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Chapter 20

Bending

Pliage
Pliage
Pure bending occurs when a prismatic member possesses a plane of symmetry and experiences couples of equal magnitudes acting within that plane. This type ...
Membre symétrique en flexion
Membre symétrique en flexion
Consider a prismatic member subjected to two couples, equal in magnitude but in opposite directions, acting within the symmetric plane of the member. A ...
Déformations d’un élément symétrique en flexion
Déformations d’un élément symétrique en flexion
Consider the deformations of a symmetric prismatic member subjected to equal and opposite couples. As the member bends uniformly, the lines on the wider ...
Contrainte de flexion
Contrainte de flexion
Consider a bending moment where a symmetric member endures stress within the elastic limit. The longitudinal stress can be expressed using Hooke's ...
Déformations d’une section transversale
Déformations d’une section transversale
When a material is subjected to uniaxial stress, the material undergoes elongation or contraction in the direction of the applied stress. At the same ...
Pliage de la matière : résolution de problèmes
Pliage de la matière : résolution de problèmes
Consider two metallic pipes having an inner radii of 1.5 cm and 1 cm, respectively, and an outer radii of 1.8 cm. If both pipes can withstand a maximum ...
Flexion d’éléments constitués de plusieurs matériaux
Flexion d’éléments constitués de plusieurs matériaux
Consider a member of two different materials that have the same cross-sectional area. The equation of stress for such a member is expressed in terms of ...
Concentrations de contraintes
Concentrations de contraintes
The equation for stress for a member under pure bending having a plane of symmetry and a uniform cross-section assumes that the stress is evenly ...
Déformations plastiques
Déformations plastiques
For pure bending, when maximum stress exceeds the yield strength of the member's material, it undergoes plastic deformation. The strain at any point ...
Éléments en matériau élastoplastique
Éléments en matériau élastoplastique
Consider a member made up of an elastoplastic material with a rectangular cross-section. Within the elastic limit, the stress distribution across the ...
Déformations plastiques des éléments avec un seul plan de symétrie
Déformations plastiques des éléments avec un seul plan de symétrie
Consider a member experiencing plastic deformation due to bending and having one plane of symmetry. The stresses are uniformly distributed above and below ...
Contraintes résiduelles en flexion
Contraintes résiduelles en flexion
If a sufficiently large bending moment is applied to an elastoplastic member, plastic zones will develop in the member. Now, if the bending moment is ...
Charge axiale excentrique dans un plan de symétrie
Charge axiale excentrique dans un plan de symétrie
Eccentric axial loading refers to the application of an axial load that is not aligned with the centroidal axis of the member. Consider a member having a ...
Flexion asymétrique
Flexion asymétrique
Unsymmetric bending occurs when the bending moment is not acting along the plane of the symmetry of the member or if the member does not possess any plane ...
Flexion asymétrique - Angle de l’axe neutre
Flexion asymétrique - Angle de l’axe neutre
Consider a member with a vertical plane of symmetry subjected to bending couples in a plane at an angle θ with respect to the vertical axis of the ...
Cas général de charge axiale excentrique
Cas général de charge axiale excentrique
Consider a member subjected to equal and opposite eccentric forces. These forces are applied at a horizontal distance of a and a vertical distance of b ...
Flexion d’éléments courbes - Analyse de déformation
Flexion d’éléments courbes - Analyse de déformation
Consider a curved member having a transverse section symmetric with the y-axis. Its upper and lower surfaces intersect with xy-planes along arcs of ...
Flexion d’éléments courbes - Surface neutre
Flexion d’éléments courbes - Surface neutre
For a curved member with a uniform cross-section, the strain equation along the section shows that it varies non-linearly with the distance from the ...
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