Cracking (Concrete Column)

Last modified by Fredrik Lagerström on 2021/06/02 10:47

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


  • 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)


  • 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


  • 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
    • kt = 0,6 for short term loading
    • kt = 0,4 for long term loading.

Effective area of Ac,eff

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


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


  • 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.

92997_-_flag_sweden.png Swedish annex

k3 = 7ø /c

92848_-_denmark_flag.png 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)


  • 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)


  • 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.
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