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Materials selection and design

In Ashby's method of materials selection, the design requirements are organized into function, constraints, objective and free variables. In selecting the material for a bicycle frame, which of these is the objective?

  1. AThe designer is free to choose the outer diameter and wall thickness of the frame tubes
  2. BThe frame must not yield under the loads in service and must always meet a specified bending stiffness
  3. CMake the mass of the frame as small as possible while meeting the required stiffness and strength
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Answer: C. Make the mass of the frame as small as possible while meeting the required stiffness and strength

Ashby's method first divides the design requirements into four parts. The function is what the component does (such as a beam carrying a load), the constraints are conditions that must be met, the objective is the quantity to be maximized or minimized, and the free variables are dimensions and the like that the designer may vary. “Make the mass as small as possible” is a quantity to minimize, so it is the objective, and the performance index used to rank materials is derived from it. “Must not yield” and “must meet a specified stiffness” are constraints that draw a pass/fail line and are used in the screening stage to eliminate materials that fail them. The outer diameter and wall thickness of the tubes are free variables; eliminating them with the constraint equations leaves the performance index, a combination of material properties only.

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More Materials selection and design questions

  1. A tie (tension member) of fixed length L must carry a tensile load F without yielding, and its cross-sectional area may be chosen freely. To make it as light as possible, which performance index should be maximized, with σf the yield strength and ρ the density of the material?
  2. A beam of square cross section with fixed length and bending stiffness is to be made as light as possible by freely varying the size of the cross section. Which performance index should be maximized, with E the Young's modulus and ρ the density?
  3. On a log–log materials selection chart (Ashby chart) with Young's modulus E on the vertical axis and density ρ on the horizontal axis, what is the slope of the guideline along which the performance index for a light, stiff beam, √E/ρ, is constant?
  4. Beams of square cross section designed for the same length and bending stiffness are made of steel (E = 210 GPa, ρ = 7.8 g/cm³) and an aluminum alloy (E = 70 GPa, ρ = 2.7 g/cm³). If the size of the cross section can be varied freely, about how many times the mass of the steel beam is the mass of the aluminum alloy beam?
  5. 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?