scholarly journals Stress Analysis of Square and Rectangular Cross Section Helical Spring

2020 ◽  
pp. 362-367
Author(s):  
Ashish M. Choube ◽  
R. U. Sambhe
Keyword(s):  
Stress Analysis ◽  
Elastic Body ◽  
Cross Section ◽  
Cross Sections ◽  
Rectangular Cross Section ◽  
Shear Stresses ◽  
Helical Spring ◽  
Free Length ◽  
Original Shape ◽  
Wide Range

Springs are nothing but the elastic body which deflects when loaded and comes back in its original shape when load removed. It has wide range of an applications, mainly used in automobile sector, in brakes and clutches, in watches, toys etc. The cross sections of spring may be circular, square or rectangular. When load is applied on spring, it will deflect and shear stresses will be generated. If the length of spring is higher, spring may buckle also. This article deals with analysis of square and rectangular cross section helical spring using FE approach and validated with analytical equations. Here, free length of spring is also changed to observe effect of shear stresses in square and rectangular cross section of spring.

On Non-Boussinesq Gravity Currents in Non-Rectangular Cross-Section Channels

2014 ◽  
Author(s):  
T. Zemach
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Rectangular Cross Section ◽  
Gravity Current ◽  
Classical Formulation ◽  
Wide Range ◽  
Front Condition ◽  
Significant Generalization ◽  
Self Similar ◽  
Cross Section Geometry

We consider the propagation of a gravity current of density ρc from a lock length x0 and height h0 into an ambient fluid of density ρa in a horizontal channel of height H along the horizontal coordinate x. The bottom and top of the channel are at z = 0, H, and the cross-section is given by the quite general −f1(z) ≤ y ≤ f2(z) for 0 ≤ z ≤ H. When the Reynolds number is large, the resulting flow is governed by the parameters R = ρc/ρa, H* = H/h0 and f(z) = f1(z) + f2(z). We show that the shallow-water one-layer model, combined with a Benjamin-type front condition, provides a versatile formulation for the thickness h and speed u of the current. The results cover in a continuous manner the range of light ρc/ρa ≪ 1, Boussinesq ρc/ρa ≈ 1 and heavy ρc/ρa ≫ 1 currents in a fairly wide range of depth ratio in various cross-section geometries. We obtain analytical solutions for the initial dam-break stage of propagation with constant speed, which appears for any cross-section geometry, and derive explicitly the trend for small and large values of the governing parameters. For large time, t, a self-similar propagation is feasible for f(z) = bzα cross-sections only, with t(2+2α)/(3+2α). The present approach is a significant generalization of the classical non-Boussinesq gravity current problem. The classical formulation for a rectangular (or laterally unbounded) channel is now just a particular case, f(z) = const., in the wide domain of cross-sections covered by this new model.

Displacement of a Ring Subject to Uniform Radial Loads

1976 ◽  
Vol 98 (1) ◽  
pp. 375-380
Author(s):  
A. K. Naghdi
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Rectangular Cross Section ◽  
Angular Speed ◽  
Theory Of Elasticity ◽  
Radial Load ◽  
Wide Range ◽  
Rotationally Symmetric ◽  
Machine Elements ◽  
Elasticity Solutions

Thick rings are extensively used in various machine elements and structures. These rings are ordinarily acted upon by irregular loadings on their boundaries. However, there are cases where the rings are subject to uniformly distributed radial loads. Examples are the cases of a ring fitted on a rotationally symmetric wheel by heating or a ring rotating with a constant angular speed, etc. The solution for stresses and displacements in a ring subject to a uniformly distributed radial load is also important for the fact that it serves as the first component in the Fourier series for the solution of the general case of inplane loading of a ring. In this investigation the displacements of rings with various cross sections under the actions of uniform radial loads are obtained. Two different methods of theory of elasticity are employed to find the solutions for rings with solid circular and tapered cross sections. An approximate third solution is also derived for the case of a ring with a symmetrical cross section having no re-entrant corners. Numerical results for the displacements of various rings indicate that the latter solution accurately matches the former elasticity solutions, and the classical solution for rectangular cross-section rings, in a wide range.

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.

Moderate Reynolds Number Mixing in a T-Channel

2010 ◽  
Author(s):  
Susan Thomas ◽  
Tim Ameel
Keyword(s):  
Reynolds Number ◽  
Cross Section ◽  
Rectangular Cross Section ◽  
Large Body ◽  
Experimental Studies ◽  
Numerical Work ◽  
Moderate Reynolds Number ◽  
Wide Range ◽  
Particle Imaging ◽  
Experimental Trials

An experimental investigation of water flow in a T-shaped channel with rectangular cross section (20 × 20 mm inlet ID and 20 × 40 mm outlet ID) has been conducted for a Reynolds number Re range of 56 to 422, based on inlet diameter. Dynamical conditions and the T-channel geometry of the current study are applicable to the microscale. This study supports a large body of numerical work, and resolution and the interrogation region are extended beyond previous experimental studies. Laser induced fluorescence (LIF) and particle imaging velocimetry (PIV) are used to characterize flow behaviors over the broad range of Re where realistic T-channels operate. Scalar structures previously unresolved in the literature are presented. Special attention is paid to the unsteady flow regimes that develop at moderate Re, which significantly impact mixing but are not yet well characterized or understood. An unsteady symmetric topology, which develops at higher Re and negatively impacts mixing, is presented, and mechanisms behind the wide range of mixing qualities predicted for this regime are explained. An optimal Re operating range is identified based on multiple experimental trials.

scholarly journals Particle separation of a modified feed nozzle hydrocyclone under different operating parameters

2021 ◽  
Vol 11 (5) ◽  
pp. 159-170
Author(s):  
Zsolt Hegyes ◽  
Máté Petrik ◽  
L. Gábor Szepesi
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Rectangular Cross Section ◽  
Circular Cross Section ◽  
Particle Separation ◽  
Baffle Plate ◽  
Important Data ◽  
Preliminary Research ◽  
All Speeds ◽  
Plate Solution

During the operation of the hydrocyclone the cut size diameter is the most important data. This is connected to feed rate, which is closely related to the feed cross section. Preliminary research has revealed that square cross-section is more effective than circular cross-section. The research compared 2 types of feed cross sections at 5 different feed rates. One is a standard rectangular cross-section and the other is a square cross-section that narrows with a baffle plate. Preliminary calculations for cut size diameter have shown that better particle separation at all speeds can be achieved with the baffle plate solution. In both types, the increased velocity created decreased cut size diameter. During the simulation, the baffle plate did not cause any abnormalities in the internal pressure and velocity distributions. The simulation revealed that the particles did not behave as previously calculated.

QCD JETS AT HERA I.: O(αs) RADIATIVE CORRECTIONS TO ELECTROWEAK CROSS SECTIONS AND JET RATES

1989 ◽  
Vol 04 (07) ◽  
pp. 1781-1825 ◽  
Author(s):  
JÜRGEN G. KÖRNER ◽  
ERWIN MIRKES ◽  
GERHARD A. SCHULER
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Neutral Current ◽  
High Energy ◽  
Coupling Constant ◽  
Bjorken Scaling ◽  
Born Cross Section ◽  
Wide Range ◽  
Lepton Polarization ◽  
Jet Cross Sections

We present the complete O(αs) corrections to the electroweak cross sections of both neutral current and charged current deep inelastic e±p scattering including lepton polarization effects. Changes in the cross section due to the inclusion of next-to-leading-log (NLL) effects are parametrized by K factors, which are defined as the ratio of the NLL O(αs) cross sections and the Born cross section. Using the standard redefinition scheme of the parton densities, we find that the K factors deviate substantially from unity for small values of the Bjorken-Scaling variable x. We also elaborate on problems that arise when defining jet cross sections in ep scattering and present numerical results for the O(αs) 3-jet and 2-jet rates. We observe that the Q2-dependence of the 3-jet rate is dominated by the running strong coupling constant αs(Q2) allowing for its determination over a wide range in Q2 at high energy ep colliders.

LOAD-BEARING CAPACITY OF CONCRETE-FILLED STEEL COLUMNS

2009 ◽  
Vol 15 (1) ◽  
pp. 21-33 ◽  
Author(s):  
Artiomas Kuranovas ◽  
Douglas Goode ◽  
Audronis Kazimieras Kvedaras ◽  
Shantong Zhong
Keyword(s):  
Bearing Capacity ◽  
Cross Section ◽  
Cross Sections ◽  
Rectangular Cross Section ◽  
Circular Cross Section ◽  
Steel Tube ◽  
Sustained Load ◽  
Load Bearing Capacity ◽  
Concrete Core ◽  
Load Bearing

This paper represents the analysis of 1303 specimens of CFST experimental data. Test results are compared with EC4 provided method for determining the load‐bearing capacity of these composite elements. Several types of CFSTs were tested: both circular and rectangular cross‐sections with solid and hollow concrete core with axial load applied without and with moment, with sustained load and preloading. For circular cross‐section columns there is a good agreement between the test failure load and the EC4 calculation for both short and long columns with and without moment. For rectangular cross‐section columns the agreement is good except when the concrete cylinder strength was greater than 75 MPa, when many tests failed below the strength predicted by EC4. Preloading the steel tube before filling with concrete seems to have no effect on the strength. This paper also presents the stress distribution, confinement distribution and complete average longitudinal stress‐strain curves for concrete‐filled steel tubular elements. Based on the definition of the “Unified Theory”, the CFST is looked upon as an entity of a new composite material. In this paper, the research achievement of the strength and stability for centrifugal‐hollow and solid concrete filled steel tube are introduced. These behaviours relate to the hollowness ratio and the confining indexes of corresponding solid CFST. If the hollow ratio equals to 0,4–0,5 and over, the N‐ϵ relationship exists in steady descending stage. The critical stress of CFST elements stability is determined as an eccentric member with the initial eccentricity by use of finite element method. Santrauka Straipsnyje analizuojami 1303 betonšerdžių plieninių strypų bandinių eksperimentiniai duomenys. Duomenys lyginami su eurokode 4 pateiktais kompozitinių elementų laikomosios galios nustatymo metodais. Analizuojami šie betonšerdžių plieninių strypų bandinių tipai: pilnaviduriai ir tuščiaviduriai, apskrito ir stačiakampio skerspjūvio kolonos, kurių galuose veikia arba neveikia momentas, su iš anksto pridėta arba ilgalaike apkrova. Apskrito skerspjūvio kolonų laikomosios galios bandymų rezultatai atitinka skaičiavimų reikšmes, apskaičiuotas pagal eurokode 4 pateiktu metodu. Stačiakampio skerspjūvio elementų laikomosios galios reikšmių bandymo rezultatai puikiai atitinka teorines reikšmes, kai betono ritininis stipris nesiekia 75 MPa. Išankstinis elementų apkrovimas poveikio elementų laikomajai galiai beveik neturi. Taip pat nagrinėjami betonšerdžių elementų įtempių būvių pasiskirstymas, betono apspaudimo poveikis ir išilginių deformacijų ir įtempių kreivės. Pateikiama S. T. Zhong „Unifikuota teorija“, kuri nagrinėja kompozitinį elementą kaip visumą. Straipsnyje nagrinėjamos kompozitinio plieninio ir betoninio elemento stiprumo ir pastovumo sąlygos. Tokių elementų reikšmėmis. Jeigu tuštumos santykis lygus 0,4–0,5 ir daugiau, N-ε sąryšis yra kritimo stadijoje. Elgsenos stadijos keičiasi pagal tuštumos koeficientą.

Electron energy distributions in uniform electric fields and the Townsend ionization coefficient

1958 ◽  
Vol 244 (1237) ◽  
pp. 166-185 ◽  
Keyword(s):  
Differential Equation ◽  
Cross Section ◽  
Electric Fields ◽  
Cross Sections ◽  
Collision Cross Section ◽  
Present Theory ◽  
Uniform Electric Field ◽  
Ionization Coefficient ◽  
Special Cases ◽  
Wide Range

The second-order differential equation which expresses the equilibrium condition of an electron swarm in a uniform electric field in a gas, the electrons suffering both elastic and inelastic collisions with the gas molecules, is solved by the Jeffreys or W.K.B. method of approximation. The distribution function F(ε) of electrons of energy ε is obtained immediately in a general form involving the elastic and inelastic collision cross-sections and without any restriction on the range of E/p (electric strength/gas pressure) save that introduced in the original differential equation. In almost all applications the approximation is likely to be of high accuracy, and easy to use. Several of the earlier derivations of F(ε) are obtained as special cases. Using the function F(ε) an attempt is made to relate the Townsend ionization coefficient a to the properties of the gas in a more general manner than hitherto, using realistic functions for the collision cross-section. It is finally expressed by the equation α/ p = A exp ( — Bp/E ) in which A and B are functions involving the properties of the gas and the ratio E/p . The important coefficient B is directly related to the form and magnitude of the total inelastic cross-section below the ionization potential and can be evaluated for a particular gas once the cross-section is known experimentally. The present theory shows clearly the influence of E/p on both A and B, a matter which has not been satisfactorily discussed previously. The theory is illustrated by calculations of F (ε) and a/p for hydrogen over a range of E/p from 10 to 1000. The agreement between the calculated results and recent reliable observations of α/ p is surprisingly good considering the nature of the calculations and the wide range of E/p .

scholarly journals NUMERICAL INVESTIGATION OF THE ELASTIC-PLASTIC LINEAR HARDENING STRESS-STRAIN STATE OF THE FRAME ELEMENT CROSS-SECTION

2016 ◽  
Vol 8 (3) ◽  
pp. 94-100
Author(s):  
Andrius Grigusevičius ◽  
Gediminas Blaževičius
Keyword(s):  
Cross Section ◽  
Axial Force ◽  
Cross Sections ◽  
Rectangular Cross Section ◽  
Bending Moment ◽  
Software Environment ◽  
Stress Strain ◽  
Hardening Material ◽  
Frame Element ◽  
Nonlinear Stress

The aim of this paper is to present a solution algorithm for determining the frame element crosssection carrying capacity, defined by combined effect of bending moment and axial force. The distributions of stresses and strains inside a cross-section made of linearly hardening material are analysed. General nonlinear stress-strain dependencies are composed. All relations are formed for rectangular cross-section for all possible cases of combinations of axial force and bending moment. To this end, five different stress-strain states are investigated and four limit axial force values are defined in the present research. The nonlinear problem is solved in MATLAB mathematical software environment. Stress-strain states in the cross-sections are investigated in detail and graphically analysed for two numerical experiments.

In-Plane Vibrations of Thick Circular Rings With T or I Cross Sections

1979 ◽  
Vol 46 (2) ◽  
pp. 470-472
Author(s):  
H. Lecoanet ◽  
J. Piranda
Keyword(s):  
Experimental Data ◽  
Eigenvalue Problem ◽  
Cross Section ◽  
Cross Sections ◽  
Rectangular Cross Section ◽  
Circular Rings ◽  
Theoretical Results ◽  
Good Agreement

This paper deals with the problem of eigenfrequencies and eigenvectors for rings whose cross section may be decomposed in basic rectangular cross sections. The solution is derived from a solution of the in-plane eigenvalue problem for rectangular cross-section thick rings. A good agreement between theoretical results and experimental data is obtained.

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