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 b6-1 introduces a reinforced concrete section with notations. The serviceability moment of resistance M_ct,ser is unknown.

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

The concrete section includes reinforcement. With the assumption of a non-cracked section, the area of the homogeneous section is defined:

A_c,eq = b h + n_e (A_s + A_sc)

(b6.2)

where :

The depth of the neutral axis is calculated as:

x = [(b h²)/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 h³)/3 + n_e (A_s d² + A_sc d'²) - A_c,eq x²

(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)