scholarly journals Considerations about the determination of γz coefficient

2013 ◽  
Vol 6 (1) ◽  
pp. 75-100
Author(s):  
D. M. Oliveira ◽  
N. A. Silva ◽  
C. F. Bremer ◽  
H. Inoue
Keyword(s):  
Reinforced Concrete ◽  
Structural Model ◽  
Steel Structures ◽  
Second Order ◽  
Order Effects ◽  
Simplified Models ◽  
Simplified Analysis ◽  
Second Order Effects ◽  
Conservative Values

In this work, the γz coefficient, used to evaluate final second order effects in reinforced concrete structures, is studied. At the start, the influence of the structural model in determination of γz coefficient is evaluated. Next, a comparative analysis of γz and B2 coefficient, usually employed to evaluate second order effects in steel structures, is performed. In order to develop the study, several reinforced concrete buildings of medium height are analysed using ANSYS-9.0 [1] software. The results show that simplified analysis provide more conservative values of γz. It means that, for structures analysed by simplified models, large values of γz don't imply, necessarily, in significant second order effects. Furthermore, it was checked that γz can be determinated from B2 coefficients of each storey of the structures and that, for all the analysed buildings, the average values of the B2 coefficients are similar to γz.

scholarly journals Evaluation of second order moments in reinforced concrete structures using the γz and B2 coefficients

2014 ◽  
Vol 7 (3) ◽  
pp. 329-348 ◽  
Author(s):  
D. M. Oliveira ◽  
N. A. Silva ◽  
P. M. Oliveira ◽  
C. C. Ribeiro
Keyword(s):  
Reinforced Concrete ◽  
Concrete Structures ◽  
Steel Structures ◽  
Second Order ◽  
Order Effects ◽  
Reinforced Concrete Structures ◽  
Ansys Software ◽  
First Order ◽  
Simplified Method ◽  
Second Order Effects

This paper presents an alternative to estimate the magnifier of first order moments to be applied on each storey of reinforced concrete structures, from the values obtained for the γz and B2 coefficients, used to evaluate second order effects in reinforced concrete structures and in steel structures, respectively. In order to develop the study, initially several reinforced concrete buildings of medium height are processed, in first order and in second order, using the ANSYS software. Next, γz, B2 and the increase in first order moments, when considering the second order effects along the height of the buildings, are calculated. Finally, from the results obtained, the magnifier of the first order moments, differentiated for each storey of the structure and calculated from both γz and B2 coefficients, is estimated and the efficiency of the simplified method of obtaining final moments using the magnifier proposed is evaluated.

scholarly journals Statistical analysis of second order effects variation with the stories height of reinforced concrete buildings

2017 ◽  
Vol 10 (2) ◽  
pp. 333-357
Author(s):  
D.M. OLIVEIRA ◽  
N.A. SILVA ◽  
C.C. RIBEIRO ◽  
S.E.C. RIBEIRO
Keyword(s):  
Reinforced Concrete ◽  
Statistical Analysis ◽  
Second Order ◽  
Order Effects ◽  
Reinforced Concrete Buildings ◽  
First Order ◽  
Concrete Buildings ◽  
Ideal Situation ◽  
Second Order Effects ◽  
The Ideal

Abstract In this paper the simplified method to evaluate final efforts using γ z coefficient is studied considering the variation of the second order effects with the height of the buildings. With this purpose, several reinforced concrete buildings of medium height are analyzed in first and second order using ANSYS software. Initially, it was checked that the (z coefficient should be used as magnifier of first order moments to evaluate final second order moments. Therefore, the study is developed considering the relation (final second order moments/ first order moments), calculated for each story of the structures. This moments relation is called magnifier of first order moments, "γ", and, in the ideal situation, it must coincide with the γ z value. However, it is observed that the reason γ /γ z varies with the height of the buildings. Furthermore, using an statistical analysis, it was checked that γ /γ z relation is generally lower than 1.05 and varies significantly in accordance with the considered building and with the presence or not of symmetry in the structure.

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

2019 ◽  
Vol 12 (2) ◽  
pp. 408-428 ◽  
Author(s):  
F. F. LEITÃO ◽  
G. H. SIQUEIRA ◽  
L. C. M. VIEIRA JR. ◽  
S. J. C. ALMEIDA
Keyword(s):  
Reinforced Concrete ◽  
Bending Moment ◽  
Second Order ◽  
Order Effects ◽  
Concrete Frames ◽  
Natural Period ◽  
Asymmetric Structures ◽  
Mass Matrices ◽  
Modes Of Vibration ◽  
Second Order Effects

Abstract The χT parameter, a simplified method recently presented, allows to estimate the global second-order effects on reinforced concrete frames using the natural period of vibration. This parameter was developed based on the fact that both natural period of vibration and global second-order effects depend essentially on the stiffness and mass matrices of the structure, being thus related. In this paper, numerical analyses are conducted on nine models with different patterns of irregularity in terms of geometry in plan and stiffness. The main purpose of these analyses is to evaluate the applicability of the χT parameter in asymmetric structures as well as that can present torsional modes as the fundamental mode of vibration. In addition, different hypotheses are tested in order to verify the influence of the different modes of vibration in the structural sensitivity to global second-order effects. Results of the simplified analyses were compared to the final bending moment values obtained through a nonlinear numerical analysis considering the P-Δ effect. It is observed that the parameter χT is a promising indicator for a simplified estimation of the global second-order effects for concrete frames, especially when higher modes of vibration are taken account in the analysis.

Simplified Approach Based on the Natural Period of Vibration for Considering Second-Order Effects on Reinforced Concrete Frames

2018 ◽  
Vol 18 (05) ◽  
pp. 1850074 ◽  
Author(s):  
Daniel G. Reis ◽  
Gustavo H. Siqueira ◽  
Luiz C. M. Vieira ◽  
Ronald D. Ziemian
Keyword(s):  
Reinforced Concrete ◽  
Amplification Factor ◽  
Flexible Structures ◽  
Second Order ◽  
Order Effects ◽  
Concrete Frames ◽  
Natural Period ◽  
Reinforced Concrete Frames ◽  
Order Analysis ◽  
Second Order Effects

Recent studies have demonstrated the existence of a relationship between a structures susceptibility to second-order effects and its natural period of vibration ([Formula: see text]) given that both these properties are fundamentally dependent on the structure stiffness and mass properties. The main advantage of the use of this characteristic is that [Formula: see text] can be obtained easily by the existing structural analysis software. In this study, different formulations are developed in order to propose an amplification factor ([Formula: see text]) to multiply first-order analysis results and satisfactorily obtain results of a second-order analysis. These formulations are based on D’Alembert’s principle, Rayleighs method, and the use of generalized coordinates to represent the dynamic displacement of flexible structures. It is observed that [Formula: see text] provides values closer to and in fact, more conservatively than, those obtained by the conventional simplified methods currently used by structural design engineers. Thus, the amplification factor [Formula: see text], which is based on the natural period of vibration, is proposed to be used as (i) an indicator of a structure susceptibility to second-order effects and (ii) an amplification factor to describe the second-order effects on reinforced concrete frames.

scholarly journals Design of slender reinforced concrete rectangular columns subjected to eccentric loads by approximate methods

2012 ◽  
Vol 5 (4) ◽  
pp. 548-554 ◽  
Author(s):  
J. M. Calixto ◽  
T. H. Souza ◽  
E. V. Maia
Keyword(s):  
Reinforced Concrete ◽  
Second Order ◽  
Order Effects ◽  
Test Results ◽  
Approximate Methods ◽  
Design Procedures ◽  
Load Combination ◽  
Second Order Effects ◽  
The Stability ◽  
Slender Columns

Reinforced concrete codes worldwide establish that the design of slender columns must ensure that under the most unfavorable load combination, there is neither instability nor material failures. Thus, it is mandatory to consider material as well as geometrical nonlinearities. The consideration of second order effects can be done using simplified methods or the general method. This work analyses second order effects based on the approximate methods shown in NBR 6118 [1]: approximate curvature method and approximate stiffness procedure. Due to the importance of the columns in the stability of buildings is essential that these simplified design methods provide safe solutions for the design of columns. In this scenario, the objective of this study is to evaluate these simplified design procedures in terms of safety, precision and economy with respect to test results of RC slender columns subjected to eccentric loads found in the literature. The comparative analysis reveals that the approximate stiffness procedure provides better results.

scholarly journals Finite Element Analysis of Bolted T-Stubs Undergoing Large Displacement: A Preliminary Study

2018 ◽  
Vol 12 (1) ◽  
pp. 170-176 ◽  
Author(s):  
Anna C. Faralli ◽  
P.J. Tan ◽  
Massimo Latour ◽  
Gianvittorio Rizzano
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Steel Structures ◽  
Second Order ◽  
Large Displacement ◽  
Order Effects ◽  
Element Analysis ◽  
Parametric Investigation ◽  
Deformation Response ◽  
Second Order Effects

Background: In recent years, there have been increased interests by the steel structures community to characterise the large-deformation response of T-stubs to evaluate the deformation capacity of bolted joints. However, little information exists on the influence of second-order effects on the response of bolted T-stubs and, consequently, there are no existing guidelines on how to include these effects in de-sign. Objective: In this paper, we assess the influence of second-order effects in T-stubs bolted to a rigid support through a parametric investigation, using finite element analysis. Methods: Both material and geometrical non-linearities were considered since they are known to have a critical impact upon the performance of T-stubs. A benchmark model is first generated and validated and then used to carry out a parametric investigation. A method to assess the contributions of membrane forces to the overall deformation response of a T-stub is also proposed based on the introduction of a non-dimensional parameter Ψ. Results: The combination of geometric parameters that are most affected by second order effects, induced by large displacement, was identified. A direct correspondence was found between the extent of second order effects that has developed and the index Ψ: a higher index implies a greater influence by second order effects.

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