# Cracking stress

A section is assumed to be in cracked state when the maximum tensile stress, calculated on basis of a uncracked section, exceeds the tensile strength of the concrete. At bending the crack condition is then expressed as:

σn + σm ≤ fctm

where:

• σn is stress of normal force
• σm is stress of moment
• fctm is the mean tensile design strength.

# Cracking moment

Cracking moment is the moment that barely causes cracking. With section forces N and M and belonging stresses σn and σm we find the factor c that induces  cracking at forces N and c M by:

c = (fctd – σn ) / σm

and cracking moment by:

Mcrack = c M

# Crack width calculation

The crack width wk may be calculated from:

wk = Sr,maxsm - εcm)

where:

• Sr,max is the maximum crack spacing
• εsm is the mean strain in the reinforcement
• εcm is the mean strain in the concrete between cracks
• εsm - εcm may be calculated from:
• εsm - εcm = [σs - kt fct,eff / ρp,eff (1 + αe ρp,eff)] / Es ≥ 0,6 σs / Es

where:

• σs is the stress in the tension reinforcement assuming cracked section
• αe is the ratio Es / Ecm
• fct,eff is the mean value of the tensile strength of the concrete when the first crack occur
• fct,eff = fctm
• ρp,eff = As / Ac,eff
• Ac,eff is the effective area of concrete as calculated below
• kt is a factor dependent on the duration of the load

# Effective area of Ac,eff

Ac,eff is the effective area of concrete of depth hc,ef

where

• hc,ef is the lesser of:
• 2,5 (h - d)
• (h - x) / 3
or
• h/2, see figure below:

# Crack spacing Sr,max

For bonded reinforcement with spacing ≤ 5(c + ø / 2) the crack spacing is calculated as:

• Sr,max = kc + k1 k2 kø/ ρp,eff

where:

• ø is the bar diameter in mm. If more than one bar size is present an average bar size øeq should be used,
• øeq = (n1 ø12 + n2 ø22) / (n1 ø1 + n2 ø2)
• c is the cover to the longitudinal reinforcement,
• k1 = 0,8 for high bond bars, 1,6 for plain bars
• k2 = 0,5 for bending, 1,0 for pure tension,
• k3 = 3,4
• k4 = 0,425
• ρp,eff as above.

Swedish annex

k3 = 7ø /c

Danish annex

k3 = 3.4 (25/c)2/3

For not bonded reinforcement or reinforcement with spacing > 5 (c + ø / 2) the crack spacing is calculated as:

• Sr,max = 1,3 (h - x)

where:

• x is the neutral axis depth.

The crack spacing should be calculated in the direction of the principle tensile stress as:

• Sr,max = 1 / (cos θ / Sr,max,y + sin θ / Sr,max,z)

where:

• θ is the angle between the reinforcement in the y-direction and the direction of the principal tensile stress
• Sr,max,y and Sr,max,z are the crack spacing’s calculated in the y and z directions respectively.