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Kirchhoff's plate theory makes which assumption equivalent to Euler-Bernoulli beam theory in 1D?
A{'text': 'Lines NORMAL to the mid-surface remain straight and perpendicular to the deformed mid-surface (no through-thickness shear)', 'label': 'B'}
B{'text': 'Plate is elastic', 'label': 'A'}
C{'text': 'Plate is square', 'label': 'C'}
D{'text': 'No load is applied', 'label': 'D'}
Answer & Solution
Correct answer: A. {'text': 'Lines NORMAL to the mid-surface remain straight and perpendicular to the deformed mid-surface (no through-thickness shear)', 'label': 'B'}
Kirchhoff hypothesis = beam's "plane sections remain plane and perpendicular to the neutral axis" generalized to 2D plates. Consequence: out-of-plane shear strain is taken as zero. Valid for thin plates, fails for thick plates (Mindlin theory needed).
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