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Chapter 20

Bending

Biegung
Biegung
Pure bending occurs when a prismatic member possesses a plane of symmetry and experiences couples of equal magnitudes acting within that plane. This type ...
Symmetrischer Stab in der Biegung
Symmetrischer Stab in der Biegung
Consider a prismatic member subjected to two couples, equal in magnitude but in opposite directions, acting within the symmetric plane of the member. A ...
Verformungen in einem symmetrischen Bauteil beim Biegen
Verformungen in einem symmetrischen Bauteil beim Biegen
Consider the deformations of a symmetric prismatic member subjected to equal and opposite couples. As the member bends uniformly, the lines on the wider ...
Biegespannung
Biegespannung
Consider a bending moment where a symmetric member endures stress within the elastic limit. The longitudinal stress can be expressed using Hooke's ...
Verformungen in einem Querschnitt
Verformungen in einem Querschnitt
When a material is subjected to uniaxial stress, the material undergoes elongation or contraction in the direction of the applied stress. At the same ...
Biegen von Material: Problemlösung
Biegen von Material: Problemlösung
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 ...
Biegen von Bauteilen aus mehreren Werkstoffen
Biegen von Bauteilen aus mehreren Werkstoffen
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 ...
Spannungskonzentrationen
Spannungskonzentrationen
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 ...
Plastische Verformungen
Plastische Verformungen
For pure bending, when maximum stress exceeds the yield strength of the member's material, it undergoes plastic deformation. The strain at any point ...
Stäbe aus elastoplastischem Material
Stäbe aus elastoplastischem Material
Consider a member made up of an elastoplastic material with a rectangular cross-section. Within the elastic limit, the stress distribution across the ...
Plastische Verformungen von Stäben mit einer einzigen Symmetrieebene
Plastische Verformungen von Stäben mit einer einzigen Symmetrieebene
Consider a member experiencing plastic deformation due to bending and having one plane of symmetry. The stresses are uniformly distributed above and below ...
Eigenspannungen beim Biegen
Eigenspannungen beim Biegen
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 ...
Exzentrische axiale Belastung in einer Symmetrieebene
Exzentrische axiale Belastung in einer Symmetrieebene
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 ...
Unsymmetrische Biegung
Unsymmetrische Biegung
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 ...
Unsymmetrische Biegung - Winkel der neutralen Achse
Unsymmetrische Biegung - Winkel der neutralen Achse
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 ...
Allgemeiner Fall der exzentrischen axialen Belastung
Allgemeiner Fall der exzentrischen axialen Belastung
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 ...
Biegen von gekrümmten Bauteilen - Dehnungsanalyse
Biegen von gekrümmten Bauteilen - Dehnungsanalyse
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 ...
Biegen von gekrümmten Bauteilen - Neutrale Oberfläche
Biegen von gekrümmten Bauteilen - Neutrale Oberfläche
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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