scholarly journals Comparison between Analytical Equation and Numerical Methods for Determining Shear Stress in a Cantilever Beam

2018 ◽  
Vol 4 (2) ◽  
pp. 258
Author(s):  
Imad Al-Qasem ◽  
A. Rasem Hasan ◽  
Mohanad Abdulwahid ◽  
Isaac Galobardes
Keyword(s):  
Cantilever Beam ◽  
Cross Section ◽  
Cross Sections ◽  
Analytical Formula ◽  
Analytical Equation ◽  
Shear Stresses ◽  
Concentrated Load ◽  
Section Shape ◽  
Show Difference ◽  
The Cross

A three meter-length cantilever beam loaded with a concentrated load at its free end is studied to determine shear stresses. In the present study, three cross sections are considered: rectangle (R); I, and T. The study presents a comparison of maximum shear stresses obtained by means of two methods: classical analytical equation derived by Collingnon, and finite element method (FEM) software. Software programs ANSYS and SAP2000 were used. The results show difference between the maximum shear stresses obtained by the analytical equation and the software, being the last is always higher. The average differences for ANSYS and SAP2000, independently of the cross section, were 12.76% and 11.96%, respectively. Considering these differences, correction factors were proposed to the classical analytical formula for each cross section case to obtain more realistic results. After the correction, the average differences decrease to 1.48% and 4.86%, regardless of the cross section shape.

scholarly journals Flexural Behaviour of Lightweight Foamed Concrete Beams Reinforced with GFRP Bars

2018 ◽  
Vol 4 (2) ◽  
pp. 278 ◽  
Author(s):  
Suhad M Abd ◽  
Dhamyaa Ghalib
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Analytical Formula ◽  
Analytical Equation ◽  
Shear Stresses ◽  
Concentrated Load ◽  
Section Shape ◽  
Foamed Concrete ◽  
Show Difference ◽  
The Cross

A three meter-length cantilever beam loaded with a concentrated load at its free end is studied to determine shear stresses. In the present study, three cross sections are considered: rectangle (R); I, and T. The study presents a comparison of maximum shear stresses obtained by means of two methods: classical analytical equation derived by Collingnon, and finite element method (FEM) software. Software programs ANSYS and SAP2000 were used. The results show difference between the maximum shear stresses obtained by the analytical equation and the software, being the last is always higher. The average differences for ANSYS and SAP2000, independently of the cross section, were 12.76% and 11.96%, respectively. Considering these differences, correction factors were proposed to the classical analytical formula for each cross section case to obtain more realistic results. After the correction, the average differences decrease to 1.48% and 4.86%, regardless of the cross section shape.

scholarly journals The Pulsed Electron Beam Time-of-flight Method for Measuring Absolute Total Cross Sections: Atomic Helium

1982 ◽  
Vol 35 (5) ◽  
pp. 559 ◽  
Author(s):  
Robert K Jones ◽  
RA Bonham
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Total Electron ◽  
Pulsed Electron Beam ◽  
Section Shape ◽  
The Cross ◽  
Scattering Cross Sections ◽  
Time Of Flight Method ◽  
New Procedures ◽  
Better Than

Improvements in a previously reported experimental method have made it possible to obtain absolute total electron-scattering cross sections with a predicted accuracy of better than � 2 % (10') for certain electron kinetic energies. As a first example of the application of the new procedures the cross section for helium is reported from O' 8 to 50� 0 eV. Error estimates for all known sources of uncertainty are discussed in detail. The results confirm the earlier work of Kennerly and Bonham and the agreement is, on the average, better than 1 % with no changes in the cross-section shape.

Experimental Studies Of Multilayer Glass Structures On Compression, Compression With Bending And Simple Bending

2019 ◽  
pp. 22-30
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Applied Load ◽  
Experimental Studies ◽  
Strength Properties ◽  
Research Topic ◽  
Normative Values ◽  
Laminated Glass ◽  
The Cross ◽  
Experimental Values

The work of multilayer glass structures for central and eccentric compression and bending are considered. The substantiation of the chosen research topic is made. The description and features of laminated glass for the structures investigated, their characteristics are presented. The analysis of the results obtained when testing for compression, compression with bending, simple bending of models of columns, beams, samples of laminated glass was made. Overview of the types and nature of destruction of the models are presented, diagrams of material operation are constructed, average values of the resistance of the cross-sections of samples are obtained, the table of destructive loads is generated. The need for development of a set of rules and guidelines for the design of glass structures, including laminated glass, for bearing elements, as well as standards for testing, rules for assessing the strength, stiffness, crack resistance and methods for determining the strength of control samples is emphasized. It is established that the strength properties of glass depend on the type of applied load and vary widely, and significantly lower than the corresponding normative values of the strength of heat-strengthened glass. The effect of the connecting polymeric material and manufacturing technology of laminated glass on the strength of the structure is also shown. The experimental values of the elastic modulus are different in different directions of the cross section and in the direction perpendicular to the glass layers are two times less than along the glass layers.

scholarly journals Designing for People’s Safety on Flooded Streets: Uncertainties and the Influence of the Cross-Section Shape, Roughness and Slopes on Hazard Criteria

Water ◽  
2021 ◽  
Vol 13 (15) ◽  
pp. 2119
Author(s):  
Luís Mesquita David ◽  
Rita Fernandes de Carvalho
Keyword(s):  
Cross Section ◽  
Overland Flow ◽  
Rectangular Cross Section ◽  
Safety Hazard ◽  
Cross Section Shape ◽  
Section Shape ◽  
Flood Flows ◽  
The Cross ◽  
Flooding Risk

Designing for exceedance events consists in designing a continuous route for overland flow to deal with flows exceeding the sewer system’s capacity and to mitigate flooding risk. A review is carried out here on flood safety/hazard criteria, which generally establish thresholds for the water depth and flood velocity, or a relationship between them. The effects of the cross-section shape, roughness and slope of streets in meeting the criteria are evaluated based on equations, graphical results and one case study. An expedited method for the verification of safety criteria based solely on flow is presented, saving efforts in detailing models and increasing confidence in the results from simplified models. The method is valid for 0.1 m2/s 0.5 m2/s. The results showed that a street with a 1.8% slope, 75 m1/3s−1 and a rectangular cross-section complies with the threshold 0.3 m2/s for twice the flow of a street with the same width but with a conventional cross-section shape. The flow will be four times greater for a 15% street slope. The results also highlighted that the flood flows can vary significantly along the streets depending on the sewers’ roughness and the flow transfers between the major and minor systems, such that the effort detailing a street’s cross-section must be balanced with all of the other sources of uncertainty.

scholarly journals Total cross sections of eγ → $$ eX\overline{X} $$ processes with X = μ, γ, e via multiloop methods

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Roman N. Lee ◽  
Alexey A. Lyubyakin ◽  
Vyacheslav A. Stotsky
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Elliptic Integral ◽  
High Energy ◽  
Calculation Methods ◽  
Complete Elliptic Integral ◽  
Total Cross Sections ◽  
Multiloop Calculation ◽  
The Cross ◽  
Analytical Expressions

Abstract Using modern multiloop calculation methods, we derive the analytical expressions for the total cross sections of the processes e−γ →$$ {e}^{-}X\overline{X} $$ e − X X ¯ with X = μ, γ or e at arbitrary energies. For the first two processes our results are expressed via classical polylogarithms. The cross section of e−γ → e−e−e+ is represented as a one-fold integral of complete elliptic integral K and logarithms. Using our results, we calculate the threshold and high-energy asymptotics and compare them with available results.

scholarly journals Asymptotic Behavior of Stable Structures Made of Beams

2021 ◽  
Author(s):  
Georges Griso ◽  
Larysa Khilkova ◽  
Julia Orlik ◽  
Olena Sivak
Keyword(s):  
Asymptotic Behavior ◽  
Cross Section ◽  
Cross Sections ◽  
Linear Elasticity ◽  
Circular Cross Section ◽  
Linear Elasticity Theory ◽  
Linear Elastic ◽  
The Cross ◽  
Small Rotation ◽  
Stable Structures

AbstractIn this paper, we study the asymptotic behavior of an $\varepsilon $ ε -periodic 3D stable structure made of beams of circular cross-section of radius $r$ r when the periodicity parameter $\varepsilon $ ε and the ratio ${r/\varepsilon }$ r / ε simultaneously tend to 0. The analysis is performed within the frame of linear elasticity theory and it is based on the known decomposition of the beam displacements into a beam centerline displacement, a small rotation of the cross-sections and a warping (the deformation of the cross-sections). This decomposition allows to obtain Korn type inequalities. We introduce two unfolding operators, one for the homogenization of the set of beam centerlines and another for the dimension reduction of the beams. The limit homogenized problem is still a linear elastic, second order PDE.

ISOSPIN DECOMPOSITION OF pp → NNππ CROSS SECTIONS — DO WE SEE A SIGN OF Δ(1600) EXCITATION IN THE nnπ+π+ CHANNEL?

2009 ◽  
Vol 24 (02n03) ◽  
pp. 450-453
Author(s):  
◽  
T. SKORODKO ◽  
M. BASHKANOV ◽  
D. BOGOSLOWSKY ◽  
H. CALÉN ◽  
...  
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Differential Cross ◽  
Pion Production ◽  
Significant Contribution ◽  
Differential Cross Sections ◽  
Pp Collisions ◽  
Theoretical Predictions ◽  
Order Of Magnitude ◽  
The Cross

The two-pion production in pp-collisions has been investigated in exclusive measurements from threshold up to Tp = 1.36 GeV . Total and differential cross sections have been obtained for the channels pnπ+π0, ppπ+π-, ppπ0π0 and also nnπ+π+. For intermediate incident energies Tp > 1 GeV , i.e. in the region, which is beyond the Roper excitation but at the onset of ΔΔ excitation the total ppπ0π0 cross section falls behind theoretical predictions by as much as an order of magnitude near 1.2 GeV, whereas the nnπ+π+ cross section is a factor of five larger than predicted. A model-unconstrained isospin decompostion of the cross section points to a significant contribution of an isospin 3/2 resonance other than the Δ(1232). As a possible candidate the Δ(1600) is discussed.

Stress concentration factors for the torsion of curved beams of arbitrary cross-section

2006 ◽  
Vol 220 (12) ◽  
pp. 1709-1726 ◽  
Author(s):  
R E Cornwell
Keyword(s):  
Finite Element ◽  
Stress Concentration ◽  
Cross Section ◽  
Cross Sections ◽  
Shear Stresses ◽  
Curved Beams ◽  
Finite Element Implementation ◽  
Out Of Plane ◽  
Concentration Factors ◽  
Stress Concentration Factors

There are numerous situations in machine component design in which curved beams with cross-sections of arbitrary geometry are loaded in the plane of curvature, i.e. in flexure. However, there is little guidance in the technical literature concerning how the shear stresses resulting from out-of-plane loading of these same components are effected by the component's curvature. The current literature on out-of-plane loading of curved members relates almost exclusively to the circular and rectangular cross-sections used in springs. This article extends the range of applicability of stress concentration factors for curved beams with circular and rectangular cross-sections and greatly expands the types of cross-sections for which stress concentration factors are available. Wahl's stress concentration factor for circular cross-sections, usually assumed only valid for spring indices above 3.0, is shown to be applicable for spring indices as low as 1.2. The theory applicable to the torsion of curved beams and its finite-element implementation are outlined. Results developed using the finite-element implementation agree with previously available data for circular and rectangular cross-sections while providing stress concentration factors for a wider variety of cross-section geometries and spring indices.

scholarly journals The Cross Section for the J = 0 → 2 Rotational Excitation of Hydrogen by Slow Electrons

1969 ◽  
Vol 22 (6) ◽  
pp. 715 ◽  
Author(s):  
RW Crompton ◽  
DK Gibson ◽  
AI McIntosh
Keyword(s):  
Momentum Transfer ◽  
Cross Section ◽  
Cross Sections ◽  
Vibrational Excitation ◽  
The Cross ◽  
Excitation Processes ◽  
Slow Electrons ◽  
And Diffusion ◽  
Momentum Transfer Cross Section ◽  
Section Analysis

The results of electron drift and diffusion measurements in parahydrogen have been analysed to determine the cross sections for momentum transfer and for rotational and vibrational excitation. The limited number of possible excitation processes in parahydrogen and the wide separation of the thresholds for these processes make it possible to determine uniquely the J = 0 → 2 rotational cross section from threshold to 0.3 eV. In addition, the momentum transfer cross section has been determined for energies less than 2 eV and it is shown that, near threshold, a vibrational cross section compatible with the data must lie within relatively narrow limits. The problems of uniqueness and accuracy inherent in the swarm method of cross section analysis are discussed. The present results are compared with other recent theoretical and experimental determinations; the agreement with the most recent calculations of Henry and Lane is excellent.

Finite-size analysis and the influence of the cross-section shape of the granular column collapses

2021 ◽  
Author(s):  
Teng Man ◽  
Herbert Huppert ◽  
Ling Li ◽  
Sergio Galindo-Torres
Keyword(s):  
Size Effect ◽  
Cross Section ◽  
Finite Size ◽  
Size Analysis ◽  
Cross Section Shape ◽  
Section Shape ◽  
The Cross ◽  
Shape Influence ◽  
Deposition Morphology ◽  
Granular Column

<p>The collapse of granular columns, which sheds light on the kinematics, dynamics, and deposition morphology of mass-driven flows, is crucial for understanding complex flows in both natural and engineering systems, such as debris flows and landslides. However, our research shows that a strong size effect and cross-section shape influence exist in this test. Thus, it is essential to better understand these effects. In this study, we explore the influence of both relative column sizes and cross-section shapes on the run-out behavior of collapsed granular columns and analyze their influence on the deposition morphology with the discrete element method (DEM) with Voronoi-based spheropolyhedron particles. We link the size effect that occurs in granular column collapse problems to the finite-size scaling functions and investigate the characteristic correlation length associated with the granular column collapses. The collapsing behavior of granular columns with different cross-section shapes is also studied, and we find that particles tend to accumulate in the direction normal to the edge of the cross-section instead of the vertex of it. The differences in the run-out behavior in different directions when the cross-section is no longer a circle can also be explained by the finite-size analysis we have performed in this study. We believe that such a study is crucial for us to better understand how granular material flows, how it deposits, and how to consider the size effect in the rheology of granular flows.</p>

Sign in / Sign up

Export Citation Format

Share Document