2.2.3 Minimum Reinforcement

Minimum Reinforcement

The minimum reinforcement area for crack control is determined according to EN 1992-1-1, clause  7.3.2 (2), Eq. (7.1), simplified as follows:

$A_{s,min} · {\sigma }_s = k_c · k · f_{ct,eff} · A_{ct}$

Equation 2.10 EN 1992-1-1, Eq. (7.1)

where

• A_s,min : minimum area of reinforcing steel in tension zone
• σ_s : allowable stress of reinforcing steel according to Figure 2.3
• k_c : factor for considering stress distribution in tension zone
  • k_c = 1.0 for pure tension
  • k_c = 0.4 for bending
  • For bending with axial force, k_c is determined as follows:

$k_c = 0.4 · \left[1 -\frac{{\sigma }_c}{k_1 · \left(h/h^{*}\right) · f_{ct,eff}}\right] \le 1$

Equation 2.11 EN 1992-1-1, Eq. (7.2)

• where
  • σ_c : mean concrete stress acting on part of section under consideration
    σ_c = N_Ed / (b ⋅ h)
  • N_Ed : axial force acting on part of cross-section under consideration
  • h^* = h < 1.0 m
  • k₁ : coefficient for considering effects of axial forces on stress distribution:
    • k₁=1.5 for N_Ed = compressive force
      k₁ = 2h^*/3h for N_Ed = tensile force
• k : coefficient to consider nonlinearly distributed self-equilibrating stresses
  • k = 1.0 for webs with h ≤ 300mm
  • k = 0.65 for h ≥ 800 mm
  • k = 1.0 for restraint caused outside (e.g. column settlement)
• f_ct,eff = f_ctm : mean value of effective tensile strength of concrete when cracks occur
• A_ct : area of concrete tension zone