Young's Modulus (E = σ/ε)

This is Hooke's law promoted from a particular spring to a whole material: stress and strain rise together in fixed proportion, and the constant of proportionality is the stiffness of the substance itself. Thomas Young presented it in his 1807 lecture series, though Leonhard Euler had the idea in 1727 and Giordano Riccati measured it in 1782 — and Young's own prose was so impenetrable that his publisher's reviewers complained they could not follow it. Steel comes in at E = 200 GPa (29 000 ksi), aluminium at 69 GPa (10 000 ksi), concrete near 30 GPa, wood along the grain around 11 GPa. Apply 200 MPa to steel and you get ε = 200 ÷ 200 000 = 0.001, one millimetre per metre.

The trap that surprises everyone new to the trade: all structural steels have the same E. A992 grade-50 steel is no stiffer than plain A36 — it is only stronger. Upgrading grade buys you more capacity before yield, never less deflection, so a bouncy floor is never fixed by a better alloy, only by a deeper section. And E only describes the straight part of the curve; past the proportional limit the material yields and this formula quietly stops being true.