Material Selection Index Strength⚠ unverified
Mechanical / Materials · Compute the strength-limited material selection index
Parameters
| Input | Symbol | Unit | Default | Description |
|---|---|---|---|---|
| Sy | Sy | Pa | 1.0 | Yield strength of the material |
| rho | ρ | kg/m**3 | 1.0 | Mass density of the material |
| Output | Symbol | Unit | Description |
|---|---|---|---|
| result | M | kg/m**3 | Strength-limited selection index, in pascals per (kg/m**3) |
The science & history
Understanding the Parameters
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Yield strength $S_y$ — the load capacity per unit area; for a tie carrying a fixed load, mass scales as $\rho/S_y$, so high $S_y/\rho$ minimises mass.
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Density $\rho$ — the mass penalty. Unlike the stiffness index, specific strength varies widely across materials, so $S_y/\rho$ genuinely discriminates: composites, titanium, and high-strength aluminium beat mild steel decisively.
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Index $M$ — a material property; the largest value wins for a strength-limited tie. Bending-limited members use $S_y^{2/3}/\rho$ (beam) instead.
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Unit caveat — the true unit is J/kg (same as specific strength); the registry's kg/m³ is a mislabel.
Derivation (Approaching a Proof)
For a tension tie of fixed length $L$ carrying load $F$ without yielding, the minimum area is $A = F/S_y$ and the mass is
$$m = \rho A L = (F L)\,\frac{\rho}{S_y}.$$
With $F$ and $L$ fixed, mass is minimised by maximising $S_y/\rho$ — the same derivation as Specific Strength. The two cards compute the identical index.
Dimensional check. $M = \dfrac{S_y}{\rho} = \dfrac{\text{Pa}}{\text{kg}/\text{m}^3} = \dfrac{\text{J}}{\text{kg}}$ — energy per mass, confirming the registry's kg/m³ label is incorrect.
History and Development
The strength index $S_y/\rho$ (or $\sigma_f/\rho$) is a core Ashby material-selection index (1980s), plotted as a slope-1 guideline on the strength–density Ashby Charts. It drove the adoption of aluminium and composites in aircraft primary structure, where strength-per-weight, not absolute strength, is the binding constraint.
Related Concepts: Specific Strength, Material Selection Index Stiffness, Ashby Chart Index, Ashby Charts, Material Selection Index Toughness, Hardness to Tensile Strength
Notes: Duplicate of Specific Strength ($S_y/\rho$). Output unit should be J/kg (registry mislabels kg/m³). Tie index — bending-limited members use $S_y^{2/3}/\rho$.