Bending stress: $\sigma = E \epsilon = 200\times10^3 \times 0.01058 = 2116$ MPa → exceeds yield → occurs. The tube will permanently deform but not fracture if $\epsilon < \epsilon_fracture$ (≈5% for steel). Minimum elastic bend radius: $R_min,elastic = \fracE \cdot D2\sigma_y = \frac200000 \times 25.42 \times 350 = 7257$ mm (7.26 m). So coiling onto a 1.2 m reel causes plastic yielding – acceptable for coiled tubing applications. 10. Conclusion The continuous tube is a critical engineering product enabling long-distance fluid transport, compact storage, and seamless flow paths. While manufacturing methods differ between seamless (extruded/drawn) and welded (roll-formed), both serve distinct markets. Modern developments in high-strength alloys, laser welding, and polymer extrusion have pushed continuous tube lengths to several kilometers, with diameters from sub-millimeter to 500+ mm. The primary trade-offs remain between installation simplicity (no joints) versus repair difficulty and transport logistics. As industries push for deeper wells, longer heat exchangers, and lighter aerospace structures, the continuous tube will remain an indispensable form of engineering material.
$$\epsilon = \fracD2 R_b$$
$$R_b,min \approx \fracE \cdot t\sigma_y$$ continuous tube
Unlike a segmented pipe, a continuous tube has no axial stress discontinuity at joints, so no stress concentration factor ($K_t \approx 1$) in the longitudinal direction. This significantly improves burst strength and fatigue life. When a continuous tube is bent to a radius $R_b$, the bending strain is: Bending stress: $\sigma = E \epsilon = 200\times10^3
$$\sigma_h = \fracP \cdot Rt, \quad \sigma_a = \fracP \cdot R2t$$ So coiling onto a 1
Bending strain: $\epsilon = \fracD2R_b = \frac25.42 \times 1200 = 0.01058$ (1.06%)