Euler-Bernoulli beam model is the most simple model to describe the behaviour of beam. Its basic assumptions are:
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The cross section of beam will remain planar in bending
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The cross section of beam will not stretch in bending
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The transversal shearing deformation of beam is insignificant
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Deformations are considered small.
The cross section of Euler-Bernoulli beam remains perpendicular to beam neutral axis in bending. The figure below illustrates Euler-Bernoulli beam.
The dependency between loading of beam and its displacement can be derived from the basic assumptions. The dependency can be presented with following equation:
,where
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EI = flexural rigidity
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w = displacement of beam neutral axis
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q = loading of beam