b6. Calculation method for moment of resistance of an uncracked rectangular section in bending at the SLS, M_{ct,ser}
Eurocode 2  Design of concrete sections
Figure b61 introduces a reinforced concrete section with notations. The serviceability moment of resistance M_{ct,ser} is unknown.
Criterion
The concrete is cracked if:
σ_{ct} > f_{ct,eff}  (b6.1) 
where:
 σ_{ct}
 is the tensile stress in concrete
 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_{ctm} or lower, (f_{ctm}(t)), if cracking is expected earlier than 28 days
Moment of resistance of an uncracked section M_{ct,ser}
The concrete section includes reinforcement. With the assumption of a noncracked section, the area of the homogeneous section is defined:
A_{c,eq} = b h + n_{e} (A_{s} + A_{sc})  (b6.2) 
where :
 n_{e}
 is the ratio E_{s}/E_{c,eff},
 with E_{c,eff} : the effective modulus of elasticity of concrete.
The depth of the neutral axis is calculated as:
x = [(b h^{2})/2 + n_{e} (A_{s} d + A_{sc} d')] / A_{c,eq}  (b6.3) 
The second moment of area of the homogeneous section is equal to:
I_{c,eq} = (b h^{3})/3 + n_{e} (A_{s} d^{2} + A_{sc} d'^{2})  A_{c,eq} x^{2}  (b6.4) 
The moment of resistance of the uncracked section M_{ct,ser} is calculated as:
M_{ct,ser} = f_{ct,eff} I_{c,eq} /(h  x)  (b6.5) 