Structural

BS 8007 — Flexural Crack Width Check

Design surface crack width for flexural cracking in water-retaining concrete structures. Long-term creep is accounted for by using a modular ratio αe ≈ 15.

Formula

w_cr = 3·a_cr·ε_m / (1 + 2(a_cr − c_min)/(h − x))

Section geometry

Per-metre strip, working in mm.

Width of section, bmm

Overall depth, hmm

Clear cover, cminmm

Reinforcement

Bar diameter, φmm

Bar spacing (c/c), smm

Loads & materials

Service moment, MkN·m / m

Steel modulus, EsN/mm²

Modular ratio, αe

Exposure / crack-width limit

Resultlive

Effective depth, d: 252mm
Steel area, As (per m): 1340.4mm²/m
Steel ratio, ρ = As/(b·d): 0.532%
Neutral axis depth, x: 82.547mm
Lever arm, z: 224.48mm
Steel stress, σs: 199.4N/mm²
ε1 (uncracked strain): 1.279e-3
εm (mean strain): 9.325e-4
acr (distance to bar): 81.045mm
Crack width, wcr: 0.1646mm
Check: PASS (≤ 0.2 mm)

Check: Crack width within allowable limit.

Inputs assume a per-metre strip in pure bending with rectangular tension steel. The check uses the cracked-section transformed area with αe accounting for creep. Compression steel and axial tension are not included — for those cases use a more detailed analysis.

Reference: BS 8007:1987 Appendix B, in conjunction with BS 8110-2 §3.8. Modular ratio αe = 15 is the standard long-term value for water-retaining work.