Refined Beam Element for Second Order Analysis of Latticed Shells

2014 ◽  
Vol 1065-1069 ◽  
pp. 1208-1211
Author(s):  
Lin Qi ◽  
Hai Feng Huo
Keyword(s):  
Geometrical Nonlinearity ◽  
Single Layer ◽  
Second Order ◽  
Order Effects ◽  
Analysis Method ◽  
Maclaurin Series ◽  
Order Analysis ◽  
Stability Functions ◽  
Beam Elements ◽  
Spatial Beam

Based on equilibrium equation of beam, the displacement interpolating functions with shear effect of spatial beam elements which are used to simulate the structure members of latticed shells are deduced. The different displacement interpolating functions in compression and tension spatial beam-column elements are unified by the method of Maclaurin series expansion, and the unified expressions which are used to simulate structure members are equivalent to those expressed by stability functions. Numerical analyses results indicate that the second-order elastic analysis method for beam structures proposed in this paper, which can perfectly incarnate the second-order effects and the geometrical nonlinearity of the single-layer cylindrical reticulated shell, is of better accurateness and higher effectiveness.

scholarly journals CONSIDERATIONS ON THE DIFFUSE SEISMICITY ASSUMPTION

2015 ◽  
Vol 12 (2) ◽  
Author(s):  
Jorge Daniel Riera ◽  
Ignacio Iturrioz
Keyword(s):  
Steel Structures ◽  
Direct Analysis ◽  
Second Order ◽  
Effective Length ◽  
Order Effects ◽  
Analysis Method ◽  
Order Analysis ◽  
3D Space ◽  
Effective Length Method ◽  
Diffuse Seismicity

Second-order effects were historically included by the effective length method (K concept). All the studies about that methodology have been developed in frame plane, with regular rectangular frames. The new way to include those effects is the use of second-order analysis, direct analysis method or alternative simplified options. This methodology was included in ANSI AISC360 in the 2005 version and in the 2010 version. As before, the studies already developed for DAM analysis are in plane. In this paper, the K concept is revisited by numerical analysis, and extended to the 3D space. Using models of symmetric and non-symmetric industrial steel structures in plane, 3D stability analyses were developed, and the results were compared with plane behavior. Several conclusions and recommendations were exposed, resulting from the analyzed models. Keywords: Second-order analyses, steel structures, irregular 3D frames.

scholarly journals ANALYSIS OF THE GLOBAL AND LOCAL IMPERFECTION OF STRUCTURAL MEMBERS AND FRAMES

2019 ◽  
Vol 25 (8) ◽  
pp. 805-818 ◽  
Author(s):  
Charlotte Mercier ◽  
Abdelouahab Khelil ◽  
Ali Khamisi ◽  
Firas Al Mahmoud ◽  
Rémi Boissiere ◽  
...  
Keyword(s):  
Second Order ◽  
Structural Defects ◽  
Order Effects ◽  
Structural Members ◽  
Buckling Mode ◽  
New Approach ◽  
Order Analysis ◽  
Main Challenge ◽  
Buckling Failure ◽  
Global And Local

Stresses of a structure are determined with a first or a second order analysis. The choice of the method is guided by the potential influence of the structure’s deformation. In general, considering their low rigidity with regard to those of buildings, scaffolding and shoring structures quickly reach buckling failure. Imperfections, such as structural defects or residual stresses, generate significant second order effects which have to be taken into account. The main challenge is to define these imperfections and to include them appropriately in the calculations. The present study suggests a new approach to define all the structure’s imperfections as a unique imperfection, based on the shape of elastic critical buckling mode of the structure. This study proposes a method allowing to determine the equation of the elastic critical buckling mode from the eigenvectors of the second order analysis of the structure. Subsequently, a comparative study of bending moments of different structures calculated according to current Eurocode 3 or 9 methods or according to the new method is performed. The obtained results prove the performance of the proposed method.

Analysis of the Overall Reliability Slender Concrete Columns

2017 ◽  
Vol 259 ◽  
pp. 203-208
Author(s):  
Vladimír Benko ◽  
Tomas Gúcky ◽  
Adrián Valašík
Keyword(s):  
Concrete Columns ◽  
Design Methods ◽  
Second Order ◽  
Order Effects ◽  
Design Strength ◽  
Order Analysis ◽  
Non Linear ◽  
Buckling Failure ◽  
Overall Reliability ◽  
General Method

Standard for designing of concrete structures STN EN 1992-1-1 offers three methods of analysis of second order effects with axial load. Namely, a general method based on non-linear second order analysis and two simplified methods: Method based on nominal stiffness and method based on nominal curvature. According to three series of the experiments of slender concrete columns and after calibration of the non-linear calculations, the authors in following paper compare the global reliability of above mentioned design methods with parametric study. According to executed research is possible to say that the differences in reliability of the design methods are considerable in several cases of the slender concrete columns design.The experiments were executed in the Central laboratory of Faculty of Civil Engineering STU in Bratislava in cooperation with company STRABAG ltd. The series of columns differed only in strength class of concrete (C45/55 for S1, C70/85 for S2, C80/95 for S3) and each series included six tested samples. The geometry and reinforcement of the columns as well as the initial eccentricity of the axial force were design so, that the buckling failure of the columns occurred earlier than the design strength of materials in the most stressed cross-section ran out.

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 Alternative Design Procedure for RC-Braced Long Columns Based on New Moment Magnifiers Matrix

2021 ◽  
Vol 2021 ◽  
pp. 1-20
Author(s):  
Mohamed Farouk ◽  
Majed Alzara ◽  
A. Ehab ◽  
A. M. Yosri
Keyword(s):  
Flexural Rigidity ◽  
Design Procedure ◽  
Bending Moment ◽  
Order Effect ◽  
Second Order ◽  
Effective Length ◽  
Column Height ◽  
Order Effects ◽  
Order Analysis ◽  
Proposed Model

Based on modified methods for the results of first-order analysis of RC columns, different codes approximate the second-order effects by using equations focusing on the maximum additional moment through the column height. These equations did not refer to the additional moments between the column and the connected beam, only the effect of the connected beams is taken into consideration by dealing with the effective length of the column, not the total length. Moreover, these equations did not take into account the second-order effect, which is caused by axial force and the inverse moments due to beam restriction for the column ends. This paper presents a new moment magnifiers matrix for the additional moments at the connection between braced columns and the connected beams as a simplified computation that can be used in the design procedure. That is through an equation based on transforming the original long column in second-order analysis to an equivalent isolated column. The equivalent column was represented as an element restricted with rotational spring support at its ends, and it is subjected to lateral distributed loads that have the same influence of the second-order effect on the induced additional moments in the long column. The suggested equivalent column can be used to form the additional bending moment diagram, also to compute the additional deformations as well. Numerous factors were analyzed linearly by using the presented new moment magnifiers matrix and finite element method, and the results proved the efficiency of the proposed model. Although the presented suggested model is based on the isolated analysis of the long column, the effect of the additional moments in the adjacent long column can be considered by presented two suggestions to improve the model. Also, development was proceeded on the model by modifying the flexural rigidity (EI) which is recommended in ACI to appropriate the time of failure. The additional moment values of the developed model were close to the values calculated by the ACI equation.

Inelastic Second-Order Analysis of Frame Structures Using the Stability-Based Beam-Column Element

2009 ◽  
Vol 12 (4) ◽  
pp. 513-527
Author(s):  
Seung-Eock Kim ◽  
Jung-Woong Park
Keyword(s):  
Composite Structures ◽  
Lateral Displacement ◽  
Uniaxial Stress ◽  
Second Order ◽  
Order Effects ◽  
Equilibrium Equations ◽  
Good Efficiency ◽  
Order Analysis ◽  
The Stability ◽  
Column Element

In this study, the stability-based beam-column element has been proposed to consider the geometric second-order effects and material inelasticity, and to take advantage of the computational efficiency of the second-order analysis. A new force interpolation function matrix is developed to consider a moment magnification due to the axial force and lateral displacement. The constitutive behaviour of the cross-section is formulated by integration of the uniaxial stress-strain response of fibres to model the material inelasticity. The generalized displacement control (GDC) method incorporating the incremental secant stiffness method is applied to solve the nonlinear equilibrium equations with multiple limit points. Evaluation of the results of this study shows that the proposed method consistently predicts well the nonlinear inelastic behaviour of steel and composite structures, and gives good efficiency.

Second-order analysis for semirigid steel frame design

2001 ◽  
Vol 28 (1) ◽  
pp. 59-76 ◽  
Author(s):  
Lei Xu
Keyword(s):  
Steel Frame ◽  
Second Order ◽  
Rotational Behaviour ◽  
Analysis Method ◽  
Frame Design ◽  
Analysis And Design ◽  
Order Analysis ◽  
Rigid Frame ◽  
Structural Responses ◽  
Fixity Factor

This paper presents an analysis method in which both the nonlinear rotational behaviour of beam-to-column connections and second-order (P-Δ and P-δ) effects of beam-column members are explicitly taken into account. By adopting the concept of an end-fixity factor, the proposed method is comprehensive regardless of the end rotational conditions of beam-column members and applies to frames with any combination of pinned, semirigid and rigid beam-to-column connections. In addition, the end-fixity factor simplifies the analysis procedure for semirigid frames. More importantly, the end-fixity factor may be valuable to the design of such structures because it provides a physical interpretation of the extent of rigidity available in a connection. Thus, it provides a convenient way for designers to compare the structural responses of a semirigid member to that of a rigid one. Examples are presented to demonstrate the validity and efficiency of the proposed approach. With only minor modifications, the proposed method is readily implemented in existing rigid frame analysis and design computer programs.Key words: steel frame, semirigid connection, second-order analysis, P-Δ effect.

Determination of Combined and Second Order Factor Effects for Simultaneous Optimization of Physical and Mechanical Properties of NR/BR Blend System

2014 ◽  
Vol 42 (4) ◽  
pp. 290-304
Author(s):  
Rajarajan Aiyengar ◽  
Jyoti Divecha
Keyword(s):  
Physical And Mechanical Properties ◽  
Second Order ◽  
Simultaneous Optimization ◽  
Order Effects ◽  
Elongation At Break ◽  
Five Factors ◽  
Rubber Compounds ◽  
Polybutadiene Rubber ◽  
Contour Plots

ABSTRACT The blends of natural rubber (NR), polybutadiene rubber (BR), and other forms of rubbers are widely used for enhancing the mechanical and physical properties of rubber compounds. Lots of work has been done in conditioning and mixing of NR/BR blends to improve the properties of its rubber compounds and end products such as tire tread. This article employs response surface methodology designed experiments in five factors; high abrasion furnace carbon black (N 330), aromatic oil, NR/BR ratio, sulfur, and N-oxydiethylene-2-benzothiazole sulfenamide for determination of combined and second order effects of the significant factors leading to simultaneous optimization of the NR/BR blend system. One of the overall optimum of eight properties existed at carbon 44 phr, oil 6.1 phr, NR/BR 78/22 phr with the following values of properties: tensile strength (22 MPa), elongation at break (528%), tear resistance (30 kg/mm), rebound resilience (67%), moderate hardness (68 International rubber hardness degrees) with low heat buildup (17 °C), permanent set (12%), and abrasion loss (57 mm3). More optimum combinations can easily be determined from the NR/BR blend system models contour plots.

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