Explicit Expressions for Buckling Analysis of Thin-Walled Beams Under Combined Loads with Laterally-Fixed Ends and Application to Stability Analysis of Saw Blades

2020 ◽  
pp. 2150032
Author(s):  
Van Binh Phung ◽  
Ngoc Doan Tran ◽  
Viet Duc Nguyen ◽  
V. S. Prokopov ◽  
Hoang Minh Dang
Keyword(s):  
Critical State ◽  
Bending Moment ◽  
Critical Issue ◽  
Eccentric Load ◽  
Concentrated Load ◽  
Combined Loads ◽  
Distributed Load ◽  
Thin Walled ◽  
The Stability ◽  
2D And 3D

This paper studies the critical issue of thin-walled beams with laterally fixed ends. The method for defining the formulae of twist moment for the beams subjected to combined loads was elucidated. Based on this, the governing differential equations of the beam were developed. The procedure for determining the critical state of the beam by the energy method was presented. With this procedure, the critical state of the beam concerned under three types of loadings such as axial force [Formula: see text], bending moment [Formula: see text] and distributed load [Formula: see text] (or concentrated load [Formula: see text]) was examined deliberately. The outcomes were presented in explicit closed-form, which can be illustrated in 2D and 3D graphs. Also, the analytical solution obtained was in agreement with the numerical one obtained by the commercial software NX Nastran. Furthermore, the analytical solutions were applied straightforwardly to explore the stability and design optimization of the tooth-blade for the new frame-type saw machine under an eccentric load. The result can also be promisingly used to study problems of thin-walled beams with laterally fixed ends subjected to other types of loads.

Improved Generalized Procedure for Determining Critical State of a Thin-Walled Beam Under Combined Symmetric Loads

2019 ◽  
Vol 19 (08) ◽  
pp. 1950098 ◽  
Author(s):  
Phung Van Binh ◽  
Nguyen Viet Duc ◽  
Prokopov Vladimir Sergeevich ◽  
Dang Hoang Minh
Keyword(s):  
Bending Moment ◽  
Complex Loading ◽  
Computational Procedure ◽  
Beam Length ◽  
Concentrated Load ◽  
Internal Forces ◽  
Thin Walled ◽  
The Stability ◽  
External Loads

This paper presents an improved generalized procedure for dealing with the stability of thin-walled beams under combined symmetric loads based on the energy method. The differential equations for the case of complex loading conditions were developed using an axis transformation matrix. The work caused by external loads was related to the work of internal forces to simplify the computational procedure. The thin-walled beam subjected to axial force [Formula: see text], bending moment [Formula: see text] at both ends, and concentrated load [Formula: see text] at midspan was studied. The case of a concentrated load [Formula: see text] replaced by a distributed load [Formula: see text] over partial beam length was also examined. The stability region boundary of the beam was derived by two approaches: one was to estimate an approximate angle of twist prior to determination of the deflection and the other was to do it in the reverse way. Numerical results reveal that the first approach yields less error than the second; however, the outcome obtained by the former was more cumbersome than the latter. Above all, both approaches provided feasible results and are useful for further applications dealing with the stability analysis of thin-walled beams.

scholarly journals Flexural-Torsional Vibration of Thin-Walled Beams Subjected to Combined Initial Axial Load and End Bending Moment: Application to the Design of Saw Tooth Blades

2019 ◽  
Vol 2019 ◽  
pp. 1-11
Author(s):  
Van Binh Phung ◽  
Anh Tuan Nguyen ◽  
Hoang Minh Dang ◽  
Thanh-Phong Dao ◽  
V. N. Duc
Keyword(s):  
Boundary Conditions ◽  
Axial Load ◽  
Stability Boundary ◽  
Bending Moment ◽  
Element Analysis ◽  
The Finite Element Analysis ◽  
Rayleigh Method ◽  
Thin Walled ◽  
The Stability ◽  
Fixed End

The present paper analyzes the vibration issue of thin-walled beams under combined initial axial load and end moment in two cases with different boundary conditions, specifically the simply supported-end and the laterally fixed-end boundary conditions. The analytical expressions for the first natural frequencies of thin-walled beams were derived by two methods that are a method based on the existence of the roots theorem of differential equation systems and the Rayleigh method. In particular, the stability boundary of a beam can be determined directly from its first natural frequency expression. The analytical results are in good agreement with those from the finite element analysis software ANSYS Mechanical APDL. The research results obtained here are useful for those creating tooth blade designs of innovative frame saw machines.

The Stability in Bending of Slightly Corrugated Plates

1952 ◽  
Vol 56 (502) ◽  
pp. 782-788 ◽  
Author(s):  
D. G. Ashwell
Keyword(s):  
Elastic Plate ◽  
Arbitrary Shape ◽  
Bending Moment ◽  
Axis Parallel ◽  
Instability Characteristic ◽  
Rectangular Elastic Plate ◽  
Thin Walled ◽  
Corrugated Plates ◽  
The Stability ◽  
Finite Bending

A previous paper was concerned with the uniform finite bending of a flat rectangular elastic plate about an axis parallel to one of its pairs of opposite edges. Expressions were obtained for the shape assumed by sections of the plate containing the axis of curvature, and the applied bending moment. In the present paper the work is extended to deal with a plate having shallow regular corrugations of arbitrary shape running along it at right angles to the axis of curvature. Such a plate may be of interest as it exhibits the type of instability characteristic of curved thin-walled members. Its solution can be derived quickly from the previous work.

scholarly journals INVESTIGATION OF THIN-WALLED COLUMN WITH VARIABLE I-SECTION STABILITY USING FINITE ELEMENT METHOD/PLONASIENĖS KINTAMOJO DVITĖJO SKERSPJŪVIO KOLONOS STABILUMO TYRIMAS BAIGTINIŲ ELEMENTŲ METODU

2000 ◽  
Vol 6 (2) ◽  
pp. 69-75
Author(s):  
Michail Samofalov ◽  
Rimantas Kačianauskas
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Stability Analysis ◽  
Numerical Experiments ◽  
Relative Length ◽  
Bending Moment ◽  
Relative Height ◽  
Thin Walled Structures ◽  
Thin Walled ◽  
The Stability

Thin-walled structures are widely used in building construction. Stability analysis [1–10] is of major importance to the design of thin-walled structures. This paper deals with the stability analysis of the thin-walled tapered column [11–18]. The aim is to investigate the influence of variation of the web height on the stability of column and combined action of axial force and plane bending moment. Critical state is defined by stability surface obtained by numerical experiments using the finite element method. Mathematical model of the linearised stability problem is presented as algebraic eigenvalue problem (1), where eigenvalues express the critical loading factor (2). Analytical solutions are known for particular cases of separate loading (4), (5). In this paper, the column with variable I-section is presented as assemblage of beam elements with constant section. Thin-walled beam element has 14 degrees of freedom (Fig 1), including linear displacements, rotations and warping displacements. Variation of cross-section of the column (Fig 2) is defined by relative height of web alb, were a and b are the height at the ends of column. Critical state is described by stability surface obtained using numerical experiments. Stability surface presents in the space of relative variation of height a/b, relative length and relative critical force and bending moment . Variation of section influences the critical bending moment only. The influence of finite element number on the with different relative height of web a/b is investigated numerically (Fig 3), and its variation of stability surface is presented in Fig 4. The numerical results show that variation of critical moment to relative web height a/b is linear (Fig 5). The shapes of buckling modes are presented in Fig 6. Variation of stability surface to relative length (6) is presented in Figs 7 and 8 and expressed by the simple expression (6) constructed on the basis of numerical experiments. Finally, the stability model (1) is compared with nonlinear calculations performed using program ANSYS [19] and shell finite elements (Figs 9 and 10).

Mathematical Analogy between Non-Uniform Torsion and Transverse Bending of Thin-Walled Open Section Beams

2015 ◽  
Vol 725-726 ◽  
pp. 746-751 ◽  
Author(s):  
Vladimir Rybakov ◽  
Alexander Sergey
Keyword(s):  
Bending Moment ◽  
Maximum Deviation ◽  
Bending Moments ◽  
Distributed Load ◽  
Transverse Bending ◽  
Open Section ◽  
Uniformly Distributed Load ◽  
Thin Walled ◽  
And Function ◽  
Mathematical Analogy

The objective of this work is to identify and make an analysis of correlation between functions of bimoments and function of bending moments arising in the beams under the same loads. This article shows the possibility of using a diagram of bending moment multiplied by a factor as a diagram of bimoment. The maximum deviation between diagram of bending moment and diagram of bimoment made up 3.6 % of maximum bending moment in case of uniformly distributed load on one side of fixed supported beam.

Circular Beams Loaded Normal to the Plane of Curvature—2

1944 ◽  
Vol 11 (1) ◽  
pp. A51-A56
Author(s):  
Mervin B. Hogan
Keyword(s):  
Deflection Angle ◽  
Bending Moment ◽  
Center Line ◽  
Concentrated Load ◽  
Simply Supported ◽  
Distributed Load ◽  
Simple Support ◽  
Circular Beam ◽  
Axis Of Symmetry ◽  
The Deflection Angle

Abstract Expressions are presented in this paper for the deflection, angle of slope, and angle of twist of the free end of a circular cantilever beam with a bending moment applied at the free end. Like expressions are also given for the same beam with a twisting moment acting at the free end. The values of the reaction and the angles of slope and twist at the simple support are given for a circular beam built in at one end, simply supported at the other, and loaded as in each of the foregoing cases. Also, equations are included for the three internal reactions, i.e., bending moment, twisting moment, and shear existing at the plane of symmetry of a cantilever arc beam, built in at both ends, with an arbitrarily placed concentrated load acting perpendicular to the plane of the beam, and at its center line. Corresponding expressions for the same element with a uniformly distributed load covering the half of the beam to one side of the axis of symmetry, and an expression for the bending moment at the plane of symmetry of the same beam when its entire length is uniformly loaded, are also stated.

The Twist Due To Bending Moment in Cantilevers Curved in flan

1956 ◽  
Vol 60 (544) ◽  
pp. 277-281
Author(s):  
W. Johnson
Keyword(s):  
Constant Curvature ◽  
Vertical Plane ◽  
Bending Moment ◽  
Shear Stresses ◽  
Bending Moments ◽  
Concentrated Load ◽  
Bending Stresses ◽  
Thin Walled ◽  
Shear Centre ◽  
The Web

The twist that arises from bending stresses in straight cantilevers of thin-walled section asymmetrical about any vertical plane, is well known and eventually leads to the concept of a shear centre. If an analysis is made along the same lines as that used for investigating straight beams, of cantilevers curved in plan, it is found that the bending moments transmitted are again responsible for shear stresses in the flanges of the beam and cause twisting.The following analyses refer, principally, to cases in which the cantilever carries a concentrated load at its end and are confined to the relatively simple forms of the channel and I-section. Each cantilever is perfectly built-in at one end and, for simplicity, it is considered that the web of a section offers no resistance to bending and that the beams are of constant curvature in plan.

The stability of rectangular thin-walled profile with loading according to the scheme of pure bending

2020 ◽  
pp. 41-45
Author(s):  
V.B. Zylev ◽  
◽  
P.O. Platnov ◽  
I.V. Alferov ◽  
◽  
...  
Keyword(s):  
Pure Bending ◽  
Thin Walled ◽  
The Stability

scholarly journals Studies on the Volumetric Stability and Mechanical Properties of Cement-Fly-Ash-Stabilized Steel Slag

Materials ◽  
2021 ◽  
Vol 14 (3) ◽  
pp. 495
Author(s):  
Mingkai Zhou ◽  
Xu Cheng ◽  
Xiao Chen
Keyword(s):  
Mechanical Properties ◽  
Fly Ash ◽  
Steel Slag ◽  
Critical Issue ◽  
Expansion Behavior ◽  
Strength Tests ◽  
Road Materials ◽  
Base Course ◽  
The Stability ◽  
Aggregate Base

The stability of steel-slag road materials remains a critical issue in their utilization as an aggregate base course. In this pursuit, the present study was envisaged to investigate the effects of fly ash on the mechanical properties and expansion behavior of cement-fly-ash-stabilized steel slag. Strength tests and expansion tests of the cement-fly-ash-stabilized steel slag with varying additions of fly ash were carried out. The results indicate that the cement-fly-ash-stabilized steel slag exhibited good mechanical properties. The expansion rate and the number of bulges of the stabilized material reduced with an increase in the addition. When the addition of fly ash was 30–60%, the stabilized material was not damaged due to expansion. Furthermore, the results of X-CT, XRD and SEM-EDS show that fly ash reacted with the expansive component of the steel slag. In addition, the macro structure of the stabilized material was found to be changed by an increase in the concentration of the fly ash, in order to improve the volumetric stability. Our study shows that the cement-fly-ash-stabilized steel slag exhibits good mechanical properties and volumetric stability with reasonable additions of fly ash.

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