Last month I discussed why steel in concrete can’t keep it from cracking. But there are a few other thing to learn about the relationship between embedded steel and concrete gaps:

Rule 14d: Any reinforcement that is not spanning a gap is serving no purpose.

Many closely jointed slabs are detailed to have general reinforcement—usually in the form of WWR—that is discontinued at both sawcuts and construction joints. If made small enough, very few of the panels bounded by the joints will ever crack. Taken together, Rules 14c (in the July issue) and 14d explain why money spent on reinforcement in such cases is wasted. However, if the joint spacing is large enough to cause a significant number of panels to crack, then the owner does receive real value for each reinforcement dollar. By binding the gaps, the steel actually is doing something useful.

Rule 14e: The use of reinforcement is a tacit admission that significant cracking is expected.

Otherwise, the specified steel has no purpose. Rules 14b through 14e all result from concrete’s inability to stretch as much as steel without breaking. Using the elastic modulus and tensile strength equations given in ACI 318, a length L of 150 pcf concrete can be stretched up to 0.000124 L before breaking in two. The same length L of Grade 60 rebar can be stretched almost 17 times more, 0.002069 L, before it yields. This offers another perspective on why rebar can’t prevent concrete cracks: By the time embedded steel has been able to assume even a small fraction of the load it is capable of carrying, the concrete encasing it must already have broken.

Rule 14f: The reinforcement must debond from the concrete at every gap it spans.

Suppose a zero-width crack forms across a perfectly embedded Grade 60 rebar, and then the crack grows wider. Can the bond between the steel and concrete remain unchanged? No. Because keeping the original bond intact would leave no steel available to stretch with the crack, some length of bar must detach from the concrete for the crack to widen. Otherwise, the additional steel length required to bridge the new gap would require the application of an infinite stress.

In reality, if the steel’s yield stress is not to be exceeded, then the debonded length between the steel and concrete at the crack must be at least 242 times the spanned gap. For a rebar to bridge a 0.010-inch-wide crack and still remain elastic, its debonded length at the crack must span 5 inches.

Rule No. 14g: Continuous steel reinforcement has only two functions: 1) to induce the formation of cracks, and 2) to stabilize gaps in the concrete.

Following Rule 12c, continuously reinforced, unjointed slabs employ steel in the top 2 1/2 inches to restrain the shrinking concrete and induce the formation of reasonably tight cracks. Because each crack derives from the work that must be done to break the local concrete-to-steel bond, increasing both the total area of the bonds and their unit strengths causes more and tighter cracks to form.

Rule No. 14h: For a given bond strength, the relative ability of a continuous layer of steel wire or bar to induce the formation of transverse cracks is given byR% t[ 3.7 -c( 4.5 -c)½ ], whereR%is the layer’s reinforcement percentage,tis the nominal thickness in inches, andcis the layer’s nominal cover in inches.

This rule relies on all standard wire and bar reinforcements having solid circles as cross sections. If such were not the case, then much less steel would be needed. Once the concrete cover has been set, it is the bond area per square foot of slab that determines the amount of reinforcement required to force a given crack spacing, not just the weight of steel per square foot of slab.

When trying to force cracks, maximizing bond strengths by keeping the reinforcement clean is also important. This suggests it might be possible to influence the induced crack locations simply by disrupting the bond along the desired lines.