A strut-and-tie model is built from three basic elements — concrete struts in compression, steel ties in tension, and the nodal zones where they meet and the forces change direction. The struts and ties are the one-dimensional members of the truss; the nodes are its pinned joints. The sections below take each element in turn: first what it is, then how its strength is checked.
The elements of an STM
Strut
A strut is the idealization of a concrete compression stress field. By the shape of that field it takes three forms: the fan, which spreads out from a concentrated load or support; the bottle, which bulges and spreads sideways; and the prism, a uniform parallel field. Because the bottle strut spreads laterally, it produces transverse tension across its axis — without crack-control reinforcement to carry it, the strut can split.
Its usable strength is below fck and depends on that shape and on what crosses it. Design codes express this with an effective compressive strength — in ACI form fce = 0.85 · βs · βc · fck — where βs accounts for the strut's condition and βc for confinement. A prismatic strut in an uncracked field keeps the full factor; a bottle-shaped strut is reduced unless crack-control reinforcement crosses it; struts crossing tension zones are reduced further.
- Three forms — fan (spreads from loads/supports) · bottle (bulges, needs crack-control steel) · prism (uniform)
- βs: prismatic ≥ bottle-shaped (reinforced) > bottle-shaped (unreinforced) > tension-zone struts — per the code tables
- AStrutTie applies the right effective strut strength per selected code (ACI 318 · AASHTO LRFD · Eurocode 2) and reports every factor used
Tie
A tie carries tension, usually resisted by reinforcement (sometimes prestressing strand). The bars are placed symmetrically about the line of action of the force, run the full length of the tie, and must be properly anchored at the nodes. Sizing the steel so the tie just yields at the ultimate load makes it yield — a ductile failure — before the concrete crushes.
A tie is designed on the assumption that the reinforcement reaches its design yield strength at the point of maximum stress; the tensile strength of the concrete is generally ignored. The governing issue is anchorage rather than strength itself — the bars must develop their full force by bond within or beyond the node, and that is the crux of tie design.
- Reinforcement placed symmetrically, run the full length, anchored at the nodes
- Sized to yield at the ultimate load → ductile failure; concrete tension ignored
- Anchorage governs — the bar must develop its full force within or beyond the node
Nodal zone
A node is where struts, ties, and applied loads or reactions meet and the forces change direction; the nodal zone is the finite volume of concrete that turns them around — the pinned joint of the truss. Nodes are of two kinds: the singular node, where concentrated stress fields meet, and the smeared node, where wide fields join through ties. The singular node is the more important to verify, its force transfer being more abrupt with higher stress concentration. Nodes matter for two reasons — controlling stress for a safe transfer of forces, and setting the anchorage of reinforcement and the size of bearing plates.
The node is classified by the forces that frame into it — C for a compression strut, T for a tie — and the strength factor βn drops as more ties connect (CCC 1.0 · CCT 0.8 · CTT 0.6), because ties must be anchored through the zone and their bond cracking softens the concrete. Geometry matters as much as the factor: in a hydrostatic node the faces are drawn perpendicular to each force so the stress is equal on every face, while an extended nodal zone borrows the overlapping concrete to raise the usable area. AStrutTie checks bearing on every nodal face and reports the governing one, so the critical node is never hidden inside a single global pass/fail.
- Two kinds — singular (concentrated, more important to check) · smeared (distributed through ties)
- CCC (all compression) βn = 1.0 · CCT (one tie) βn = 0.8 · CTT (two or more ties) βn = 0.6 — ACI 318
- Hydrostatic node: faces ⟂ to each force · extended node: larger effective bearing area · face bearing checked per node