고체역학 (Beer) — Stress and Strain—Axial Loading: Problem 2.86

2.86 Determine the change in volume of the 50-mm gage length segment AB in Prob. 2.64 (a) by computing the dilatation of the material, (b) by subtracting the original volume of portion AB from its final volume. (Reference Problem 2.64): A 2.75-kN tensile load is applied to a test coupon made from 1.6-mm flat steel plate (\(E = 200 \text{ GPa}\), \(\nu = 0.30\)). Determine the resulting change in (a) the 50-mm gage length, (b) the width of portion AB of the test coupon, (c) the thickness of portion AB, (d) the cross-sectional area of portion AB. (Dimensions from Fig. P2.64: width of segment AB = 12 mm).