K., "Concrete01 Material-Zero Tensile Strength", (2006). http://opensees.berkeley.edu/OpenSees/manuals/usermanual/164.htm.

27. Kent, D.C. and Park, R., "Inelastic Behavior of Reinforced Concrete Members with Cyclic Loading", Bulletin of the New Zealand Society for Earthquake Engineering, Vol. 4, pp. 108-125, (1971).

28. Asprone, D., Frascadore, R., Di Ludovico , M., Prota, A. and Manfredi, G., "Influence of Strain Rate on the Seismic Response of RC Structures", Engineering Structures, Vol. 35, pp. 29–36, (2012).

29. Ožbolt, J. and Sharma, A., "Numerical Simulation of Reinforced Concrete Beams with Different Shear Reinforcements under Dynamic Impact Loads", International Journal of Impact Engineering, Vol. 38, pp. 940-950, (2011).

30. Krauthammer, T., Shanaa, H.M. and Assadi, A., "Response of Structural Concrete Elements to Severe Impulsive Loads", Computers Structures, Vol. 53, pp. 119-130, (1994).

31. Razaqpur, G., Mekky, W. and Foo, S., "Fundamental Concepts in Blast Resistance Evaluation of Structures", Canadian Journal of Civil Engineering, Vol. 36, pp. 1292-1304, (2009).

32. Malvar, L.J. and Crawford J.E., "Dynamic Increase Factors for Steel Reinforcing Bars", In: 28th DDESB Seminar, Orlando, USA, (1998).

33. Federal Institute of Technology, Model Code 2010, First Complete Draft, Volume 1: fib Bulletin 55, Switzerland, (2010).

34. Izadifard, R.A., Nourizadeh, A. and Shamshirgar, A., "A Material Model for Static and Dynamic Nonlinear Finite Element Modeling of Reinforced Concrete Elements", In: Proceedings of the 4th International Conference on Seismic Retrofitting, Tabriz, Iran, (2012).

35. Smith, G.D., "Numerical Solution of Partial Differential Equations: Finite Difference Methods", 3rd ed., Oxford University Press, (1985).

36. Parks, D.M., "Euler-Bernoulli Beams Bending, Buckling, and Vibration", MIT OpenCourseWare, Massachusetts Institute of Technology, Department of Mechanical Engineering, (2004).

37. Farouk, S., "Near-Field Explosion Effects on Reinforced Concrete Columns: An Experimental Investigation", Master of Civil Engineering thesis, Carleton University Ottawa, (2014).

38. Braimah, A., Farouk S. and Von-Rosen B., "Near-field Explosion Effects on Reinforced Concrete Column", In: Proceeding of 5th International Workshop on Performance, Protection & Strengthening of Structures under Extreme Loading, pp. 505-514, (2015).

39. Shi, H.J., Salim, H. and Ma, G., "Using P–I Diagram Method to Assess the Failure Modes of Rigid-Plastic Beams Subjected to Triangular Impulsive Loads", International Journal of Protection Structures, Vol. 3, pp. 333–353, (2012).