The modulus of elasticity E measures how stiff a material is, independent of the member’s shape: it is the constant that ties stress to recoverable strain while the material stays elastic. In beam calculations E always appears multiplied by the second moment of area I — the product EI is the bending stiffness — so a simply supported beam under a uniformly distributed load deflects 5wL⁴/(384EI). Doubling E halves the deflection without changing the member’s strength at all, which is why stiffness and strength are checked separately.
Typical design values: structural carbon steels such as ASTM A36 and A992 use E = 200 GPa regardless of grade, austenitic stainless runs slightly lower at 193 GPa, and aluminum 6061-T6 is 68.9 GPa — roughly a third of steel, which is why aluminum members deflect so much more at the same load. Concrete has no single value; its modulus tracks the strength class through the ACI 318 relation E ≈ 4700·√f′c, landing in the 20–40 GPa range for normal-weight mixes.
Wood needs extra care because it is orthotropic: the published 8–16 GPa range for softwoods and hardwoods applies along the grain, while across the grain the modulus drops by roughly an order of magnitude. Note also that a higher-strength steel grade does not deflect less — A992 yields at 345 MPa versus 250 MPa for A36, yet both share the same 200 GPa modulus, so swapping grades never fixes a serviceability problem.