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 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.

scholarly journals Comparative Analysis and Design of Bridge Pier for Various Geometries Along Height Comparing the Parameters Deflection and Bending Stresses

2021 ◽  
Vol 9 (12) ◽  
pp. 571-580
Author(s):  
Prof. G. C. Jawalkar
Keyword(s):  
Bending Moment ◽  
Moment Equation ◽  
Second Order ◽  
Bridge Pier ◽  
Column Buckling ◽  
Circular Section ◽  
Analysis And Design ◽  
Order Analysis ◽  
Bending Stresses ◽  
Slender Column

Abstract: Slender member is subjected to axial load and biaxial bending moment and fails due to buckling. This buckling is caused due to slenderness effect also known as ‘P∆’ effect. This buckling gives rise to excessive bending moment occurring at a point of maximum deflection. This additional bending moment is considered in second order analysis. The objective of the research reported in this paper is to formulate bending moment equation by using beam column theory and to study the behaviour of solid circular section and hollow circular section of bridge pier. The optimization in area of cross section is done by providing a combination of solid and hollow circular section in place of a solid circular section of pier within permissible limits. A comparative study on behaviour for all three conditions is been carried out. Keywords: slender column, buckling, ‘P∆’ effect, beam-column, second order analysis, bridge pier.

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 Comparative Analysis and Design of Bridge Pier for various Geometries along height

2021 ◽  
Vol 9 (12) ◽  
pp. 431-440
Author(s):  
Prof. G.C. Jawalkar
Keyword(s):  
Bending Moment ◽  
Moment Equation ◽  
Second Order ◽  
Bridge Pier ◽  
Biaxial Bending ◽  
Column Buckling ◽  
Circular Section ◽  
Analysis And Design ◽  
Order Analysis ◽  
Slender Column

Abstract: Slender member is subjected to axial load and biaxial bending moment and fails due to buckling. This buckling is caused due to slenderness effect also known as ‘P∆’ effect. This buckling gives rise to excessive bending moment occurring at a point of maximum deflection. This additional bending moment is considered in second order analysis. The objective of the research reported in this paper is to formulate bending moment equation by using beam column theory and to study the behaviour of solid circular section and hollow circular section of bridge pier. The optimization in area of cross section is done by providing a combination of solid and hollow circular section in place of a solid circular section of pier within permissible limits. A comparative study on behaviour for all three conditions is been carried out. Keywords: slender column, buckling, ‘P∆’ effect, beam-column, second order analysis, bridge pier.

scholarly journals Accelerating Symmetric Rank-1 Quasi-Newton Method with Nesterov’s Gradient for Training Neural Networks

2021 ◽  
Author(s):  
S. Indrapriyadarsini ◽  
Shahrzad Mahboubi ◽  
Hiroshi Ninomiya ◽  
Takeshi Kamio ◽  
Hideki Asai
Keyword(s):  
Neural Networks ◽  
Newton Method ◽  
Trust Region ◽  
Nonlinear Problems ◽  
Classification Problem ◽  
Second Order ◽  
Highly Nonlinear ◽  
Gradient Based ◽  
Quasi Newton ◽  
Second Order Methods

Gradient based methods are popularly used in training neural networks and can be broadly categorized into first and second order methods. Second order methods have shown to have better convergence compared to first order methods, especially in solving highly nonlinear problems. The BFGS quasi-Newton method is the most commonly studied second order method for neural network training. Recent methods have shown to speed up the convergence of the BFGS method using the Nesterov’s acclerated gradient and momentum terms. The SR1 quasi-Newton method though less commonly used in training neural networks, are known to have interesting properties and provide good Hessian approximations when used with a trust-region approach. Thus, this paper aims to investigate accelerating the Symmetric Rank-1 (SR1) quasi-Newton method with the Nesterov’s gradient for training neural networks and briefly discuss its convergence. The performance of the proposed method is evaluated on a function approximation and image classification problem.

scholarly journals Accelerating Symmetric Rank-1 Quasi-Newton Method with Nesterov’s Gradient for Training Neural Networks

2021 ◽  
Author(s):  
S. Indrapriyadarsini ◽  
Shahrzad Mahboubi ◽  
Hiroshi Ninomiya ◽  
Takeshi Kamio ◽  
Hideki Asai
Keyword(s):  
Neural Networks ◽  
Newton Method ◽  
Trust Region ◽  
Nonlinear Problems ◽  
Classification Problem ◽  
Second Order ◽  
Highly Nonlinear ◽  
Gradient Based ◽  
Quasi Newton ◽  
Second Order Methods

Gradient based methods are popularly used in training neural networks and can be broadly categorized into first and second order methods. Second order methods have shown to have better convergence compared to first order methods, especially in solving highly nonlinear problems. The BFGS quasi-Newton method is the most commonly studied second order method for neural network training. Recent methods have shown to speed up the convergence of the BFGS method using the Nesterov’s acclerated gradient and momentum terms. The SR1 quasi-Newton method though less commonly used in training neural networks, are known to have interesting properties and provide good Hessian approximations when used with a trust-region approach. Thus, this paper aims to investigate accelerating the Symmetric Rank-1 (SR1) quasi-Newton method with the Nesterov’s gradient for training neural networks and briefly discuss its convergence. The performance of the proposed method is evaluated on a function approximation and image classification problem.

Service-load Behaviour of Braced Reinforced Concrete Columns with Rotational Spring Supports

1998 ◽  
Vol 1 (3) ◽  
pp. 193-201
Author(s):  
M.A. Bradford
Keyword(s):  
Reinforced Concrete ◽  
Concrete Columns ◽  
Second Order ◽  
Effective Length ◽  
Reinforced Concrete Columns ◽  
Effective Length Factor ◽  
Codes Of Practice ◽  
Service Load ◽  
Creep And Shrinkage ◽  
Time Dependent Analysis

A simplified mathematical model for the short-term and time dependent analysis of reinforced concrete columns subjected to eccentric loading and with rotational springs is developed. Such a column is typical of that in a sway-prevented frame. The analysis includes cracking at service loads, creep and shrinkage deformations, and second order slenderness effects. The second order deflections are compared with those predicted by use of the contentious effective length factor given in design codes of practice.

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