The dynamic lateral instability of beams

1954 ◽  
Vol 226 (1164) ◽  
pp. 111-128
Keyword(s):  
Theoretical Analysis ◽  
Reasonable Agreement ◽  
Vertical Plane ◽  
Bending Moment ◽  
Critical Value ◽  
The Other ◽  
Lateral Bending ◽  
Lateral Instability ◽  
Maximum Stiffness ◽  
The Moment

The vibrations of a deep slender beam, bent to uniform curvature by in variant moments acting in a vertical plane, which is also the plane of maximum stiffness, have been studied. It is shown that the moments couple up the lateral bending and torsional modes of the beam, those modes being replaced by two independent modes, each involving torsion and flexure. One of these m odes is associated with a frequency which decreases with increasing bending moment, the frequency becoming zero when the moment reaches the critical value for lateral instability. The other mode is associated with a frequency which increases with bending moment. Experiments were carried out on an I-section cantilever carrying an end mass. Owing to the varying bending moment, the theoretical analysis of this case is more complicated, and an iterative method, originated by Schwarz (1890), has been employed. Results are in reasonable agreement with experiment.

Large Deflections of a Simply Supported Beam Subjected to Moment at One End

1984 ◽  
Vol 51 (3) ◽  
pp. 519-525 ◽  
Author(s):  
P. Seide
Keyword(s):  
Linear Theory ◽  
Bending Moment ◽  
Critical Value ◽  
The Other ◽  
Large Deflections ◽  
Simply Supported Beam ◽  
Simply Supported ◽  
Elastica Theory ◽  
Angle Of Rotation

The large deflections of a simply supported beam, one end of which is free to move horizontally while the other is subjected to a moment, are investigated by means of inextensional elastica theory. The linear theory is found to be valid for relatively large angles of rotation of the loaded end. The beam becomes transitionally unstable, however, at a critical value of the bending moment parameter MIL/EI equal to 5.284. If the angle of rotation is controlled, the beam is found to become unstable when the rotation is 222.65 deg.

scholarly journals Stability and Bifurcation of Two Kinds of Three-Dimensional Fractional Lotka-Volterra Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Jinglei Tian ◽  
Yongguang Yu ◽  
Hu Wang
Keyword(s):  
Hopf Bifurcation ◽  
Asymptotic Stability ◽  
Theoretical Analysis ◽  
Fractional Order ◽  
Three Dimensional ◽  
Sufficient Conditions ◽  
Critical Value ◽  
The Other ◽  
Bifurcation Parameter ◽  
Volterra Systems

Two kinds of three-dimensional fractional Lotka-Volterra systems are discussed. For one system, the asymptotic stability of the equilibria is analyzed by providing some sufficient conditions. And bifurcation property is investigated by choosing the fractional order as the bifurcation parameter for the other system. In particular, the critical value of the fractional order is identified at which the Hopf bifurcation may occur. Furthermore, the numerical results are presented to verify the theoretical analysis.

scholarly journals Measurements of the absolute indices of refraction in strained glass

1910 ◽  
Vol 83 (566) ◽  
pp. 572-579 ◽  
Keyword(s):  
Plane Wave ◽  
Cross Section ◽  
Rectangular Cross Section ◽  
Vertical Plane ◽  
Bending Moment ◽  
The Other ◽  
Double Refraction ◽  
Light Passing ◽  
The Absolute ◽  
The Cross

1. In June, 1907, the author described a method by which the double-refraction in strained glass could be measured by observing the deviation of a ray of light passing through a slab of glass under flexure. If a slab or beam of glass of rectangular cross-section be bent in a vertical plane under a bending moment M, and if a plane wave be transmitted through the glass in a direction perpendicular to the plane of flexure, the light is broken up into two components, one polarised horizontally ( i. e . perpendicular to the cross-section and along the line of stress) and the other vertically.

Theoretical analysis of short backfire antenna by using Moment of method

2021 ◽  
Vol 13 (01) ◽  
pp. 24-32
Author(s):  
Ali K Al-zuwaini ◽  
◽  
Zeki A. Ahmed ◽  
Wa'i A. Godaymi ◽  
◽  
...  
Keyword(s):  
Theoretical Analysis ◽  
Mathematical Analysis ◽  
Moment Method ◽  
Theoretical Study ◽  
The Other ◽  
Axially Symmetric ◽  
Radiation Fields ◽  
Best Value ◽  
Back Reflector ◽  
The Moment

The short backfire antenna is one of the important types of antennas due to its high directional and other characteristics. Therefore, this research deals with, a theoretical study to calculate the radiative structures of a short backfire antenna as an axially symmetric body using the moment method. The main goal is to theoretically calculate the radiation fields and compare them with previous practical researches. Where the mathematical analysis with the used software was verified by comparing the results and noting the extent of the match. The other goal is to study the effect of the antenna dimensions on its performance by studying the effect of adding a rim to the edge of the large back reflector, as well as studying the change of the radius of the two reflectors (large and small), where it was confirmed that the best value for the radius of the large reflectors and small (Rm=1λ) (Rs= 0.25 λ) respectively.

Experimental Investigation on Cold-formed Steel Beams under Pure Bending

2012 ◽  
pp. 13-20 ◽  
Author(s):  
Yeong Huei Lee ◽  
Yee Ling Lee ◽  
Cher Siang Tan
Keyword(s):  
Local Buckling ◽  
Bending Moment ◽  
Steel Beams ◽  
Pure Bending ◽  
Lateral Instability ◽  
Moment Capacity ◽  
British Standard ◽  
Cold Formed Steel ◽  
The Moment ◽  
Design Yield

This paper presents the flexural behaviour of cold-formed double lipped channels beams under pure bending action. Two channel sections are bolted back-to-back to form an I-shape structural beam member. A series of six experiment tests were carried out on beam specimens DC200 and DC250, each with 200 mm depth and 250 mm depth respectively. The thickness of beam section is 2 mm and the design yield strength is 350 N/mm2. All beams failed at local buckling at top-flange due to lateral instability of the cold-formed steel structural members. The moment resistance for DC200 is 17.87 kNm and DC250 is 31.53 kNm. The experimental results are compared to theoretical resistance prediction based on British Standard and Eurocode. The comparison showed that the experimental moment capacity is lower than the theoretical bending moment resistance but higher than theoretical buckling moment resistance from Eurocode. This showed that a better agreement is achieved between experimental data and Eurocode buckling moment resistance for cold-formed steel beam under pure bending. Kertas kerja ini membentangkan sifat lenturan rasuk keluli tergelek sejuk di bawah tindakan lenturan tulen. Dua channel dihimpunkan berkembar dan diperketatkan dengan bolt untuk membentuk rasuk struktur bentuk-I. Satu siri ujian lenturan telah dijalankan ke atas spesimen rasuk DC200 dan DC250, dengan kedalaman 200 mm dan 250 mm masing-masing. Ketebalan keratan rasuk adalah 2 mm dan kekuatan reka bentuk adalah 350 N/mm2. Semua rasuk gagal pada momen kilasan sisi di bahagian atas bebibir akibat ketakstabilan sisi anggota keluli tergelek sejuk. Rintangan momen bagi DC200 adalah 17.87 kNm dan DC250 adalah 31.53 kNm. Keputusan eksperimen dibanding dengan ramalan teori yang berdasarkan British Standard dan Eurocodes. Perbandingan tersebut menunjukkan bahawa rintangan momen lenturan eksperimen adalah lebih rendah daripada ramalan teori momen lenturan tetapi lebih tinggi daripada ramalan teori momen rintangan kilasan sisi mengikut Eurocode. Ini menunjukkan bahawa persetujuan baik dicapai di antara keputusan eksperimen dengan ramalan teori Eurocode momen rintangan kilasan sisi bagi rasuk keluli tergelek sejuk.

The Final ‘Thank You’

Derrida Today ◽  
2010 ◽  
Vol 3 (1) ◽  
pp. 21-36
Author(s):  
Grant Farred
Keyword(s):  
South Africa ◽  
South African ◽  
Jacques Derrida ◽  
Political Transition ◽  
The Other ◽  
World Cup ◽  
The Core ◽  
Nelson Mandela ◽  
Black President ◽  
The Moment

‘The Final “Thank You”’ uses the work of Jacques Derrida and Friedrich Nietzsche to think the occasion of the 1995 rugby World Cup, hosted by the newly democratic South Africa. This paper deploys Nietzsche's Zarathustra to critique how a figure such as Nelson Mandela is understood as a ‘Superman’ or an ‘Overhuman’ in the moment of political transition. The philosophical focus of the paper, however, turns on the ‘thank yous’ exchanged by the white South African rugby captain, François Pienaar, and the black president at the event of the Springbok victory. It is the value, and the proximity and negation, of the ‘thank yous’ – the relation of one to the other – that constitutes the core of the article. 1

Macaronics as What Eludes Translation

Paragraph ◽  
2015 ◽  
Vol 38 (2) ◽  
pp. 214-230
Author(s):  
Haun Saussy
Keyword(s):  
Print Culture ◽  
The Other ◽  
Digital Code ◽  
Avant Garde ◽  
The Moment

‘Translation’ is one of our all-purpose metaphors for almost any kind of mediation or connection: we ask of a principle how it ‘translates’ into practice, we announce initiatives to ‘translate’ the genome into predictions, and so forth. But the metaphor of translation — of the discovery of equivalents and their mutual substitution — so attracts our attention that we forget the other kinds of inter-linguistic contact, such as transcription, mimicry, borrowing or calque. In a curious echo of the macaronic writings of the era of the dawn of print, the twentieth century's avant-garde, already foreseeing the end of print culture, experimented with hybrid languages. Their untranslatability under the usual definitions of ‘translation’ suggests a revival of this avant-garde practice, as the mainstream aesthetic of the moment invests in ‘convergence’ and the subsumption of all media into digital code.

Action-Minimizing Curves for Tonelli Lagrangians

2017 ◽  
Author(s):  
Alfonso Sorrentino
Keyword(s):  
Critical Value ◽  
The Other ◽  
Invariant Sets ◽  
Simple Pendulum ◽  
New Concepts ◽  
Peierls Barrier ◽  
Average Action

This chapter discusses the notion of action-minimizing orbits. In particular, it defines the other two families of invariant sets, the so-called Aubry and Mañé sets. It explains their main dynamical and symplectic properties, comparing them with the results obtained in the preceding chapter for the Mather sets. The relation between these new invariant sets and the Mather sets is described. As a by-product, the chapter introduces the Mañé's potential, Peierls' barrier, and Mañé's critical value. It discusses their properties thoroughly. In particular, it highlights how this critical value is related to the minimal average action and describes these new concepts in the case of the simple pendulum.

Computational and experimental studies of the strength of full-scale samples of pipes with defects "metal loss" and "dent with groove"

2020 ◽  
Vol 10 (3) ◽  
pp. 226-233
Author(s):  
Dmitry A. Neganov ◽  
◽  
Victor M. Varshitsky ◽  
Andrey A. Belkin ◽  
◽  
...  
Keyword(s):  
Internal Pressure ◽  
Experimental Studies ◽  
Full Scale ◽  
The Other ◽  
Metal Loss ◽  
Calculation Methods ◽  
Reliable Operation ◽  
Sufficient Stability ◽  
Comparative Results ◽  
The Moment

The article contains the comparative results of the experimental and calculated research of the strength of a pipeline with such defects as “metal loss” and “dent with groove”. Two coils with diameter of 820 mm and the thickness of 9 mm of 19G steel were used for full-scale pipe sample production. One of the coils was intentionally damaged by machining, which resulted in “metal loss” defect, the other one was dented (by press machine) and got groove mark (by chisel). The testing of pipe samples was performed by applying static internal pressure to the moment of collapse. The calculation of deterioration pressure was carried out with the use of national and foreign methodical approaches. The calculated values of collapsing pressure for the pipe with loss of metal mainly coincided with the calculation experiment results based on Russian method and ASME B31G. In case of pipe with dent and groove the calculated value of collapsing pressure demonstrated greater coincidence with Russian method and to a lesser extent with API 579/ASME FFS-1. In whole, all calculation methods demonstrate sufficient stability of results, which provides reliable operation of pipelines with defects.

Experimental study of moment carrying behavior of typical Tibetan timber beam-column joints

2021 ◽  
pp. 136943322110015
Author(s):  
Ting Guo ◽  
Na Yang ◽  
Huichun Yan ◽  
Fan Bai
Keyword(s):  
Bending Moment ◽  
Structural Performance ◽  
Test Results ◽  
Timber Beam ◽  
Rotational Stiffness ◽  
Trilinear Model ◽  
Column Joint ◽  
Loading Tests ◽  
The Moment ◽  
Relationship Of

This study aimed to investigate the moment carrying behavior of typical Tibetan timber beam-column joints under monotonic vertical static load and also evaluate the influence of length ratio of Gongmu to beam (LRGB) and dowels layout on the structural performance of the joint. Six full-scale specimens were fabricated with same construction but different Gongmu length and dowels position. The moment carrying performance of beam-column joints in terms of failure mode, moment resistance, and rotational stiffness of joints were obtained via monotonic loading tests. Test results indicated that all joints are characterized by compressive failure perpendicular to grain of Ludou. Additionally, it was found that greater LRGB leads to greater initial rotational stiffness and maximum moment of the joint by an increase of restraint length for beam end; however, offsetting dowels toward column resulted smaller stiffness and ultimate bending moment of joints, particularly, offsetting Beam-Gongmu dowels toward column changed the moment-rotation curve pattern of the beam-column joint, accompanied by a hardening stiffness at last phase. Furthermore, a simplified trilinear model was proposed to represent the moment-rotation relationship of the typical Tibetan timber beam-column joint.

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