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.

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.

scholarly journals Silo with a Corrugated Sheet Wall

2013 ◽  
Vol 21 (3) ◽  
pp. 19-30 ◽  
Author(s):  
Csaba Németh ◽  
Ján Brodniansky
Keyword(s):  
Computational Models ◽  
Bending Moment ◽  
Physical Models ◽  
Experimental Measurements ◽  
Bending Moments ◽  
Bulk Materials ◽  
Production And Consumption ◽  
Thin Walled ◽  
The Mathematical Model

Abstract Silos and tanks are currently being used to create reserves of stored materials. Their importance is based on balancing the production and consumption of bulk materials to establish an adequate reserve throughout the year. The case study introduced within the framework of this paper focuses on thin-walled silos made of corrugated sheets and on an approach for designing these types of structures. The storage of bulk materials causes compression or tensile stresses in the walls of a silo structure. The effect of a frictional force in the silo walls creates an additional bending moment in a wave, which ultimately affects the resulting bending moments. Several mathematical and physical models were used in order to examine various types of loading and their effects on a structure. Subsequently, the accuracy of the computational models was verified by experimental measurements on a grain silo in Bojničky, Slovakia. A comparison of the experimental and mathematical models shows a reasonable match and confirms the load specifications, while indicating that the mathematical model was correct.

Variational Equation of Motion for Coupled Flexure and Torsion of Bars of Thin-Walled Open Section Including Thermal Effect

1971 ◽  
Vol 38 (2) ◽  
pp. 502-506 ◽  
Author(s):  
Yi-Yuan Yu
Keyword(s):  
Thermal Effect ◽  
Structural Dynamics ◽  
Variational Equation ◽  
Equation Of Motion ◽  
Bending Moments ◽  
Open Section ◽  
Thermal Bending ◽  
Axis Of Symmetry ◽  
Thin Walled ◽  
Special Case

Literature on flexure and torsion of bars of thin-walled open section is reviewed. The use of the variational equation of motion in solving problems of structural dynamics is further advocated. The variational equation of motion, together with the associated stress-displacement relations, is then derived for coupled flexure and torsion of the open section. Thermal effect is included, leading to a thermal twisting moment in addition to the usual thermal bending moments. For the special case of an open section with one axis of symmetry and with symmetrical heat input, only flexure is shown to be thermally inducible. The general result then reduces to the simple variational equation of flexural motion used in a separate study of the thermal flutter of a spacecraft boom.

scholarly journals Numerical analysis of symmetrical and asymmetrical reinforced concrete flat slabs - an integrated slab/ column analysis

2016 ◽  
Vol 9 (3) ◽  
pp. 306-356
Author(s):  
A. Puel ◽  
D. D. Loriggio
Keyword(s):  
Numerical Analysis ◽  
Axial Force ◽  
Three Dimensional ◽  
Bending Moment ◽  
Bending Moments ◽  
Flat Slabs ◽  
Distributed Load ◽  
Significant Difference ◽  
Local Support ◽  
Internal Forces

ABSTRACT This paper studies the modeling of symmetric and asymmetric flat slabs, presenting alternatives to the problem of singularity encountered when the slab is modeled considering columns as local support. A model that includes the integrated slab x column analysis was proposed, distributing the column reactions under the slab. The procedure used transforms the bending moment and column axial force in a distributed load, which will be applied to the slab in the opposite direction of gravitational loads. Thus, the bending moment diagram gets smooth in the punching region with a considerable reduction of values, being very little sensible to the variation of used mesh. About the column, it was not seen any significant difference in the axial force, although the same haven't occurred with the bending moments results. The final part of the work uses geoprocessing programs for a three-dimensional view of bending moments, allowing a new comprehension the behavior of these internal forces in the entire slab.

The Influence of Hyperbolic Notches on the Transverse Flexure of Elastic Plates

1940 ◽  
Vol 7 (2) ◽  
pp. A53-A56
Author(s):  
George H. Lee
Keyword(s):  
Infinite Plate ◽  
Bending Moment ◽  
Bending Moments ◽  
Elastic Plates ◽  
Transverse Bending ◽  
Narrow Section ◽  
Kirchhoff Theory

Abstract This paper considers the solution of the two problems of the infinite plate, with two symmetrically disposed hyperbolic notches, subjected to (a) transverse bending and (b) twisting. The transverse-bending moments and torsional couples are so applied that the narrow section between the notches transmits the bending moment or the torsional couple. Using the Poisson-Kirchhoff theory, finite expressions were obtained for the deflection and stress in each problem.

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.

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