Continuous beams and slabs, and beams in frames - Composite Structures of Steel and Concrete - page 144

that allows for the non-uniform tension in the concrete prior to cracking.
In Equation 4.32, h c is the thickness of the concrete flange, excluding any
ribs, and z 0 is the distance of the centroid of the uncracked composite
section (for short-term loading) below the centroid of the concrete flange.
For composite beams, the ratio z 0 / h c typically increases with the span.
Where it exceeds 1.17, k c 1.0, and the tension is effectively treated as

uniform over the thickness of the concrete flange.
Finally, f sk in Equation 4.31 is replaced by

=

σ s , the maximum stress
permitted in the reinforcement immediately after cracking ( ≤ f sk ), which

influences the crack width. This leads to the design rule

A s ≥ 0.8 k c f ct,eff A ct / σ s (4.33)

To use this rule, it is necessary to estimate the value of the tensile
strength f ct,eff when the concrete first cracks. If the intrinsic deformation
due to the heat of hydration or the shrinkage of the concrete is large,
cracking could occur within a week of casting, when f ct,eff is still low.
Where this is uncertain, EN 1994-1-1 permits the use of the mean value
of the tensile strength corresponding to the specified 28-day strength of
the concrete, f ctm , which is approximately 0.1 f ck , or 0.08 f cu , where f cu is the
specified cube strength.
The choice of the stress

σ s depends on the design crack width, w k , the

diameter φ of the reinforcing bars, and the value of f ct,eff . Figure 4.7 gives

Figure 4.7 Maximum steel stress for minimum reinforcement, high

bond bars