Evaluation of effective length factors in braced frames

1983 ◽  
Vol 10 (1) ◽  
pp. 18-26 ◽  
Author(s):  
Donald J. Fraser
Keyword(s):  
Iterative Method ◽  
Effective Length ◽  
Braced Frames ◽  
Buckling Loads ◽  
Numerical Examples ◽  
Analysis And Design ◽  
Stability Functions ◽  
Axial Forces ◽  
Stabilizing Effect ◽  
Tension Members

A designer-oriented iterative method for the evaluation of effective length factors in braced frames is described. The formulae used in the method have been expressed in terms of effective length factors because designers use this parameter, rather than the values of critical buckling loads, in the analysis and design of columns. The method takes into account the reduced stiffness of restraining members due to the presence of significant axial forces and also allows for the stabilizing effect of tension members. Application of the method is demonstrated by numerical examples. Keywords: braced structures, buckling of continuous columns, frame buckling, truss buckling, effective length factors, accurate stability functions, linear approximations of stability functions, structural stability.

Buckling of Double Layer Grid Edge Members

1997 ◽  
Vol 12 (2) ◽  
pp. 81-87
Author(s):  
Erling Murtha-Smith ◽  
Thuyen P. Nguyen
Keyword(s):  
Double Layer ◽  
External Load ◽  
Stiffness Matrix ◽  
Diagonal Matrix ◽  
Moment Of Inertia ◽  
Effective Length ◽  
Stiffness Coefficient ◽  
Stability Functions

Stability equations are developed for edge joints for Double Layer Grids. Translations are neglected and rotations at each joint are related. Hence, the stiffness matrix reduces to a diagonal matrix of unit bandwidth so each joint becomes an independent substructure. Instability of an edge joint occurs when the minimum principal stiffness coefficient of the joint goes to zero. Using stability functions and the regular geometric relationships of DLG topology, the buckling forces in the members and hence the external load on the system are determined. A simple example in which the members were all of the same length, material and moment of inertia, gives effective length factors for the edge members of between 0.77 to 0.81.

An Accelerated Iterative Method with Third-Order Convergence

2012 ◽  
Vol 220-223 ◽  
pp. 2658-2661
Author(s):  
Zhong Yong Hu ◽  
Liang Fang ◽  
Lian Zhong Li
Keyword(s):  
Iterative Method ◽  
Fourth Order ◽  
Newton’S Method ◽  
Newton's Method ◽  
New Method ◽  
Order Convergence ◽  
Third Order ◽  
Numerical Examples ◽  
Modified Newton’S Method ◽  
Jarratt Method

We present a new modified Newton's method with third-order convergence and compare it with the Jarratt method, which is of fourth-order. Based on this new method, we obtain a family of Newton-type methods, which converge cubically. Numerical examples show that the presented method can compete with Newton's method and other known third-order modifications of Newton's method.

scholarly journals The Krylov problem in the case of a beam on Vlasov inertial foundation

2018 ◽  
Vol 19 (6) ◽  
pp. 728-736
Author(s):  
Wacław Szcześniak ◽  
Magdalena Ataman
Keyword(s):  
Closed Form ◽  
Compressive Force ◽  
Elastic Beam ◽  
Forced Vibrations ◽  
Critical Force ◽  
Winkler Foundation ◽  
Static Deflection ◽  
Numerical Examples ◽  
Moving Force ◽  
Axial Forces

The paper deals with vibrations of the elastic beam caused by the moving force traveling with uniform speed. The function defining the pure forced vibrations (aperiodic vibrations) is presented in a closed form. Dynamic deflection of the beam caused by moving force is compared with the static deflection of the beam subjected to the force , and compressed by axial forces . Comparing equations (9) and (13), it can be concluded that the effect on the deflection of the speed of the moving force is the same as that of an additional compressive force . Selected problems of stability of the beam on the Winkler foundation and on the Vlasov inertial foundation are discussed. One can see that the critical force of the beam on Vlasov foundation is greater than in the case of Winkler's foundation. Numerical examples are presented in the paper

scholarly journals A fourth order method for finding a simple root of univariate function

2015 ◽  
Vol 34 (2) ◽  
pp. 197-211
Author(s):  
D. Sbibih ◽  
Abdelhafid Serghini ◽  
A. Tijini ◽  
A. Zidna
Keyword(s):  
Iterative Method ◽  
Fourth Order ◽  
Newton’S Method ◽  
Simple Root ◽  
Newton's Method ◽  
Order Method ◽  
Numerical Examples ◽  
Quadratic Interpolation ◽  
Univariate Function ◽  
Fourth Order Method

In this paper, we describe an iterative method for approximating asimple zero $z$ of a real defined function. This method is aessentially based on the idea to extend Newton's method to be theinverse quadratic interpolation. We prove that for a sufficientlysmooth function $f$ in a neighborhood of $z$ the order of theconvergence is quartic. Using Mathematica with its high precisioncompatibility, we present some numerical examples to confirm thetheoretical results and to compare our method with the others givenin the literature.

scholarly journals A Family of Fourteenth-Order Convergent Iterative Methods for Solving Nonlinear Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Fiza Zafar ◽  
Gulshan Bibi
Keyword(s):  
Iterative Method ◽  
Iterative Methods ◽  
Nonlinear Equations ◽  
Order Of Convergence ◽  
Efficiency Index ◽  
Numerical Examples ◽  
New Class ◽  
First Derivative ◽  
New Methods ◽  
Specific Step

We present a family of fourteenth-order convergent iterative methods for solving nonlinear equations involving a specific step which when combined with any two-step iterative method raises the convergence order by n+10, if n is the order of convergence of the two-step iterative method. This new class include four evaluations of function and one evaluation of the first derivative per iteration. Therefore, the efficiency index of this family is 141/5 =1.695218203. Several numerical examples are given to show that the new methods of this family are comparable with the existing methods.

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).

BUCKLING OF COLUMNS WITH INTERNAL SLIDE RELEASE

2002 ◽  
Vol 02 (04) ◽  
pp. 593-598 ◽  
Author(s):  
M. EISENBERGER ◽  
H. AMBARSUMIAN
Keyword(s):  
Stiffness Matrix ◽  
Buckling Load ◽  
Buckling Loads ◽  
Simply Supported ◽  
Axial Forces ◽  
Exact Stiffness Matrix

The exact buckling loads of columns with internal slide release are found using the exact stiffness matrix of the column including the effect of the axial forces. Two types of columns are considered: clamped–clamped and clamped-simply supported with internal slide release at variable locations along the member. It is found that for both the clamped–clamped and the clamped-simply supported columns the buckling load is constant and does not depend on the location of the slide discontinuity.

Sign in / Sign up

Export Citation Format

Share Document