scholarly journals VII.—Rupture Stresses in Beams and Crane Hooks.

1914 ◽  
Vol 50 (1) ◽  
pp. 211-223
Author(s):  
Angus R. Fulton
Keyword(s):  
Compressive Stress ◽  
Cross Section ◽  
Bending Moment ◽  
Neutral Axis ◽  
Sectional Area ◽  
Inverse Proportion ◽  
Direct Loading ◽  
The Cross ◽  
External Forces ◽  
Distribution Of Stress

CONCLUSIONS1. It may be taken as conclusive that the final distribution of stress at rupture point in a member subjected to an external bending moment is a rectangular one, unless where the cohesion of adjacent layers is not sufficient to withstand the shear induced by the resisting moment of the section.2. That, provided shear does not take place, the neutral axis moves always to the position which reduces the summation of the tensile and compressive stress areas, across a section, to the equilibrant of the external forces. (In the case of a beam this reduces to zero; in that of a hook, at the principal section to the suspended weight.)3. That the total resisting moment of these stresses must be equal to the external bending moment as measured to the neutral axis at rupture point, but that these balancing moments do not differ materially from those measured to an axis obtained by dividing the sectional area into tensile and compressive stress areas which are in inverse proportion to the magnitude of their respective ultimate direct stresses.The advantage of these formulæ are important. It is possible to indicate with certainty the magnitude of the load which will cause rupture in a beam or a hook provided there is known the point of application or the effective arm of the load, the cross-section of the beam or hook, and the breaking strengths of the material when subjected to the different forms of direct loading.

Creep Relaxation of a Beam of General Cross Section Subjected to Mechanical and Thermal Loads

1978 ◽  
Vol 100 (4) ◽  
pp. 626-629 ◽  
Author(s):  
M. R. Eslami
Keyword(s):  
Cross Section ◽  
Thermal Load ◽  
Opposite Sign ◽  
Neutral Axis ◽  
Allowable Stress ◽  
Sectional Area ◽  
Lower Stress ◽  
Cross Sectional ◽  
The Cross ◽  
Mechanical Moment

Creep relaxation of a beam of general cross-sectional area subjected to mechanical and thermal load is obtained. Temperature is assumed to be a function of Z, the height of the beam, and the mechanical moment on the cross section M. The stress in the beam is obtained as a function of time. It is concluded that the point of zero stress shifts, and therefore, the neutral axis of the beam moves toward the lower stress magnitude portion of the cross section, and as time passes it sharply drops to a large stress of the opposite sign that for a large enough time will exceed the allowable stress, and therefore causes failure of the beam.

The Design and Simulation for a Novel Electroosmotic Micromixer

2006 ◽  
Author(s):  
Hongjun Song ◽  
Xie-Zhen Yin ◽  
Dawn J. Bennett
Keyword(s):  
Electric Field ◽  
Cross Section ◽  
Chemical Reactions ◽  
Electroosmotic Flow ◽  
Chaotic Advection ◽  
Microfluidic Systems ◽  
Mixing Effect ◽  
Passive Mixers ◽  
The Cross ◽  
External Forces

The analysis of fluid mixing in microfluidic systems is useful for many biological and chemical applications at the micro scale such as the separation of biological cells, chemical reactions, and drug delivery. The mixing of fluids is a very important factor in chemical reactions and often determines the reaction velocity. However, the mixing of fluids in microfluidics tends to be very slow, and thus the need to improve the mixing effect is a critical challenge for the development of the microfluidic systems. Micromixers can be classified into two types, active micromixers and passive micromixers. Passive micromixers depend on changing the structure and shape of microchannels in order to generate chaotic advection and to increase the mixing area. Thus, the mixing effect is enhanced without any help from external forces. Although passive micromixers have the advantage of being easily fabricated and requiring no external energy, there are also some disadvantages. For example, passive mixers often lack flexibility and power. Passive mixers rely on the geometrical properties of the channel shapes to induce complicated fluid particle trajectories thereby enhancing the mixing effect. On the other hand, active micromixers induce a time-dependent perturbation in the fluid flow. Active micromixers mainly use external forces for mixing including ultrasonic vibration, dielectrophoresis, magnetic force, electrohydrodynamic, and electroosmosis force. However, the complexity of their fabrication limits the application of active micromixers. In this paper we present a novel electroosmotic micromixer using the electroosmotic flow in the cross section to enhance the mixing effect. A DC electric field is applied to a pair of electrodes which are placed at the bottom of the channel. A transverse flow is generated in the cross section due to electroosmotic flow. Numerical simulations are investigated using a commercial software Fluent® which demonstrates how the device enhances the mixing effect. The mixing effect is increased when the magnitude of the electric field increased. The influences of Pe´clet number are also discussed. Finally, a simple fabrication using polymeric materials such as SU-8 and PDMS is presented.

Online Monitoring of Functional Electrical Properties in Aerosol Jet Printing Additive Manufacturing Process Using Shape-From-Shading Image Analysis

2017 ◽  
Vol 139 (10) ◽  
Author(s):  
Roozbeh (Ross) Salary ◽  
Jack P. Lombardi ◽  
Prahalad K. Rao ◽  
Mark D. Poliks
Keyword(s):  
Cross Section ◽  
Electrical Resistance ◽  
Online Monitoring ◽  
Shape From Shading ◽  
Sectional Area ◽  
Cross Sectional ◽  
Jet Printing ◽  
The Cross ◽  
Aerosol Jet Printing ◽  
Line Resistance

The goal of this research is online monitoring of functional electrical properties, e.g., resistance, of electronic devices made using aerosol jet printing (AJP) additive manufacturing (AM) process. In pursuit of this goal, the objective is to recover the cross-sectional profile of AJP-deposited electronic traces (called lines) through shape-from-shading (SfS) analysis of their online images. The aim is to use the SfS-derived cross-sectional profiles to predict the electrical resistance of the lines. An accurate characterization of the cross section is essential for monitoring the device resistance and other functional properties. For instance, as per Ohm’s law, the electrical resistance of a conductor is inversely proportional to its cross-sectional area (CSA). The central hypothesis is that the electrical resistance of an AJP-deposited line estimated online and in situ from its SfS-derived cross-sectional area is within 20% of its offline measurement. To test this hypothesis, silver nanoparticle lines were deposited using an Optomec AJ-300 printer at varying sheath gas flow rate (ShGFR) conditions. The four-point probes method, known as Kelvin sensing, was used to measure the resistance of the printed structures offline. Images of the lines were acquired online using a charge-coupled device (CCD) camera mounted coaxial to the deposition nozzle of the printer. To recover the cross-sectional profiles from the online images, three different SfS techniques were tested: Horn’s method, Pentland’s method, and Shah’s method. Optical profilometry was used to validate the SfS cross section estimates. Shah’s method was found to have the highest fidelity among the three SfS approaches tested. Line resistance was predicted as a function of ShGFR based on the SfS-estimates of line cross section using Shah’s method. The online SfS-derived line resistance was found to be within 20% of offline resistance measurements done using the Kelvin sensing technique.

scholarly journals Analytical Model of a Multi-Step Straightening Process for Linear Guideways Considering Neutral Axis Deviation

Symmetry ◽  
2018 ◽  
Vol 10 (8) ◽  
pp. 316 ◽  
Author(s):  
Yongquan Zhang ◽  
Hong Lu ◽  
He Ling ◽  
Yang Lian ◽  
Mingtian Ma
Keyword(s):  
Analytical Model ◽  
Cross Section ◽  
Predictive Accuracy ◽  
Neutral Axis ◽  
Longitudinal Stress ◽  
Linear Superposition ◽  
Element Analysis ◽  
Cross Sectional ◽  
The Cross ◽  
Sectional Shape

The cross-sectional shape of a linear guideway has been processed before the straightening process. The cross-section features influence not only the position of the neutral axis, but also the applied and residual stresses along the longitudinal direction, especially in a multi-step straightening process. This paper aims to present an analytical model based on elasto-plastic theory and three-point reverse bending theory to predict straightening stroke and longitudinal stress distribution during the multi-step straightening process of linear guideways. The deviation of the neutral axis is first analyzed considering the asymmetrical features of the cross-section. Owing to the cyclic loading during the multi-step straightening process, the longitudinal stress curves are then calculated using the linear superposition of stresses. Based on the cross-section features and the superposition of stresses, the bending moment is corrected to improve the predictive accuracy of the multi-step straightening process. Finite element analysis, as well as straightening experiments, have been performed to verify the applicability of the analytical model. The proposed approach can be implemented in the multi-step straightening process of linear guideways with similar cross-sectional shape to improve the straightening accuracy.

Two Secondary Effects in Bending of Slit Thin-Walled Tubes

1966 ◽  
Vol 33 (1) ◽  
pp. 75-78 ◽  
Author(s):  
F. P. J. Rimrott
Keyword(s):  
Cross Section ◽  
Circular Tube ◽  
Bending Moment ◽  
Approximate Equation ◽  
Neutral Axis ◽  
Secondary Effects ◽  
Theoretical Predictions ◽  
Thin Walled ◽  
Brazier Effect ◽  
Free Edges

During bending of a slit, thin-walled circular tube two secondary effects are observed to occur simultaneously. One, the so-called Brazier effect, occurs in thin-walled tubes generally when they are subjected to bending, and consists of an ovaling of the cross section. The second effect is a peculiarity of slit tubes only and manifests itself as an overlap of the free edges. The severity of both effects depends upon the location of the slit. The bending moment and the radial and tangential displacements have been determined as function of the curvature for four different slit locations with respect to the neutral axis. The value of the curvature at instability has also been derived. Subsequently an approximate equation has been obtained for the cantilever. The results of experiments on a cantilever are compared with the theoretical predictions.

Static Stress Redesign of Structures by Large Admissible Perturbations

2003 ◽  
Vol 127 (2) ◽  
pp. 122-129 ◽  
Author(s):  
Michael M. Bernitsas ◽  
Bhineka M. Kristanto
Keyword(s):  
Cross Section ◽  
Forced Response ◽  
Static Stress ◽  
Neutral Axis ◽  
Perturbation Equation ◽  
Cross Sectional ◽  
Structure Changes ◽  
Large Admissible Perturbations ◽  
The Cross ◽  
Outer Fiber

The LargeE Admissible Perturbation (LEAP) methodology is developed further to solve static stress redesign problems. The static stress general perturbation equation, which expresses the unknown nodal stresses of the objective structure in terms of the baseline structure stresses, is derived first. This equation depends on the redesign variables for each element or group of elements; namely, the cross-sectional area and moment of inertia, and the distance between the neutral axis and the outer fiber of the cross section. This equation preserves the shape of the cross section in the redesign process. LEAP enables the designer to redesign a structure to achieve specifications on modal properties, static displacements, forced response amplitudes, and static stresses. LEAP is implemented in code RESTRUCT which post-processes the FEA results of the baseline structure. Changes on the order of 100% in the above performance particulars and in redesign variables can be achieved without repetitive finite element (FE) analyses. Several numerical applications on a simple cantilever beam and an offshore tower are used to verify the LEAP algorithm for stress redesign.

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 Numerical simulation of cutting layer in internal corners milling

Mechanik ◽  
2019 ◽  
Vol 92 (7) ◽  
pp. 412-414
Author(s):  
Jan Burek ◽  
Rafał Flejszar ◽  
Barbara Jamuła
Keyword(s):  
Numerical Simulation ◽  
Numerical Model ◽  
Cross Section ◽  
Cross Sectional Area ◽  
Sectional Area ◽  
Cross Sectional ◽  
Cross Section Area ◽  
Section Area ◽  
The Cross ◽  
The Stability

The analytical and numerical model of the cross-section of the machined layer in the process of milling of concave rounding is presented. Simulation tests were carried out to determine the cross-sectional area of the cutting layer. A strategy has been developed that allows to increase the stability of the cross-section area of the cutting layer when the mill enters the inner corner area.

scholarly journals The Ovalisation of Steel Circular Hollow Sections under Bending

2018 ◽  
Vol 11 (1) ◽  
Author(s):  
Manahel Sh. Khalaf ◽  
Amer M. Ibrahim
Keyword(s):  
Cross Section ◽  
Local Buckling ◽  
Bending Moment ◽  
Thickness Ratio ◽  
Experimental Results ◽  
Experimental Program ◽  
Specimen Length ◽  
Specimen Cross Section ◽  
The Cross

This paper investigates the ovalisation behavior of the Steel Circular Hollow Sections (CHSs) when subjected to bending moment. The experimental program included testing of ten specimens in four groups in order to examine the influence of changing the diameter, thickness, length and the presence of openings on the ovalisation phenomenon of these specimens.The experimental results showed that the ovalisation of the specimen cross-section appears clearly when the diameter to thickness ratio (D/t) is ranging from 17 to 50, while the ovalisation of the specimens that have D/t ratio greater than 50 is very little or unclear because the instability of these specimens are controlled by the local buckling. In addition, the change of the specimen length and the presence of openings didn’t cause the cross-section ovalisation

Part II. The Flattening of Monocoque Cylinders

1938 ◽  
Vol 42 (328) ◽  
pp. 302-319
Keyword(s):  
Variational Method ◽  
Potential Energy ◽  
Cross Section ◽  
Radial Displacement ◽  
Bending Moment ◽  
Experimental Investigations ◽  
Pure Bending ◽  
Centre Line ◽  
Thin Walled ◽  
The Cross

It is known from both theoretical and experimental investigations that St. Venant's assumption on the constancy of the shape of the cross section of girders in pure bending does not hold true in case of thin-walled sections. The greater flexibility than calculated according to ordinary bending theory of initially curved tubes, as experimentally found by Professor Bantlin, was perfectly explained by Professor von Kármán in 1911 on the assumption of a flattening of the section.In 1927 Brazier with the aid of the variational method determined exactly that the shape of an originally circular thin-walled bent cylinder corresponding to the least potential energy is quasi elliptical and that the cross section of the cylinder, therefore, must flatten, even if the centre line of the cylinder was originally straight. In consequence of the flattening St. Venant's linear law for the curvature loses its validity and the curvature increases more rapidly than the bending moment. For a certain value of the curvature the bending moment is a maximum, and after this value was reached the curvature increases even if the applied moment remains unchanged or decreases, fulfilling thereby the criterion of instability. This instability occurs when the rate of flattening, i.e., the maximum radial displacement of any point of the circumference of the tube divided by the original radius of the tube, will equal 2/9.

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