The beam theory delivers values for deflection and stress of a pipe depending on wall thickness, material, medium, insulation, fixation and span.
In the pipes cross section we only take into consideration the tensile stress and the compression stress, which are in equilibrium with the local bending moment. Shear tension, responsible for vertical force balance, is neglected. Tensile stress (elongation), responsible for horizontal force balance, can be neglected for reasonable short pipe span. The load is free of torsion. The load lies vertical on the pipe axis. Fibres on the concave side are compressed. On the convex side fibres are stressed. In between the neutral fibres. Neutral fibres span the horizontal plain of symmetry. The deflection of the pipe is the distance of the neutral fibres from their location without load. Navier [Navier 1833, page 43 ff., see literature] approaches the bending line in every point by a circle.
Théorie des barres
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In the pipes cross section we only take into consideration the tensile stress and the compression stress, which are in equilibrium with the local bending moment. Shear tension, responsible for vertical force balance, is neglected. Tensile stress (elongation), responsible for horizontal force balance, can be neglected for reasonable short pipe span. The load is free of torsion. The load lies vertical on the pipe axis. Fibres on the concave side are compressed. On the convex side fibres are stressed. In between the neutral fibres. Neutral fibres span the horizontal plain of symmetry. The deflection of the pipe is the distance of the neutral fibres from their location without load. Navier [Navier 1833, page 43 ff., see literature] approaches the bending line in every point by a circle.
Théorie des barres
allemand  C. Meyer |
anglais C. Meyer |
You like that explanation? Feel invited to contribute a translation to any other language. If you like your name will be mentioned in the table and the document. Contact us: Mentions légales
| Littérature | 1833 Navier Résumé des leçons sur l´application de la méchanique | Bibliothèque national de France at http://gallica.bnf.fr |