Calculation of crack widths wk
Eurocode 2 part 1-1: Design of concrete structures 7.3 Crack control
The crack width, wk, may be calculated as follows:
|wk = sr,max⋅(εsm - εcm)||(7.8)|
- is the maximum crack spacing
- is the mean strain in the reinforcement under the relevant combination of loads, including the effect of imposed deformations and taking into account the effects of tension stiffening
- is the mean strain in the concrete between cracks.
- is the stress in the tension reinforcement assuming a cracked section,
see application for a rectangular section or application for a T-section
- is the design value of the modulus of elasticity of the reinforcing steel, see § 3.2.7 (4)
- is the ratio Es/Ecm
- is the mean value of the tensile strength of the concrete effective at the time when the cracks may first be expected to occur:
fct,eff = fctm or lower, (fctm(t)), if cracking is expected earlier than 28 days
= (As + ξ1⋅A'p)/Ac,eff (7.10)
- the cross sectional area of reinforcement
- the area of pre or post-tensioned tendons within Ac,eff
- the effective area of concrete in tension surrounding the reinforcement or prestressing tendons of depth, hc,ef, where hc,ef is the lesser of 2,5(h - d), (h - x)/3 or h/2 (see Figure 7.1)
- the adjusted ratio of bond strength taking into account the different diameters of prestressing and reinforcing steel:
ξ1 = (7.5)
- the ratio of bond strength of prestressing and reinforcing steel, according to Table 6.2
- the largest bar diameter of the reinforcing steel
- the diameter or equivalent diameter of prestressing steel:
Φp = 1,6⋅√AP for bundles, where AP is the area of a prestressing steel,
Φp = 1,75⋅Φwire for single 7 wire strands,
Φp = 1,20⋅Φwire for single 3 wire strands, where Φwire is the wire diameter.
- is a factor dependent on the duration of the load:
kt = 0,6 for short term loading,
kt = 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 sr,max may be calculated as follows:
|sr,max = k3c + k1k2k4Φ / ρp,eff||(7.11)|
- is the bar diameter. Where a mixture of bar diameters is used in a section, an equivalent diameter, Φeq, should be used.
- is the cover to the longitudinal reinforcement
- see the difference of the mean strains above
- 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).
- 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.
- is a Nationally Determined Parameter, see § 7.3.4 (3)
- 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 sr,max may be calculated as follows:
|sr,max = 1,3(h - x)||(7.14)|
This application calculates the crack width wk from your inputs. Intermediate results will also be given.
First, change the following option if necessary: