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.

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.

Elastic Torsion in the Presence of Initial Axial Stress

1950 ◽  
Vol 17 (4) ◽  
pp. 383-387
Author(s):  
J. N. Goodier
Keyword(s):  
Cross Section ◽  
Axial Stress ◽  
Torsional Rigidity ◽  
Torsional Stiffness ◽  
Lateral Buckling ◽  
Initial Tension ◽  
Open Section ◽  
Thin Walled ◽  
The Cross

Abstract The torsional rigidity, for small elastic torsion, of bars of thin-walled open section, is, in general, altered by initial tension, compression, bending, or other axial stress. This appears in the increase of torsional stiffness of strips due to tension, in the decrease to zero in open sections which buckle torsionally as columns, and also has an influence on lateral buckling of beams. This paper contains an extension of the Saint Venant solution for ordinary torsion to the problem of torsion in the presence of initial axial stress with any distribution on the cross section. The results are confirmed by tests, and validate the intuitively derived formulas which are in use.

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.

Unsymmetrical Bending of Beams: A Matrix Formulation

1996 ◽  
Vol 24 (2) ◽  
pp. 144-149 ◽  
Author(s):  
T. Tarnai
Keyword(s):  
Normal Stress ◽  
Cross Section ◽  
Inertia Tensor ◽  
Shearing Stress ◽  
Deflection Curve ◽  
Matrix Formulation ◽  
The Matrix ◽  
The Subject ◽  
Thin Walled ◽  
Bending Of Beams

In this note the bending of uniform straight beams of unsymmetrical cross-section is investigated by matrices. The importance of the matrix of the inertia tensor of the cross-section is shown. Matrix formulae are presented for the normal stress, the flexural shearing stress in the case of thin-walled open sections, and the deflection curve in the case of small displacements. Matrix formulation makes this problem easy to handle; and so it provides an aid in teaching the subject.

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.

First and Second Order Elastoplastic Analyses of Thin-Walled Metal Members using Generalized Beam Theory

2018 ◽  
Author(s):  
Miguel Abambres
Keyword(s):  
Finite Element ◽  
Stainless Steel ◽  
Cross Section ◽  
Beam Theory ◽  
Second Order ◽  
Flow Rule ◽  
Non Linear ◽  
Thin Walled ◽  
Shell Finite Element ◽  
Generalized Beam Theory

Original Generalized Beam Theory (GBT) formulations for elastoplastic first and second order (postbuckling) analyses of thin-walled members are proposed, based on the J2 theory with associated flow rule, and valid for (i) arbitrary residual stress and geometric imperfection distributions, (ii) non-linear isotropic materials (e.g., carbon/stainless steel), and (iii) arbitrary deformation patterns (e.g., global, local, distortional, shear). The cross-section analysis is based on the formulation by Silva (2013), but adopts five types of nodal degrees of freedom (d.o.f.) – one of them (warping rotation) is an innovation of present work and allows the use of cubic polynomials (instead of linear functions) to approximate the warping profiles in each sub-plate. The formulations are validated by presenting various illustrative examples involving beams and columns characterized by several cross-section types (open, closed, (un) branched), materials (bi-linear or non-linear – e.g., stainless steel) and boundary conditions. The GBT results (equilibrium paths, stress/displacement distributions and collapse mechanisms) are validated by comparison with those obtained from shell finite element analyses. It is observed that the results are globally very similar with only 9% and 21% (1st and 2nd order) of the d.o.f. numbers required by the shell finite element models. Moreover, the GBT unique modal nature is highlighted by means of modal participation diagrams and amplitude functions, as well as analyses based on different deformation mode sets, providing an in-depth insight on the member behavioural mechanics in both elastic and inelastic regimes.

scholarly journals Analytical solution for torsion of cylindrical orthotropic annular wedge-shaped bars reinforced by thin shells

2021 ◽  
Author(s):  
István Ecsedi ◽  
Attila Baksa
Keyword(s):  
Analytical Solution ◽  
Cross Section ◽  
Analytical Method ◽  
Torsional Rigidity ◽  
Circular Ring ◽  
Thin Shells ◽  
Elastic Wedge ◽  
Curved Boundary ◽  
Cylindrically Orthotropic ◽  
Boundary Surfaces

AbstractThis paper deals with the Saint-Venant torsion of elastic, cylindrically orthotropic bar whose cross section is a sector of a circular ring shaped bar. The cylindrically orthotropic homogeneous elastic wedge-shaped bar strengthened by on its curved boundary surfaces by thin isotropic elastic shells. An analytical method is presented to obtain the Prandtl’s stress function, torsion function, torsional rigidity and shearing stresses. A numerical example illustrates the application of the developed analytical method.

Sign in / Sign up

Export Citation Format

Share Document