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Which value is closest to the ratio CFRP/steel of the specific modulus (Young's modulus/density) in the fiber direction, for unidirectional CFRP (Young's modulus 140 GPa in the fiber direction, density 1.6 g/cm³) and steel (Young's modulus 210 GPa, density 7.9 g/cm³)?

  1. AAbout 0.67
  2. BAbout 3.3
  3. CAbout 4.9
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Answer: B. About 3.3

The specific modulus is 140/1.6 = 87.5 for CFRP and 210/7.9 ≈ 26.6 for steel (both in GPa/(g/cm³)), so the ratio is 87.5/26.6 ≈ 3.3. CFRP has the lower Young's modulus itself, but its density is about one fifth, so at equal weight it is about 3.3 times as stiff. About 0.67 compares only the moduli (140/210), and about 4.9 looks only at the density ratio (7.9/1.6). Note that this value applies only in the fiber direction; perpendicular to the fibers, the specific modulus is far lower than that of steel. Real structures compensate for direction by laminating, so the specific-stiffness advantage is smaller than this value.

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