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.

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.

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.

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 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.

Corrosion-Induced Concrete Cracking, Steel-Concrete Bond Loss, and Mechanical Degradation of Steel Bars

2014 ◽  
Vol 919-921 ◽  
pp. 1760-1770 ◽  
Author(s):  
Fu Jian Tang ◽  
Gen Da Chen ◽  
Wei Jian Yi
Keyword(s):  
Cross Section ◽  
Crack Width ◽  
Surface Profile ◽  
Concrete Surface ◽  
Cross Sectional Area ◽  
Mechanical Degradation ◽  
Sectional Area ◽  
Cross Sectional ◽  
Steel Bars ◽  
The Cross

This study experimentally investigated corrosion-induced deterioration in reinforced concrete (RC) structures: concrete cover cracking, steel-concrete bond loss, and mechanical degradation of corroded steel bars. Pullout and RC beam specimens were prepared, subjected to accelerated corrosion in a wet sand bath, and tested under loading. A 3D laser scan was employed to measure the surface profile of corroded steel bars and determine the corrosion effect on the distribution of residual cross section area. The crack width on the concrete surface was sampled randomly and analyzed statistically. Corrosion reduced the bond strength between steel bars and concrete, particularly in the form of corrosion-induced number and width of cracks. Both the yield and ultimate strengths depended upon the critical cross sectional area of steel bars, whereas the elongation changed with the cross section distribution over the length of the steel bars. Corrosion also changed the distribution of the cross sectional area of steel bars. The crack width on the concrete surface can be well represented by a normal distribution regardless of corrosion levels.

Analysis of the Cross-Sectional Area of the Adductor Longus Tendon

2007 ◽  
Vol 35 (6) ◽  
pp. 996-999 ◽  
Author(s):  
Eric J. Strauss ◽  
Kirk Campbell ◽  
Joseph A. Bosco
Keyword(s):  
Cross Section ◽  
Muscle Fibers ◽  
Cross Sectional Area ◽  
Sectional Area ◽  
Cross Sectional ◽  
Sectional Anatomy ◽  
Longus Muscle ◽  
The Cross ◽  
Adductor Longus ◽  
Muscle Origin

Background Strain injury to the adductor longus muscle is a common cause of groin pain in athletes and generally occurs in the proximal portion of the muscle, near its origin from the anterior aspect of the pubis. The composition and cross-sectional anatomy of this muscle's origin has not been previously described. Hypothesis We hypothesize that the adductor longus muscle origin is composed mainly of muscle fibers and that the tendon composes only a small part of the cross section at the origin of the muscle. Study Design Descriptive laboratory study. Methods We harvested 42 adductor longus muscles from 28 cadavers and measured the cross-sectional dimensions of the tendon with microcalipers. Next, we determined the relative contributions of the tendon and muscle fibers to the cross-sectional anatomy of the muscle using optical scanning. These 2 sets of measurements were obtained at 3 locations: at the muscle origin and 1.0 and 2.0 cm distal to the origin. Results The average length and width of the tendon was 11.6 and 3.7 mm, respectively, at the origin. The average cross-sectional areas of the tendon were 49.3, 27.9, and 25.7 mm2 at points 0.0, 1.0, and 2.0 cm from its origin, respectively. The origin of the adductor longus muscle was composed of 37.9% tendon and 62.1% muscle tissue. At 1.0 cm from the origin, the percentage of tendon decreased to 34%. At 2.0 cm from the origin, the tendon composed 26.7% of the cross section. Conclusion The cross-sectional area of the tendon of the adductor longus muscle is relatively small. The muscle origin is composed predominantly of direct attachment of muscle fibers. Clinical Relevance Knowledge of the cross-sectional anatomy of the adductor longus muscle at its origin may help clinicians better understand the complex nature of injuries in this area.

Scanning esophageal impedance probe for measurement of luminal cross section.

1979 ◽  
Vol 236 (5) ◽  
pp. E545
Author(s):  
D A Mary ◽  
P J North ◽  
J N Hunt
Keyword(s):  
Cross Section ◽  
Cross Sectional Area ◽  
Sectional Area ◽  
Dynamic Changes ◽  
Cross Sectional ◽  
Variable Voltage ◽  
Electrode Assemblies ◽  
Impedance Probe ◽  
The Cross ◽  
Esophageal Impedance

A scanning esophageal probe for measuring luminal cross section is described. Current is injected into electrode assemblies so that a variable voltage output directly proportional to interelectrode impedance and inversely proportional to cross-sectional area of the medium around the electrodes may be measured. The device is capable of measuring the cross section of glass cylinders. It was used in one esophagus to measure the cross-sectional area of different sizes of swallowed bolus. The probe offers a safe and repeatable method of studying dynamic changes in luminal dimensions of the esophagus.

A New Method of Measuring the Cross-Sectional Area of Connective Tissue Structures

1988 ◽  
Vol 110 (2) ◽  
pp. 104-109 ◽  
Author(s):  
N. G. Shrive ◽  
T. C. Lam ◽  
E. Damson ◽  
C. B. Frank
Keyword(s):  
Cross Section ◽  
Rectangular Cross Section ◽  
Cross Sectional Area ◽  
Sectional Area ◽  
Connective Tissues ◽  
Maximum Width ◽  
Cross Sectional ◽  
Elliptical Cross ◽  
The Cross

There appears to be no generally accepted method of measuring in-situ the cross-sectional area of connective tissues, particularly small ones, before mechanical testing. An instrument has therefore been devised to measure the cross-sectional area of one such tissue, the rabbit medial collateral ligament, directly and nondestructively. However, the methodology is general and could be applied to other tissues with appropriate changes in detail. The concept employed in the instrument is to measure the thickness of the tissue as a function of position along the width of the tissue. The plot obtained of thickness versus width position is integrated to provide the cross-sectional area. This area is accurate to within 5 percent, depending mainly on alignment of the instrument and pre-load of the ligament. Results on the mid-substance of the rabbit medial collateral ligaments are repeatable and reproducible. Values of maximum width and thickness are less variable than those obtained with a vernier caliper. The measured area is considerably less than that estimated assuming rectangular cross-section and slightly less than that estimated on the assumption of elliptical cross-section.

Static Stress Redesign of Structures by Large Admissible Perturbations

2003 ◽  
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 LargE 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 the 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 FE analyses. Several numerical applications on a simple cantilever beam and an offshore tower are used to verify the LEAP algorithm for stress redesign.

Sign in / Sign up

Export Citation Format

Share Document