Abstract: In this paper, a semi empirical formula is presented based on the experimental results to predict the first pick (maximum force) value in the instantaneous folding force- axial distance diagram of a square column. To achieve this purpose, the maximum value of the folding force was assumed to be a function of the average folding force. Using the experimental results, the maximum value of the force necessary to initiate the first fold in a square column was obtained with respect to the geometrical quantities and material properties. Finally, the results obtained from the semi empirical relation in this paper, were compared to the experimental results which showed a good correlation.
Abstract: In this paper, a theoretical formula is presented to
predict the instantaneous folding force of the first fold creation in a
square column under axial loading. Calculations are based on analysis
of “Basic Folding Mechanism" introduced by Wierzbicki and
Abramowicz. For this purpose, the sum of dissipated energy rate under
bending around horizontal and inclined hinge lines and dissipated
energy rate under extensional deformations are equated to the work rate
of the external force on the structure. Final formula obtained in this
research, reasonably predicts the instantaneous folding force of the first
fold creation versus folding distance and folding angle and also predicts
the instantaneous folding force instead of the average value. Finally,
according to the calculated theoretical relation, instantaneous folding
force of the first fold creation in a square column was sketched
versus folding distance and was compared to the experimental results
which showed a good correlation.