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In solid mechanics, a bending moment is the reaction induced in a structural element when an external force or moment is applied to the element, causing the element to bend. [ 1 ] [ 2 ] The most common or simplest structural element subjected to bending moments is the beam .
In molecular biology, an axoneme, also called an axial filament, is the microtubule-based cytoskeletal structure that forms the core of a cilium or flagellum. [ 1 ] [ 2 ] Cilia and flagella are found on many cells , organisms , and microorganisms , to provide motility.
Stress resultants are simplified representations of the stress state in structural elements such as beams, plates, or shells. [1] The geometry of typical structural elements allows the internal stress state to be simplified because of the existence of a "thickness'" direction in which the size of the element is much smaller than in other directions.
The bending moment applied to the beam also has to be specified. The rotation φ {\displaystyle \varphi } and the transverse shear force Q x {\displaystyle Q_{x}} are not specified. Clamped beams : The displacement w {\displaystyle w} and the rotation φ {\displaystyle \varphi } are specified to be zero at the clamped end.
Shear and Bending moment diagram for a simply supported beam with a concentrated load at mid-span. Shear force and bending moment diagrams are analytical tools used in conjunction with structural analysis to help perform structural design by determining the value of shear forces and bending moments at a given point of a structural element such as a beam.
An influence line for a given function, such as a reaction, axial force, shear force, or bending moment, is a graph that shows the variation of that function at any given point on a structure due to the application of a unit load at any point on the structure. An influence line for a function differs from a shear, axial, or bending moment diagram.
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The starting point is the relation from Euler-Bernoulli beam theory = Where is the deflection and is the bending moment. This equation [7] is simpler than the fourth-order beam equation and can be integrated twice to find if the value of as a function of is known.