FSS,
Your question is perfectly valid. An individual element, when
stressed to the limits, will behave differently (inelastic, plastic,
in contrast to elastic behaviour assumed in analysis). The
structural system will not fail until the structure is unable to
carry any additional load, i.e., the structure behaves like a
'mechanism'. This behaviour can be analysed using nonlinear
analysis FEM packages. The analysis is called "pushover
analysis" and is used to determine the overload factor available
prior to collapse of the structure.
In your specific situation, you are right that the structure will
not fail if only a tension pile reaches the limits. Strictly, the load-
deformation characteristic of axial load transfer between pile
and soil is nonlinear. As the load nears the limiting value, some
of the loads
will be redistributed among the other 3 piles until a structural
or soil failure takes place. This behaviour can be studied using
the pushover analysis. However, in this kind of behaviour, the
deformations resulting from nonlinear behaviour will distort
the original results you got from linear analysis and stress
other connected elements more. The benefits of considering the
nonlinear behaviour are not substantial for general structures
and should be ignored, considering the uncertainties in soil
properties and foundation design.
This is the theoretical aspect. As a practical designer, I wouldn't
take any benefits from such behaviour unless it is fully
justified (e.g. in some cases where we have to evaluate the safety
of an existing structure). The situation you have described is
usually encountered in piled jetty structures.
We recently tried to verify the effects of higher pile settlement
on the safety of a jetty structure. The pile was quite safe, but the
connecting beam elements at the superstructure were getting
overstressed.
Hope this helps.
M. Hariharan