Structural Engineering & Statics
where the load goes
Concept

Stirrup — where it appears

A closed or open link of reinforcement wrapping a beam's longitudinal bars, carrying the tension across a diagonal shear crack. Its spacing rather than its size usually governs, because a crack must be crossed by at least one link to be controlled at all.

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

Also named here as web crushing — the same set of essays touches all of them, so they are one junction rather than several.

The cut that severs the stirrups is the cut that counts them. A cracked web drawn as the truss it has become: a tension chord along the bottom, a compression chord along the top, concrete struts between the cracks and stirrups crossing them. The free body is a cut parallel to the cracks, which over a lever arm of 495 mm severs z·cot θ/s = 8.3 stirrups at cot θ = 2.5. Every one of them is at yield, so the shear is their number times their strength, and flattening the crack raises the count rather than the strength. The same cut passes through the bottom chord, which is where the chord force the moment diagram does not contain comes from.

The beam that becomes a truss

Once a web has cracked in shear there is no shear stress field in it any more. There are concrete struts, two chords and whatever crosses the cracks, and the angle of those cracks is not a property of the material — it is something the designer chooses, and every quantity in the beam moves when it changes.

internal-forces · Shear truss analogy Flattening the truss saves stirrups and crushes the web. Two capacities against the angle of the cracks, for a web 350 mm wide with a lever arm of 630 mm. The rising line is the stirrups: a cut along the crack severs z·cot θ/s of them, so flattening the crack from 45° to cot θ = 2.5 takes the 315 kN they carry to 787 — 2.5 times as much from the same steel. The falling line is the concrete strut, whose stress is V(cot θ + tan θ)/b_w z and therefore least at 45°. They do not cross in this range, so the stirrups govern throughout and the angle is a free choice.

The angle is a choice, not a property

The truss inside a cracked concrete web has a strut angle, and nothing measures it. The designer picks it, the stirrup requirement falls as it flattens, the web stress rises, and every choice in between is a different structure that carries the same load.

internal-forces · Concrete shear

Named alongside it

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

EquilibriumFree bodyReinforcementShift ruleStrut-and-tieWeb crushingAggregate interlockConcrete shearConcrete strutCracked sectionLever armLower-bound theorem

All concepts