# Crack control: the minimum reinforcement area `A`_{s,min}

_{s,min}

## Eurocode 2 part 1-1: Design of concrete structures 7.3.2 (2)

If crack control is required, a minimum amount of bonded reinforcement is required to control cracking in areas where tension is expected. The required minimum areas of reinforcement may be calculated as follows:

A _{s,min}σ = _{s}k _{c}k f _{ct,eff}A_{ct} | (7.1) |

where:

`A`_{s,min}- is the minimum area of the reinforcing steel within the tensile zone
`A`_{ct}- is the area of concrete within tensile zone.
`σ`_{s}- is the absolute value of the maximum stress permitted in the reinforcement immediately after formation of the crack. This may be taken as the yield strength of the reinforcement,
`f`. A lower value may, however, be needed to satisfy the crack width limits according to the maximum bar size or spacing (cf. 7.3.3 (2))_{yk} `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`or lower, (_{ctm}`f`), if cracking is expected earlier than 28 days_{ctm}(t) `k`- is the coefficient which allows for the effect of non-uniform self-equilibrating stresses, which lead to a reduction of restraint forces

= 1,0 for webs with`h`≤ 300 mm or flanges with widths less than 300 mm,

= 0,65 for webs with`h`≥ 800 mm or flanges with widths greater than 800 mm,

intermediate values may be interpolated `k`_{c}- is a coefficient which takes account of the stress distribution within the section immediately prior to cracking and of the change of the lever arm:

* For pure tension`k`= 1,0;_{c}

* For bending or bending combined with axial forces:

- For rectangular sections and webs of box sections and T-sections:

(7.2) where:

`σ`_{c}- is the mean stress of the concrete acting on the part of the section under consideration:
`σ`=_{c}`N`/(_{Ed}`b`⋅`h`)(7.4) with

`N`_{Ed}- the axial force at the serviceability limit state acting on the part of the cross-section under consideration (compressive force positive).
`N`should be determined considering the characteristic values of prestress and axial forces under the relevant combination of actions_{Ed} `b`- the width of the section
`h`- the height of the section

`h`^{*}-
`h`=^{*}`h`for`h`< 1,0 m

`h`= 1,0 m for^{*}`h`≥ 1,0 m `k`_{1}- is a coefficient considering the effects of axial forces on the stress distribution:

`k`= 1,5 if_{1}`N`is a compressive force_{Ed}

`k`= 2_{1}`h`/(3^{*}`h`) if`N`is a tensile force_{Ed}

(7.3) where:

`F`_{cr}- is the absolute value of the tensile force within the flange immediately prior to cracking due to the cracking moment calculated with
`f`_{ct,eff}.

This application calculates
the minimum reinforcement area `A _{s,min}`
from your inputs.
Intermediate results will also be given.

First, change the following option if necessary: