Crack control, cover and congestion

Crack control without calculating a crack width

Module 6 calculated a crack width from first principles: spacing times strain difference. In routine design that calculation is usually skipped, and a deemed-to-satisfy rule used instead.

The rule limits either the bar diameter or the bar spacing, as a function of the steel stress under the quasi-permanent combination. Both are tabulated, and both get tighter as the stress rises.

Either limit is sufficient on its own. They are two routes to the same end, not two requirements.

That is worth stating plainly because reading them as simultaneous requirements is a common error, and it makes many perfectly ordinary details appear to fail. A beam with large bars at close centres satisfies the spacing route and needs no further justification.

Cover fights crack control

From Module 6, the crack spacing is

s_r,max = 3.4c + 0.425 k₁k₂φ/ρ_p,eff

The first term is proportional to cover. So increasing cover from 35 mm to 50 mm adds 51 mm to the crack spacing, and since crack width is spacing times strain, the surface cracks get proportionately wider.

This is a genuine conflict, not a modelling artefact. A bar deep inside the concrete cannot control what happens at a surface far away from it.

• Durability wants more cover, to keep chlorides and carbonation away from the steel.
• Crack control wants less cover, so the bars are closer to the surface they are controlling.
• Fire wants more cover, to keep the steel cool.
• Effective depth wants less cover, because every millimetre of cover is a millimetre off d.

Three of the four pull the same way, and durability and fire usually win — cover is set by exposure class and fire rating, and is not a free variable. What the designer then adjusts is bar size and spacing, which is why crack control is a detailing decision rather than a calculation.

Congestion: the check that does not exist

There is no code check for whether a detail can be built. There is a minimum clear spacing, which is necessary but nowhere near sufficient: a beam can satisfy it and still be impossible in practice, because the calculation does not know about

• the links, which occupy the corners and cannot be moved;
• the column bars passing through the joint, which arrive wherever the column put them;
• the beam bars coming in from the other direction, at the same level;
• the laps, which double the bar count wherever they occur;
• the poker, which needs somewhere to go.

Congestion is caught by someone looking at a drawing, or by a steel fixer on site who cannot get the bars in and moves them. The second is much worse, because nobody tells the designer.

One thing that can be reasoned about

For bars of 25 mm and above, the minimum clear gap equals the bar diameter. So a full layer of n bars needs nφ of bar and (n − 1)φ of gap:

nφ + (n − 1)φ ≤ W, which rearranges to nφ/W ≤ (W + φ)/2W

A single layer is therefore about half bar and half air — 47% for H25 in a 300 mm web, 53% for H32 in a 400 mm web. It can never approach being solid steel, whatever the drawing looks like.

That bounds the problem usefully. It means the congestion signal is not how full a layer looks, because a full layer always looks about half empty. The signal is whether the bars fit in one layer at all, and whether a layer near its ceiling still has to accommodate links, column bars and laps.