Nonlinear Finite Element Modeling of Shear-Critical Reinforced Concrete Beams Using a Set of Interactive Constitutive Laws
Tóm tắt
Complex nature of diagonal tension accompanied by the formation of new cracks as well as closing and propagating preexisting cracks has deterred researchers to achieve an analytical and mathematical procedure for accurate predicting shear behavior of reinforced concrete, and there is the lack of a unique theory accepted universally. Shear behavior of reinforced concrete is studied in this paper based on recently developed constitutive laws for normal strength concrete and mild steel bars using the nonlinear finite element method. The salient feature of these stress–strain relations is to account the interactive effects of concrete and embedded bars on each other in a smeared rotating crack approach. Implementing the considered constitutive laws into an efficient secant-stiffness-based finite element algorithm, a procedure for the nonlinear analysis of reinforced concrete is achieved. The resulted procedure is capable of predicting load-deformation behavior, cracking pattern, and failure mode of reinforced concrete. Corroboration with data from shear-critical beam test specimens with a wide range of properties showed the model to predict responses with a good accuracy. The results were also compared with those from the well-known theory of modified compression field and its extension called disturbed stress field model which revealed the present study to provide more accurate predictions.
Tài liệu tham khảo
Joint ASCE-ACI Committee 445 (1998) Recent approaches to shear design of structural concrete. J Struct Eng ASCE 124 (12):1375–1417
CEB (1997) Concrete Tension and Size Effect, Contribution from CEB Task Group 2.7, Comité Euro-International du Béton, Lausanne, Switzerland
Lucas W, Oehlers DJ, Ali M (2011) Formulation of a shear resistance mechanism for inclined cracks in RC beams. J Struct Eng ASCE 137(12):1480–1488
Arslan G (2008) Cracking shear strength of RC slender beams without stirrups. J Civil Eng Manage 14(3):177–182
Pérez Caldentey A, Padilla P, Muttoni A, Fernández RM (2012) Effect of load distribution and variable depth on shear resistance of slender beams without stirrups. ACI Struct J 109(5):595–603
Keskin RS, Arslan G (2013) Predicting diagonal cracking strength of rc slender beams without stirrups using ANNs. Comp Conc 12(5):697–715
Jeong JP, Kim W (2014) Shear resistant mechanism into base components: beam action and arch action in shear-critical RC members. Int J Conc Struct Mater 8(1):1–14
Fernández RM, Muttoni A, Sagaseta J (2015) Shear strength of concrete members without transverse reinforcement: a mechanical approach to consistently account for size and strain effects. Eng Struct 99:360–372
Cavagnis F, Ruiz MF, Muttoni A (2015) Shear failures in reinforced concrete members without transverse reinforcement: an analysis of the critical shear crack development on the basis of test results. Eng Struct 113:157–173
Kazemi MT, Broujerdian V (2006) Reinforced concrete beams without stirrups considering shear friction and fracture mechanics. Can J Civ Eng 33:161–168
Kazemi MT, Broujerdian V (2006) Discussion of repeating a classic set of experiments on size effect in shear of membranes without stirrups, by Bentz EC and Buckley S. ACI Struct J 103(5):754–755
Bazant ZP, Kazemi MT (1991) Size effect on diagonal shear failure of beams without stirrups. ACI Struct J 88(3):268–276
Bažant ZP, Yu Q (2005) Designing against size effect on shear strength of reinforced concrete beams without stirrups: I-formulation. J Struct Eng ASCE 131(12):1855–1877
Bažant ZP, Yu Q (2005) Designing against size effect on shear strength of reinforced concrete beams without stirrups: II-verification. J Struct Eng ASCE 131(12):1886–1897
Xu S, Zhang X, Reinhardt HW (2012) Shear capacity prediction of reinforced concrete beams without stirrups using fracture mechanics approach. ACI Struct J 109(5):705–714
Gastebled OJ, May IM (2001) Fracture mechanics model applied to shear failure of reinforced concrete beams without stirrups. ACI Struct J 98(2):184–190
Collins MP (1978) Towards a rational theory for RC members in shear. J Struct Eng ASCE 104(4):649–666
Vecchio FJ, Collins MP (1986) The modified compression-field theory for reinforced concrete elements subjected to shear. ACI J Proceed 83(2):219–231
Vecchio FJ (1989) Nonlinear finite element analysis of reinforced concrete membranes. ACI Structural Journal 86(1):26–35
Vecchio FJ (2000) Disturbed stress field model for reinforced concrete: formulation. J Struct Eng ASCE 126(8):1070–1077
Vecchio FJ (2001) Disturbed stress field model for reinforced concrete: implementation. J Struct Eng ASCE 127(1):12–20
Vecchio FJ, Lai D, Shim W, Ng J (2001) Disturbed stress field model for reinforced concrete: validation. J Struct Eng ASCE 127(4):350–358
Vecchio FJ (2000) Analysis of shear-critical reinforced concrete beams. ACI Struct J 97(1):102–110
Hsu TTC, Zhang LX (1997) Nonlinear analysis of membrane elements by fixed-angle softened-truss model. ACI Struct J 94(5):483–492
Dabbagh H, Foster SJ (2006) A smeared-fixed crack model for FE analysis of RC membranes incorporating aggregate interlock. Adv Struct Eng 9(1):91–102
Bhatt P, Kader MA (1998) Prediction of shear strength of reinforced concrete beams by nonlinear finite element analysis. Comput Struct 68(1):139–155
Lee J, Kim SW, Mansour M (2011) Nonlinear analysis of shear-critical reinforced concrete beams using fixed angle theory. J Struct Eng ASCE 137(10):1017–1029
Broujerdian V, Kazemi MT (2010) Smeared rotating crack model for reinforced concrete membrane elements. ACI Struct J 107(4):411–418
Ayoub A, Flippou FC (1998) Nonlinear finite element analysis of reinforced concrete shear panels and walls. J Struct Eng ASCE 124(3):298–308
Sadeghi K (2014) Analytical stress-strain model and damage index for confined and unconfined concretes to simulate RC structures under cyclic loading. Int J Civil Eng 12(3):333–343
Arslan G, Hacisalihoglu M, Balci M, Borekci M (2014) An investigation on seismic design indicators of RC columns using finite element analyses. Int J Civil Eng 12(2):237–243
ACI Committee 446 (1991) Fracture mechanics of concrete: concepts, models and determination of material properties. ACI 446.1R-91, ACI, Detroit
ACI Committee 446 (1997) Finite Element Analysis of Fracture in Concrete Structures, ACI Committee 446 Report, American Concrete Institute, Farmington Hills, Mich
Bazant ZP, Oh BH (1983) Crack band theory for fracture of concrete. Matériaux et Constr 16(3):155–177
Prasad MVKV, Krishnamoorthy CS (2002) Computational model for discrete crack growth in plain and reinforced concrete. Comp Methods Appl Mech Eng 191(25):2699–2725
Slobbe AT, Hendriks MAN, Rots JG (2014) Smoothing the propagation of smeared cracks. Eng Fract Mech 132:147–168
Hsu TTC, Zhang LX (1996) Tension softening in reinforced concrete membrane elements. ACI Struct J 93(1):108–115
Belarbi A, Hsu TTC (1995) Compressive laws of softened concrete in biaxial tension-compression. ACI Struct J 92(5):562–573
Hognestad E (1951) Study of combined bending and axial load in reinforced concrete members, bulletin series No. 399, University of Illinois Engineering Experimental Section
Kent DC, Park R (1971) Flexural members with confined concrete. J Struct Div ASCE 97(7):1969–1990
Wollrab E, Kulkarni SM, Ouyang C, Shah SP (1996) Response of reinforced concrete panels under uniaxial tension. ACI Struct J 93(6):648–657
Bresler B, Scordelis AC (1963) Shear strength of reinforced concrete beams. ACI J 60(1):51–74
Vecchio FJ, Shim W (2004) Experimental and analytical reexamination of classic concrete beam tests. ASCE J Struct Eng 130(3):460–469