고체역학 (Gere) — Axially Loaded Members: Problem 2.3-11

2.3-11 A steel bar is 2.4 m long and has a circular cross section of diameter \(d_1 = 20 \text{ mm}\) over one-half of its length and diameter \(d_2 = 12 \text{ mm}\) over the other half (see figure on following page part a). The modulus of elasticity is \(E = 205 \text{ GPa}\). (a) How much will the bar elongate under a tensile load \(P = 22 \text{ kN}\)? (b) If the same volume of material is made into a bar of constant diameter \(d\) and length 2.4 m, what will be the elongation under the same load \(P\)? (c) If the uniform axial centroidal load \(q = 18.33 \text{ kN/m}\) is applied to the left over segment 1 (see figure part b), find the ratio of the total elongation of the bar to that in parts (a) and (b).