Abstract
An automated computationally efficient two-stage procedure has been proposed for service load analysis of reinforced concrete (RC) flexural members considering concrete cracking and tension stiffening. The proposed procedure yields cracked lengths, redistributed bending moments and inelastic deflections. The computation of final state, including cracked lengths and interpolation coefficients for tension stiffening, is automated by the initialization of second stage from the results of first stage. The procedure combines the analytical–numerical procedure developed by authors and the neural networks methodology. The cracked lengths and corresponding interpolation coefficients are rapidly estimated in the first stage using the closed-form expressions which are obtained from the trained neural networks. Eight separate neural networks are trained for the estimation of final cracked lengths and interpolation coefficients at in-span locations and supports. The use of estimated cracked lengths and interpolation coefficients of the first stage, in the beginning of second stage, significantly reduces number of iterations in the second stage. The deflections and bending moments obtained from the two-stage procedure are compared with those from the analytical–numerical procedure for a number of beams. The analytical–numerical procedure requires around six analyses to yield results with sufficient accuracy for design purpose (within 2–3%); whereas, in the two-stage procedure, only two analyses, one in each stage, are required to yield results with similar accuracy. The developed two-stage procedure requires a significantly small computational effort as compared to similarly accurate methods available in literature.
Similar content being viewed by others
References
Channakeshava C, Iyengar KTSR (1988) Elasto-plastic cracking analysis of reinforced concrete. J Struct Eng 114(11):2421–2438
Hu HT, Schnobrich WC (1990) Nonlinear analysis of cracked reinforced concrete. ACI Struct J 87(2):199–207
Rasheed HAS, Dinno KS (1994) An efficient nonlinear analysis of RC sections. Comput Struct 53(3):613–623
Polak MA, Blackwell KG (1998) Modeling tension in reinforced concrete members subjected to bending and axial load. J Struct Eng 124(9):1018–1024
Gerstle WH, Martha LF, Ingraffea AR (1987) Finite and boundary element modeling of crack propagation in two and three dimensions. Eng Comput 2(3):167–183
Stramandinoli RSB, Rovere HLL (2008) An efficient tension-stiffening model for nonlinear analysis of reinforced concrete members. Eng Struct 30(7):2069–2080
Casanova A, Jason L, Davenne L (2012) Bond slip model for the simulation of reinforced concrete structures. Eng Struct 39:66–78
Stramandinoli RSB, Rovere HLL (2012) FE model for nonlinear analysis of reinforced concrete beams considering shear deformation. Eng Struct 35:244–253
Dai JG, Ueda T, Sato Y, Nagai K (2012) Modeling of tension stiffening behavior in FRP-strengthened RC members based on rigid body spring networks. Comput-aided Civ Inf Eng 27(6):406–718
Cosenza E (1990) Finite element analysis of reinforced concrete elements in a cracked state. Comput Struct 36(1):71–79
Mickleborough NC, Ning F, Chan CM (1999) Prediction of stiffness of reinforced concrete shearwalls under service loads. ACI Struct J 96(6):1018–1026
Ning F, Mickleborough NC, Chan CM (1999) The effective stiffness of reinforced concrete flexural members under service load conditions. Aust J Struct Eng 2(2&3):135–144
Chan CM, Mickleborough NC, Ning F (2000) Analysis of cracking effects on tall reinforced concrete buildings. J Struct Eng 126(9):995–1003
Chan CM, Ning F, Mickleborough NC (2000) Lateral stiffness characteristics of tall reinforced concrete buildings under service loads. Struct Design Tall Build 9(5):365–383
Tanrikulu AK, Dundar C, Cagatay IH (2000) A computer program for the analysis of reinforced concrete frames with cracked beam elements. Struct Eng Mech 10(5):463–478
Kara IF, Dundar C (2009) Effect of loading types and reinforcement ratio on an effective moment of inertia and deflection of a reinforced concrete beam. Adv Eng Softw 40(9):836–846
Kara IF, Dundar C (2010) Three-dimensional analysis of tall reinforced concrete buildings with nonlinear cracking effects. Mech Based Des Struct Mach 38(3):388–402
Patel KA, Chaudhary S, Nagpal AK (2016) A tension stiffening model for analysis of reinforced concrete flexural members subjected to service load. Comput Concr 17(1):29–51
Patel KA (2016) Development of computationally efficient techniques for instantaneous and time-dependent analysis of reinforced concrete beams and frames at service load. Ph.D. thesis, Indian Institute of Technology Delhi, New Delhi
Singh Y, Nagpal AK (1994) Two stage condensation procedure for free vibration characteristics of framed tube buildings. Struct Des Tall Build 3(1):37–49
Singh Y, Nagpal AK (1994) Two-stage gravity load analysis of framed-tube buildings. Struct Des Tall Build 3(1):65–83
Singh Y, Nagpal AK (1994) Two-stage solution for framed tube buildings. Comput Struct 50(5):655–663
Patel KA, Chaudhary S, Nagpal AK (2014) Analytical-numerical procedure incorporating cracking in RC beams. Eng Comput 31(5):986–1010
Ghali A, Favre R, Elbadry M (2002) Concrete structures: stresses and deformations, 3rd edn. E and Spon, London
Chaudhary S, Pendharkar U, Patel KA, Nagpal AK (2014) Neural networks for deflections in continuous composite beams considering concrete cracking. Iran J Sci Tech T Civil Eng 38(C1+):205–221
Pendharkar U, Chaudhary S, Nagpal AK (2010) Neural networks for inelastic mid-span deflections in continuous composite beams. Struct Eng Mech 36(2):165–179
Chaudhary S, Pendharkar U, Nagpal AK (2007) Bending moment prediction for continuous composite beams by neural networks. Adv Struct Eng 10(4):439–454
Pendharkar U, Chaudhary S, Nagpal AK (2007) Neural network for bending moment in continuous composite beams considering cracking and time effects in concrete. Eng Struct 29(9):2069–2079
MATLAB 7.8 (2009) Neural networks toolbox user’s guide. USA
Kim JI, Kim DK, Feng MQ, Yazdani F (2004) Application of neural networks for estimation of concrete strength. J Mater Civil Eng 16(3):257–264
Khandelwal M, Kumar DL, Yellishetty M (2011) Application of soft computing to predict blast-induced ground vibration. Eng Comput 27(2):117–125
Rajasekaran S, Suresh D, Pai GV (2002) Application of sequential learning neural networks to civil engineering modeling problems. Eng Comput 18(2):138–147
Tohidi S, Sharifi Y (2015) Neural networks for inelastic distortional buckling capacity assessment of steel I-beams. Thin Wall Struct 94:359–371
Mohammadhassani M, Nezamabadi-Pour H, Jumaat MZ, Jameel M, Arumugam AMS (2013) Application of artificial neural networks (ANNs) and linear regressions (LR) to predict the deflection of concrete deep beams. Comput Concr 11(3):237–252
Tadesse Z, Patel KA, Chaudhary S, Nagpal AK (2012) Neural networks for prediction of deflection in composite bridges. J Constr Steel Res 68(1):138–149
Gupta RK, Patel KA, Chaudhary S, Nagpal AK (2013) Closed form solution for deflection of flexible composite bridges. Proc Eng 51:75–83
Gupta RK, Kumar S, Patel KA, Chaudhary S, Nagpal AK (2015) Rapid prediction of deflections in multi-span continuous composite bridges using neural networks. Int J Steel Struct 15(4):893–909
Patel KA, Bhardwaj A, Chaudhary S, Nagpal AK (2015) Explicit expression for effective moment of inertia of RC beams. Lat Am J Solid Struct 12(3):542–560
Yu WW, Winter G (1960) Instantaneous and long-time deflections of reinforced concrete beams under working loads. ACI J Proc 57(7):29–50
ABAQUS (2011) ABAQUS standard user’s manuals: version 6.11. Hibbitt, Karlsson and Sorensen, Pawtucket
Patel KA, Chaudhary S, Nagpal AK (2016) An element incorporating cracking for reinforced concrete skeletal structures at service load. Adv Struct Eng. doi:10.1177/1369433216673642
Patel KA, Chaudhary S, Nagpal AK (2016) Rapid prediction of inelastic bending moments in reinforced concrete beams considering cracking. Comput Concr. 18(6):1113–1134
ACI 318 (2008) Building code requirements for structural concrete and commentary. American Concrete Institute (ACI) Committee 318, USA
Author information
Authors and Affiliations
Corresponding author
Electronic supplementary material
Below is the link to the electronic supplementary material.
Rights and permissions
About this article
Cite this article
Patel, K.A., Chaudhary, S. & Nagpal, A.K. An automated computationally efficient two-stage procedure for service load analysis of RC flexural members considering concrete cracking. Engineering with Computers 33, 669–688 (2017). https://doi.org/10.1007/s00366-016-0496-4
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00366-016-0496-4