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302 New Trends in Eco-efficient and Recycled Concrete

penetration depth is of RAC and NAC is considered. The simplifications result in
the square root of the ratio between the diffusion coefficients in RAC and RC.

11.4.1.4 Creep

Creep affects the long-term deformation in reinforced concrete structures, influencing
the SLSs. Usually, the creep coefficient is used indirectly in the design computations,
by affecting instant elastic deformations or adjusting elastic parameters, such as the
modulus of elasticity. For example, the effective modulus of elasticity, E c,eff ,consid-
ers the influence of creep and is used to determine the long-term behaviour.

11.4.2 Simplified approach (based on the compressive strength
classes only)

One possible criteria to define an EFU can be based on simple ULS considering
just the changes in compressive strength of RAC versus NAC. This change in com-
pressive strength would have to affect the beam/slab cross section, by means of an
increase in its height (in pure bending), the effective height (d). Considering this,
and the ratios χ and ξ that relate the compressive strength (11.1) and effective
height (11.2) between RAC and NAC, respectively (Table 11.1), it is possible to
establish a relationship between these two factors, for a common resisting bending
moment (M Rd ), tension rebar area (A s ) and steel yielding strength (f yd ).
Knowing that the ULS resisting moment (M Rd ) in pure bending, assuming a rect-
angular compressive stress block and tension reinforcement at yielding, is equal to:

M Rd 5 A s f yd d 2 0:4xð Þ (11.3)

and that the neutral axis (x) can be computed from the equilibrium of normal stres-
ses at the cross-section as follows:

A s f yd
x 5 (11.4)
0:8bf cd
It is possible to establish the variation of ξ as a function of χ, as seen in
Eq. (11.5), where ω has the physical meaning indicated in Eq. (11.6)

Table 11.1 Ratios that relate the compressive strength and effective height between RAC
and NAC

Equation Meaning
(11.1) f cd,RAC , f cd,NAC design compressive strength
f cd;RAC 5 χf cd;NAC
of RAC and NAC elements, respectively
(11.2) d RAC , d NAC effective height of the cross section
d RAC 5 ξd NAC
of RAC and NAC elements, respectively