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.

STABILITY AND SIMULATION-BASED DESIGN OF STEEL SCAFFOLDING WITHOUT USING THE EFFECTIVE LENGTH METHOD

2003 ◽  
Vol 03 (04) ◽  
pp. 443-460 ◽  
Author(s):  
S. L. CHAN ◽  
A. Y. T. CHU ◽  
F. G. ALBERMANI
Keyword(s):  
Bending Moment ◽  
Nonlinear Problems ◽  
Second Order ◽  
Effective Length ◽  
Analysis And Design ◽  
Order Analysis ◽  
Effective Length Factor ◽  
Highly Nonlinear ◽  
Reliable Design ◽  
Effective Length Method

A robust computer procedure for the reliable design of scaffolding systems is proposed. The design of scaffolding is not detailed in design codes and considered by many researchers and engineers as intractable. The proposed method is based on the classical stability function, which performs excellently in highly nonlinear problems. The method is employed to predict the ultimate design load capacities of four tested 3-storey steel scaffolding units, and for the design of a 30 m×20 m×1.3 m 3-dimensional scaffolding system. As the approach is based on the rigorous second-order analysis allowing for the P-δ and P-Δ effects and for notional disturbance forces, no assumption of effective length is required. It is superior to the conventional second-order analysis of plotting only the bending moment diagram with allowance for P-Δ effect since it considers both P-Δ and P-δ effects such that section capacity check is adequate for strength and stability checking. The proposed method can be applied to large deflection and stability analysis and design of practical scaffolding systems in place of the conventional and unreliable effective length method which carries the disadvantages of uncertain assumption of effective length factor (L e /L).

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.

Second Order Analysis on a Typical Steel Industrial Plant

2011 ◽  
Vol 243-249 ◽  
pp. 1405-1408
Author(s):  
Bo Li ◽  
Shao Bin Hu ◽  
Ya Xin Sun ◽  
Yan Wang
Keyword(s):  
Finite Element ◽  
Order Effect ◽  
Second Order ◽  
Nonlinear Finite Element ◽  
Effective Length ◽  
Industrial Plant ◽  
Order Analysis ◽  
First Order ◽  
Engineering Steel ◽  
Analysis Design

The deficiency of effective length approach and the necessity of second order analysis design on nonferrous engineering steel industrial plant are emphasized. Second order analysis approach by nonlinear finite-element with ANSYS is used to design an industrial plant. The example indicates that second-order effect should not be neglect and the result of first order analysis is not safe enough for industrial plant.

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.

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 Analysis of Second-Order Effect on Staggered Truss Structure

2012 ◽  
Vol 446-449 ◽  
pp. 857-862
Author(s):  
Qi Shi Zhou ◽  
Xu Hong Zhou ◽  
Li Ming Yang
Keyword(s):  
Structural Characteristics ◽  
Order Effect ◽  
Second Order ◽  
Truss Structure ◽  
Order Effects ◽  
Good Precision ◽  
Finite Element Software ◽  
Load Carrying ◽  
Second Order Effects ◽  
Lateral Displacements

Based on the structural characteristics that the distribution of mass and stiffness is symmetrical in staggered truss structure, the load-carrying performance of staggered truss structure is equivalent to a pressure-bend combinational strut in this paper. By analyzing the relationship among curvatures , bending moments and shear forces of the pressure-bend combinational strut, the balance differential equations of the pressure-bend combinational strut is erected. Based on Runge-Kutta method, the lateral iteration equation derived by considering the influence of the second-order effects is derived. This paper analyzes the lateral displacements of floors of the staggered truss structure examples considering second-order effects or not, and gives a comparative analysis with the existing finite element software Ansys. The results show that the calculation method of second-order effects proposed in this paper has a good precision.

Second order effects in dissipative media

1966 ◽  
Vol 292 (1428) ◽  
pp. 14-50 ◽  
Keyword(s):  
Strain Hardening ◽  
Tensile Load ◽  
Order Effect ◽  
Elastic Cylinder ◽  
Second Order ◽  
Tensile Creep ◽  
Order Effects ◽  
Elastic Solids ◽  
Viscoelastic Media ◽  
Second Order Effects

Second order or ‘cross’ effects arise as a result of quadratic terms in the constitutive equations of isotropic elastic, viscous and viscoelastic media, which are required by the condition of tensor invariance of those relations. The most pronounced second order effects arise when these are clearly separable from the first order deformation, as in the case of second order elongation and volume change of an elastic cylinder subject to a twisting moment, or of second order normal stress in the case of shear flow of polymeric liquids. The recent I. U. T. A. M. Conference on Second Order Effects (Pergamon Press, London, 1964) was mainly concerned with these two phenomena. The paper discusses second order effects in dissipative (viscoelastic, plastic and strain ­ hardening) solids and reports the results of experiments in which these effects were observed. While the experiments on elastomers confirm the Rivlin-Ericksen theory of those effects in viscoelastic media, the existence of a new accumulating second order effect has been discovered by experiments on aluminium specimens in reversed torsion (Ronay 1965). This effect, which has not been observed before, is probably responsible for the rapid acceleration of tensile creep in metals by small amplitudes of reversed torsion. While the second order effects in elastic solids vanish at zero strain since they are reversible, and vanish at zero velocity in polymeric fluids, they accumulate with the number of repeated torsion cycles in strain-hardening media. Hence their observation is very simple and does not require the elaborate procedures necessary for the observation of second order effects in elastic solids and viscous fluids. The theory of accumulating second order effects in strain-hardening media is developed; the linearity of the interaction between tensile load and torsion amplitude is demonstrated by the experiments.

Second-Order Effect of Staggered Truss and Simplified Formula

2010 ◽  
Vol 163-167 ◽  
pp. 808-811
Author(s):  
Lin Feng Lu ◽  
Li Lin
Keyword(s):  
Critical Factor ◽  
Order Effect ◽  
Internal Force ◽  
Second Order ◽  
Order Effects ◽  
Magnification Factor ◽  
Design Code ◽  
The World ◽  
Second Order Effects ◽  
Simplified Formula

This paper summarizes the regulations about steel frame second-order effect of some design code in the world, and find out a critical factor of controlling second-order effect. The second-order effects of staggered truss were studied systematically by using ETABS program, and put forward design proposals the second-order effects of internal force and displacement, the simplified formula on second-order effect magnification factor of displacement was given.

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.

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