Torsional Shear Stress in Prismatic Beams With Arbitrary Cross-Sections Using Finite Element Method

Tran, Dang-Bao

doi:10.14311/cej.2021.02.0030

Cited by 4 publications

(3 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Amulu & Ezeagu [10] investigated the effect of combined actions of torsion moments, bending moments and shear forces in reinforced concrete beams with concrete compressive strength of 30N/mm 2 ; the ultimate torsion moments, bending moments, and shear forces of the beams were determined experimentally. Tran [11] used isoparametric eight-noded quadrilateral elements in order to improve Gruttmann's isoparametric four-noded quadrilateral elements; MATLAB was the language for programming the numerical method.…”

Section: Cross-sectional Analysis Of Beams Subjected To Saint-venant ...mentioning

confidence: 99%

Cross-sectional Analysis of Beams Subjected to Saint-Venant Torsion Using the Green’s Theorem and the Finite Difference Method

Fogang¹

2022

Preprint

View full text Add to dashboard Cite

This paper presents an approach to the elastic analysis of beams subjected to Saint-Venant torsion using Green’s theorem and the finite difference method (FDM). The Saint-Venant torsion of beams, also called free torsion or unrestrained torsion, is characterized by the absence of axial stresses due to torsion; only shear stresses are developed. The solution to this torsion problem consists of finding a stress function that satisfies the governing equation and the boundary conditions. The FDM is an approximate method for solving problems described with differential or partial differential equations; it does not involve solving differential equations, equations are formulated with values at selected nodes of the structure. In this paper, the beam’s cross-section was discretized with a two-dimensional grid and additional nodes were introduced at the boundaries. The introduction of additional nodes allowed us to apply the governing equations at boundary nodes and satisfy the boundary conditions. Beam’s cross-sections of various shapes and openings were analyzed using this model; shear stresses, torsion constant, and warping were determined. Furthermore, beams with thin-walled closed sections, single-cell or multiple-cell, were analyzed using the stress function whereby the linear distribution of the shear stresses over the thickness was considered; closed-form solutions for shear stresses and torsion constant were presented. For rectangular cross-sections, the results obtained in this study showed good agreement with the exact results, and the accuracy was increased through a grid refinement. For thin-walled closed sections the values of torsion constant and maximal shear stress were higher than those calculated using Bredt’s analysis; moreover, regarding the closed-form solution, the maximal shear stress in the cross-section does not necessarily occur at the position with the smallest thickness.

show abstract

Section: Cross-sectional Analysis Of Beams Subjected To Saint-venant ...mentioning

confidence: 99%

Cross-sectional Analysis of Beams Subjected to Saint-Venant Torsion Using the Green’s Theorem and the Finite Difference Method

Fogang¹

2022

Preprint

View full text Add to dashboard Cite

show abstract

“…Ritz [3] and Trefftz [4] used energy methods whereby the stress function was approximately determined from the minimum condition of the strain energy of the twisted beam. Tran [5] used isoparametric eight-noded quadrilateral elements in order to improve Gruttmann's isoparametric four-noded quadrilateral elements. Fogang [6] used finite difference method for the torsional analysis of beams with arbitrary cross-sections; a grid network was considered for the cross-section and additional nodes were introduced at the boundaries.…”

Section: Introductionmentioning

confidence: 99%

Saint-Venant Torsion of Beams with Rectangular Cross-Section Using the Fourier Analysis

Fogang

2024

Preprint

View full text Add to dashboard Cite

This paper presents an approach to the analysis of beams with rectangular cross-sections subjected to Saint-Venant torsion using the Fourier analysis, body forces being not considered. The Saint-Venant torsion of beams, also called free torsion or unrestrained torsion, is characterized by the absence of axial stresses due to torsion; only shear stresses are developed. The solution to this torsion problem consists of finding the Prandtl stress function that satisfies the governing equation and the boundary conditions, the governing equation being such that the Laplacian of the stress function has a constant value within the cross-section. In this paper, Fourier sine series was utilized to describe the constant value of the above mentioned Laplacian, while double sine series or simple sine series was utilized to describe the Prandtl stress function. Closed-form solutions in form of infinite series were derived for shear stresses, torsional constant and warping function. Those solutions were identical to the exact solutions.

show abstract

“…Amulu & Ezeagu [11] investigated the effect of combined actions of torsion moments, bending moments and shear forces in reinforced concrete beams with concrete compressive strength of 30N/mm 2 ; the ultimate torsion moments, bending moments, and shear forces of the beams were determined experimentally. Tran [12] used isoparametric eight-noded quadrilateral elements in order to improve Gruttmann's isoparametric four-noded quadrilateral elements; MATLAB was the language for programming the numerical method.…”

Section: Introductionmentioning

confidence: 99%

Cross-sectional Analysis of Beams Subjected to Saint-Venant Torsion Using the Green’s Theorem and the Finite Difference Method

Fogang¹

2022

Preprint

View full text Add to dashboard Cite

This paper presents an approach to the elastic analysis of beams subjected to Saint-Venant torsion using Green’s theorem and the finite difference method (FDM). The Saint-Venant torsion of beams, also called free torsion or unrestrained torsion, is characterized by the absence of axial stresses due to torsion; only shear stresses are developed. The solution to this torsion problem consists of finding a stress function that satisfies the governing equation and the boundary conditions. The FDM is an approximate method for solving problems described with differential or partial differential equations; it does not involve solving differential equations, equations are formulated with values at selected nodes of the structure. In this paper, the beam’s cross-section was discretized using a two-dimensional grid and additional nodes were introduced at the boundaries. The introduction of additional nodes allowed us to apply the governing equations at boundary nodes and satisfy the boundary conditions. Beam’s cross-sections of various shapes and openings were analyzed using this model; shear stresses, torsion constant, and warping were determined. Furthermore, beams with thin-walled closed sections, single-cell or multiple-cell, were analyzed using the stress function whereby the linear distribution of the shear stresses over the thickness was considered; closed-form solutions for shear stresses and torsion constant were presented. For rectangular cross-sections, the results obtained in this study showed good agreement with the exact results, and the accuracy was increased through a grid refinement. For thin-walled closed sections it was noted that the maximal shear stress in the midline occurs at the position with the smallest thickness, which is in agreement with Bredt’s analysis, but the maximal shear stress in the cross-section did not necessarily occur at that position; moreover, the values of torsion constant were higher than those calculated using Bredt’s analysis

show abstract

Torsional Shear Stress in Prismatic Beams With Arbitrary Cross-Sections Using Finite Element Method

Cited by 4 publications

References 18 publications

Cross-sectional Analysis of Beams Subjected to Saint-Venant Torsion Using the Green’s Theorem and the Finite Difference Method

Cross-sectional Analysis of Beams Subjected to Saint-Venant Torsion Using the Green’s Theorem and the Finite Difference Method

Saint-Venant Torsion of Beams with Rectangular Cross-Section Using the Fourier Analysis

Cross-sectional Analysis of Beams Subjected to Saint-Venant Torsion Using the Green’s Theorem and the Finite Difference Method

Contact Info

Product

Resources

About