Calculation of crack widths w_k

(7.9)

where:

σ_s

is the stress in the tension reinforcement assuming a cracked section,
see application for a rectangular section or application for a T-section

E_s

is the design value of the modulus of elasticity of the reinforcing steel, see § 3.2.7 (4)

α_e

is the ratio E_s/E_cm

with

E_cm

the secant modulus of elasticity of concrete

f_ct,eff

is the mean value of the tensile strength of the concrete effective at the time when the cracks may first be expected to occur:
f_ct,eff = f_ctm or lower, (f_ctm(t)), if cracking is expected earlier than 28 days

ρ_p,eff

= (As + ξ1⋅A'p)/Ac,eff

(7.10)

with

A_s

the cross sectional area of reinforcement

A'_p

the area of pre or post-tensioned tendons within A_c,eff

A_c,eff

the effective area of concrete in tension surrounding the reinforcement or prestressing tendons of depth, h_c,ef, where h_c,ef is the lesser of 2,5(h - d), (h - x)/3 or h/2 (see Figure 7.1)

ξ₁

the adjusted ratio of bond strength taking into account the different diameters of prestressing and reinforcing steel:

ξ1 =

(7.5)

with

ξ

the ratio of bond strength of prestressing and reinforcing steel, according to Table 6.2

Φ_S

the largest bar diameter of the reinforcing steel

Φ_P

the diameter or equivalent diameter of prestressing steel:
Φ_p = 1,6⋅√A_P for bundles, where A_P is the area of a prestressing steel,
Φ_p = 1,75⋅Φ_wire for single 7 wire strands,
Φ_p = 1,20⋅Φ_wire for single 3 wire strands, where Φ_wire is the wire diameter.

k_t

is a factor dependent on the duration of the load:
k_t = 0,6 for short term loading,
k_t = 0,4 for long term loading.

• Where the bonded reinforcenlent is fixed at reasonably close centres within the tension zone (spacing ≤ 5(c + Φ/2), cf. Figure 7.2), the maximum crack spacing s_r,max may be calculated as follows:

where:

Φ

is the bar diameter. Where a mixture of bar diameters is used in a section, an equivalent diameter, Φ_eq, should be used.

c

is the cover to the longitudinal reinforcement

ρ_p,eff

see the difference of the mean strains above

k₁

is a coefficient which takes account of the bond properties of the bonded reinforcement:
k₁ = 0,8 for high bond bars,
k₁ = 1,6 for bars with an effectively plain surface (e.g. prestressing tendons).

k₂

is a coefficient which takes account of the distribution of strain:
k₂ = 0,5 for bending,
k₂ = 1,0 for pure tension.
Intermediate values of k₂ should be used for cases of eccentric tension or for local areas:

k2 = (ε1 + ε2)/(2ε1)

(7.13)

where ε₁ is the greater and ε₂ is the lesser tensile strain at the boundaries of the section considered, assessed on the basis of a cracked section.

k₃

is a Nationally Determined Parameter, see § 7.3.4 (3)

k₄

is a Nationally Determined Parameter, see § 7.3.4 (3).

• Where the spacing of the bonded reinforcement exceeds 5(c + Φ/2) (cf. Figure 7.2), or where there is no bonded reinforcement within the tension zone, the maximum crack spacing s_r,max may be calculated as follows:

where:

h

is the overall depth of the section (see Figure 7.1)

x

is the neutral axis depth of the section (see Figure 7.1).