)
varies linearly with the applied load and the stress (
) varies linearly according
to: 
, where E is the modulus of elasticity.It is assumed that the beam element is initially straight and
unstressed. It is also assumed that the material does not yield,
therefore the beam will be straight after the load is released.
These assumptions mean that the beam must be made of an elastic
material, one which will return to it's original size and shape
when all loads are removed, if not stressed past the materials
elastic or proportional limit. It is also assumed that the beam
is not stressed past the proportional limit, at which point the
beam will take a permanent set and will not fully return to it's
original size and shape, when all loads are removed. Below the
proportional limit an elastic material is in the linear elastic
range, where the strain ()
varies linearly with the applied load and the stress () varies linearly according
to: , where E is the modulus of elasticity.
