Displacements of cracked members - Concrete Structures: Stresses and Deformations - page 270

or

2

N r
N

ζ = 1 − (with N > N r ) (8.12)

In Equation (8.10), the mean strain in steel is determined by interpolation
between the steel strains ε s1 and ε s2 in states 1 and 2. The interpolation co-

e σ s2 in a fully

cracked section when the applied forces are N r and N , respectively. The use of
this equation will be extended in the following sections to be applied for
members subjected to bending.
In order to take into account the bond properties of the reinforcing bars
and the in

cient ζ depends upon the ratio of the steel stresses σ sr and

uence of duration of the application or the repetition of loading,
the Eurocode 2-1991 2 (EC2-91) introduces the coe

fl

cients β 1 and β 2 into

Equation (8.11) as follows:

σ sr
σ s2

2

ζ = 1 − β 1 β 2 (with σ s2 σ sr ) (8.13)

where β 1 = 1 and 0.5 for high bond bars and for plain bars, respectively. β 2 = 1

and 0.5, respectively for rst loading and for loads applied in a sustained

manner or for a large number of load cycles.
With this modi

fi

ε sm (Fig. 8.2) will have a horizontal
plateau at cracking level as shown in Fig. 8.3 (line AC).
The second term in Equation (8.10) (

fi cation, the graph of

ζε s2 ) represents the supplementary
strain of steel compared with the strain of concrete. 3 Thus, the average width
of a crack is

w m = s rm ζε s2 (8.14)

Figure 8.3 Mean strain in the reinforcement of a cracked member (according to EC2-91).