Torsion of Uniform Rods With Particular Reference to Rods of Triangular Cross Section

1952 ◽  
Vol 19 (4) ◽  
pp. 554-557
Author(s):  
Henry Nuttall
Keyword(s):  
Incompressible Fluid ◽  
Cross Section ◽  
Viscous Incompressible Fluid ◽  
Torsional Rigidity ◽  
Isosceles Triangle ◽  
Shearing Stress ◽  
Torsion Problem ◽  
Approximate Evaluation ◽  
Triangular Cross Section ◽  
Hydrodynamic Analogy

Abstract A solution of the Saint-Venant torsion problem is presented which is alternative to that usually adopted. When the cross section has the shape of an isosceles triangle the method also provides a close and useful Rayleigh-Ritz solution. The torsional rigidity has been evaluated for a range of section proportions, and simple expressions for an approximate evaluation of the maximum shearing stress are provided. Use is made of the hydrodynamic analogy to extend the application of these solutions to the problem of the flow of a viscous incompressible fluid in a tube of triangular section.

Analysis of Twisting Stiffness for a Multifiber Composite Layer

1974 ◽  
Vol 41 (3) ◽  
pp. 658-662 ◽  
Author(s):  
C. W. Bert ◽  
S. Chang
Keyword(s):  
Cross Section ◽  
Least Squares Method ◽  
Rectangular Cross Section ◽  
Torsional Rigidity ◽  
Composite Layer ◽  
Circular Cross Section ◽  
Relaxation Method ◽  
Fiber Composites ◽  
Numerical Results ◽  
Torsion Problem

The twisting stiffness of a rectangular cross section consisting of a single row of solid circular cross-section fibers embedded in a matrix is analyzed. The problem is formulated as a Dirichlet torsion problem of a multielement region and solved by the boundary-point least-squares method. Numerical results for a single-fiber square cross section compare favorably with previous relaxation-method results. New numerical results for three and five-fiber composites suggest that the torsional rigidity of a multifiber composite can be approximated from the torsional rigidities of single and three-fiber models.

Torsional Stress Concentration in Angle and Square Tube Fillets

1950 ◽  
Vol 17 (4) ◽  
pp. 388-390
Author(s):  
J. H. Huth
Keyword(s):  
Stress Concentration ◽  
Cross Section ◽  
Torsional Rigidity ◽  
Relaxation Method ◽  
Torsional Stress ◽  
Shearing Stress ◽  
Thin Walled ◽  
Two Sides

Abstract This paper points out the wide variation in the results of previous investigations into the stress concentration at the fillets of angle sections subjected to uniform torsion. The relaxation method is applied and new results are given (not in agreement with previous results) for both angle sections and thin-walled square tube sections. These results are believed to be within about 4 per cent of the correct values, and they cover a complete range of fillets of all sizes. Also, the maximum shearing stress and torsional rigidity are given for a prismatical bar whose cross section is formed by a circular quadrant tangent to two sides of a square. It is pointed out that the stress concentration in angle sections with generous fillets may be lowered considerably by rounding off the outside corner in such a way as to keep the thickness of the section everywhere approximately constant.

scholarly journals The torsion and flexure of shafting with keyways or cracks

1932 ◽  
Vol 138 (836) ◽  
pp. 607-634 ◽  
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Torsional Rigidity ◽  
Circular Cross Section ◽  
Transverse Load ◽  
Torsion Problem ◽  
Circular Section ◽  
Physical Conditions ◽  
The Cross ◽  
Straight Lines

The object of the paper is to investigate the properties of shafts of circular cross-section into which keyways or slits have been cut, first when subjected to torsion, and second when bent by a transverse load at one end. The torsion problem for similar cases has been treated by several writers. Filon has worked out an approximation to the case of a circular section with one or two keyways ; in his method the boundary of the cross-section was a nearly circular ellipse and the boundaries of the keyways were confocal hyperbolas. In particular he considered the case when the hyperbola degenerated into straight lines starting from the foci. The solution for a circular section with one keyway in the form of an orthogonal circle has been obtained by Gronwall. In each case the solution has been obtained by the use of a conformal trans­formation and this method is again used in this paper, the transformations used being ρ = k sn 2 t . ρ = k 1/2 sn t , ρ = k 1/2 sn 1/2 t where ρ = x + iy , t = ξ + i η. No work appears to have been done on the flexure problem which is here worked out for several cases of shafts with slits. 2. Summary of the Problems Treated . We first consider the torsional properties of shafts with one and with two indentations. In particular cases numerical results have been obtained for the stresses at particular points and for the torsional rigidity. The results for one indentation and for two indentations of the same width and approximately the same depth have been compared. We next consider the solution of the torsion problem for one, two or four equal slits of any depth from the surface towards the axis. The values of the stresses have not been worked out in these cases since the stress is infinite at the bottom of the slits. This in stress occurs because the physical conditions are not satisfied at the bottom of the slits, but as had been pointed out by Filon this does not affect the validity of the values of the torsional rigidity. We compare the effect on the torsional rigidity of the shaft of one, two and four slits of the same depth in particular cases. We also compare the results for one slit with those obtained by Filon by another method, and find very good agreement which is illustrated by a graph. The reduction in torsional rigidity due to a semicircular keyway is compared with that due to a slit of approximately the same depth. Finally the distortion of the cross-sections at right angles to the planes is investigated, and in this, several interesting and perhaps unexpected features appear. The relative shift of the two sides of the slits is calculated in several cases.

Torsion of a Circular Compound Bar With Imperfect Interface

2000 ◽  
Vol 68 (6) ◽  
pp. 955-958 ◽  
Author(s):  
T. Chen ◽  
I. S. Weng
Keyword(s):  
Cross Section ◽  
Series Solution ◽  
Torsional Rigidity ◽  
Jump Condition ◽  
Imperfect Interface ◽  
Warping Function ◽  
Torsion Problem ◽  
Perfect Bonding ◽  
Circular Compound ◽  
Circular Bar

The Saint-Venant torsion problem of a circular cylinder reinforced by a nonconcentric circular bar of a different material with an imperfect interface is studied. Conformal mapping together with a Laurent series expansion are employed to analyze the problem. The jump condition in either the warping function or the shear traction, characterizing the imperfect interface, is simulated in the transformed domain in an exact manner. Unlike the problem with perfectly bonded interface, the series solution has to be resolved by a truncation. Numerical illustrations are provided for the torsional rigidity of the cross section. In the case of perfect bonding case, our results agree with that reported in Muskhelishvili.

scholarly journals Saint-Venant’s torsion of thin-walled nonhomogeneous open elliptical cross section

2021 ◽  
Vol 11 (5) ◽  
pp. 151-158
Author(s):  
István Ecsedi ◽  
Ákos József Lengyel ◽  
Attila Baksa ◽  
Dávid Gönczi
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Torsional Rigidity ◽  
Elliptical Cross Section ◽  
Curvilinear Coordinates ◽  
Torsion Problem ◽  
Cross Sectional ◽  
Elliptical Cross ◽  
Thin Walled ◽  
The One

This paper deals with the Saint-Venant’s torsion of thin-walled isotropic nonhomogeneous open elliptical cross section whose shear modulus depends on the one of the curvilinear coordinates which define the cross-sectional area of the beam. The approximate solution of torsion problem is obtained by variational method. The usual simplification assumptions are used to solve the uniform torsion problem of bars with thin-walled elliptical cross-sections. An example illustrates the application of the derived formulae of shearing stress and torsional rigidity.

scholarly journals Колебания неосесимметричного цилиндра в заполненной жидкостью полости, совершающей вращательные осцилляции

2020 ◽  
Vol 46 (15) ◽  
pp. 43
Author(s):  
В.Д. Щипицын
Keyword(s):  
Incompressible Fluid ◽  
Layer Thickness ◽  
Cross Section ◽  
Cylindrical Cavity ◽  
High Speed ◽  
Viscous Incompressible Fluid ◽  
Stokes Layer ◽  
High Speed Video ◽  
Video Registration ◽  
Cylindrical Solid

The behavior of a cylindrical solid of nonaxisymmetric cross section in a horizontal cylindrical cavity filled with a viscous incompressible fluid under rotational vibrations is experimentally investigated. The effect of the vibrational suspension of a heavy nonaxisymmetric cylinder near the bottom of the vibrating cavity was found and studied at a distance comparable with the Stokes layer thickness. The character of oscillations of the cylinder and its interaction to the wall of the cavity is studied by high-speed video registration of process.

The Acceleration of Thin Cylindrical Bodies in a Viscous Fluid

1978 ◽  
Vol 45 (1) ◽  
pp. 1-6 ◽  
Author(s):  
H. J. Lugt ◽  
H. J. Haussling
Keyword(s):  
Viscous Fluid ◽  
Incompressible Fluid ◽  
Cross Section ◽  
Viscous Incompressible Fluid ◽  
Cylindrical Body ◽  
Elliptic Cross Section ◽  
Trailing Edges ◽  
Elliptic Cross

The start from rest of a thin cylindrical body with elliptic cross section in a viscous incompressible fluid is studied numerically for various acceleration models. Force and moment coefficients are computed. The role of the starting vortices behind the leading and trailing edges in the generation of lift is investigated.

Extinction cross section of an arbitrary body in a viscous incompressible fluid

1995 ◽  
Vol 52 (2) ◽  
pp. 1857-1865 ◽  
Author(s):  
Scott A. Wymer ◽  
Akhlesh Lakhtakia ◽  
Renata S. Engel
Keyword(s):  
Incompressible Fluid ◽  
Cross Section ◽  
Viscous Incompressible Fluid ◽  
Extinction Cross Section ◽  
Arbitrary Body
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