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.

This article is about the structural behavior. For other meanings see Bending (disambiguation). 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. ... Bending can refer to the following: Bending - the behavior of a structural element subjected to a lateral load Bending (metalworking) - a sheet metalworking process used in manufacture Elemental Bending - the mental manipulation of the four classical elements - Water, Earth, Fire, Air as seen in Avatar: The Last Airbender The flection...

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. 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. ... Load may mean: Look up Load in Wiktionary, the free dictionary. ... 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 compression members experiencing bending. In physics, force is an influence that may cause a body to accelerate. ... Shear stress is a stress state where the stress is parallel to a face of the material, as opposed to normal stress when the stress is perpendicular to the face. ... Physical compression is the result of the subjection of a material to compressive stress, resulting in reduction of volume. ... Tension is a reaction force applied by a stretched string (rope or a similar object) on the objects which stretch it. ... For other meanings, see Couple A Couple is or are two equal and opposite forces whose lines of action do not coincide. ... It has been suggested that this article or section be merged with torque. ... A bending moment in physics is an example of an internal force that is induced in a structure when loads are applied to that structure. ... Columns Ionic column base A compression member is a general class of structural elements of which a column is the most common specific example. ...

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. Stress is the internal distribution of force per unit area that balances and reacts to external loads applied to a body. ... The word linear comes from the Latin word linearis, which means created by lines. ... In mathematics, a locus (Latin for place, plural loci) is a collection of points which share a common property. ... In architecture and structural engineering, a truss is a static structure consisting of straight slender members inter-connected at joints into triangular units. ... This page is a candidate to be copied to Wiktionary. ...

Simple or Symmetrical Bending

Beam bending is analyzed with the Euler-Bernoulli beam equation. The classic formula for determining the bending stress in a member is: The elementary Euler-Bernoulli beam theory is a simplification of the linear isotropic theory of elasticity which allows quick calculation of the load-carrying capacity and deflection of common structural elements called beams. ...

simplified for a beam of rectangular cross-section to:

• σ is the bending stress
• M - the moment at the neutral axis
• y - the perpendicular distance to the neutral axis
• I_x - the area moment of inertia about the neutral axis x
• b - the width of the section being analyzed
• h - the depth of the section being analyzed

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. Stress is the internal distribution of force per unit area that balances and reacts to external loads applied to a body. ... It has been suggested that this article or section be merged with torque. ... An axis in the cross section of a beam, shaft or the like along which there are no longitudinal stresses / strains. ... An axis in the cross section of a beam, shaft or the like along which there are no longitudinal stresses / strains. ... 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 and deflection. ... An axis in the cross section of a beam, shaft or the like along which there are no longitudinal stresses / strains. ... 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. ...

Complex or Unsymmetrical Bending

The equation above is, also, only valid if the cross-section is symmetrical. For unsymmetrical sections, the full form of the equation must be used (presented below):

Complex Bending of Homogeneous Beams

The complex bending stress equation for elastic, homogeneous beams is given as where Mx and My are the bending moments about the x and y centroid axes, respectively. Ix and Iy are the second moments of area (also known as moments of inertia) about the x and y axes, respectively, and Ixy is the product of inertia. Using this equation it would be possible to calculate the bending stress at any point on the beam cross section regardless of moment orientation or cross-sectional shape. Note that Mx, My, Ix, Iy, and Ixy are all unique for a given section along the length of the beam. In other words, they will not change from one point to another on the cross section. However, the x and y variables shown in the equation correspond to the coordinates of a point on the cross section at which the stress is to be determined. Centroid of a triangle In geometry, the centroid or barycenter of an object in -dimensional space is the intersection of all hyperplanes that divide into two parts of equal moment about the hyperplane. ...

See also

• Contraflexure
• Deflection
• Shear strength
• Shear stress
• Bending (metalworking)