Structural Engineering & Statics
where the load goes
Concept

Crack width — where it appears

How far the two faces of a crack have separated, which decides how much shear the roughness on them can carry. It scales with the member's depth while the aggregate bridging it does not, which is the whole of the size effect in the shear strength of a member with no links.

Named by 2 essays across 2 fields — each of them below, with the objects they name alongside it.

Cover enters twice, and the strength of the concrete enters once. How long a 20 mm bar has before the cover over it splits, against the cover, split into the two halves it is always split into. Initiation is the time for the chloride front to reach the bar, which goes as the square of the cover — Fick's law and nothing else — and it is 9.1 years at 35 mm and 36.2 at 70. Propagation is the time from there to a split cover, which is short: 0.9 years, because the cover cracks at a section loss of 0.21% and no strength check in this collection would notice a loss that small. The pressure the cover can take grows with the cover too, so cover appears in both terms and the concrete's own tensile strength appears in one of them, linearly. That asymmetry is why every durability clause in every code is about cover and crack width, and hardly at all about strength.

The load that comes from inside

Every action in this collection has been applied from outside — a weight, a pressure, a movement, a temperature. Corrosion is not applied at all, and the reason it belongs to statics rather than to durability is that what does the damage is a load: rust occupies three times the volume of the steel it came from, and the only place to make room is by pushing the cover apart.

materials · corrosion A strength with no mechanism in it, made of four. The shear a member carries with no links in it, split into the mechanisms that carry it, against the member's effective depth on a logarithmic axis. The three bands are calibrated to Taylor's measured shares at one 300 mm × 500 mm member and are then evaluated everywhere else, so the shape of the total is a prediction. Aggregate interlock is the band that dies: it depends on how tightly the crack faces are held together, crack width grows with member depth, and it falls from 62% of a shallow member's strength to 22% of a deep one's. That decay is the whole of the size effect, and the dashed line is the code's fitted k = 1 + √(200/d), which knows nothing about interlock and falls by a factor of 1.52 where the model falls by 2.05 over the same twentyfold range. Dowel action is why the expression contains the flexural reinforcement ratio, which nothing in a truss analogy would predict.

The strength with no mechanism in it

A concrete member with no links in it carries shear, and the expression that says how much is three variables raised to fitted powers with a size term in front. There is no free body anywhere in it. What it is fitting is a competition between four things that carry shear across a crack, and only one of them explains why a deeper member is worse at it.

internal-forces · concrete shear

Named alongside it

The objects these essays reach for when they reach for this one.

BondAggregate interlockAnchorageCorrosionCoverCracked sectionDiffusionDowel actionDurabilityEmpirical formulaExpansionFailure surface

All concepts