The designer is concerned however with the maximum crack width which has an acceptably low probability of being exceeded. For design purposes the design maximum crack width, iv^, can be based on the maximum spacing. .vr.TOX. Hence the design crack width at any level defined by y in a member will thus be given by
The expression for the design crack width given in EC2 is of the above form and is given as
vi'k = the design crack width
■V.max ~ the maximum crack spacing esin the mean strain in the reinforcement allowing for the effects of tension stiffening of the concrete, shrinkage etc.
fcm the mean strain in the concrete between cracks
The mean strain. £sm. will be less than the apparent value £\ and - -:cm) is given by the expression where <t, is the stress in the tension steel calculated using the cracked concrete section. k, is a factor that accounts for the duration of loading (0.6 for short-term load. 0.4 for long-term load).
The maximum crack spacing. .yr.mux. is given by the empirical formula where <!> is the bar size in mm or an average bar size where a mixture of different sizes have been used and c is the cover to the longitudinal reinforcement. k\ is a coefficient accounting for the bond properties of the reinforcement (0.8 for high bond, 1.6 for plain bars) and ki is a coefficient accounting for the nature of the strain distribution which for cracking due to flexure can be taken as 0.5. pp,cfi is the effective reinforcement ratio, ^sMc.eff. where /I, is the area of reinforcement within an effective tension area of concrete Ac,efr, as shown in figure 6.12.
The effective tension area is that area of the concrete cross-section which will crack due to the tension developed in bending. This is the cracking which will he controlled by the presence of an appropriate type, amount and distribution of reinforcement. Generally the effective tension area should be taken as having a depth equal to 2.5 times the distance from the tension face of the concrete to the centroid of the reinforcement.
where
Figure 6.12
Typical examples of effective concrete tension area
Effective tension area d r-V
Effective tension area for this face
Effective tension area for this face
Effective tension area
Slab
Member in tension
Slab
although for slabs the depth of this effective area should be limited to [li — x)/3. An overall upper depth limit of h/2 also applies.
Although not directly incorporated into the above formulae, it should be noted that crack widths may vary across the width of the soffit of a beam and are generally likel> to be greater at positions mid-way between longitudinal reinforcing bars and at the corners of the beam. Where the maximum crack spacing exceeds 5(c + <j>/2) then an upper bound to crack width can be estimated by using sr max - 1.3(/i —x).
To use the formula of EC2 it is necessary to carry out an elastic analysis of the cracked concrete section using an effective modulus £,. Cft , as given in equation 6.8 to allow for creep effects.
The methods discussed in section 4.10.1 should be used to lind the neutral axi-position, .v, and hence the stresses. <rs and nsr. in the tensile reinforcement from which \m (equation 6.16) can he obtained.
Calculation of flexural crack widths
Calculate the design flexural crack widths for the beam shown in figure 6.13 when subject to a quasi-permanent moment of 650 kN m. The concrete is class C25/30 and the reinforcement is high bond with a total cross-sectional area of 3770 mm2.
(a) Calculate the mean strain esm
From table 6.11. Et,,, 31 kN/mnr. From table 6.12, assuming loading at 28 days with indoor exposure, the creep coefficient o « 2.63 (because 2Aju = 2x [ 1000 x 4001/2800 - 285) and hence the effective modulus is given by equation 6.8 as
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