Crack widths are calculated per 7.3.4. Cracked equilibrium strains are calculated assuming that concrete has no tensile strength. Creep is not considered.

Un-tensioned reinforcement is added to keep crack widths at or below the required limits.

UK National Annex crack width limits are in accordance with Table NA.4 of the applied National Annex.

This criterion is applied to two-way slabs and other wide cross sections, but will not provide accurate crack width predictions for these wide cross sections when reinforcement is not spaced according to the varying stress patterns across the section. For narrower cross sections with a uniform stress pattern, the bonded reinforcement should be spaced uniformly. For this reason it may not be appropriate to do a "crack width" only design on full panel strip widths.

The crack-limiting capabilities of appropriately placed bonded tendons are considered, and the balance loading will be considered if included in the load combinations. Bonded tendons are only considered effective if the average spacing of the bonded tendons and un-tensioned reinforcement within h_c,eff is less than or equal to 300 mm in accordance with 7.3.2(3).

Crack width = s_r,max(εsm- εcm)

• εsm - εcm = [σ_s - k_t(f_ct,eff/ρ_p,eff ) (1 + α_e ρ_p,eff )] / E_s ≥ 0.6 σ_s / E_s

  RAM Concept uses a rearranged form of this equation, which utilizes strains instead of stresses

• εsm - εcm = σ_s / E_s - k_t[ (f_ct,eff/(ρ_p,eff E_s) + (f_ct,eff/E_cm)] ≥ 0.6 σ _s / E_s
• σ_s = tension stress in un-tensioned reinforcement from a cracked section analysis, or maximum differential bonded tendon stress from tendon stress level at zero strain in the concrete at the same level
• k_t = 0.6 for frequent service design
  • 0.4 for quasi-permanent service design
• f_ct,eff = f_ctm
• ρ_p,eff = (A_s + ξ₁ ² A_p’)/A_c,eff
• A_s = area of un-tensioned reinforcement within depth h_c,eff
• A_p’ = area of bonded tendons within depth h_c,eff
• A_c,eff = area of concrete within depth h_c,eff
• h_c,eff = minimum of 2.5(h-d), (h-x)/3, or h/2
• d = depth to the outermost layer of reinforcement
• ${\xi }_1=\sqrt{\xi \frac{{\varphi }_s}{{\varphi }_p}}$
• ξ = 0.5 for f_ck ≤ C50/60
  • 0.25 for f_ck ≤ C70/85
  • Linearly interpolated between C50/60 and C70/85
• φ_s = largest diameter of reinforcement contained within depth h_c,eff
• φ_p = 1.6A_p’
• α_e = E_s/E_cm
• s_r,max = k₃c + k₁k₂k₄φ_eq /ρ_p,eff = crack spacing (eq. 7.11)
• k₃ = 3.4 (UK National Annex)
• c = average cover to reinforcement, weighted by bar/tendon units
• k₁ = 0.8 for un-tensioned reinforcement
  • 1.6 for bonded tendons
  • averaged for cross sections containing both tendons and un-tensioned reinforcement,
  • weighted by bar/tendon units
• k₂ = 0.5 for bending (compression strain on one face)
  • (ε₁ + ε₂ ) / 2ε₁ for tension (tension strain on both faces)
• k₄ = 0.425 (UK National Annex)
• φ_eq = n₁φ₁² + n₂φ₂² + n_i φ_i ² / (n₁φ₁ + n₂φ₂ + n_i φ_i )

If the bonded reinforcement within h_c,eff is less than or equal to 5(c+ ϕ_eq /2), RAM Concept uses equation 7.11 for s_r,max. If a larger spacing exists, RAM Concept uses a crack spacing of 1.3(h-x) in accordance with equation 7.14. RAM Concept always assumes the maximum crack spacing is 1.3(h - x).

For bonded PT systems, decompression is checked for exposure class XC2, XC3, and XC4 for the quasi-permanent load combination and for exposure class XD and XS for the frequent load combination. For the decompression checks, a check is made that the entire bonded tendon lies within 25 mm of concrete in compression, using cracked section properties. For this purpose, a constant 25 mm duct depth representing the depth of a typical flat duct is assumed. Further, it is assumed that the strand is centered in the duct (i.e., at 12.5 mm).