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At a free edge the three physical conditions are those of vanishing transverse force, vanishing bending couple and vanishing twisting couple. The two Kirchhoff conditions which take their places are vanishing bending couple and vanishing of the sum of transverse force and edgewise rate of change of twisting couple.
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E. Reissner (Tue,) studied this question.
synapsesocial.com/papers/6a1d1b9f68a6eca4522f2f30 — DOI: https://doi.org/10.1090/qam/20440
E. Reissner
Massachusetts Institute of Technology
Quarterly of Applied Mathematics
Massachusetts Institute of Technology
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