Elastic Section Modulus (S = I/c)

Bending stress is Mc/I, and for a given shape the c and the I never change — so designers precombine them into one number, S = I/c, and the stress check becomes the one-liner σ = M/S. A 50 mm × 100 mm rectangle has I = 4.167 × 10⁻⁶ m⁴ and c = 0.05 m, so S = 8.333 × 10⁻⁵ m³. Every steel manual on every job site is really a table of S values: pick the lightest beam whose S beats M/σ_allow and the sizing is done.

Two cautions. This engine has no m³ unit type, so S is a plain number in m³ (1 in³ = 1.6387 × 10⁻⁵ m³, 1 mm³ = 10⁻⁹ m³). And a section that is not symmetric about its bending axis — a channel, a tee, an unequal-flange girder — has two different values of c and therefore two section moduli, one for the tension face and one for the compression face. Use the smaller S, which belongs to the fibre furthest from the neutral axis, or you will check the wrong face. Note also that S here is the elastic modulus; plastic design uses Z, which for a rectangle is 1.5 times larger.