Deflection of a Thick Ring in Diametral Compression by Test and by Strength-of-Materials Theory

1959 ◽  
Vol 26 (2) ◽  
pp. 294-295
Author(s):  
Alexander Blake
Keyword(s):  
Cross Section ◽  
Strain Energy ◽  
Rectangular Cross Section ◽  
Theoretical Estimate ◽  
Shear Stresses ◽  
Strength Of Materials ◽  
Diametral Compression ◽  
Normal And Shear Stresses

Abstract Experimental and theoretical deflection studies are briefly described for several steel rings, of uniform rectangular cross section, compressed by two forces along a diameter and having D/d ratios ranging from 1.3 to 1.9. The calculations are based on the principle of Castigliano and expressions for strain energy due to bending, normal, and shear stresses. Discrepancies between the theoretical estimate and the tests are shown.

Thermoelasticity Solutions for Straight Beams

2002 ◽  
Vol 69 (3) ◽  
pp. 224-229 ◽  
Author(s):  
C. D. Copper ◽  
W. D. Pilkey
Keyword(s):  
Temperature Distribution ◽  
Cross Section ◽  
Solution Technique ◽  
Shear Stresses ◽  
Stress Distributions ◽  
Strength Of Materials ◽  
Numerical Efficiency ◽  
Temperature Distributions ◽  
Normal And Shear Stresses

This paper presents a thermoelastic solution technique for beams with arbitrary quasi-static temperature distributions that create large transverse normal and shear stresses. This technique calculates the stress resultants and centroid displacements along a beam. Then, the stress resultants and temperature distribution are used to calculate the stress distributions on a cross section of the beam. Simple examples demonstrate the numerical efficiency of the proposed technique and the inadequacy of the strength of materials theory to solve these types of problems.

Naturally Twisted Layered Anisotropic Rod Made of Reinforced Materials Research

2015 ◽  
Vol 736 ◽  
pp. 30-38 ◽  
Author(s):  
Alibek Nurimbetov ◽  
Amangeldy Bekbayev ◽  
Seitzhan Orynbayev ◽  
Muratkali Dzhamanbayev ◽  
Meruyert Keikimanova
Keyword(s):  
Cross Section ◽  
Strain State ◽  
Rectangular Cross Section ◽  
Shear Stresses ◽  
Anisotropy Coefficient ◽  
Centrifugal Forces ◽  
Materials Research ◽  
Limit Stress ◽  
The Individual ◽  
Normal And Shear Stresses

In this paper, we consider the deformation of multilayer bars in torsion and tension. Thus, in the analyzed strength calculations rod having a rectangular cross section of the composite material. Namely, the choice of the structure of the material, satisfy the specifications of the rod in terms of stress-strain state in a torsion-bending coherence taking into account features of the composite materials. On the example with a layered core, being under the influence of centrifugal forces shows the effect of shifts between the layers on the redistribution of normal and shear stresses in layers. Depending on the magnitude of the anisotropy coefficient of the material used, normal and shear stresses in the outer layers is increased by 2-5 times. Comparison of these values ​​with limit stress for these layers allows you to select how the reinforcement of these layers. Collection of data about the influence of the stiffness of the individual layers by an angle promotion rod and durability allow the optimal folding of the reinforcing layers and the type of reinforcement and matrix.

Small Indentations of Rubber Blocks: Effect of Size and Shape of Block and of Lateral Compression

2006 ◽  
Vol 79 (4) ◽  
pp. 674-693 ◽  
Author(s):  
A. N. Gent ◽  
O. H. Yeoh
Keyword(s):  
Cross Section ◽  
Strain Energy ◽  
Rectangular Cross Section ◽  
Strain Energy Function ◽  
Elastic Solid ◽  
Biaxial Compression ◽  
Rigid Surface ◽  
Lateral Compression ◽  
Block Width ◽  
Rubber Block

Abstract Many gaskets and seals consist of a long rubber strip or thin-walled ring, placed on a flat rigid surface and indented by a flat-ended rigid indenter. We have examined their resistance to small indentations by FEA. They are treated as infinitely-long elastic blocks of rectangular cross-section, resting on a rigid frictionless base. The indentation stiffness is calculated for various ratios of indenter tip width to block width and to block thickness, using two restraint conditions on the outer surfaces: frictionless walls (zero outwards displacement), as for a gasket placed in a recess; or stress-free, as for a gasket with no lateral restraint. For an infinitely-wide and infinitely-thick block, the theoretical resistance to indentation is zero. For comparison, the indentation stiffness is calculated for cylindrical rubber blocks of varied radius and thickness, indented by a flat-ended cylindrical indenter. In this case the result for an infinitely-large block is finite. A second study treats indentation of a rubber block, pre-compressed in the surface plane. Biot showed that the indentation stiffness of a half-space becomes zero at a critical compression, about 33% for equi-biaxial compression and 44 % for plane strain compression, for both a neo-Hookean and a Mooney-Rivlin elastic solid. FEA calculations were made of the indentation stiffness of neo-Hookean blocks of various sizes, pre-compressed to various degrees. The results are compared with Biot's result. In an Appendix, the critical degree of compression is calculated for a more realistic strain energy function than either the neo-Hookean or the Mooney-Rivlin approximation.

Generation and Investigation of Embedded Micro-Channels Network Using Three Dimensional Printing Technology

2017 ◽  
Author(s):  
Austin Smith ◽  
Hamzeh Bardaweel
Keyword(s):  
Additive Manufacturing ◽  
3D Printing ◽  
Cross Section ◽  
Rectangular Cross Section ◽  
Hydrodynamic Characteristics ◽  
Shear Stresses ◽  
Printing Technology ◽  
Micro Channels ◽  
3D Printed ◽  
Printing Direction

The work presented here is motivated by the recent growing interest in using additive manufacturing to fabricate micro-channels networks. Distorted shapes and rough geometries influence hydrodynamic characteristics of micro-channels by increasing their flow resistance and pressure drop or altering wall shear stresses inside them. Since geometric conformity and shape fidelity of micro-channels networks are greatly influenced by manufacturing process, this work is focused on dimensional characterization of micro-channels fabricated using additive manufacturing. In this work, circular and rectangular cross-section micro-channels are 3D printed. Shapes and dimensions of 3D printed micro-channels are examined using Scanning Electron Microscope (SEM) imaging. In this work, 500 μm diameter and 200 μm square transparent PolyLactic Acid (PLA) micro-channels are 3D printed with average errors 0.25% and 1.65%, respectively. SEM images confirmed geometric conformity and shape fidelity of the 3D printed circular and rectangular cross-section micro-channels. Statistical analysis is performed on multiple prints to verify reproducibility and shape conformity. Results show that factors such as printing direction play essential role in the shape conformity and geometric fidelity of the micro-channels. Although 3D printing is a promising route for attaining micro-channels there are still significant improvements that can be made to the precision of the printer in the XY plane for printing small geometric figures. This improvement will likely come as the printing technology and software both improve to allow the operator more control over the outcome of the print. Additionally, new 3D printing materials may open the gate for new applications in different fields such as thermal management and microfluidics.

Analysis of Buckling Column Spring With Pivoted Ends and Uniform Rectangular Cross Section

1961 ◽  
Vol 83 (1) ◽  
pp. 61-66
Author(s):  
Alexander Blake
Keyword(s):  
Cross Section ◽  
Rectangular Cross Section ◽  
Experimental Results ◽  
Strength Of Materials ◽  
Bending Stresses ◽  
Deflection Analysis ◽  
Uniform Cross Section

Design formulas and working charts are derived for predicting load-deflection characteristics and maximum bending stresses in initially straight buckling column springs, of uniform cross section, considered to be pin jointed at the supports. Load-deflection analysis is based on the study of a slender bar, compressed beyond critical buckling, made by Lagrange. Stresses are calculated using the elementary strength of materials theory. The predicted load-deflection curves for typical spring proportions are compared with the experimental results.

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.

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