Abstract
ABSTRACT The symmetry limit theory of the present authors for beam-columns subjected to idealized completely reversed tip deflection cycling programs is extended to a general branching problem of steady-state paths. It is shown that transition to asymmetric steady states may occur from any symmetric steady state whose tip deflection amplitude is greater than or equal to the symmetry limit amplitude but is less than the upper limit of branching with increasing tip deflection amplitude. It is verified that the smallest amplitude among those at which transition to asymmetric steady states may occur coincides exactly with the symmetry limit, yielding a mathematical proof of the validity of the symmetry limit theory.
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