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The STRESS RESULTANTS used in plate theory are integrals through the thickness. The bending moment resultant per unit width M_x is:
A{'text': '$M_x = \\int \\sigma_x \\, dz$', 'label': 'C'}
B{'text': '$M_x = t \\cdot \\sigma_x$', 'label': 'D'}
C{'text': '$M_x = \\sigma_x$', 'label': 'A'}
D{'text': '$M_x = \\int_{-t/2}^{t/2} \\sigma_x \\cdot z \\, dz$ — moment of σ_x about the mid-plane, per unit width', 'label': 'B'}
Answer & Solution
Correct answer: D. {'text': '$M_x = \\int_{-t/2}^{t/2} \\sigma_x \\cdot z \\, dz$ — moment of σ_x about the mid-plane, per unit width', 'label': 'B'}
Stress resultants are statically equivalent forces (N_x) and moments (M_x) integrated through the thickness, per unit width. M_x = ∫z·σ_x dz captures the bending effect. Units: force·length/length = force (or moment per unit width).
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