# Plastic bending

**Plastic bending**is a nonlinear behaviour peculiar to members made of ductile materials that frequently achievemuch greater ultimate bending strength than indicated by a linear elastic bending analysis. In both the plastic andelastic bending analyses of a straight beam, it is assumed that the strain distribution is linear about the neutralaxis (plane sections remain plane). In an elastic analysis this assumption leads to a linear stress distribution butin a plastic analysis the resulting stress distribution is nonlinear and is dependent on the beam’s material.The limiting

**plastic bending**strength $M\_r$ can generally be thought of as an upper limit to a beam’s load–carrying capability as it only represents the strength at a particular cross–section and not the load–carrying capability of the overall beam. A beam may fail due to global or local instability before Mr is reached at any point on its length. Therefore, beams should also be checked for local buckling, local crippling, and global lateral–torsional buckling modes of failure.**Note**that the deflections necessary to develop the stresses indicated in a plastic analysis are generally excessive, frequently to the point of incompatibility with the function of the structure. Therefore, separate analysis may be required to ensure design deflection limits are not exceeded. Also, since working materials into the plastic range can lead to permanent deformation of the structure, additional analyses may be required at limit load to ensure no detrimental permanent deformations occur. The large deflections and stiffness changes usually associated with plastic bending can significantly change the internal load distribution, particularly in statically indeterminate beams. The internal load distribution associated with the deformed shape and stiffness should be used for calculations.**Plastic bending**occurs when an applied moment causes the outside fibers of a cross-section to exceed the material's yield strength. Loaded with only a moment, the peak bending stresses occurs at the outside fibers of a cross-section. The cross-section will not yield simultaneously through the section. Rather, outside regions will yield first, redistributing stress and delaying failure beyond what would be predicted elastic analytical methods. The stress distribution from theneutral axis is the same as the shape of the stress-strain curve of the material (this assumes a non-composite cross-section). After a structural member reaches a sufficiently high condition of plastic bending, it acts as aPlastic hinge .Elementary Elastic Bending theory requires that bending stress varies linearly with distance from the

neutral axis , but plastic bending shows a more accurate and complex stress distribution. The yielded areas of the cross-section will vary somewhere between the yield and ultimate strength of the material. In the elastic region of the cross-section, the stress distribution varies linearly from the neutral axis to the beginning of the yielded area. Predicted failure occurs when the stress distribution approximates the material's stress-strain curve. The largest value being that of the ultimate strength. Not every area of the cross-section will have exceeded the yield strength.As in the basic Elastic Bending theory, the moment at any section is equal to an

area integral of bending stress across the cross-section. From this and the above additional assumptions, predictions of deflections and failure strength are made.Plastic theory was validated at the beginning of the last century by C. v. Bach. [

*Bach, C. and Baumann, R., "Elastizitat und Festigkeit", 9th ed., 1908.*]**ee also**Bending **References**

*Wikimedia Foundation.
2010.*

### Look at other dictionaries:

**Bending**— For other uses, see Bending (disambiguation). Flexure redirects here. For joints that bend, see living hinge. For bearings that operate by bending, see flexure bearing. Continuum mechanics … Wikipedia**Plastic hinge**— A plastic hinge is a type of energy damping device allowing plastic rotation [deformation] of an otherwise rigid column connection [ [http://mceer.buffalo.edu/education/reu/04Proceedings/12Long Bergad.pdf Analysis of Rotational Column with… … Wikipedia**plastic**— [adj1] flexible, soft; made of manufactured, treated compounds bending, ductile, elastic, fictile, formable, moldable, molded, pliable, pliant, resilient, shapeable, supple, workable; concept 604 Ant. hard, inflexible, stiff plastic [adj2] easily … New thesaurus**Bending (metalworking)**— Metal bending redirects here. For the form of stage magic, see Spoon bending. Bending … Wikipedia**Plastic Moment**— In plastic limit analysis of members subjected to bending, it is assumed that an abrupt transition from elastic to ideally plastic behaviour occurs at a certain value of moment, known as plastic moment (Mp). Member behaviour between My and Mp is… … Wikipedia**plastic**— Synonyms and related words: Bakelite, Buna, Celluloid, Formica, Lucite, Mylar, PVC, Perspex, Plexiglas, Styrofoam, Teflon, able to adapt, acaroid resins, accessible, accordant, acetate, acetate nitrate, acquiescent, acrylic, adaptable, adaptive,… … Moby Thesaurus**Pole bending**— Western riding Timed events Barrel race Pole bending Stake race (Figure 8) Keyhole race Flag race Pole bending is timed event that feat … Wikipedia**Circuit bending**— Probing for bends using a jeweler s screwdriver and alligator clips Circuit bending is the creative customization of the circuits within electronic devices such as low voltage, battery powered guitar effects, children s toys and small digital… … Wikipedia**Reinforced concrete biaxial bending**— Reinforced Concrete Biaxial BendingReinforced concrete biaxial bending is the stress state of a reinforced concrete element subjected to axial force and two orthogonal moments and is usually found in column design. This page is entended to give… … Wikipedia**Buckling**— In engineering, buckling is a failure mode characterized by a sudden failure of a structural member subjected to high compressive stresses, where the actual compressive stress at the point of failure is less than the ultimate compressive stresses … Wikipedia