Bending

Bend referred to in the technical mechanics, a mechanical change in the geometry of slender components (beams or arcs ) or thin components ( trays or plates). By dimensional reduction of the original 3D problem, the description of the change in geometry is approximated by a 1D theory and in the case of ( bowls or plates) by a 2D theory in the case of (beams or arcs). With the determination of the bending deformation of the center line ( elastic line ) when using a 1D theory or central surface ( 2D theory ), can be calculated using the kinematic laws of the respective bending theories of deformation and stress state at any point of the component. Typical of bending are changes in curvature of the center line or the center area by static and dynamic stresses with respect to the curvature, which had the part in the unstressed state. Such curvatures result in bending stresses in each point and bending moments with respect to the center line or central area.

Depending on whether the deflection is small, moderate or large compared with the cross-sectional dimensions (bar and bends) and the thickness ( trays or plates ), various 1-D or 2-D bending theories must be used to provide a physical and mathematical sufficient approximation of the original 3D problem to get. The most popular 1D bending theory is the Bernoulli beams. It is valid if the deflections of the originally straight center line are small compared to the cross-sectional dimensions. For validity of the Kirchhoff plate theory, the bending of the originally flat central surface must be small compared to the plate thickness. The plate theory according to von Kármán is valid if the deflection is in the same order of magnitude as the plate thickness. Similar differences exist for beams, arches and shells.

Straight bending: bending a bar or a curved only in one plane in the direction of the arc of the major axes of the cross section.

Oblique bending: bending of a beam or a curved only in one plane sheet in a different direction of the principal axes.

The bending line of a beam for the linear theory is applicable to can be determined on the basis of the composite stress superposition of bending standard cases. For standard bending cases there are corresponding tables.

With a claimed to just bend component, there is a stress-free surface that separates the claimed to train and pressure regions of the part of each other. The stresses are greatest at the points that are furthest away from the stress-free plane.

A loaded in bending component can use two mechanisms fail ( beam theory ):

Bending

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