Mechanics of Materials · Strain and stiffness
Strain, and the price of it
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Strain, and the price of it

Strain first. ε=δL\varepsilon = \dfrac{\delta}{L}epsilon equals delta over L. δ\delta (delta) is the change in length, how much the specimen grew under load; LL is the original gauge length, the marked span the instrument watches; ε\varepsilon is the strain, the growth per unit of original length. Both lengths must be in the SAME unit before you divide — that is the entire difficulty of this formula, and it catches somebody every year.

Then the price. E=σεE = \dfrac{\sigma}{\varepsilon}E equals sigma over epsilon — is Young's modulus: the stress it takes to buy one unit of strain. σ\sigma is the stress in the specimen, ε\varepsilon the strain it produced, EE the material's stiffness. Steel lands near 200 GPa, aluminium near 70, copper near 110 — and those numbers belong to the ALLOY, never to your particular bar. A thicker bar is stronger; it is not stiffer per unit of stress.

Because strain is a bare ratio, σ/ε\sigma / \varepsilon comes back wearing the stress's own unit. Feed it megapascals and megapascals come out; the gigapascal on the datasheet is one division by a thousand away, never a different quantity.