Minimum reinforcement for crack control - Flanges of sections

Concrete characteristic strength

f_ck

MPa

e.g. 30 MPa for concrete class C30/37. For a list of concrete classes see Table of Concrete Design Properties. For bridges, according to EN 1992-2 §7.3.2(105) in calculating the minimum reinforcement to cater for shrinkage the effective tensile strength of concrete f_ct,eff should not be taken less than 2.9 MPa. This can be effected by selecting concrete compressive strength f_ck at least equal to 30 MPa corresponding to concrete class C30/37.

Steel characteristic yield strength

f_yk

MPa

Overall height of cross-section

h

m

Width of the examined flange

b_f

m

Thickness of the examined flange

t_f

m

Normalized location of the centroid of the overall cross-section from the most compressive edge

z_cm/h

It describes the location of the centroid of the overall composite cross-section where the stress value σ_c is applicable. A value of 0.5 corresponds to the middle of the height h.

Mean axial stress in the examined section part in the uncracked state - SLS combination (positive when compressive)

σ_c

MPa

Mean elastic stress acting on the part of the section under consideration (=N_Ed/A) considering the characteristic values of prestress and axial forces at the appropriate SLS combination (typically the quasi-permanent combination for reinforced concrete, see EN1992-1-1 §7.3.1). Compression positive. Any value of the stress σ_c less than the tensile strength of concrete -f_ct,eff is treated as pure tension.

Apply coefficient k (effect of non-uniform self-equilibrating stresses reducing restraint)

Selecting 'Yes' is appropriate for members where tensile stresses are the result of restraint due to internal stresses (e.g. shrinkage, hydration heat). Selecting 'No' is a conservative option. This option may be appropriate for cases where the imposed deformations are external to the member (e.g. support settlement), see also German National Annex to EN 1991-1-1 §7.3.1.

Diameter of reinforcement bars

Φ

mm

Distance from centroid of reinforcement layer to nearest concrete edge

c'

m

Concrete cover to tensile reinforcement surface

c

mm

Crack control verification is strongly affected by the concrete cover c (distance between the surface of longitudinal reinforcement closest to the nearest concrete surface). Larger values of c produce more unfavorable results.

Calculation method for maximum steel stress permitted in the reinforcement after crack formation

The steel stress can be limited automatically to satisfy the crack width requirement according to the direct calculation method in EN 1991-1-1 §7.3.4. Otherwise the maximum permitted steel stress can be specified manually e.g. as a function of the bar diameter and bar spacing according to the tables in EN 1991-1-1 §7.3.3.

Maximum steel stress permitted in the reinforcement

σ_s

MPa

Limiting value for the calculated crack width

w_max

mm

According to the National Annex to EN1992-1-1 §7.3.1(5). Typically for crack control verification of reinforced concrete a value of w_max = 0.3 mm is applicable. Enter very large value (e.g. 999) if crack control is not required and the steel stress should be limited to the yield strength of the reinforcement f_yk.

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Eurocode 2 Minimum reinforcement for crack control of flanges of profiled sections (box-shaped, I-shaped)

Minimum reinforcement for flanges of profiled sections