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.

Measurements of Torsional Stiffness Changes and Instability Due to Tension, Compression, and Bending

1953 ◽  
Vol 20 (4) ◽  
pp. 553-560
Author(s):  
H. L. Engel ◽  
J. N. Goodier
Keyword(s):  
Nonlinear Behavior ◽  
Torsional Stiffness ◽  
Open Section ◽  
Thin Walled

Abstract The measurements reported verify theoretically predicted effects of tension, compression, and bending, on the torsional stiffness of uniform bars of thin-walled open section. Related modes of buckling and types of nonlinear behavior in torsion are indicated analytically and exhibited in tests, some of these being apparently new.

Torsional and Flexural Buckling of Bars of Thin-Walled Open Section Under Compressive and Bending Loads

1942 ◽  
Vol 9 (3) ◽  
pp. A103-A107 ◽  
Author(s):  
J. N. Goodier
Keyword(s):  
Lateral Buckling ◽  
Flexural Buckling ◽  
Open Section ◽  
Bending Loads ◽  
Thin Walled ◽  
General Section ◽  
Observed Behavior

Abstract The observed behavior of torsionally weak columns in buckling by twisting rather than, or as well as, bending is analyzed in this paper on the basis of a hypothesis due to Wagner. The theory is simplified, and extended to the general section, where results simpler than some already obtained by Kappus are given. It is further extended to bars, restrained by flexible sheets, and bars with constrained axes of rotation. Wagner’s hypothesis is applied to the problem of lateral buckling, where it yields the accepted theory for symmetrical sections, but indicates results of novel form for unsymmetrical cases. Similar results are obtained in the problem of eccentric thrust, whatever the section.

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.

Design variation of thin-walled composite beam cross-section properties

2016 ◽  
Vol 12 (3) ◽  
pp. 558-576 ◽  
Author(s):  
Aníbal J.J. Valido ◽  
João Barradas Cardoso
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Laminated Composite ◽  
Adjoint System ◽  
Design Sensitivity ◽  
Content Type ◽  
Design Elements ◽  
Thin Walled ◽  
The Cross ◽  
Cross Section Geometry

Purpose The purpose of this paper is to present a design sensitivity analysis continuum formulation for the cross-section properties of thin-walled laminated composite beams. These properties are expressed as integrals based on the cross-section geometry, on the warping functions for torsion, on shear bending and shear warping, and on the individual stiffness of the laminates constituting the cross-section. Design/methodology/approach In order to determine its properties, the cross-section geometry is modeled by quadratic isoparametric finite elements. For design sensitivity calculations, the cross-section is modeled throughout design elements to which the element sensitivity equations correspond. Geometrically, the design elements may coincide with the laminates that constitute the cross-section. Findings The developed formulation is based on the concept of adjoint system, which suffers a specific adjoint warping for each of the properties depending on warping. The lamina orientation and the laminate thickness are selected as design variables. Originality/value The developed formulation can be applied in a unified way to open, closed or hybrid cross-sections.

scholarly journals Computation of Thin-Walled Cross-Section Resistance to Local Buckling with the Use of the Critical Plate Method

2016 ◽  
Vol 62 (2) ◽  
pp. 229-264 ◽  
Author(s):  
A. Szychowski
Keyword(s):  
Cross Section ◽  
Critical Stress ◽  
Analytical Calculation ◽  
Local Buckling ◽  
Stability Loss ◽  
Longitudinal Stress ◽  
Plate Method ◽  
Thin Walled ◽  
The Cross ◽  
Elastically Restrained

Abstract Thin-walled bars currently applied in metal construction engineering belong to a group of members, the cross-section res i stance of which is affected by the phenomena of local or distortional stability loss. This results from the fact that the cross-section of such a bar consists of slender-plate elements. The study presents the method of calculating the resistance of the cross-section susceptible to local buckling which is based on the loss of stability of the weakest plate (wall). The “Critical Plate” (CP) was identified by comparing critical stress in cross-section component plates under a given stress condition. Then, the CP showing the lowest critical stress was modelled, depending on boundary conditions, as an internal or cantilever element elastically restrained in the restraining plate (RP). Longitudinal stress distribution was accounted for by means of a constant, linear or non-linear (acc. the second degree parabola) function. For the critical buckling stress, as calculated above, the local critical resistance of the cross-section was determined, which sets a limit on the validity of the Vlasov theory. In order to determine the design ultimate resistance of the cross-section, the effective width theory was applied, while taking into consideration the assumptions specified in the study. The application of the Critical Plate Method (CPM) was presented in the examples. Analytical calculation results were compared with selected experimental findings. It was demonstrated that taking into consideration the CP elastic restraint and longitudinal stress variation results in a more accurate representation of thin-walled element behaviour in the engineering computational model.

Collapse of Thin-Walled Elliptical Tubes for High Values of Major-to-Minor Axis Ratio

1993 ◽  
Vol 115 (4A) ◽  
pp. 432-440 ◽  
Author(s):  
C. Ribreau ◽  
S. Naili ◽  
M. Bonis ◽  
A. Langlet
Keyword(s):  
Contact Pressure ◽  
Cross Section ◽  
External Pressure ◽  
Straight Line Segment ◽  
Minor Axis ◽  
Cross Sectional ◽  
Axis Ratio ◽  
Straight Line ◽  
Thin Walled ◽  
The Cross

The topic of this study concerns principally representative models of some elliptical thin-walled anatomic vessels and polymeric tubes under uniform negative transmural pressure p (internal pressure minus external pressure). The ellipse’s ellipticity ko, defined as the major-to-minor axis ratio, varies from 1 up to 10. As p decreases from zero, at first the cross-section becomes somewhat oval, then the opposite sides touch in one point at the first-contact pressure pc. If p is lowered beneath pc, the curvature of the cross-section at the point of contact decreases until it becomes zero at the osculation pressure or the first line-contact pressure p1. For p<p1, the contact occurs along a straight-line segment, the length of which increases as p decreases. The pressures pc and p1 are determined numerically for various values of the wall thickness of the tubes. The nature of contact is especially described. The solution of the related nonlinear, two-boundary-values problem is compared with previous experimental results which give the luminal cross-sectional area (from two tubes), and the area of the mid-cross-section (from a third tube).

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.

Structural bionic design for thin-walled cylindrical shell against buckling under axial compression

2011 ◽  
Vol 225 (11) ◽  
pp. 2619-2627 ◽  
Author(s):  
D Xing ◽  
W Chen ◽  
J Ma ◽  
L Zhao
Keyword(s):  
Cylindrical Shell ◽  
Axial Compression ◽  
Cross Section ◽  
Cylindrical Shells ◽  
High Load ◽  
Vascular Bundles ◽  
Bionic Design ◽  
Load Bearing ◽  
Thin Walled ◽  
The Cross

In nature, bamboo develops an excellent structure to bear nature forces, and it is very helpful for designing thin-walled cylindrical shells with high load-bearing efficiency. In this article, the cross-section of bamboo is investigated, and the feature of the gradual distribution of vascular bundles in bamboo cross-section is outlined. Based on that, a structural bionic design for thin-walled cylindrical shells is presented, of which the manufacturability is also taken into consideration. The comparison between the bionic thin-walled cylindrical shell and a simple hollow one with the same weight showed that the load-bearing efficiency was improved by 44.7 per cent.

Effects of Cross-Section Ovalization of Subsea Thin-Walled Bends Under In-Plane Bending

2010 ◽  
Author(s):  
Ranil Banneyake ◽  
Ayman Eltaher ◽  
Paul Jukes
Keyword(s):  
Cross Section ◽  
Computational Cost ◽  
Straight Pipe ◽  
Limit States ◽  
Element Analysis ◽  
High Tendency ◽  
Thin Walled ◽  
Plane Bending ◽  
The Cross ◽  
The Impact

Ovalization of the cross-section of bends under in-plane bending (a.k.a. Brazier effect) is a known phenomenon caused by the longitudinal stress acting on the cross-section as the pipe bends. Besides its tendency to induce stresses in the bend above what is predicted using simple beam theory, excessive cross-section ovalization is particularly critical to subsea pipes, as it can lead to collapse of the pipe under external pressure. Also, being in a plastic regime may cause the bend material to ratchet and undergo excessive strains under cyclic operational loads, especially under high-pressure high-temperature (HPHT) conditions. Ovalization normally results in local increase of stresses and could lead to failure of the bend before the bend globally reaches its limiting capacity. The offshore industry standards and design codes address the impact of initial ovality in straight pipes, but their applicability to bends is not clear. Therefore, this paper presents an investigation into the increased tendency of thin-walled bends to ovalize, and the effect of bend cross-section ovalization on their stiffness and yielding and collapse limit states, with emphasis on offshore applications. Due to the lack of analytical solutions for the bend response taking into account cross-section ovalization, finite element analysis (FEA) is used in this study. Predictions of the bend models are compared with those of straight pipe models and predictions of models of the bend made of beam elements (with pipe section) are compared with those of models made of brick /shell elements. The increased tendency of thin-walled bends to ovalize compared to straight pipes is investigated (e.g. 100 times in the linear range), and the impact and significance of ovalization in bends are assessed (e.g., stress increase of the order of 35% has been observed in some example situations). Also discussed in the paper is the selection of proper element specifications in order to accurately capture the ovalization response while keeping the computational cost manageable. Recommendations as to how to account for ovalization effects are presented. This paper helps to gain a better understanding of the response of subsea thin-walled bends under in-plane bending and their comparatively high tendency to ovalize compared to straight pipe, and emphasizes the significance of local effects such as cross-section ovalization, the overlooking of which may result in a significant underestimation of involved stresses and strains.

scholarly journals Primary Response Assessment Method for Concept Design of Monotonous Thin-Walled Structures

10.14311/750 ◽  
2005 ◽  
Vol 45 (4) ◽  
Author(s):  
V. Zanic ◽  
P. Prebeg
Keyword(s):  
Cross Section ◽  
Response Assessment ◽  
Assessment Method ◽  
Primary Response ◽  
Concept Design ◽  
Fem Model ◽  
Feasibility Assessment ◽  
Thin Walled Structures ◽  
Thin Walled ◽  
The Cross

A concept design methodology for monotonous, tapered thin-walled structures (wing/fuselage/ship/bridge) is presented including modules for: model generation; loads; primary (longitudinal) and secondary (transverse) strength calculations; structural feasibility (buckling/fatigue/ultimate strength criteria); design optimization modules based on ES/GA/FFE; graphics. A method for primary strength calculation is presented in detail. It provides the dominant response field for design feasibility assessment. Bending and torsion of the structure are modelled with the accuracy required for concept design. A ‘2.5D-FEM’ model is developed by coupling a 1D-FEM model along the ‘monotonity’ axis and a 2D-FEM model(s) transverse to it. The shear flow and stiffness characteristics of the cross-section for bending and pure/restrained torsion are given, based upon the warping field of the cross-section. Examples: aircraft wing and ship hull. 

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