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Pure bending occurs only under a constant bending moment (M) since the shear force (V), which is equal to , has to be equal to zero. In reality, a state of pure bending does not practically exist, because such a state needs an absolutely weightless member. The state of pure bending is an approximation made to derive formulas.
In the absence of a qualifier, the term bending is ambiguous because bending can occur locally in all objects. Therefore, to make the usage of the term more precise, engineers refer to a specific object such as; the bending of rods, [2] the bending of beams, [1] the bending of plates, [3] the bending of shells [2] and so on.
Note that this equation implies that pure bending (of positive sign) will cause zero stress at the neutral axis, positive (tensile) stress at the "top" of the beam, and negative (compressive) stress at the bottom of the beam; and also implies that the maximum stress will be at the top surface and the minimum at the bottom. This bending stress ...
Values for the flexural strength measured with four-point bending will be significantly lower than with three-point bending., [7] Compared with three-point bending test, this method is more suitable for strength evaluation of butt joint specimens. The advantage of four-point bending test is that a larger portion of the specimen between two ...
Deformation of a thin plate highlighting the displacement, the mid-surface (red) and the normal to the mid-surface (blue) The Kirchhoff–Love theory of plates is a two-dimensional mathematical model that is used to determine the stresses and deformations in thin plates subjected to forces and moments.
Simple model for transpression: strike-slip zone with an additional and simultaneous shortening across the zone.Also induces vertical uplift. In geology, transpression is a type of strike-slip deformation that deviates from simple shear because of a simultaneous component of shortening perpendicular to the fault plane.
Orientations of the line perpendicular to the mid-plane of a thick paperback book under bending. The Timoshenko–Ehrenfest beam theory was developed by Stephen Timoshenko and Paul Ehrenfest [1] [2] [3] early in the 20th century.
The last terms, involving second derivatives, are the flexural (bending) strains. They involve the curvatures. They involve the curvatures. These zero terms are due to the assumptions of the classical plate theory, which assume elements normal to the mid-plane remain inextensible and line elements perpendicular to the mid-plane remain normal to ...