고체역학 (Gere) — Axially Loaded Members: Problem 2.3-26

2.3-26 A uniformly tapered tube AB of circular cross section and length L is shown in the figure. The average diameters at the ends are \( d_A \) and \( d_B = 2d_A \). Assume E is constant. Find the elongation \( \delta \) of the tube when it is subjected to loads P acting at the ends. Use the following numerical data: \( d_A = 35 \text{ mm} \), \( L = 300 \text{ mm} \), \( E = 2.1 \text{ GPa} \), and \( P = 25 \text{ kN} \). Consider the following cases: (a) A hole of constant diameter \( d_A \) is drilled from B toward A to form a hollow section of length \( x = L/2 \). (b) A hole of variable diameter d(x) is drilled from B toward A to form a hollow section of length \( x = L/2 \) and constant thickness \( t = d_A/20 \).