A New Unified Strength of Materials Solution for Stresses in Curved Beams and Rings

1992 ◽  
Vol 114 (2) ◽  
pp. 231-237 ◽  
Author(s):  
C. Bagci
Keyword(s):  
Cross Sections ◽  
Solution Method ◽  
Normal Force ◽  
Neutral Axis ◽  
Curved Beams ◽  
Strength Of Materials ◽  
Special Cases ◽  
Elasticity Solutions ◽  
Simplified Solution ◽  
Force Equilibrium

Presently existing strength of materials solutions for stresses in curved beams use an incorrect normal force equilibrium condition to define neutral axis location, and to reach a simplified solution, which neglects the curvature effect on stresses due to normal force. This article presents a new but a most general form of the strength of materials solution for determining tangential normal stresses in curved beams, including reductions to special cases. The neutral axis phenomenon is clarified and experimentally verified. Several numerical examples are included, some of which offer photoelastic experimental results, where results predicted by the exact elasticity solution, method of the article, Winkler’s theory, and the conventional simplified method are compared. The hook, diametrically loaded cut, and full ring applications are included. It is shown that simplified theory leads to very large errors. Results by the method offered are very reliable with small errors which are comparable with those of exact elasticity solutions. Stress and deflection analyses of curved beams with varying thicknesses of cross-sections by exact elasticity solutions are given in a separate article [6].

Exact Elasticity Solutions for Stresses and Deflections in Curved Beams and Rings of Exponential and T-Sections

1991 ◽  
Author(s):  
Cemil Bagci
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Plane Stress ◽  
Numerical Results ◽  
Neutral Axis ◽  
Curved Beams ◽  
Equilibrium Stress ◽  
Different Boundary Conditions ◽  
Stress Functions ◽  
Elasticity Solutions

Abstract Exact elasticity solutions for stresses and deflections (displacements) in curved beams and rings of varying thicknesses are developed using polar elasticity and state of plane stress. Basic forms of differential equations of equilibrium, stress functions, and differential equations of compatibility are given. They are solved to develop expressions for radial, tangential, and shearing stresses for moment, force, and combined loadings. Neutral axis location for each type of loading is determined. Expressions for displacements are developed utilizing strain-displacement relationships of polar elasticity satisfying boundary conditions on displacements. In case of full rings stresses are as in curved beams with properly defined moment loading, but displacements differ satisfying different boundary conditions. The developments for constant thicknesses are used to develop solutions for curved beams and rings with T-sections. Comparative numerical results are given.

A unified relaxed approach easing the practical application of a paradox in curved beams

2020 ◽  
Vol 234 (22) ◽  
pp. 4535-4542 ◽  
Author(s):  
HMA Abdalla ◽  
D Casagrande ◽  
A Strozzi
Keyword(s):  
Finite Element ◽  
Stress Reduction ◽  
Normal Force ◽  
Bending Moment ◽  
Neutral Axis ◽  
Mathematical Approach ◽  
Bending Stress ◽  
Practical Application ◽  
Curved Beams ◽  
Closed Form Solutions

The paper deals with an arising paradox in curved beams subjected to bending moment and normal force. This paradox consists in the fact that by laterally removing material from section zones close to the neutral axis, not only an obvious reduction of the beam mass can be obtained, but also an unexpected, though technically negligible, reduction of the bending stress. It has recently been shown that the relaxation of the demanding achievement of a concurrent mass and stress reduction may practically lead to interesting results, yet solvable numerically. In this paper we show that, under some mild assumptions, a remarkable simplification of the intrados stress functional is obtained. Hence, a unified approximate mathematical approach based on linearization is developed for the derivation of analytical closed-form solutions for the lateral grooved zones. A practical example of the application of the relaxed paradox to optimize a crane hook subjected to bending and normal force is illustrated and compared to finite element forecasts.

Exact Elasticity Solutions for Stresses and Deflections in Curved Beams and Rings of Exponential and T-Sections

1993 ◽  
Vol 115 (3) ◽  
pp. 346-358 ◽  
Author(s):  
C. Bagci
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Plane Stress ◽  
Numerical Results ◽  
Neutral Axis ◽  
Curved Beams ◽  
Equilibrium Stress ◽  
Different Boundary Conditions ◽  
Stress Functions ◽  
Elasticity Solutions

Exact elasticity solutions for stresses and deflections (displacements) in curved beams and rings of varying thicknesses are developed using polar elasticity and state of plane stress. Basic forms of differential equations of equilibrium, stress functions, and differential equations of compatibility are given. They are solved to develop expressions for radial, tangential, and shearing stresses for moment, force, and combined loadings. Neutral axis location for each type of loading is determined. Expressions for displacements are developed utilizing strain-displacement relationships of polar elasticity satisfying boundary conditions on displacements. In case of full rings stresses are as in curved beams with properly defined moment loading, but displacements differ satisfying different boundary conditions. The developments for constant thicknesses are used to develop solutions for curved beams and rings with T-sections. Comparative numerical results are given.

A PSO-Based Method for Tracing the Motion of Neutral Axis Plane of Asymmetric Hull Cross-Sections and its Application

2018 ◽  
Author(s):  
Chenfeng Li ◽  
Chao Gao ◽  
Xueqian Zhou ◽  
Sen Dong ◽  
Peng Fu ◽  
...  
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
International Association ◽  
Random Search ◽  
Two Dimensions ◽  
Neutral Axis ◽  
Force Vector ◽  
Hull Girder ◽  
Vector Equilibrium ◽  
Force Equilibrium

The Smith’s method is stipulated by the International Association of Classification Societies in the Common Structure Rules as a standard method for estimating ultimate/residual strength of hull girder in both intact and damaged conditions. However, for the latter case where the effective hull cross-section is asymmetric and the neutral axis of damaged cross-section not only translates but also rotates, the additional force vector equilibrium also needs to be applied so as to determine the neutral axis plane. The commonly adopted iterative methods for the two-force-equilibrium problem do not always converge for the desired accuracy. This paper proposes a Particle Swarm Optimization based iteration method to trace the motion of the neutral axis plane of asymmetric cross sections. The translation and rotation of the neutral axis are taken as the two dimensions of particles in the model, and the force equilibrium error and the force vector equilibrium error are the objective functions. The neutral axis is determined by performing a random search within the entire range of possible position of neutral axis. The proposed method has been implemented and validated for the case of the DOW’s 1/3 frigate model, the analysis of efficiency and accuracy shows that the method performs in general better than traditional ones.

Stress concentration factors for the torsion of curved beams of arbitrary cross-section

2006 ◽  
Vol 220 (12) ◽  
pp. 1709-1726 ◽  
Author(s):  
R E Cornwell
Keyword(s):  
Finite Element ◽  
Stress Concentration ◽  
Cross Section ◽  
Cross Sections ◽  
Shear Stresses ◽  
Curved Beams ◽  
Finite Element Implementation ◽  
Out Of Plane ◽  
Concentration Factors ◽  
Stress Concentration Factors

There are numerous situations in machine component design in which curved beams with cross-sections of arbitrary geometry are loaded in the plane of curvature, i.e. in flexure. However, there is little guidance in the technical literature concerning how the shear stresses resulting from out-of-plane loading of these same components are effected by the component's curvature. The current literature on out-of-plane loading of curved members relates almost exclusively to the circular and rectangular cross-sections used in springs. This article extends the range of applicability of stress concentration factors for curved beams with circular and rectangular cross-sections and greatly expands the types of cross-sections for which stress concentration factors are available. Wahl's stress concentration factor for circular cross-sections, usually assumed only valid for spring indices above 3.0, is shown to be applicable for spring indices as low as 1.2. The theory applicable to the torsion of curved beams and its finite-element implementation are outlined. Results developed using the finite-element implementation agree with previously available data for circular and rectangular cross-sections while providing stress concentration factors for a wider variety of cross-section geometries and spring indices.

The Theory of Curved Beams

1946 ◽  
Vol 13 (4) ◽  
pp. A294-A296
Author(s):  
G. C. Best
Keyword(s):  
Neutral Axis ◽  
Curved Beams ◽  
Slide Rule ◽  
Special Formula ◽  
Satisfactory Accuracy ◽  
Orderly Fashion ◽  
Approximate Integration

Abstract In this paper, the theory of curved beams is developed by a somewhat different procedure from that customarily employed. Deflections at the centroid are first assumed and then loads and stresses resulting from these deflections are estimated. This process works out in a somewhat more orderly fashion than the conventional development. Throughout, all measurements are to the centroidal axis rather than to the neutral axis. Final results are presented in such a form that satisfactory accuracy may be obtained from slide-rule computations and approximate integration. Hence the procedure is applicable to any section, it being unnecessary first to develop a special formula for each different section. An illustrative example is given. The theory is extended to cover the case of unsymmetrical bending of curved beams. The effects of torsion, which will probably also occur in the generalized case, are not treated. These can be superimposed upon stresses due to bending.

scholarly journals Dynamic modeling of tunnel survey spatiotemporal data

2014 ◽  
Vol 20 (2) ◽  
pp. 354-375
Author(s):  
Xiaolong Li ◽  
Jiansi Yang ◽  
Bingxuan Guo ◽  
Hua Liu ◽  
Jun Hua
Keyword(s):  
Survey Data ◽  
Cross Section ◽  
Cross Sections ◽  
3D Modeling ◽  
3D Model ◽  
Three Dimensional ◽  
Spatiotemporal Data ◽  
Excavation Process ◽  
Special Cases ◽  
Time Stamps

Currently, for tunnels, the design centerline and design cross-section with time stamps are used for dynamic three-dimensional (3D) modeling. However, this approach cannot correctly reflect some qualities of tunneling or some special cases, such as landslips. Therefore, a dynamic 3D model of a tunnel based on spatiotemporal data from survey cross-sections is proposed in this paper. This model can not only playback the excavation process but also reflect qualities of a project typically missed. In this paper, a new conceptual model for dynamic 3D modeling of tunneling survey data is introduced. Some specific solutions are proposed using key corresponding technologies for coordinate transformation of cross-sections from linear engineering coordinates to global projection coordinates, data structure of files and database, and dynamic 3D modeling. A 3D tunnel TIN model was proposed using the optimized minimum direction angle algorithm. The last section implements the construction of a survey data collection, acquisition, and dynamic simulation system, which verifies the feasibility and practicality of this modeling method.

MOMENTS IN REINFORCED CONCRETE STRUCTURES UNDER BENDING WITH TORSION

2021 ◽  
Vol 95 (3) ◽  
pp. 27-46
Author(s):  
VL.I. KOLCHUNOV ◽  
◽  
A.I. DEMYANOV ◽  
M.V. PROTCHENKO ◽  
◽  
...  
Keyword(s):  
Reinforced Concrete ◽  
Computational Model ◽  
Cross Sections ◽  
Neutral Axis ◽  
Reinforced Concrete Structures ◽  
The Third ◽  
Straight Line ◽  
The Family ◽  
Third Stage ◽  
Concrete Blocks

The moments in reinforced concrete during bending with torsion were determined, the new first hypothesis of linear deformations and its filling of the diagram during bending with torsion for the analytical second functional as a function of three functions - an exponent, a straight line and a parabola curve. A simple new method is found (from the family of mesh methods) and a summed function of additional deplanation is proposed. The new second hypothesis of angular deformations and its filling of the diagram in reinforced concrete during bending with torsion is constructed. The analytical first general undefined functional is a function of functions, as well as transitions, operations between functions. At the same time, a spatial triple integral of arguments from longitudinal deformations for the first hypothesis was obtained, as well as the third and fourth functionals (indefinite and definite) from moments (bending and twisting) with the projection of the coefficients of the diagram of "deformations - stresses" of compressed concrete and the filling coefficients of the diagrams of compressed concrete for their shoulders to the neutral axis for a field of small squares. The bending and torque moments from the compressed area of concrete and working reinforcement are determined (folded for their levels or expanded into algebraic functions from the synthesis of the computational model of reinforced concrete blocks). In this case, we have new functionals (from the first to the fourth functional), proposed hypotheses (first and second), as well as cross sections (from small squares) to a spatial crack. There are also jumps (cracks) lateral, normal, etc., from the first - third stage of average deformations of concrete and working reinforcement.

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