A platform for research: civil engineering, architecture and urbanism
A platform for research: civil engineering, architecture and urbanism
Application of the Saint‐Venant theory to thin‐walled sections warping
The Saint‐Venant theory proposes an exact solution to the elastic equations for beams including warping strains due to shear force and torsion. It has been at the centre of recent developments in the field of beam theory: normal stress may at first be determined as if plane sections would remain plane but under torsion and shear force, restrain warping introduces secondary normal stress.
For thin‐walled sections, the analysis of warping due to torsion is conventional and uses the concept of sectorial area. However, the problem of shear flows due to shear force is generally solved by using an energy approach in which warping only appears indirectly. By introducing a static moment function, similar to the sectorial function used for torsion, this paper proposes to take explicit account of the warping of thin‐walled sections under the effect of shear force. In the case of sections with straight walls, it is convenient to use third degree polynomials. The proposed method can easily be calculated with a spreadsheet and may be extended to any type of arch, in particular those which consist of B‐spline functions or NURBS.
Different examples are analyzed.
Application of the Saint‐Venant theory to thin‐walled sections warping
The Saint‐Venant theory proposes an exact solution to the elastic equations for beams including warping strains due to shear force and torsion. It has been at the centre of recent developments in the field of beam theory: normal stress may at first be determined as if plane sections would remain plane but under torsion and shear force, restrain warping introduces secondary normal stress.
For thin‐walled sections, the analysis of warping due to torsion is conventional and uses the concept of sectorial area. However, the problem of shear flows due to shear force is generally solved by using an energy approach in which warping only appears indirectly. By introducing a static moment function, similar to the sectorial function used for torsion, this paper proposes to take explicit account of the warping of thin‐walled sections under the effect of shear force. In the case of sections with straight walls, it is convenient to use third degree polynomials. The proposed method can easily be calculated with a spreadsheet and may be extended to any type of arch, in particular those which consist of B‐spline functions or NURBS.
Different examples are analyzed.
Application of the Saint‐Venant theory to thin‐walled sections warping
Vié, Dominique (author)
ce/papers ; 4 ; 495-504
2021-09-01
10 pages
Article (Journal)
Electronic Resource
English
| Springer Verlag | 2019
De Saint-Venant Equations Experimentally Verified
| ASCE | 2021
Numerical Solution of Saint-Venant Equations
| ASCE | 2021