6.8
. 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. To make the usage of the term more precise, engineers refer to the bending of rods,[2] the bending of beams,[1] the bending of plates,[3] the bending of shells[2] and so on.
Bending Stress
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Bending stress is the normal stress that is induced at a point in a body subjected to loads that cause it to bend. When a load is applied perpendicular to the length of a beam (with two supports on each end), bending moments are induced in the beam.
Flexural theory states that most materials will exhibit linear-plastic behaviour, i.e. they will respond to an applied load by deflecting in accordance to Hooke s Law, and will return to their original shape and form when the load is removed. This stress-strain relation exists only up to a certain load, after which the material will undergo some irretrievable deformation. Hooke s Law states that deformation of an object under loading is proportional to the magnitude of the load.
Materials which are said to be "elastic" become distorted when they are compressed, stretched, or bent. This behaviour is due to the forces that different parts of a member exert on each other when a structure is subjected to loads. A simply supported beam of length L, subjected to a concentrated transverse load P at midspan would exhibit vertical deflection (and start to curve) due to bending caused by the two reaction loads at the supports. At midspan, the top of the beam would be the location at which the maximum compression occurs in the beam due to contraction in the top fibers. The bottom of the beam would experience maximum tension due to the elongation in the bottom fibers.
The maximum bending moment due to applied transverse load of P, occurs at mid span of a beam of length L, and is given by the following equation: