Stress Analysis of a Helical Coil

1963 ◽  
Vol 30 (1) ◽  
pp. 122-126 ◽  
Author(s):  
Irving Stein
Keyword(s):  
Exact Solution ◽  
Stress Analysis ◽  
Cross Section ◽  
Small Angle ◽  
Rectangular Cross Section ◽  
Helical Coil ◽  
Torsional Stress ◽  
Stress Problem

The solution for the torsional-stress problem in a small-angle helical coil of rectangular cross section is derived. The exact solution is then approximated for validity at small coil indices. This work complements the solution of Gohner,2 which is valid at larger coil indices.

Torsion of Curved Beams of Rectangular Cross Section

1952 ◽  
Vol 19 (1) ◽  
pp. 49-53
Author(s):  
H. L. Langhaar
Keyword(s):  
Exact Solution ◽  
Cross Section ◽  
Approximation Method ◽  
Rectangular Cross Section ◽  
Circular Cross Section ◽  
Curved Beams ◽  
Previously Treated

Abstract Recently, W. Freiberger obtained an exact solution of the problem of uniform torsion of a segment of a ring of circular cross section. This paper presents a solution of the problem for the rectangular cross section. O. Göhner previously treated this case by an approximation method.

Characterization of TEMPO-oxidized cellulose nanofibers in aqueous suspension by small-angle X-ray scattering

2014 ◽  
Vol 47 (2) ◽  
pp. 788-798 ◽  
Author(s):  
Ying Su ◽  
Christian Burger ◽  
Benjamin S. Hsiao ◽  
Benjamin Chu
Keyword(s):  
Cross Section ◽  
Small Angle ◽  
Structural Information ◽  
Rectangular Cross Section ◽  
Aqueous Suspension ◽  
Cellulose Nanofibers ◽  
Weighted Average ◽  
X Ray ◽  
X Ray Scattering ◽  
Ray Scattering

Cellulose nanofibers, extracted from wood pulps using the (2,2,6,6-tetramethylpiperidine-1-yl)oxyl (TEMPO)-mediated oxidation method, are low-cost, sustainable and high-performance materials with potential usage in many applications. The structural information of these cellulose nanofibers in aqueous suspension was characterized by synchrotron small-angle X-ray scattering (SAXS). A simplified ribbon model having a near rectangular cross section was found to give the best fit to the SAXS results. The analytical expression of the ribbon model also led to a higher calculation efficiency compared with the more conventional parallelepiped model. The extracted structural information included the cross-section size and size distribution of the cellulose nanofibers. For example, for nanofibers prepared from the dried pulp of the maritime pine, the size-weighted averages of thickness and width were 3.2 and 12.7 nm, respectively, and the corresponding standard deviations were 2.2 and 5.5 nm, respectively. The scattering results of the size-weighted average of the nanofiber width are also consistent with those determined directly from transmission electron microscopy.

Vibrations and Waves in Elastic Bars of Rectangular Cross Section

1960 ◽  
Vol 27 (1) ◽  
pp. 152-158 ◽  
Author(s):  
R. D. Mindlin ◽  
E. A. Fox
Keyword(s):  
Exact Solution ◽  
Cross Section ◽  
Rectangular Cross Section ◽  
Modes Of Vibration

An exact solution of the equations of elasticity is found for a family of modes of vibration, or waves, in an infinite bar of rectangular cross section for certain ratios of width to depth. The solution is composed of coupled dilatational and equivoluminal waves and the four faces of the bar are free of traction.

Stress Concentration Factors in Angled Flexural Members of Rectangular Cross-Section

1989 ◽  
Vol 111 (4) ◽  
pp. 490-491 ◽  
Author(s):  
F. M. A. Siddiqui ◽  
J. W. Beseler
Keyword(s):  
Stress Concentration ◽  
Stress Analysis ◽  
Cross Section ◽  
Rectangular Cross Section ◽  
Finite Element Program ◽  
Flexural Members ◽  
Reentrant Corner ◽  
Element Program ◽  
Concentration Factors ◽  
Stress Concentration Factors

The results of stress analysis of angled members subjected to pure flexure are presented. The stress analysis was performed using the ANSYS finite element program. Stress concentration factors varying from 1.25 to 2.5 can be expected at the reentrant corner of the member depending on the ratio of the fillet radius to the width and the deviating angle.

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