Investigating the effect of probabilistic distribution of crack at the limit state on the seismic reliability of concrete buildings

Document Type : Research Paper

Authors

1 Assistant Professor, Department of Civil, Water and Environmental Engineering, Shahid Beheshti University, Tehran, Iran.

2 Ph.D. Student, Faculty of Civil, Water and Environmental Engineering, Shahid Beheshti University, Tehran, Iran

3 Ph.D. Student, Faculty of Civil, Water and Environmental Engineering, Shahid Beheshti University, Tehran, Iran.

Abstract

Description of the real behavior of the structures depends on the sources of uncertainty or effective random parameters of the inputs and structural characteristics. These uncertainties may appear as changes and dispersal in external forces and environmental conditions, boundary conditions, geometric parameters or specification of the materials. One of the effective factors in the analysis of concrete structures is consideration of the effect of cracking on the structural elements, which directly affects the calculation of the natural periods, the story displacement and other response parameters. In different codes for design of concrete structures, cracking effect is considered as a mean and constant coefficient for each element, while clearly the condition of various components will be different based on loading situation and specifications. In this paper, reliability of stiffness reduction coefficients of the beams and columns due to cracking of concrete in the ACI code is investigated under random distribution of floor live loads using Monte Carlo simulation method. By considering 1000 modelling loops, calculating accurate crack coefficients of beams and columns and applying them in each model, the reliability of cracking coefficients has been obtained. The results show that the reliability index of these coefficients is very low. Also, other results of this modeling and applying accurate cracking coefficients, show that the story displacements and time period of first and second modes decrease about 40-55% and 20-30%, respectively and the reaction forces of the elements, especially the axial forces and torsional moments increase about 20-30%.

Keywords

References

[1] E. Basler, Untersuchungen über den Sicherheitsbegriff von Bauwerken, ETH Zurich, 1960.
[2] C.A. Cornell, A probability-based structural code, in:  Journal Proceedings, 1969, pp. 974-985.
[3] S.H. Ghasemi, A. Nowak, Reliability index for non-normal distributions of limit state functions, Structural Engineering and Mechanics, 62(3) (2017) 365-372.
[4] H.O. Madsen, S. Krenk, N.C. Lind, Methods of structural safety, Courier Corporation, 2006.
[5] A.S. Nowak, K.R. Collins, Reliability of structures, CRC Press, 2012.
[6] D. Li, Z. Zheng, Y. Tian, J. Sun, X. He, Y. Lu, Stochastic nonlinear vibration and reliability of orthotropic membrane structure under impact load, Thin-Walled Structures, 119 (2017) 247-255.
[7] I. Skrzypczak, J. Kujda, L. Buda-Ożóg, The use of probabilistic methods in assessing the reliability of masonry structures, Procedia Engineering, 193 (2017) 160-167.
[8] H. Zhang, Durability reliability analysis for corroding concrete structures under uncertainty, Mechanical Systems and Signal Processing, 101 (2018) 26-37.
[9] Z. Zheng, J. Guo, W. Song, X. He, F. Lu, C. Xie, J. Sun, Nonlinear free vibration analysis of axisymmetric polar orthotropic circular membranes under the fixed boundary condition, Mathematical Problems in Engineering, 2014 (2014).
[10] J. Van de Lindt, Damage-based seismic reliability concept for woodframe structures, Journal of Structural Engineering, 131(4) (2005) 668-675.
[11] K.T. Wieghaus, R.A. Atadero, Effect of existing structure and FRP uncertainties on the reliability of FRP-based repair, Journal of Composites for Construction, 15(4) (2010) 635-643.
[12] B. Teplý, Interrelation among service life, reliability index, and costs of concrete structures subjected to aggressive exposure, Journal of Performance of Constructed Facilities, 28(4) (2013) 04014003.
[13] D.L. Kozak, A.B. Liel, Reliability of steel roof structures under snow loads, Structural Safety, 54 (2015) 46-56.
[14] N.M. Okasha, M. Aichouni, Proposed structural reliability-based approach for the classification of concrete quality, Journal of Materials in Civil Engineering, 27(5) (2014) 04014169.
[15] M.L. Beconcini, P. Croce, F. Marsili, M. Muzzi, E. Rosso, Probabilistic reliability assessment of a heritage structure under horizontal loads, Probabilistic engineering mechanics, 45 (2016) 198-211.
[16] E. Kianfar, V. Toufigh, Reliability analysis of rammed earth structures, Construction and Building Materials, 127 (2016) 884-895.
[17] M. Gordini, M. Habibi, M. Tavana, M. TahamouliRoudsari, M. Amiri, Reliability Analysis of Space Structures Using Monte-Carlo Simulation Method, in:  Structures, Elsevier, 2018, pp. 209-219.
[18] M. Khuntia, S. Ghosh, Flexural stiffness of reinforced concrete columns and beams: experimental verification, Structural Journal, 101(3) (2004) 364-374.
[19] C.S. Association, Design of concrete structures, Mississauga, Ont.: Canadian Standards Association, 2004.
[20] ACI, Building code requirements for reinforced concrete, in, 2014.
[21] T.M. Fayyad, J.M. Lees, Experimental investigation of crack propagation and crack branching in lightly reinforced concrete beams using digital image correlation, Engineering Fracture Mechanics, 182 (2017) 487-505.
[22] I. Luchko, Basic concepts of the fracture mechanics of reinforced concrete, Materials Science, 31(4) (1996) 448-453.
[23] H. Nahvi, M. Jabbari, Crack detection in beams using experimental modal data and finite element model, International Journal of Mechanical Sciences, 47(10) (2005) 1477-1497.
[24] E. Ooi, Z. Yang, A hybrid finite element-scaled boundary finite element method for crack propagation modelling, Computer Methods in Applied Mechanics and Engineering, 199(17-20) (2010) 1178-1192.
[25] E.T. Ooi, Z.J. Yang, Modelling crack propagation in reinforced concrete using a hybrid finite element–scaled boundary finite element method, Engineering Fracture Mechanics, 78(2) (2011) 252-273.
[26] Z. Yang, J. Chen, Finite element modelling of multiple cohesive discrete crack propagation in reinforced concrete beams, Engineering Fracture Mechanics, 72(14) (2005) 2280-2297.
[27] B.H.R. Center, Standard No.2800. Iranian Code of Practice for Seismic Resistant Design of Buildings, in, BHRC Publication, Forth Edition, In persian,Tehran.Iran, 2016.
[28] D.E. Branson, G.A. Metz, Instantaneous and time-dependent deflections of simple and continuous reinforced concrete beams, Department of Civil Engineering and Auburn Research Foundation, Auburn University, 1963.
[29] A.W. Beeby, Short-term deformations of reinforced concrete members, Cement and Concrete Association, 1968.
[30] C. CEB-FIP, Model code for concrete structures, Bulletin D'Information,  (1990).
[31] D.E. Branson, Deformation of concrete structures, McGraw-Hill New York, 1977.
[32] D.E. Branson, M. Christiason, Time Dependent Concrete Properties Related To Design-Strength and Elastic Properties, Creep, and Shrinkage, Special Publication, 27 (1971) 257-278.
[33] D.E. Branson, K. Kripanarayanan, Loss of prestress, camber and deflection of non-composite and composite prestressed concrete structures, PRECAST/PRESTRESSED CONCRETE INSTITUTE. JOURNAL,  (1971).
[34] ACI Committee 435, Control of deflection in concrete structures, ACI 435R-95, in, ACI, Farmington Hills, Michigan 2003.

Files

Share

How to cite

Statistics