Non-Linear Analysis of Cracked Tensile Reinforced Concrete Bars: A Comparison of Numerical Methods

Bajc, Urška; Saje, Miran; Planinc, Igor; Bratina, Sebastjan

doi:10.4203/ccp.102.116

Cited by 1 publication

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“…Principle of virtual work states that virtual work of internal forces equals virtual work of external forces. Here, we begin with modified principle as it is given in Bajc et al (2013Bajc et al ( , 2018 for RC bar with discrete cracks at nodes of finite element, however, applicable adaptations for RC bar with discrete crack at 'excluded' point (at material coordinates À x r c and þ x r c somewhere along the length of finite element) are introduced…”

Section: Modified Principle Of Virtual Work For a Rc Bar With One Crackmentioning

confidence: 99%

“…In the finite element, where the crack appears during the numerical analysis, the equations for cracked finite element (as presented in previous sections of this paper) are applied. In the remaining finite elements, the equations for uncracked finite element (as in Bajc et al (2013;2018)) are used. All equations are then combined into the equation of system through well established procedures of numerical theory of structures Gðx,λÞ ¼ RðxÞ À λP ¼ 0 (45)…”

Section: Solving Algorithmmentioning

confidence: 99%

“…However, a system of discrete generalized equilibrium equations of finite element without crack is briefly presented first. This system of equations is applicable in the model of RC bar with discrete crack at 'excluded' point previous to cracking, and has already been presented in detail by Bajc et al (2013Bajc et al ( , 2018.…”

Section: Finite Element Formulationmentioning

confidence: 99%

“…Cracking of concrete in the first model is considered through occurrence of discrete cracks (e.g. in Bajc et al, 2013;Dias-da-Costa et al, 2009;Federation internationale du beton, 2013;Yang et al, 2008 and others). When the tensile strength of concrete, f ct , is exceeded, a discontinuity in the geometry of the element occurs (see Figure 1(a)).…”

Section: Introductionmentioning

confidence: 99%

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A novel strain-based finite element family for mesh-independent analysis of the tensile failure of reinforced concrete bars

Ogrin

Planinc

Bratina

2021

Advances in Structural Engineering

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The paper presents a novel family of strain-based beam finite elements (FE) for analysis of tensile failure of a reinforced concrete bar (RC bar), with results of the analysis being independent of the applied FE mesh. The composite bar consists of a continuous longitudinal ductile reinforcing bar(s) surrounded by brittle concrete cover, which are considered separately in the model. Longitudinal slip at the contact between the concrete cover and reinforcing bars is allowed, while their relative displacements perpendicular to the axis of the RC bar are prevented. Cracks in concrete cover occur when tensile stress in concrete exceeds its tensile strength. Propagation of partially connected crack, that is, softening of the material at the crack, is described through constitutive law in form of nonlinear relationship between stresses in concrete at the crack and the width of the crack. Each separate crack is considered discretely as a discontinuity in geometry of the element. In the analysis of cracking of concrete, it is commonly assumed that the discrete crack can occur at the nodes of FE only. However, this assumption leads to dependence of the analysis results on the employed FE mesh. The presented family of FE enables occurrence of the crack anywhere along the FE. In order to achieve this, the discrete crack is excluded from equations of FE and additional boundary conditions are introduced at the discontinuity. This approach ensures that the location of the cracks, their number and their propagation are independent of the applied FE mesh. Advantages of the novel family of FE are thoroughly presented in a parametric study which investigates influence of number of FE as well as influence of degrees of interpolation and integration on the cracking of RC bar under tensile loading. Experimental results of tensile tests on the analysed bar are available in literature. It can be concluded that the results obtained with the minimal possible number of novel FE and sufficiently high degree of numerical integration scheme, applied for solving integrals in equations of FE, are considerably more accurate than the results of previous analyses with model of discrete crack at the nodes of FE only.

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Section: Modified Principle Of Virtual Work For a Rc Bar With One Crackmentioning

confidence: 99%

Section: Solving Algorithmmentioning

confidence: 99%

Section: Finite Element Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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