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Encyclopedia > Bending
Figure 1. A side view of a simply supported beam (top) bending under a distributed lateral load (bottom).
Figure 2. The internal forces and the axial stress distribution across the cross-section of a beam in bending.

In engineering mechanics, bending (also known as flexure) characterizes the behavior of a structural element subjected to a lateral load. A structural element subjected to bending is known as a beam. A closet rod sagging under the weight of clothes on clothes hangers is an example of a beam experiencing bending. Image File history File links A simply supported beam before and after the application of a uniform lateral load. ... The internal forces and the cross-sectional stress distribution in a beam in bending. ... Engineering mechanics is a branch of the physical sciences which looks to understand the actions and reactions of bodies at rest or in motion. ... The structure of a thing is how the parts of it relate to each other, how it is put together. This contrast with process, which is how the thing works; but process requires a viable structure. ... Look up element in Wiktionary, the free dictionary. ... Load is what is carried, or a force. ... A statically determinate beam, bending under an evenly distributed load. ... Wall closet in a residential house in the U.S. It is common for a mirror to be placed on the inside of a closet door. ... [[ Deflection happens when an object hits a plane surface In physics In physics deflection is the event where an object collides and bounces against a plane surface. ... Wire (top) and wooden (bottom) clothes hangers A clothes hanger, or coat hanger, is a device in the shape of human shoulders designed to facilitate the hanging of a coat, jacket, sweater, shirt, blouse or dress in a manner that prevents wrinkles, with a lower bar for the hanging of...

Bending produces reactive forces inside a beam as the beam attempts to accommodate the flexural load: in the case of the beam in Figure 1, the material at the top of the beam is being compressed while the material at the bottom is being stretched. There are three notable internal forces caused by lateral loads (shown in Figure 2): shear parallel to the lateral loading, compression along the top of the beam, and tension along the bottom of the beam. These last two forces form a couple or moment as they are equal in magnitude and opposite in direction. This bending moment produces the sagging deformation characteristic of members experiencing bending. In physics, a force is defined as a rate of change of momentum (Newtonian definition). ... Shear stress is a stress state where the shape of a material tends to change (usually by sliding forces -- torque by transversely-acting forces) without particular volume change. ... Compression in material science, physics or structural engineering, is the stress state of materials where the volume tends to decrease (compaction). ... Tension is a reaction force applied by a stretched string (rope or a similar object) on the objects which stretch it. ... Couple, as a noun, is close in meaning to pair, can refer to: two of any similar items; the publicly social bond between two people (most often heterosexual, but common use has also increasingly included homosexuals) in a sexual relationship: husband and wife; girlfriend and boyfriend; two girlfriends (ed. ... In physics, the moment of force (often just moment, though there are other quantities of that name such as moment of inertia) is a quantity that represents the magnitude of force applied to a rotational system at a distance from the axis of rotation. ...

The compressive and tensile forces shown in Figure 2 induce stresses on the beam. The maximum compressive stress is found at the uppermost edge of the beam while the maximum tensile stress is located at the lower edge of the beam. Since the stresses between these two opposing maxima vary linearly, there therefore exists a point on the linear path between them where there is no bending stress. The locus of these points is the neutral axis. Because of this area with no stress and the adjacent areas with low stress, using uniform cross section beams in bending is not a particularly efficient means of supporting a load as it does not use the full capacity of the beam until it is on the brink of collapse. Wide-flange beams (I-Beams) and truss girders effectively address this inefficiency as they minimize the amount of material in this under-stressed region. Figure 1  Stress tensor In physics, stress is a measure of the internal distribution of force per unit area within a body that balances and reacts to the loads applied to it. ... The word linear comes from the Latin word linearis, which means created by lines. ... In mathematics, a locus (plural loci) is a collection of points which share a common property. ... Truss bridge for a single track railway, converted to pedestrian use and pipeline support. ... This page is a candidate to be copied to Wiktionary. ...

## Stress in a beam

Beam bending is analyzed with the Euler-Bernoulli beam equation. The classic formula for determining the bending stress in a member is: ${sigma}= frac{M y}{I_x}$ The elementary Euler-Bernoulli beam theory is a simplfication of the linear isotropic theory of elasticity which allows quick calculation of the load-carrying capacity and deflection of common structural elements called beams. ...

This equation is valid only when the stress at the extreme fiber (i.e. the portion of the beam furthest from the neutral axis) is below the yield stress of the material it is constructed from. At higher loadings the stress distribution becomes non-linear, and ductile materials will eventually enter a plastic hinge state where the magnitude of the stress is equal to the yield stress everywhere in the beam, with a discontinuity at the neutral axis where the stress changes from tensile to compressive. This plastic hinge state is typically used as a limit state in the design of steel structures. Figure 1  Stress tensor In physics, stress is a measure of the internal distribution of force per unit area within a body that balances and reacts to the loads applied to it. ... In physics, the moment of force (often just moment, though there are other quantities of that name such as moment of inertia) is a quantity that represents the magnitude of force applied to a rotational system at a distance from the axis of rotation. ... The second moment of area, also known as the second moment of inertia and the area moment of inertia, is a property of a shape that is used to predict its resistance to bending. ... Yield strength, or the yield point, is defined in engineering and materials science as the stress at which a material begins to plastically deform. ... This article needs to be wikified. ...

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