A Macro-element Model for Nonlinear Analysis of Masonry Structures

Document Type : Research Article

Authors

Tarbiat Modares University

Abstract

In this study, the macro modeling of masonry structures is used based on homogenous models, and an equivalent planar-frame model-based analytical method is proposed for masonry structure assessment. The equivalent frame model is a simple applicable approach that is almost accurate and time-saving. Also, it holds proper convergence compared to the exact analytical and experimental methods. In the formulation of beam-column elements, the distribution of nonlinearity is chosen. The nonlinear constitutive model is simulated in the cross-sections and also along the length by the usage of fiber elements. For the consideration of shear behavior, bed joint sliding mode of failure, and diagonal tension mode, a smeared crack approach-based interface element is developed in the MATLAB framework. To consider the seismic assessment of masonry walls, constitutive models are considered according to Instruction for seismic rehabilitation of existing buildings (No. 360) through a subroutine in the main program. The accuracy of the suggested approach is verified through a comparison of experimental results and existing analytical methods.

Keywords

Main Subjects


  1. Taucer, E. Spacone, F.C. Filippou, A fiber beam-column element for seismic response analysis of reinforced concrete structures, Earthquake Engineering Research Center, College of Engineering, University of California Berkeley, California, 1991.
  2. Spacone, F.C. Filippou, F.F. Taucer, Fibre Beam–Column Model for Non‐Linear Analysis of R/C Frames: Part II. Applications, Earthquake engineering & structural dynamics, 25(7) (1996) 727-742.
  3. H. Scott, G.L. Fenves, Plastic hinge integration methods for force-based beam–column elements, Journal of Structural Engineering, 132(2) (2006) 244-252.
  4. Demirlioglu, S. Gonen, S. Soyoz, M.P. Limongelli, In-Plane Seismic Response Analyses of a Historical Brick Masonry Building Using Equivalent Frame and 3D FEM Modeling Approaches, International Journal of Architectural Heritage, (2018) 1-19.
  5. Manojlović, D. Jovanovic, V. Vukobratovic, PUSHOVER ANALYSIS OF A FOUR-STOREY MASONRY BUILDING DESIGNED ACCORDING TO EUROCODE, 2018.
  6. Siano, P. Roca, G. Camata, L. Pelà, V. Sepe, E. Spacone, M. Petracca, Numerical investigation of non-linear equivalent-frame models for regular masonry walls, Engineering Structures, 173 (2018) 512-529.
  7. Quagliarini, G. Maracchini, F. Clementi, Uses and limits of the Equivalent Frame Model on existing unreinforced masonry buildings for assessing their seismic risk: A review, Journal of Building Engineering, 10 (2017) 166-182.
  8. Ceresa, L. Petrini, R. Pinho, R. Sousa, A fibre flexure–shear model for seismic analysis of RC‐framed structures, Earthquake Engineering & Structural Dynamics, 38(5) (2009) 565-586.
  9. -X. Li, Y. Gao, Q. Zhao, A 3D flexure–shear fiber element for modeling the seismic behavior of reinforced concrete columns, Engineering Structures, 117(Supplement C) (2016) 372-383.
  10. S. Stramandinoli, H.L. La Rovere, FE model for nonlinear analysis of reinforced concrete beams considering shear deformation, Engineering structures, 35 (2012) 244-253.
  11. Mullapudi, A. Ayoub, Analysis of reinforced concrete columns subjected to combined axial, flexure, shear, and torsional loads, Journal of Structural Engineering, 139(4) (2012) 561-573.
  12. Sasani, A. Werner, A. Kazemi, Bar fracture modeling in progressive collapse analysis of reinforced concrete structures, Engineering Structures, 33(2) (2011) 401-409.
  13. R. Valipour, S.J. Foster, Finite element modelling of reinforced concrete framed structures including catenary action, Computers & structures, 88(9) (2010) 529-538.
  14. Raka, E. Spacone, V. Sepe, G. Camata, Advanced frame element for seismic analysis of masonry structures: model formulation and validation, Earthquake Engineering & Structural Dynamics, 44(14) (2015) 2489-2506.
  15. Ghiassi, M. Soltani, A.A. Tasnimi, Seismic evaluation of masonry structures strengthened with reinforced concrete layers, Journal of Structural Engineering, 138(6) (2011) 729-743.
  16. Salvatori, P. Spinelli, A Continuum-Discrete Multiscale Model for In-Plane Mechanical Modeling of Masonry Panels, Journal of Multiscale Modelling, 9(03) (2018) 1840004.
  17. Caliò, M. Marletta, B. Pantò, A new discrete element model for the evaluation of the seismic behaviour of unreinforced masonry buildings, 2012.
  18. Vanin, D. Zaganelli, A. Penna, K. Beyer, Estimates for the stiffness, strength and drift capacity of stone masonry walls based on 123 quasi-static cyclic tests reported in the literature, Bulletin of Earthquake Engineering, 15(12) (2017) 5435-5479.
  19. Marques, P.B. Lourenço, Unreinforced and confined masonry buildings in seismic regions: Validation of macro-element models and cost analysis, Engineering Structures, 64 (2014) 52-67.
  20. Orakcal, L.M.M. Sanchez, J.W. Wallace, Analytical modeling of reinforced concrete walls for predicting flexural and coupled-shear-flexural responses, Pacific Earthquake Engineering Research Center, College of Engineering, University of California, Berkeley, 2006.
  21. Bazoune, Y. Khulief, N. Stephen, Shape functions of three-dimensional Timoshenko beam element, Journal of Sound and Vibration, 259(2) (2003) 473-480.
  22. Puchegger, S. Bauer, D. Loidl, K. Kromp, H. Peterlik, Experimental validation of the shear correction factor, Journal of sound and vibration, 261(1) (2003) 177-184.
  23. Yu, D.H. Hodges, Elasticity solutions versus asymptotic sectional analysis of homogeneous, isotropic, prismatic beams, Journal of Applied Mechanics, 71(1) (2004) 15-23.
  24. Hutchinson, Shear coefficients for Timoshenko beam theory, TRANSACTIONS-AMERICAN SOCIETY OF MECHANICAL ENGINEERS JOURNAL OF APPLIED MECHANICS, 68(1) (2001) 87-92.
  25. Dong, C. Alpdogan, E. Taciroglu, Much ado about shear correction factors in Timoshenko beam theory, International Journal of Solids and Structures, 47(13) (2010) 1651-1665.
  26. Chan, K. Lai, N. Stephen, K. Young, A new method to determine the shear coefficient of Timoshenko beam theory, Journal of Sound and Vibration, 330(14) (2011) 3488-3497.
  27. P. Timoshenko, X. On the transverse vibrations of bars of uniform cross-section, The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 43(253) (1922) 125-131.
  28. Maekawa, H. Okamura, A. Pimanmas, Non-linear mechanics of reinforced concrete, Spon Press, 2003.
  29. Jirásek, Z.P. Bazant, Inelastic analysis of structures, John Wiley & Sons, 2002.
  30. -B.D. Pang, T.T. Hsu, Behavior of reinforced concrete membrane elements in shear, Structural Journal, 92(6) (1995) 665-679.
  31. دستورالعمل بهسازی لرزه ای ساختمان‌های موجود نشریه 360، 1392.
  32. R. Herrmann, Finite element analysis of contact problems, Journal of the Engineering Mechanics Division, 104(5) (1978) 1043-1057.
  33. Zhuge, D. Thambiratnam, J. Corderoy, Nonlinear dynamic analysis of unreinforced masonry, Journal of structural engineering, 124(3) (1998) 270-277.
  34. J.B.B. Lourenço, Computational strategies for masonry structures, Delft University of Technology, Delft, The Netherlands, 1997.
  35. Li, Contact density model for stress transfer across cracks in concrete, Journal of the Faculty of Engineering, the University of Tokyo, (1) (1989) 9-52.
  36. Soltani, X. An, K. Maekawa, Computational model for post cracking analysis of RC membrane elements based on local stress–strain characteristics, Engineering structures, 25(8) (2003) 993-1007.
  37. M.M. Salem, Enhanced tension stiffening model and application to nonlinear dynamic analysis of reinforced concrete, 1998.
  38. Jin, M. Soltani, X. An, Experimental and numerical study of cracking behavior of openings in concrete dams, Computers & structures, 83(8) (2005) 525-535.
  39. Ramm, The Riks/Wempner approach-An extension of the displacement control method in nonlinear analysis, nonlinear computational mechanics, (1982) pp. 63-86.
  40. A. Felippa, Nonlinear finite element methods, Department of Aerospace Engineering Sciences and Center for Space Structures and Controls, 2001.
  41. Schweizerhof, P. Wriggers, Consistent linearization for path following methods in nonlinear FE analysis, Computer Methods in Applied Mechanics and Engineering, 59(3) (1986) 261-279.
  42. Ganz, B. Thürlimann, Tests on the biaxial strength of masonry, Rep. No. 7502, 3 (1982).
  43. Paquette, M. Bruneau, Pseudo-dynamic testing of unreinforced masonry building with flexible diaphragm, Journal of structural engineering, 129(6) (2003) 708-716.
  44. یعقوبی‌فر، ا.، بررسی رفتار دیوارهای آجری تقویت شده با شبکه فولادی و پوشش بتن به روش آزمایشگاهی و تحلیلی، پایان‌نامه کارشناسی ارشد مهندسی عمران- سازه، دانشکده عمران‌محیط‌زیست، دانشگاه تربیت‌مدرس، شهریور 1387.