## ::Bending

### ::concepts

**Bending**::cfrac Alpha::theory Partial::mathrm Stress::equation Where::moment Section::beams

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In applied mechanics, **bending** (also known as **flexure**) characterizes the behavior of a slender structural element subjected to an external load applied perpendicularly to a longitudinal axis of the element.

The structural element is assumed to be such that at least one of its dimensions is a small fraction, typically 1/10 or less, of the other two.<ref name=Boresi>Boresi, A. P. and Schmidt, R. J. and Sidebottom, O. M., 1993, **Advanced mechanics of materials**, John Wiley and Sons, New York.</ref> When the length is considerably longer than the width and the thickness, the element is called a beam. For example, a closet rod sagging under the weight of clothes on clothes hangers is an example of a beam experiencing bending. On the other hand, a shell is a structure of any geometric form where the length and the width are of the same order of magnitude but the thickness of the structure (known as the 'wall') is considerably smaller. A large diameter, but thin-walled, short tube supported at its ends and loaded laterally is an example of a shell experiencing bending.

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*,<ref name=Libai/> the *bending of beams*,<ref name=Boresi/> the *bending of plates*,<ref name=Timo>Timoshenko, S. and Woinowsky-Krieger, S., 1959, **Theory of plates and shells**, McGraw-Hill.</ref> the *bending of shells*<ref name=Libai>Libai, A. and Simmonds, J. G., 1998, **The nonlinear theory of elastic shells**, Cambridge University Press.</ref> and so on.

**Bending sections**

Intro Quasistatic bending of beams Dynamic bending of beams Quasistatic bending of plates Dynamic bending of plates See also References External links

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