Analysis of the global second-order effects on irregular reinforced concrete structures using the natural period of vibration

Leitão, Fábio Fleming; Siqueira, Gustavo Henrique; Vieira, Lucélia Gonçalves; Almeida, Saulo José de Castro

doi:10.1590/s1983-41952019000200012

Cited by 4 publications

(2 citation statements)

References 12 publications

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“…Reis et al [12] uses a similar procedure applied in Statler [11], however, it uses a dynamic model of a flexible structure based on equivalent cantilever beam-column to estimate the first natural frequency. In another work by Leitão et al [13], the proposed method by Reis et al [12] was used to evaluate the applicability of the amplification factor based on natural frequencies in an asymmetric structure in which torsional vibration modes can become fundamental vibration modes.…”

Section: Introductionmentioning

confidence: 99%

Modal P-delta – simplified geometric nonlinear method by using modal and buckling analysis

Ferreira

Cruz

Araújo

et al. 2023

Rev. IBRACON Estrut. Mater.

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Recent works show that in structures, there is a relationship between the natural period of vibration and global second-order effects. This relationship occurs because both depend on the stiffness matrix and the mass matrix of the structure. In this work, a non-linear geometric method - modal P-delta – is proposed that takes advantage of the relationship between the dynamic parameters and the non-linear effects. The methodology establishes an association between the buckling instability modes and the structural vibration modes. An interpolation of the vibration modes without axial loading and vibration modes with critical axial loading is proposed to approximate the vibration modes and frequencies of the loaded structure. In this way, through a simple formulation, the vibration modes and the natural frequencies of the loaded structure can be used to evaluate the displacements of the structures including the non-linear effects. Several numerical examples were simulated in regular structures in the plane, such as a free-fixed column and a plane frame with two different loading configurations. The results generated with the modal P-delta method provide information about the nonlinear behavior of the pre-buckling equilibrium path. These results are different from the findings in the literature, where the relationship between dynamic parameters and non-linear effects is used as a simple indicator or amplification factors to determine non-linear effects. Furthermore, our results indicate that the modal P-delta reduces the computational time spent considerably compared to the traditional P-delta iterative method.

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Section: Introductionmentioning

confidence: 99%

Modal P-delta – simplified geometric nonlinear method by using modal and buckling analysis

Ferreira

Cruz

Araújo

et al. 2023

Rev. IBRACON Estrut. Mater.

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“…Leitão et al [11] follow the development of the χT parameter, focusing specially in structures with geometric asymmetry and with vibration fundamental mode of torsional shape. The results of the simplified analysis are compared with those obtained through non-linear numerical analysis considering the P-Δ effect.…”

Section: Introductionmentioning

confidence: 99%

Second-order torsion effects in concrete buildings

Andrade

Nóbrega

2021

Rev. IBRACON Estrut. Mater.

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The internal forces due to torsion in global analysis of buildings, and its second-order effects, usually are not properly considered in structural design or even in design code’s prescriptions. Although the γZ coefficient, which is used to the evaluation of global second-order effects, has a wide, useful and consolidated application, it is true that specific torsional aspects are not well considered by it. This paper discusses the little-known γθ coefficient, an analogous proposition to the γZ coefficient, but focused specifically on the consideration of torsional effects. After the discussion on the concepts and the design methodology, several buildings are evaluated and their displacements and the coefficients γZ and γθ are calculated. Comparing these parameters, and also the results obtained by the P–Δ method, it is demonstrated the importance and the reliability of the γθ coefficient.

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Evaluation of limit state of stress and strain of free-fixed columns with variable geometry according to criteria from the Brazilian code for concrete structures

Wahrhaftig

Magalhães

Siqueira

2020

Lat. Am. j. solids struct.

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The ultimate limit state of stability by equilibrium bifurcation, the limit states for stress and strain resulting from this condition were evaluated for an extremely slender real structure of reinforced concrete, with geometry varying along its length. The aspects related to nonlinearities of the material were considered through the recommendations on NBR 6118:2014, from the Brazilian Association of Technical Standards (ABNT). In the analytical solution, developed for stability analysis, all elements of the structural dynamics present in the system were taken into account, including the column self-weight. The critical buckling load was then dynamically defined to different instants of time. Reductions of 70% for the modulus of elasticity and 59% for the critical buckling force were found in analyses performed from zero and five thousand days. It was also possible to obtain the induced stresses on the homogenized cross-sections and those transferred to reinforcement steel bars. KeywordsLimit states, critical buckling load, analytical solution, NBR 6118:2014. Graphical AbstractEvaluation of limit state of stress and strain of free-fixed columns with variable geometry according to criteria from the Brazilian code for concrete structures Alexandre de Macêdo Wahrhaftig et al.

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Analysis of the global second-order effects on irregular reinforced concrete structures using the natural period of vibration

Cited by 4 publications

References 12 publications

Modal P-delta – simplified geometric nonlinear method by using modal and buckling analysis

Modal P-delta – simplified geometric nonlinear method by using modal and buckling analysis

Second-order torsion effects in concrete buildings

Evaluation of limit state of stress and strain of free-fixed columns with variable geometry according to criteria from the Brazilian code for concrete structures

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