Analysis of Helical Torsion Spring for Epicyclic Traction Drive

2017 ◽  
Vol 261 ◽  
pp. 408-415
Author(s):  
Geza Nemeth
Keyword(s):  
Cross Section ◽  
Rectangular Cross Section ◽  
Bending Moment ◽  
Initial Shape ◽  
Traction Drive ◽  
Torsion Spring ◽  
Spring Wire ◽  
Tangential Forces ◽  
Radial Forces ◽  
Proper Operation

Let us consider a simple epicyclic traction drive containing a sun wheel, an annular wheel, planetary wheels and a planet carrier. The annular wheel is substituted by a helical torsion spring with rectangular cross section. The spring has initial tensioning, tightened to the planetary wheels. When the number of coils is z and the number of planet wheels is N, there are zN piece of concentrated forces acting to the spring from inside towards outside. The main load of the spring is bending, it is computable along the spring wire. The bending moment is limited by the spring material and the cross section of spring. The radial forces acting to the spring are governed by the constraint of stress equality, the deflections of the contacting parts are determined by the radial (and slightly the tangential) forces. An initial shape of the spring that assures the proper operation of the drive after the assembly, is calculated by elementary mechanical calculation methods. The main goal is the developing of a traction drive in which the clamping force is proportional to the torque which should be transmitted, for the sake of the favourable life rating and the efficiency.

Bearing Capacity of Structures Made of Materials with Different Tensile and Compression Strengths

2019 ◽  
Vol 968 ◽  
pp. 200-208
Author(s):  
Mykola Soroka
Keyword(s):  
Cross Section ◽  
Rectangular Cross Section ◽  
Limit State ◽  
Analytical Calculation ◽  
Bending Moment ◽  
Maximum Load ◽  
Longitudinal Force ◽  
Plastic State ◽  
Limiting State ◽  
Tension And Compression

The paper considers the problem of the ultimate load finding for structures made of a material with different limits of tensile strength and compression. The modulus of elasticity under tension and compression is the same. It is assumed that upon reaching the ultimate strength, the material is deformed indefinitely. The calculations use a simplified material deformation diagram — Prandtl diagrams. The limiting state of a solid rectangular section under the action of a longitudinal force and a bending moment is considered. The dependences describing the boundary of the strength of a rectangular cross section are obtained. Formulas allowing the calculation of the values of the limit forces and under the action of which the cross section passes into the plastic state are derived. Examples of the analytical calculation of the maximum load for the frame and two-hinged arch are given. An algorithm is proposed and a program for calculating arbitrary flat rod systems according to the limit state using the finite element method is compiled. The proposed algorithm does not involve the use of iterative processes, which leads to an exact calculation of the maximum load within the accepted assumptions.

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.

scholarly journals Cross-Sectional Analysis of the Resistance of Rc Members Subjected to Bending With/without Axial Force

2021 ◽  
Author(s):  
Marek Lechman
Keyword(s):  
Cross Section ◽  
Axial Force ◽  
Rectangular Cross Section ◽  
Bending Moment ◽  
Equilibrium Equations ◽  
Cross Sectional ◽  
Cross Sectional Analysis ◽  
Nonlinear Stress ◽  
The Cross ◽  
Sectional Analysis

The paper presents section models for analysis of the resistance of RC members subjected to bending moment with or without axial force. To determine the section resistance the nonlinear stress-strain relationship for concrete in compression is assumed, taking into account the concrete softening. It adequately describes the behavior of RC members up to failure. For the reinforcing steel linear elastic-ideal plastic model is applied. For the ring cross-section subjected to bending with axial force the normalized resistances are derived in the analytical form by integrating the cross-sectional equilibrium equations. They are presented in the form of interaction diagrams and compared with the results obtained by testing conducted on RC columns under eccentric compression. Furthermore, the ultimate normalized bending moment has been derived for the rectangular cross-section subjected to bending without axial force. It was applied in the cross-sectional analysis of steel and concrete composite beams, named BH beams, consisting of the RC rectangular core placed inside a reversed TT welded profile. The comparisons made indicated good agreements between the proposed section models and experimental results.

scholarly journals STRESS-STRAIN STATE OF REINFORCED CONCRETE BEAMS STRENGTHENED WITH A NEW EXTERNAL STEEL STRUCTURE

2017 ◽  
Vol 1 (48) ◽  
pp. 90-99
Author(s):  
V. P. Zhyrakhivskyi ◽  
М. G. Chekanovych ◽  
О. М. Chekanovych
Keyword(s):  
Reinforced Concrete ◽  
Cross Section ◽  
Concrete Beams ◽  
Rectangular Cross Section ◽  
Bending Moment ◽  
Steel Structure ◽  
Research Data ◽  
Reinforced Concrete Beams ◽  
Reinforced Beams ◽  
Steel Bars

The study presents a new structure for strengthening of one-span reinforced concrete beams in rectangular cross-section using external steel bars. The specific feature of the proposed strengthening is the unloading of the compressed upper zone of a beam with simultaneous compression of its lower stretched zone. The article considers some variants of making the strengthening structure with rigid and flexible reinforcement elements for faster tension of external bars, and the variant including only flexible elements. It provides a design scheme and method for such reinforced beams. The study provides experimental research data on the series of beams with different parameters of the strengthening structure in the form of «bending moment – deflection» and «bending moment - deformation of concrete» dependencies.

Shape Memory Elements in Bending: Influence of the Shape of their Cross-Section

2000 ◽  
Vol 11 (12) ◽  
pp. 977-984 ◽  
Author(s):  
Vratislav Kafka ◽  
David Vokoun
Keyword(s):  
Shape Memory ◽  
Cross Section ◽  
Elastic Limit ◽  
Rectangular Cross Section ◽  
Circular Cross Section ◽  
Bending Moment ◽  
Internal Variables ◽  
Memory Recovery ◽  
The Cross ◽  
The Mathematical Model

The effect of the shape of the cross-section of a bent prismatic bar on its shape memory recovery moment is investigated. The analysis is based on the mathematical model of the first author (Kafka, 1994a, 1994b, 2001). The area of the cross-section of the bar is assumed to be constant, the shape of the cross-section is varied. The investigated shapes are rectangles with various relations of their sides, and a circular cross-section. It is assumed that the rod is bent above elastic limit and unloaded at room temperature, which results in macroscopic residual stresses giving zero bending moment, and in residual internal variables descriptive of the change of the state of the material. Then, the resulting form is held fixed and temperature of the rod is raised. Due to the increase of temperature there arise recovery stresses resulting in recovery moments. These moments—depending on the shape of the cross-section—are calculated, and in this way the effectiveness of the shape of the cross-section is evaluated. In the case of a rectangular cross-section the effect of the relation of the sides is strongly non-linear, the effect of the circular cross-section is lower by 20% than that of a square cross-section.

On the Experimental Analysis of Temperature Influence on Stiffness of Reinforced Concrete Beams

2015 ◽  
Vol 6 (1) ◽  
pp. 49-58 ◽  
Author(s):  
Robert Kowalski ◽  
Michal Glowacki ◽  
Marian Abramowicz
Keyword(s):  
Reinforced Concrete ◽  
Cross Section ◽  
Cross Sections ◽  
Concrete Beams ◽  
Rectangular Cross Section ◽  
Thermal Strain ◽  
Bending Moment ◽  
Reinforced Concrete Beams ◽  
Stiffness Reduction ◽  
Tensile Zone

The paper presents results of experimental research whose main topic was determination of stiffness reduction in bent reinforced concrete beams in two cases: when only tensioned or only compressed zone was exposed to high temperature. Twenty four reinforced concrete beams with rectangular cross-section were prepared for the experiment. Eight groups of beams were prepared in total: 2 with reinforcement ratio - 0.44 and 1.13% x 2 levels of load - 50 or 70% of destructive force ensuring the constant value of bending moment in the centre part of heated beams x 2 static schemes. Three beams were used in each group. Significant cross-section stiffness reduction was observed in beams where the tensile zone was heated. This was due to considerable elongation of the bars where the steel load elongation summed up with the free thermal strain. In beams where the compressed zone was heated the stiffness reduction was observed only after the time where the tensile zone heated cross-sections were already destroyed.

The Effect of Shear and Normal Forces on the Fully Plastic Moment of a Beam of Rectangular Cross Section

1961 ◽  
Vol 28 (2) ◽  
pp. 269-274 ◽  
Author(s):  
B. G. Neal
Keyword(s):  
Cantilever Beam ◽  
Cross Section ◽  
Lower Bounds ◽  
Rectangular Cross Section ◽  
Bending Moment ◽  
Upper And Lower Bounds ◽  
Collapse Load ◽  
Shear Forces ◽  
Normal Forces ◽  
Interaction Relations

The value of the fully plastic moment of a beam is known to be reduced by both normal and shear forces, and their separate effects have been studied in some detail, but little attention has been paid to the reduction caused by normal and shear forces acting simultaneously. This problem is discussed with reference to a cantilever beam of rectangular cross section subjected to both shear and normal forces at the free end. Upper and lower bounds to the collapse load are determined, and the results are presented in the form of interaction relations between the shear and normal forces and the bending moment at the clamped end of the cantilever at collapse.

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.

scholarly journals Analytical modeling of the shape memory effect in SMA beams with rectangular cross section under reversed pure bending

2021 ◽  
pp. 1045389X2098878
Author(s):  
Enrico Radi
Keyword(s):  
Martensitic Transformation ◽  
Cross Section ◽  
Rectangular Cross Section ◽  
Axial Stress ◽  
Bending Moment ◽  
Integral Form ◽  
Loading Path ◽  
Martensite Variant ◽  
Young’S Moduli ◽  
The Cross

An analytical model is developed for a prismatic SMA beam with rectangular cross section subjected to alternating bending at temperature below the austenitic transformations. The loading path consists in a loading-unloading cycle under bending and then under reversed bending. Two opposite martensitic variants take place, whose volume fractions evolve linearly with the axial stress. Different Young’s moduli are taken for the austenitic and martensitic phases. As the bending moment is increased, the martensitic transformation starts from the top and bottom and then it extends inwards. If the maximum applied bending moment is large enough, then the complete Martensitic transformation takes place at the upper and lower parts of the cross section. During unloading and the following reversed bending, reorientation of the Martensite variant into the opposite one takes place starting from the boundary between the fully martensitic region and the intermediate transforming region. Special attention is devoted to calculate analytically the axial stress and Martensite variant distributions within the cross section at each stage of the process. A closed form moment-curvature relation is provided for loading and elastic unloading and in integral form for the rest of the process. The approach is then validated by comparison with analytical results available in the literature.

Design and Optimization of Variable Rectangular Cross Section Chassis for On-Road Heavy Vehicles

2016 ◽  
Vol 8 (1) ◽  
Author(s):  
K. Rajasekar ◽  
R. Saravanan ◽  
N.V. Dhandapani
Keyword(s):  
Genetic Algorithm ◽  
Uniform Distribution ◽  
Cross Section ◽  
Rectangular Cross Section ◽  
Bending Moment ◽  
3D Models ◽  
Heavy Vehicle ◽  
Variable Cross ◽  
Element Analysis ◽  
Section Modulus

All the loads generated by other components of heavy vehicle are transferred to its chassis. Chassis related failures are few but the damages to the safety of occupant are huge; sometimes it leads to fatal accidents. In order to overcome this, the chassis has to be optimized based on static and dynamic loads by ensuring a uniform distribution of stress and strain. The shape and cross section of the chassis gives a resistance to the above mentioned loads. The cross section of the chassis structure of all on-road vehicles is uniform despite the variable loads. In this work, variable cross section chassis of an on-road heavy vehicle is designed by keeping optimum sections. Bending moment of the chassis has been mathematically related with section modulus of the chassis. Genetic algorithm based procedures have been used to optimize the height, width and thickness of the chassis cross section. Coding in C language is used to automate the genetic algorithm procedures. For benchmark study, 3D models of optimized and existing chassis of an on-road heavy vehicle were developed. Finite element analysis reveals that the optimized chassis has less failure possibilities due to lower stress values and uniform distribution when compared to those from the model of existing chassis.

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