In plastic limit analysis of structural 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 Myp and Mp
is considered to be elastic. When Mp is reached, a plastic hinge is
formed in the member. In contrast to a frictionless hinge
permitting free rotation, it is postulated that the plastic hinge
allows large rotations to occur at constant plastic moment Mp.
Plastic hinges extend along short lengths of beams. Actual
values of these lengths depend on cross-sections and load
distributions. But detailed analyses have shown that it is
sufficiently accurate to consider beams rigid-plastic, with
plasticity confined to plastic hinges at points. While this
assumption is sufficient for limit analysis, finite element
formulations are available to account for the spread of plasticity
along plastic hinge lengths.
By inserting a plastic hinge at a plastic limit load into a
statically determinate beam, a kinematic mechanism permitting an
unbounded displacement of the system can be formed. It is known as
the collapse mechanism. For each degree of static indeterminacy of
the beam, an additional plastic hinge must be added to form a
collapse mechanism.
