Proposed soft computing models for moment capacity prediction of reinforced concrete columns

Abstract

Computational intelligence (CI) is a powerful approach to determine the response values of complex systems. Despite their benefits, the way to reach the solution in these approaches is difficult and cannot be expressed in a clear and simple formulation. In recent years, some methods have been proposed to provide simple and efficient mathematical forms in such approaches. In this paper, five of these methods are investigated to estimate the amount of moment capacity in rectangular concrete columns based on the extracted equations of CI. To train, validate and also test the proposed equations, a set of experimental laboratory tests of RC columns were collected from PEER database, and then mathematical frameworks for calculating the target were extracted. The obtained results of the proposed structures are also compared with each other, and it was concluded that all methods with high accuracy were able to estimate the moment capacity, but equation-based neuro-fuzzy system had better results than other presented models. The proposed equations are very powerful tools for determining the final capacity of RC columns as a key element in concrete structures.

This is a preview of subscription content, log in to check access.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13

Abbreviations

A :

Coefficient of linear function

A s :

Area of longitudinal reinforcement

b :

Bias value

\( b_{1} \) :

Bias for the hidden layer

\( b_{2} \) :

Bias for the output layer

C :

Membership function

c :

Mean for x

C(As):

Correction factor for As

C(\( f'_{c} \)):

Correction factor for \( f'_{c} \)

C(\( f_{y,l} \)):

Correction factor for \( f_{y,l} \)

C(L/r):

Correction factor for L/r

D :

Depth or longer side of the column

f :

Linear function

\( f'_{c} \) :

Compressive strength of concrete

\( f_{y,t} \) :

Yield stress of longitudinal reinforcement

\( f_{y,l} \) :

Yield stress of transverse reinforcement

I :

Moment of inertia of the cross section

IW :

Input weights of hidden layer

L :

Length of equivalent cantilever

L/r :

Length of column to gyration ratio

LW :

Layer weights of output layer

M :

Moment capacity of concrete column

\( M_{0} \) :

ANFIS output

Mean:

Mean of error

N :

Number of data

StDev:

Standard deviation

V :

Output layer for ANN-8-Purelin

W :

Width or shorter side of the column

w :

Weights

X :

Input parameter

\( x_{ \hbox{max} } \) :

Maximum value for x

\( x_{ \hbox{min} } \) :

Minimum value for x

\( x_{n} \) :

Normal value of x

\( x_{r} \) :

Real value of x

Y :

Polynomial equation

Z :

Output layer for ANN-1-Tansig

\( \rho_{l} \) :

Longitudinal reinforcement ratio

\( \rho_{t} \) :

Transverse reinforcement ratio

σ :

Variance for x

References

  1. Aguilar V, Sandoval C, Adam JM, Garzón-Roca J, Valdebenito G (2016) Prediction of the shear strength of reinforced masonry walls using a large experimental database and artificial neural networks. Struct Infrastruct Eng. https://doi.org/10.1080/15732479.2016.1157824

    Article  Google Scholar 

  2. Ang BG (1981) Ductility of reinforced concrete bridge piers under seismic loading. Department of Civil Engineering, University of Canterbury, Christchurch

    Google Scholar 

  3. Atalay MB, Penzien J (1975) The seismic behavior of critical regions of reinforced concrete components as influenced by moment, shear and axial force. University of California, Berkeley

    Google Scholar 

  4. Barrera A, Bonet J, Romero ML, Fernández M (2012) Ductility of slender reinforced concrete columns under monotonic flexure and constant axial load. Eng Struct 40:398–412. https://doi.org/10.1016/j.engstruct.2012.03.012

    Article  Google Scholar 

  5. Bayrak O (1998) Seismic performance of rectilinearly confined high strength concrete columns. National Library of Canada = Bibliothèque nationale du Canada

  6. Bayrak O, Sheikh S (1996) Confinement steel requirements for high strength concrete columns. In: 11th world conference on earthquake engineering, Acapulco, Mexico

  7. Berry M, Parrish M, Eberhard M (2004) PEER structural performance database user’s manual (version 1.0). University of California, Berkeley

    Google Scholar 

  8. Del Zoppo M, Di Ludovico M, Prota A (2016) Deformation capacity of non-conforming rc columns under compressive axial load and biaxial bending. Eng Struct 124:480–493. https://doi.org/10.1016/j.engstruct.2016.06.019

    Article  Google Scholar 

  9. Galal K, Arafa A, Ghobarah A (2005) Retrofit of RC square short columns. Eng Struct 27(5):801–813. https://doi.org/10.1016/j.engstruct.2005.01.003

    Article  Google Scholar 

  10. Galeota D, Giammatteo M, Marino R (1996) Seismic resistance of high strength concrete columns. In: 11th world conference on earthquake engineering, Acapulco, Mexico

  11. Gill WD (1979) Ductility of rectangular reinforced concrete columns with axial load. Department of Civil Engineering, University of Canterbury, Christchurch

    Google Scholar 

  12. Guide to simplified design for reinforced concrete building (2012) (trans: 314 AC). American concrete institute, USA

  13. Huang Q, Gardoni P, Hurlebaus S (2009) Probabilistic capacity models and fragility estimates for reinforced concrete columns incorporating NDT data. J Eng Mech 135(12):1384–1392. https://doi.org/10.1061/(ASCE)0733-9399(2009)135:12(1384)

    Article  Google Scholar 

  14. Hwang S-K, Yun H-D (2004) Effects of transverse reinforcement on flexural behaviour of high-strength concrete columns. Eng Struct 26(1):1–12. https://doi.org/10.1016/j.engstruct.2003.08.004

    Article  Google Scholar 

  15. Inel M (2007) Modeling ultimate deformation capacity of RC columns using artificial neural networks. Eng Struct 29(3):329–335. https://doi.org/10.1016/j.engstruct.2006.05.001

    Article  Google Scholar 

  16. Ivakhnenko A (1971) Polynomial theory of complex systems. IEEE Trans Syst Man Cybern 4:364–378

    MathSciNet  Article  Google Scholar 

  17. Jang J-S (1993) ANFIS: adaptive-network-based fuzzy inference system. IEEE Trans Syst Man Cybern 23(3):665–685. https://doi.org/10.1109/21.256541

    Article  Google Scholar 

  18. Kabeyasawa T, Kabeyasawa T, Kim Y (2010) Progressive collapse simulation of reinforced concrete buildings using column models with strength deterioration after yielding. In: Paper presented at the ATC and SEI conference on improving the seismic performance of existing buildings and other structures

  19. Kanda M, Shirai N, Adachi H, Sato T (1988) Analytical study on elasto-plastic hysteretic behaviors of reinforced concrete members. Trans Jpn Concr Inst 10(1):257–264

    Google Scholar 

  20. Kono S, Watanabe F (2000) Damage evaluation of reinforced concrete columns under multiaxial cyclic loadings. In: The second US-Japan workshop on performance-based earthquake engineering methodology for reinforced concrete building structures, pp 221–231

  21. Kono S, Bechtoula H, Sakashita M, Tanaka H, Watanabe F, Eberhard M (2006) Damage assessment of reinforced concrete columns under high axial loading, vol 165. ACI Special Publications, Farmington Hills

    Google Scholar 

  22. Kotsovos GM (2011) Assessment of the flexural capacity of RC beam/column elements allowing for 3D effects. Eng Struct 33(10):2772–2780. https://doi.org/10.1016/j.engstruct.2011.06.002

    Article  Google Scholar 

  23. Kumar R, Gardoni P (2011) Modeling structural degradation of RC bridge columns subjected to earthquakes and their fragility estimates. J Struct Eng 138(1):42–51. https://doi.org/10.1061/(ASCE)ST.1943-541X.0000450

    Article  Google Scholar 

  24. Legeron F, Paultre P (2000) Behavior of high-strength concrete columns under cyclic flexure and constant axial load. ACI Struct J 97(4):591–601

    Google Scholar 

  25. Leung CK, Ng MY, Luk HC (2006) Empirical approach for determining ultimate FRP strain in FRP-strengthened concrete beams. J Compos Constr 10(2):125–138. https://doi.org/10.1061/(ASCE)1090-0268(2006)10:2(125)

    Article  Google Scholar 

  26. Matamoros AB (1999) Study of drift limits for high-strength concrete columns. University of Illinois, Urbana-Champaign

    Google Scholar 

  27. Mirrashid M (2014) Earthquake magnitude prediction by adaptive neuro-fuzzy inference system (ANFIS) based on fuzzy C-means algorithm. Nat Hazards 74(3):1577–1593. https://doi.org/10.1007/s11069-014-1264-7

    Article  Google Scholar 

  28. Mirrashid M, Givehchi M, Miri M, Madandoust R (2016) Performance investigation of neuro-fuzzy system for earthquake prediction. Asian J Civil Eng (BHRC) 17(2):213–223

    Google Scholar 

  29. Mo Y-L, Wang S (2000) Seismic behavior of RC columns with various tie configurations. J Struct Eng 126(10):1122–1130. https://doi.org/10.1061/(ASCE)0733-9445(2000)126:10(1122)

    Article  Google Scholar 

  30. Montejo LA, Kowalsky MJ, Hassan T (2009) Seismic behavior of flexural dominated reinforced concrete bridge columns at low temperatures. J Cold Reg Eng 23(1):18–42. https://doi.org/10.1061/(ASCE)0887-381X(2009)23:1(18)

    Article  Google Scholar 

  31. Mostafaei H, Vecchio FJ, Kabeyasawa T (2009) A simplified axial-shear-flexure interaction approach for load and displacement capacity of reinforced concrete columns. In: Conference on improving the seismic performance of existing buildings and other structures. Berkeley, CA, USA, pp 753–764

  32. Muguruma H, Watanabe F, Komuro T (1989) Applicability of high strength concrete to reinforced concrete ductile column. Trans Jpn Concr Inst 11(1):309–316

    Google Scholar 

  33. Naderpour H, Mirrashid M (2017) Compressive strength of mortars admixed with wollastonite and microsilica. In: Materials science forum. Trans Tech Publications, pp 415–418. http://www.scientific.net/MSF.890.415

  34. Naderpour H, Mirrashid M (2018a) Shear strength prediction of rc beams using adaptive neuro-fuzzy inference system. Sci Iran. https://doi.org/10.24200/sci.2018.50308.1624

    Article  Google Scholar 

  35. Naderpour H, Mirrashid M (2018b) An innovative approach for compressive strength estimation of mortars having calcium inosilicate minerals. J Build Eng 19:205–215. https://doi.org/10.1016/j.jobe.2018.05.012

    Article  Google Scholar 

  36. Naderpour H, Mirrashid M (2019a) Classification of failure modes in ductile and non-ductile concrete joints. Eng Fail Anal 103:361–375. https://doi.org/10.1016/j.engfailanal.2019.04.047

    Article  Google Scholar 

  37. Naderpour H, Mirrashid M (2019b) Shear failure capacity prediction of concrete beam–column joints in terms of ANFIS and GMDH. Pract Period Struct Des Constr 24(2):04019006. https://doi.org/10.1061/(ASCE)SC.1943-5576.0000417

    Article  Google Scholar 

  38. Naderpour H, Nagai K, Haji M, Mirrashid M (2019a) Adaptive neuro-fuzzy inference modelling and sensitivity analysis for capacity estimation of fiber reinforced polymer strengthened circular reinforced concrete columns. Expert Syst 36(4):e12410. https://doi.org/10.1111/exsy.12410

    Article  Google Scholar 

  39. Naderpour H, Mirrashid M, Nagai K (2019b) An innovative approach for bond strength modeling in FRP strip-to-concrete joints using adaptive neuro–fuzzy inference system. Eng Comput. https://doi.org/10.1007/s00366-019-00751-y

    Article  Google Scholar 

  40. Nauck D, Klawonn F, Kruse R (1997) Foundations of neuro-fuzzy systems. Wiley, Hoboken

    Google Scholar 

  41. Nosho K, Stanton J, MacRae G (1996) Retrofit of rectangular reinforced concrete columns using Tonen Forca tow sheet carbon fiber wrapping. Report No SGEM:96-92

  42. Ohno T, Nishioka T (1984) An experimental study on energy absorption capacity of columns in reinforced concrete structures. Proc JSCE Struct Eng Earthq Eng 1(2):137–147

    Google Scholar 

  43. Park R, Paulay T (1990) Use of interlocking spirals for transverse reinforcement in bridge columns. Strength Ductility Concr Substruct Bridges RRU Road Res Unit Bull 84(1):77–92

    Google Scholar 

  44. Paultre P, Legeron F, Mongeau D (2001) Influence of concrete strength and transverse reinforcement yield strength on behavior of high-strength concrete columns. Struct J 98(4):490–501

    Google Scholar 

  45. Pham TM, Hadi MN (2014) Predicting stress and strain of FRP-confined square/rectangular columns using artificial neural networks. J Compos Constr 18(6):04014019. https://doi.org/10.1061/(ASCE)CC.1943-5614.0000477

    Article  Google Scholar 

  46. Prakash S, Belarbi A, You Y-M (2010) Seismic performance of circular RC columns subjected to axial force, bending, and torsion with low and moderate shear. Eng Struct 32(1):46–59. https://doi.org/10.1016/j.engstruct.2009.08.014

    Article  Google Scholar 

  47. Pujol S (2002) Drift capacity of reinforced concrete columns subjected to displacement reversals. Purdue University, West Lafayette

    Google Scholar 

  48. Saatcioglu M, Grira M (1999) Confinement of reinforced concrete columns with welded reinforced grids. Struct J 96(1):29–39

    Google Scholar 

  49. Saatcioglu M, Ozcebe G (1989) Response of reinforced concrete columns to simulated seismic loading. Struct J 86(1):3–12

    Google Scholar 

  50. Sakai Y (1990) Experimental studies on flexural behavior of reinforced concrete columns using high-strength concrete. Japan Concrete Institute, Sapporo

    Google Scholar 

  51. Sezen H, Lodhi M (2009) Response estimation of non-ductile reinforced concrete columns subjected to lateral loads. In: ATC-SEI conference on improving the seismic performance of existing buildings and other structures. San Francisco, USA, pp 9–11

  52. Shirmohammadi F, Esmaeily A (2015) Performance of reinforced concrete columns under bi-axial lateral force/displacement and axial load. Eng Struct 99:63–77. https://doi.org/10.1016/j.engstruct.2015.04.042

    Article  Google Scholar 

  53. Soesianawati M (1986) Limited ductility design of reinforced concrete columns. Department of Civil Engineering, University of Canterbury, Christchurch

    Google Scholar 

  54. Sugano S (1996) Seismic behavior of reinforced concrete columns which used ultra-high-strength concrete. In: Proceedings of the 11th world conference on earthquake engineering

  55. Takemura H, Kawashima K (1997) Effect of loading hysteresis on ductility capacity of reinforced concrete bridge piers. J Struct Eng 43:849–858

    Google Scholar 

  56. Tanaka H (1990) Effect of lateral confining reinforcement on the ductile behaviour of reinforced concrete columns. University of Canterbury, Christchurch

    Google Scholar 

  57. Thomson JH, Wallace JW (1994) Lateral load behavior of reinforced concrete columns constructed using high-strength materials. Struct J 91(5):605–615

    Google Scholar 

  58. Wang P, Han Q, Du X (2014) Experimental study on circular RC bridge columns under combined cyclic flexural and torsional loadings. In: International efforts in lifeline earthquake engineering, ASCE, pp 417–424

  59. Watson S, Park R (1989) Design of reinforced concrete frames of limited ductility. Department of Civil Engineering, University of Canterbury, Christchurch

    Google Scholar 

  60. Watson S, Zahn F, Park R (1994) Confining reinforcement for concrete columns. J Struct Eng 120(6):1798–1824. https://doi.org/10.1061/(ASCE)0733-9445(1994)120:6(1798)

    Article  Google Scholar 

  61. Xiao Y, Martirossyan A (1998) Seismic performance of high-strength concrete columns. J Struct Eng 124(3):241–251. https://doi.org/10.1061/(ASCE)0733-9445(1998)124:3(241)

    Article  Google Scholar 

  62. Zahn FA (1985) Design of reinforced concrete bridge columns for strength and ductility. Department of Civil Engineering, University of Canterbury, Christchurch

    Google Scholar 

  63. Zhou X, Satoh T, Jiang W, Ono A, Shimizu Y (1987) Behavior of reinforced concrete short column under high axial load. Trans Jpn Concr Inst 9(2):541–548

    Google Scholar 

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to Masoomeh Mirrashid.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Communicated by V. Loia.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Naderpour, H., Mirrashid, M. Proposed soft computing models for moment capacity prediction of reinforced concrete columns. Soft Comput 24, 11715–11729 (2020). https://doi.org/10.1007/s00500-019-04634-8

Download citation

Keywords

  • Flexure failure
  • Moment capacity
  • Reinforced concrete columns
  • Soft computing
  • Structural capacity