Graphical limit state analysis

The art of structural design requires specific methods and tools. One of those
consists
in modelling the structural behaviour through a network of straight bars,
whether
in compression (struts) or in tension (ties), and in expressing its static
equilibrium
through classic graphic statics reciprocal diagrams: a form diagram describing
the
geometry of a strut-and-tie network and a force diagram representing the
vector
equilibrium of its nodes.
When it comes to statically indeterminate structures, the lower-bound theorem
of
Plasticity avoids any overestimation of the load bearing capacity, which
allows the
designer to select one of the possible equilibrium states.
Considering that a limit state analysis of these indeterminate equilibriums
can better
support the design process when it shares the same graphical environment, the
thesis
consists in proposing a graphical methodology for constructing a parametric
force
diagram resulting from the combination of independent force diagrams. The
stress
distribution is then modified by manipulating the relative position of some
vertices
of the force diagram until it reaches limit states; hence, the possibility of
identifying
the collapse state and the corresponding load bearing capacity of various
types of
structures such as pin-jointed trusses, beams or masonry arches.
The analysis of the admissible geometrical domains for these specific vertices
allows
a better understanding of the behaviour of statically indeterminate structures
at
limit state and may be helpful when designing them.