고체역학 (Gere) — Axially Loaded Members: Problem 2.3-16

2.3-16 A prismatic bar \(AB\) of length \(L\), cross-sectional area \(A\), modulus of elasticity \(E\), and weight \(W\) hangs vertically under its own weight (see figure). (a) Derive a formula for the downward displacement \(\delta_C\) of point \(C\), located at distance \(h\) from the lower end of the bar. (b) What is the elongation \(\delta_B\) of the entire bar? (c) What is the ratio \(\beta\) of the elongation of the upper half of the bar to the elongation of the lower half of the bar? (d) If bar \(AB\) is a riser pipe hanging from a drill rig at sea, what is the total elongation of the pipe? Let \(L = 1500\text{ m}\), \(A = 0.0157\text{ m}^2\), and \(E = 210\text{ GPa}\). See Appendix I for weight densities of steel and sea water. (See Probs. 1.4-2 and 1.7-13 for additional figures.)