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Materials selection and design

A tie of fixed length and tensile stiffness is made of steel (E = 210 GPa, ρ = 7.8 g/cm³, price per kg taken as 1) and of quasi-isotropic CFRP laminate (E = 70 GPa, ρ = 1.6 g/cm³, price per kg 20 times that of steel). If the cross-sectional area can be varied freely, about how many times the material cost of the steel tie is that of the CFRP tie?

  1. AAbout 0.62 times
  2. BAbout 20 times
  3. CAbout 12 times
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Answer: C. About 12 times

The mass of a stiffness-limited tie is proportional to ρ/E, so the mass ratio CFRP/steel is (1.6/70)/(7.8/210) = 0.0229/0.0371 ≈ 0.62. Material cost is mass times price per kg, so 0.62 × 20 ≈ 12.3, about 12 times. About 0.62 times compares only mass and ignores price. About 20 times looks only at the ratio of prices per kg and ignores that less CFRP mass is needed. When cost is the objective, the performance index becomes E/(Cmρ) (Cm is the price per kg), and CFRP, advantageous in weight, is far worse than steel in material cost. In practice, the decision also includes processing costs and the fuel saved in service by being lighter.

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