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b7. Calculation method for moment of resistance of an uncracked T-section in bending at the SLS, Mct,ser

Eurocode 2 - Design of concrete sections

Figure b7-1 introduces a reinforced concrete T-section with notations. The serviceability moment of resistance Mct,ser is unknown.


The concrete is cracked if:

σct > fct,eff (b7.1)


is the tensile stress in concrete
is the mean value of the tensile strength of the concrete effective at the time when the cracks may first be expected to occur:
fct,eff = fctm or lower, (fctm(t)), if cracking is expected earlier than 28 days

Moment of resistance of an uncracked section Mct,ser

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

Ac,eq = bw h + (beff - bw) hf + ne (As + Asc) (b7.2)

where :

is the ratio Es/Ec,eff,
with Ec,eff : the effective modulus of elasticity of concrete.

The depth of the neutral axis is calculated as:

x = [(bw h2)/2 + (beff - bw) hf2/2 + ne (As d + Asc d')] / Ac,eq (b7.3)

The second moment of area of the homogeneous section is equal to:

Ic,eq = (bw h3)/3 + (beff - bw) hf3/3 + ne (As d2 + Asc d'2) - Ac,eq x2 (b7.4)

The moment of resistance of the uncracked section Mct,ser is calculated as:

Mct,ser = fct,eff Ic,eq /(h - x) (b7.5)