| Summary: | In the critical state of a beam under central compression
a flexural-torsional equilibrium shape becomes
possible in addition to the fundamental straight equilibrium
shape and the Euler bending. Particularly, torsional
configuration takes place in all cases where the line of
shear centres does not correspond with the line of centres
of mass. This condition is obtained here about a z-axis
highly variable section beam; with the assumptions that
shear centres are aligned and line of centres is bound to
not deform.
For the purpose, let us evaluate an open thin wall C-cross
section with flanges width and web height linearly variables
along z-axis in order to have shear centres axis approximately
aligned with gravity centres axis.
Thus, differential equations that govern the problem are
obtained.
Because of the section variability, the numerical integration
of differential equations that gives the true critical
load is complex and lengthy. For this reason, it is given
an energetic formulation of the problem by the theorem of
minimum total potential energy (Ritz-Rayleigh method).
It is expected an experimental validation that proposes the
model studied.
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