Limit analysis of 3D reinforced concrete frames

Larsen, Kasper Paaske; Poulsen, Peter Noe; Nielsen, Leif Otto

doi:10.1201/b10546-42

Cited by 9 publications

(15 citation statements)

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“…In this equation, F(x)≽O means that the matrix F is a semidefinite positive. For a given stress state σc in the concrete, the yield criteria can be written as two linear matrix inequalities and two linear inequalities (Larsen, 2009)α1 and α2 are scalar variables.…”

Section: Materials Yield Criteria and Programmingmentioning

confidence: 99%

Numerical and analytical evaluation of stirrup-induced confinement on resistance of RC beams using lower bound limit analysis

Mohammadiasl

Bagherieh

2022

Advances in Structural Engineering

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In this paper, a modified three-dimensional element is introduced for limit analysis of RC structures, which considers more aspects of structural behaviour. Using the introduced element, the influence of stirrup confinement on the shear and moment resistance of RC beams is evaluated by lower bound limit analysis. To analyse and solve the relevant optimization problem, the semidefinite programming method, SDP, is employed. The modified Mohr–Coulomb yield criterion is utilized to constrain the concrete stress state. Beams with a constant amount of shear reinforcement per unit length, with different values of stirrup spacing, are studied. It means that they only differed in the effect of confinement induced by stirrup reinforcements. The performance of the proposed element is verified by comparing the results of numerical limit analyses with experimental results. This comparison revealed the efficiency and accuracy of the proposed model and the capability of the introduced element to take the effect of stirrup-induced confinements into account. After modelling and investigating the effect of stirrup confinement in load bearing of RC beams, a simplified equation for the design and practical purposes is proposed. Using this equation, the shear resistance of the beams could be modified for different stirrup space choices. The results obtained from this simplified equation are compared with numerical limit analysis and experimental results. The comparisons indicate the reasonable accuracy of the proposed equation.

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Section: Materials Yield Criteria and Programmingmentioning

confidence: 99%

Numerical and analytical evaluation of stirrup-induced confinement on resistance of RC beams using lower bound limit analysis

Mohammadiasl

Bagherieh

2022

Advances in Structural Engineering

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“…k = 4 corresponding to µ = 0.75 and θ ≈ 37 • is commonly used for normal strength concrete. The principal stresses are the eigenvalues of the concrete stress tensor σ c , thus, (4) can be represented using linear matrix inequalities [26,29,30].…”

Section: Conic Representation Of the Mohr-coulomb Criterionmentioning

confidence: 99%

Lower bound multiscale element for in situ cast joints in triaxial stress

Herfelt

Poulsen

Hoang

et al. 2018

Engineering Structures

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In practice, precast concrete structures are often being designed by manual methods and linear finite element analysis in the ultimate limit state. This practice leads to suboptimal structures, and the behaviour of the in-situ cast joints are unaccounted for. More accurate and efficient means of design are therefore needed, and a framework based on finite element limit analysis is being developed. In this paper, a one-dimensional multiscale joint element is presented, and a mechanical model is proposed as the yield function of the macro element. The scope of the model is to capture the behaviour of joints in three dimensions subjected to triaxial stress, and the resulting mathematical optimisation problem fits the format of semidefinite programming. The presented joint element is analysed and a real size example of a four-storey stairwell subjected to shear and torsion of precast concrete is presented. The influence of the joints on the behaviour of the stairwell is assessed.

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“…For ultimate limit state (ULS) analysis of appropriately reinforced concrete structures, finite element limit analysis (FELA) has proven to be a reliable and computationally efficient method for a variety of types of RC structures. [4][5][6][7][8] By adopting rigid-plastic material models for the reinforcement and the concrete, the method determines the ultimate capacity and collapse mode of RC structures with great computational robustness and efficiency owing to the use of convex optimization algorithms. However, due to the rigid-plastic material models, FELA cannot provide information on finite deformations, ruling out its use in serviceability limit state (SLS) analysis or buckling analysis.…”

Section: Introductionmentioning

confidence: 99%

A shell element for design‐oriented elasto‐plastic analysis of reinforced concrete wall structures using convex optimization

Vestergaard

Poulsen

Hoang

et al. 2022

Structural Concrete

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The iterative nature of the design processes for building structures requires computational models to be robust, efficient, and accessible while reflecting the actual structural behavior with sufficient accuracy. For limit state analysis of reinforced concrete structures, efficient linear-elastic models are generally inaccurate, while the modeling and computational complexity of most high-accuracy nonlinear models inhibit their use in design processes for large-scale structures. A recently proposed framework for elasto-plastic analysis of cracked reinforced concrete panels was demonstrated to be capable of analyzing models with more than 10,000 finite elements within minutes on a standard personal computer. This paper proposes an extension of this work in terms of a finite shell element for elastoplastic analysis of fully cracked reinforced concrete wall structures subjected to monotonic loading. Using nonlinear-elastic constitutive models to imitate elastoplasticity, the proposed shell element couples the in-plane section force variation to the nonlinear through-thickness stress variation in a stress-based formulation using a layer-based submodel. The method is validated with exact solutions, and its applicability in design processes involving large-scale structures is demonstrated using a finite element model of a four-story stairwell with more than three million variables, which is solved within minutes on a personal computer.

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Limit analysis of 3D reinforced concrete frames

Cited by 9 publications

References 0 publications

Numerical and analytical evaluation of stirrup-induced confinement on resistance of RC beams using lower bound limit analysis

Numerical and analytical evaluation of stirrup-induced confinement on resistance of RC beams using lower bound limit analysis

Lower bound multiscale element for in situ cast joints in triaxial stress

A shell element for design‐oriented elasto‐plastic analysis of reinforced concrete wall structures using convex optimization

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