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Mechanical properties and fracture

A steel rod 2.0 m long with a Young's modulus of 200 GPa is loaded in tension to 100 MPa within its elastic range. Which value is closest to the elongation of the rod?

  1. AAbout 0.10 mm
  2. BAbout 1.0 mm
  3. CAbout 10 mm
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Answer: B. About 1.0 mm

From Hooke's law, the strain is ε = σ/E = 100×10⁶ / (200×10⁹) = 5.0×10⁻⁴. The elongation is ΔL = εL = 5.0×10⁻⁴ × 2000 mm = 1.0 mm. About 0.10 mm and about 10 mm are off by one order of magnitude from a slip in the GPa–MPa conversion (1 GPa = 1000 MPa) or the m–mm conversion. Even in a steel with a yield stress of several hundred MPa, the elastic strain stays at only about 0.1–0.2%. At the same stress, an aluminum alloy with about one third the modulus (about 70 GPa) stretches about three times as much, a difference that matters in stiffness-critical design.

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