Geomechanics and Engineering

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Nonlinear shear-flexure-interaction RC frame element on Winkler-Pasternak foundation

  • Suchart, Limkatanyu (Department of Civil and Environmental Engineering, Faculty of Engineering, Prince of Songkla University) ;
  • Worathep, Sae-Long (Civil Engineering Program, School of Engineering, University of Phayao) ;
  • Nattapong, Damrongwiriyanupap (Civil Engineering Program, School of Engineering, University of Phayao) ;
  • Piti, Sukontasukkul (Construction and Building Materials Research Center, Department of Civil Engineering, King Mongkut's University of Technology North Bangkok) ;
  • Thanongsak, Imjai (School of Engineering and Technology, Walailak University) ;
  • Thanakorn, Chompoorat (Civil Engineering Program, School of Engineering, University of Phayao) ;
  • Chayanon, Hansapinyo (Center of Excellence in Natural Disaster Management, Department of Civil Engineering, Chiang Mai University)
  • Received : 2022.01.06
  • Accepted : 2022.12.23
  • Published : 2023.01.10
⟨ Previous Next ⟩

Abstract

This paper proposes a novel frame element on Winkler-Pasternak foundation for analysis of a non-ductile reinforced concrete (RC) member resting on foundation. These structural members represent flexural-shear critical members, which are commonly found in existing buildings designed and constructed with the old seismic design standards (inadequately detailed transverse reinforcement). As a result, these structures always experience shear failure or flexure-shear failure under seismic loading. To predict the characteristics of these non-ductile structures, efficient numerical models are required. Therefore, the novel frame element on Winkler-Pasternak foundation with inclusion of the shear-flexure interaction effect is developed in this study. The proposed model is derived within the framework of a displacement-based formulation and fiber section model under Timoshenko beam theory. Uniaxial nonlinear material constitutive models are employed to represent the characteristics of non-ductile RC frame and the underlying foundation. The shear-flexure interaction effect is expressed within the shear constitutive model based on the UCSD shear-strength model as demonstrated in this paper. From several features of the presented model, the proposed model is simple but able to capture several salient characteristics of the non-ductile RC frame resting on foundation, such as failure behavior, soil-structure interaction, and shear-flexure interaction. This confirms through two numerical simulations.

Keywords

Acknowledgement

The financial support of this work was provided by the Office of the Permanent Secretary, Ministry of Higher Education, Science, Research and Innovation (Grant No. RGNS 64-134), by the Thailand Research Fund (Grant No. RTA 6280012) and by the Thailand Science Research and Innovation Fund and the University of Phayao (Grant No. FF66-UoE023). Furthermore, we would like to sincerely thank the copy-editing service of Research and Development Office, and Assoc. Prof. Dr. Seppo Karrila who dedicated his time to provide valuable comments, and gratefully acknowledge the support and assistance received.

References

  1. Ayoub, A. (2003), "Mixed formulation of nonlinear beam on foundation elements", Comput. Struct., 81(7), 411-421. https://doi.org/10.1016/S0045-7949(03)00015-4. 
  2. Bao, T. and Liu, Z.L. (2020), "Evaluation of Winkler model and Pasternak model for dynamic soil-structure interaction analysis of structures partially embedded in soils", Int. J. Geomech., 20(2), 04019167. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001519. 
  3. Basha, S.H. and Kaushik, H.B. (2019), "Investigation on improving the shear behavior of columns in masonry infilled RC frames under lateral loads", Bull. Earthq. Eng., 17, 3995-4026. https://doi.org/10.1007/s10518-019-00622-3. 
  4. Beirao da Veiga, V., Lovadina, C. and Reali, A. (2012), "Avoiding shear locking for the Timoshenko beam problem via isogeometric collocation methods", Comput. Method. Appl. Mech. Eng., 241-244, 38-51. https://doi.org/10.1016/j.cma.2012.05.020. 
  5. Biskinis, D., Roupakias, G. and Fardis, M. (2004), "Degradation of shear strength of reinforced concrete members with inelastic cyclic displacement", ACI Struct. J., 101(6), 773-783. https://doi.org/10.14359/13452. 
  6. Boussinesq, H. (1885), Applications des Potentiels al'Etude de l'Equilibre et du Mouvement des Solids Elastique, GauthierVillars, Paris, France. 
  7. Ceresa, P., Petrini, L. and Pinho, R. (2007), "Flexure-shear fiber beam-column elements for modeling frame structures under seismic loading: State of the art", J. Earthq. Eng., 11(1), 46-88. https://doi.org/10.1080/13632460701280237. 
  8. Chaimahawan, P. and Pimanmas, A. (2009), "Nonlinear FEM analysis of RC beam-column joint strengthened by cast in-situ joint expansion", J. Adv. Concr. Technol., 7(3), 307-326. https://doi.org/10.3151/jact.7.307. 
  9. Chaimahawan, P., Hansapinyo, C. and Phuriwarangkhakul, P. (2018), "Test and finite element analysis of gravity load designed precast concrete wall under reversed cyclic loads", Eng. J., 22(2), 185-200. https://doi.org/10.4186/ej.2018.22.2.185. 
  10. Chaimahawan, P. and Shaingchin, S. (2019), "Deflection control of reinforced concrete slab strengthened with CFRP plates", J. Eng. Sci. Technol., 14(6), 3387-3405. 
  11. Chapra, S.C. and Canale, R.P. (2002), Numerical methods for engineers, McGraw-Hill, New York, USA. 
  12. Chindaprasirt, P., Lao-un, J., Zaetang, Y., Wongkvanklom, A., Phoo-ngernkham, T., Wongsa, A. and Sata, V. (2022), "Thermal insulating and fire resistance performances of geopolymer mortar containing auto glass waste as fine aggregate", J. Build. Eng., 60, 105178. https://doi.org/10.1016/j.jobe.2022.105178. 
  13. Damrongwiriyanupap, N., Limkatanyu, S. and Xi, Y. (2015), "A thermo-hygro-coupled model for chloride penetration in concrete structures", Adv. Mater. Sci. Eng., 682940. https://doi.org/10.1155/2015/682940. 
  14. Dutta, S.C. and Roy, R.A. (2002), "Critical review on idealization and modeling for interaction among soil-foundation-structure system", Comput. Struct., 80(20-21), 1579-1594. https://doi.org/10.1016/S0045-7949(02)00115-3. 
  15. Eurocode No. 2 (1991), Design of concrete structures-part 1-1: General rules and rules for buildings, ENV 1992-1-1; Brusse, Belgium. 
  16. Feng, D.C. and Xu, J. (2018a), "An efficient fiber beam-column element considering flexure-shear interaction and anchorage bond-slip effect for cyclic analysis of RC structures", Bull. Earthquake Eng., 16, 5425-5452. https://doi.org/10.1007/s10518-018-0392-y. 
  17. Feng, D.C., Ren, X.D. and Li, J. (2018b), "Softened damage-plasticity model for analysis of cracked reinforced concrete structures", J. Struct. Eng., 144(6), 04018044. https://doi.org/10.1061/(ASCE)ST.1943-541X.0002015. 
  18. Filonenko-Borodich, M.M. (1940), "Some approximate theories of the elastic foundation", Uch. Zap. Mosk. Gos, Univ. Mekh., 46, 3-18. 
  19. Gan, J., Yuan, H. and Li, S. (2020), "A computing method for bending problem of thin plate on Pasternak foundation", Adv. Mech. Eng., 12(7), 168781402093933. https://doi.org/10.1177/1687814020939333. 
  20. Ghee, A., Priestley, M.J.N. and Paulay, T. (1989), "Seismic shear strength of circular reinforced concrete columns", ACI Struct. J., 86(1), 45-59.  https://doi.org/10.14359/2634
  21. Gulkan, P. and Alemdar, B.N. (1999), "An exact finite element for a beam on a two-parameter elastic foundation: A revisit", Struct. Eng. Mech., 7(3), 259-276. https://doi.org/10.12989/sem.1999.7.3.259. 
  22. Hetenyi, M. (1971), Beams on elastic foundation: theory with applications in the fields of civil and mechanical engineering, University of Michigan, Ann Arbor, Michigan, USA. 
  23. Janwaen, W., Barros, J.A.O. and Costa, I.G. (2020), "New hybrid FRP strengthening technique for rectangular RC columns subjected to eccentric compressive loading", J. Compos. Constr., 24(5), 4020043. https://doi.org/10.1061/(ASCE)CC.1943-5614.0001052. 
  24. Jung, W., Kim, J. and Kwon, M. (2018), "Performance evaluation of RC beam-column joints with different bonding interfaces", Sci. Iran., 25(1), 11-21. https://doi.org/10.24200/sci.2017.4175. 
  25. Karimi, S., Ahmadi, H. and Foroutan, K. (2022), "Nonlinear vibration and resonance analysis of a rectangular hyperelastic membrane resting on a Winkler-Pasternak elastic medium under hydrostatic pressure", J. Vib. Control, https://doi.org/10.1177/10775463211062339. 
  26. Kent, D.C. and Park, R. (1971), "Flexural members with confined concrete", J. Struct. Div., 97(7), 1964-1990. https://doi.org/10.1061/JSDEAG.0002957. 
  27. Li, X. (1994), "Reinforced concrete columns under seismic lateral force and varying axial load", Ph.D. Dissertation, Department of Civil Engineering, University of Canterbury, Christchurch, New Zealand. 
  28. Limkatanyu, S., Kuntiyawichai, K., Spacone, E. and Kwon, M. (2012), "Natural stiffness matrix for beams on Winkler foundation: exact force-based derivation", Struct. Eng. Mech., 42(1), 39-53. https://doi.org/10.12989/sem.2012.42.1.039. 
  29. Limkatanyu, S., Prachasaree, W., Damrongwiriyanupap, N., Kwon, M. and Jung, W. (2013a), "Exact stiffness for beams on Kerr-type foundation: the virtual force approach", J. Compos. Constr., 626287. https://doi.org/10.1155/2013/626287. 
  30. Limkatanyu, S., Kuntiyawichai, K., Spacone, E. and Kwon, M. (2013b), "Nonlinear Winkler-based beam element with improved displacement shape functions", KSCE J. Civ. Eng., 17, 192-201. https://doi.org/10.1007/s12205-013-1606-0. 
  31. Limkatanyu, S., Prachasaree, W., Damrongwiriyanupap, N. and Kwon, M. (2014), "Exact stiffness matrix for nonlocal bars embedded in elastic foundation media: the virtual-force approach", J. Eng. Math., 89, 163-176. https://doi.org/10.1007/s10665-014-9707-4. 
  32. Limkatanyu, S., Sae-Long, W., Prachasaree, W. and Kwon, M. (2015), "Improved nonlinear displacement-based beam element on a two-parameter foundation", Eur. J. Environ. Civ. Eng., 19(6), 649-671. https://doi.org/10.1080/19648189.2014.965847. 
  33. Limkatanyu, S., Sae-Long, W., Damrongwiriyanupap, N., Imjai, T., Chaimahawan, P. and Sukontasukkul, P. (2022), "Shear-flexure interaction frame model on Kerr-type foundation for analysis of non-ductile RC members on foundation", J. Appl. Comput. Mech., 8(3), 1076-1090. https://doi.org/10.22055/jacm.2022.39597.3440. 
  34. Liu, W., Tian, Y. and Cassidy, M.J. (2021), "An interface to numerically model undrained soil-structure interactions", Comput. Geotech., 138(5), 104327. https://doi.org/10.1016/j.compgeo.2021.104327. 
  35. Lodhi, M.S. and Sezen, H. (2012), "Estimation of monotonic behavior of reinforced concrete columns considering shear-flexure-axial load interaction", Earthquake Eng. Struct. Dyn., 41(15), 2159-2175. https://doi.org/10.1002/eqe.2180. 
  36. Lopez, C.N., Massone, L.M. and Kolozvari, K. (2022), "Validation of an efficient shear-flexure interaction model for planar reinforced concrete walls", Eng. Struct., 252, 113590. https://doi.org/10.1016/j.engstruct.2021.113590. 
  37. Lynn, A.C. (2001), "Seismic evaluation of existing reinforced concrete building columns", Ph.D. Dissertation, Department of Civil and Environmental Engineering, University of California, Berkeley, USA. 
  38. Marini, A. and Spacone, E. (2006), "Analysis of reinforced concrete elements including shear effects", ACI Struct. J., 103(5), 645-655. https://doi.org/10.14359/16916. 
  39. Mauludin, L.M. and Oucif, C. (2019), "Modeling of self-healing concrete: A review", J. Appl. Comput. Mech., 5, 526-539. https://doi.org/10.22055/jacm.2017.23665.1167. 
  40. Menegotto, M. and Pinto, P.E. (1973), "Method of analysis for cyclically loaded reinforced concrete plane frames including changes in geometry and nonelastic behavior of elements under combined normal force and bending", Proceedings of the IABSE Symp. Resist. Ultimate Deformability Struct. Acted on by Well-Defined Repeated Loads, Lisbon. 
  41. Menglin, L., Huaifeng, W., Xi, C. and Yongmei, Z. (2011), "Structure-soil-structure interaction: Literature review", Soil Dyn. Earthquake Eng., 31(12), 1724-1731. https://doi.org/10.1016/j.soildyn.2011.07.008. 
  42. Mergos, P.E. and Kappos, A.J. (2008), "A distributed shear and flexural flexibility model with shear-flexure interaction for R/C members subjected to seismic loading", Earthq. Eng. Struct. D., 37(12), 1349-1370. https://doi.org/10.1002/eqe.812. 
  43. Mergos, P.E. and Kappos, A.J. (2012), "A gradual spread inelasticity model for R/C beam-columns, accounting for flexure, shear and anchorage slip", Eng. Struct., 44, 94-106. https://doi.org/10.1016/j.engstruct.2012.05.035. 
  44. Mukherjee, S. and Prathap, G. (2001), "Analysis of shear locking in Timoshenko beam elements using the function space approach", Commun. Numer. Method. Eng., 17(6), 385-393. https://doi.org/10.1002/cnm.413. 
  45. Onate, E. (2013), Structural analysis with the finite element method volume 2: beams, plates and shells, Springer, Netherlands. 
  46. Onu, G. (1996), "Equivalences in the soil-structure interaction", Comput. Struct., 58(2), 367-380. https://doi.org/10.1016/0045-7949(95)00129-5. 
  47. Orakcal, K., Wallace, J.W. and Conte, J.P. (2004), "Nonlinear modeling and analysis of slender reinforced concrete walls", ACI Struct. J., 101(5), 688-698. 
  48. Park, R. and Paulay, T. (1975), Reinforced concrete structures, John Wiley & Sons, New York, USA. 
  49. Pasternak, P.L. (1954), On a new method of analysis of an elastic foundation by means of two constants, Gosudarstvennoe Izdatelstvo Literaturi po Stroitelstvu I Arkhitekture, Moscow, Russia. 
  50. Phoo-Ngernkham, T., Hanjitsuwan, S., Li, L.Y., Damrongwiriyanupap, N. and Chindaprasirt P. (2019), "Adhesion characterisation of Portland cement concrete and alkali-activated binders", Adv. Cem. Res., 31(2), 69-79. https://doi.org/10.1680/jadcr.17.00122. 
  51. Prachasaree, W., Sangkaew, A., Limkatanyu, S. and GangaRao, H.V.S. (2015), "Parametric study on dynamic response of fiber reinforced polymer composite bridges", Int. J. Polym. Sci., Article No 565301. https://doi.org/10.1155/2015/565301. 
  52. Prachasaree, W., Limkatanyu, S., Wangapisit, O. and Kraidam, S. (2018), "Field investigation of service performance of concrete bridges exposed to tropical marine environment", Int. J. Civ. Eng., 16(12), 1757-1769. https://doi.org/10.1007/s40999-017-0250-3. 
  53. Prendergast, L.J., Hester, D., Gavin, K. and O'Sullivan, J.J. (2013), "An investigation of the changes in the natural frequency of a pile affected by scour", J. Sound Vib., 332(25), 6685-6702. https://doi.org/10.1016/j.jsv.2013.08.020. 
  54. Priestley, M.J.N., Seible, F., Verma, R. and Xiao, Y. (1993), "Seismic shear strength of reinforced concrete columns", Structural Systems Research Project Report No. SSRP 93/06; University of California, San Diego, USA. 
  55. Qian, J., Mu, L., Zhang, Y. and Zhang, Y. (2021), "Behavior of a structured piled beam-slab foundation for a wind turbine under multidirectional loads in sand", Int. J. Geomech., 21(3), 04020267. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001934. 
  56. Sae-Long, W. and Limkatanyu, S. (2018), "Shear model with shear-flexure interaction for non-linear analysis of reinforced concrete frame element", MATEC Web Conf., 192, 02003. https://doi.org/10.1051/matecconf/201819202003. 
  57. Sae-Long, W., Limkatanyu, S., Prachasaree, W., Horpibulsuk, S. and Panedpojaman, P. (2019), "Nonlinear frame element with shear-flexure interaction for seismic analysis of non‑ductile reinforced concrete columns", Int. J. Concr. Struct. Mater., 13, 32. https://doi.org/10.1186/s40069-019-0343-2. 
  58. Sae-Long, W., Limkatanyu, S., Hansapinyo, C., Imjai, T. and Kwon, M. (2020), "Forced-based shear-flexure-interaction frame element for nonlinear analysis of non-ductile reinforced concrete columns", J. Appl. Comput. Mech., 6, 1151-1167. https://doi.org/10.22055/jacm.2020.32731.2065. 
  59. Sae-Long, W., Limkatanyu, S., Hansapinyo, C., Prachasaree, W., Rungamornrat, J. and Kwon, M. (2021a), "Nonlinear flexibility-based beam element on Winkler-Pasternak foundation", Geomech. Eng., 24(4), 371-388. https://doi.org/10.12989/gae.2021.24.4.371. 
  60. Sae-Long, W., Limkatanyu, S., Panedpojaman, P., Prachasaree, W., Damrongwiriyanupap, N., Kwon, M. and Hansapinyo, C. (2021b), "Nonlinear Winkler-based frame element with inclusion of shear-flexure interaction effect for analysis of non-ductile RC members on foundation", J. Appl. Comput. Mech., 7(1), 148-164. https://doi.org/10.22055/jacm.2020.34699.2460. 
  61. Sanches, R., Simoes, F.M.F. and Pinto da Costa, A. (2019), "Physical and geometrical nonlinear dynamic analysis of beams on foundations under moving loads", J. Eng. Mech., 146(1), 04019114. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001692. 
  62. Sapountzakis, E.J. and Kampitsis, A.E. (2013), "Inelastic analysis of beams on two-parameter tensionless elastoplastic foundation", Eng. Struct., 48, 389-401. https://doi.org/10.1016/j.engstruct.2012.09.012. 
  63. Senjanovic, I., Vladimir, N. and Cho, D.S. (2013), "A shear locking-free beam finite element based on the modified Timoshenko beam theory", Trans. FAMENA, 37(4), 1-16. 
  64. Sezen, H. (2002), "Seismic behavior and modeling of reinforced concrete building columns", Ph.D. Dissertation, Department of Civil and Environmental Engineering, University of California, Berkeley, USA. 
  65. Sezen, H. and Moehle, J.P. (2004), "Shear strength model for lightly reinforced concrete columns", J. Struct. Eng., 130(11), 1692-1703. https://doi.org/10.1061/(ASCE)0733-9445(2004)130:11(1692). 
  66. Spacone, E. and Limkatanyu, S. (2000), "Responses of reinforced concrete members including bond-slip effects", ACI Struct. J., 97(6), 831-839. https://doi.org/10.14359/9628. 
  67. Tan, Y.-Z., Liu, Y.-X., Wang, P.-Y. and Zhang, Y. (2016), "A predicting model for thermal conductivity of high permeability-high strength concrete materials", Geomech. Eng., 10(1), 49-57. https://doi.org/10.12989/gae.2016.10.1.049. 
  68. Taylor, R.L. (2000), FEAP: A finite element analysis program, User manual: version 7.3, Department of Civil and Environmental Engineering, University of California, Berkeley, USA. 
  69. Teodoru, I.B. (2009), "Beams on elastic foundation. the simplified continuum approach", Bull. Polytech. Inst. Jassy, LV(LIX), 37-46. 
  70. Timoshenko, S.P. and Gere, J.M. (1961), Theory of elastic stability engineering societies monographs, McGraw-Hill Book Company, New York, USA. 
  71. Tonzani, G.M. and Elishakoff, I. (2020), "Three alternative versions of the theory for a Timoshenko-Ehrenfest beam on a Winkler-Pasternak foundation", Math. Mech. Solids, 26(3), 299-324. https://doi.org/10.1177/1081286520947775. 
  72. Vecchio, F.J. and Collins, M.P. (1986), "The modified compression-field theory for reinforced concrete elements subjected to shear", ACI J., Proc., 83(2), 219-231. https://doi.org/10.14359/10416. 
  73. Wankhade, R. and Ghugal, Y.M. (2016), "Study on soil-structure interaction: A review", Int. J. Eng. Res., 5(3), 737-741. https://doi.org/10.17950/ijer/v5i3/047. 
  74. Whitman, R.V. and Luscher, U. (1962), "Basic experiment into soil-structure interaction", ASCE Soil Mech. Found. Div. J., 88(2), 135-167. https://doi.org/10.1061/JSFEAQ.0000461. 
  75. Winkler, E. (1867), Theory of elasticity and strength, Dominicus, Prague, Czechoslovakia. 
  76. Younesian, D., Hosseinkhani, A., Askari, H. and Esmailzadeh, E. (2019), "Elastic and viscoelastic foundations: A review on linear and nonlinear vibration modeling and applications", Nonlinear Dyn., 97, 853-895. https://doi.org/10.1007/s11071-019-04977-9. 
  77. Zhaohua, F. and Cook, R.D. (1983), "Beam elements on two-parameter elastic foundations", J. Eng. Mech., 109(6), 1390-1402. https://doi.org/10.1061/(ASCE)0733-9399(1983)109:6(1390).