Strut-and-Tie Model Calculator

What it solves

Strut-and-tie modelling is how EN 1992-1-1 §6.5 handles the parts of a concrete structure where ordinary beam theory does not apply - regions where plane sections do not remain plane. That covers deep beams, corbels, pile caps, walls with openings and the zone immediately around a concentrated load or support.

This calculator builds the truss model for a deep beam, resolves the strut and tie forces from the geometry, and checks the compression struts, the nodes and the tension tie against the code limits. It reports the governing check and the strut angle, and warns when the geometry falls outside the range where the model is valid.

Worked example - 3.0 m deep beam carrying 2000 kN

The tool defaults: a 3000 mm span by 2000 mm deep beam, 400 mm wide, 400 mm bearing, carrying a 2000 kN central point load in C30/37 with 500 MPa reinforcement. Span-to-depth is 1.5, comfortably in deep beam territory. These figures come from calling the engine directly, so they are what the tool shows on load.

Support reaction R_A

1000 kN

Internal lever arm z (auto)

1400 mm

Strut inclination theta

43.03 degrees

cot theta

1.071

Strut force

1465.6 kN

Tie force

1071.4 kN

Design concrete strength f_cd

17.0 N/mm2

Strength reduction factor nu

0.88

Strut check

8.74 / 8.98 N/mm2, utilisation 0.974

Node check

6.25 / 12.72 N/mm2, utilisation 0.492

Tie check

1071.4 / 1071.4 kN, utilisation 1.000 - GOVERNS

The tie governs at exactly 1.000 because the tool sizes the reinforcement to match the tie force - that is the design outcome, not a coincidence. What matters is the margin on the other two: the strut is at 0.974, almost fully utilised, while the node has plenty of room at 0.492.

A strut utilisation that close to 1.0 is the number to watch. If the load increased even slightly, the concrete strut - not the reinforcement - would be the limit, and adding more steel would not help. Widening the beam or increasing the bearing length is what relieves a strut.

The strut angle is the design decision

Everything follows from theta. A shallower strut gives a longer lever arm and a smaller tie force, but the strut itself carries more load and the node stresses rise; a steeper strut does the opposite. EN 1992-1-1 constrains the angle to a usable range precisely because the extremes are unserviceable, and the tool flags a model outside it rather than returning a number that looks fine.

At 43 degrees the example sits near the middle of the permitted band, which is where a well-proportioned deep beam usually lands. If your model is being pushed to an extreme angle to make a check pass, the truss layout is probably wrong rather than the section being inadequate.

Formula reference

Design concrete strength

$f_{cd} = \dfrac{\alpha_{cc}\,f_{ck}}{\gamma_C}$

Strut strength, cracked

$\sigma_{Rd,\max} = 0.6\,\nu'\,f_{cd}$

Strength reduction factor

$\nu' = 1 - \dfrac{f_{ck}}{250}$

CCC node (compression only)

$\sigma_{Rd,\max} = k_1\,\nu'\,f_{cd}$

CCT node (one tie anchored)

$\sigma_{Rd,\max} = k_2\,\nu'\,f_{cd}$

Tie reinforcement

$A_s = \dfrac{F_{tie}}{f_{yd}}$

Design steel strength

$f_{yd} = \dfrac{f_{yk}}{\gamma_S}$

Strut force from geometry

$F_{strut} = \dfrac{R}{\sin\theta}$

Assumptions and limits

A strut-and-tie model is a lower-bound plasticity solution: any statically admissible truss that satisfies equilibrium and the stress limits is safe, but different valid trusses give different amounts of reinforcement. The model here is the standard single-strut deep beam layout, which is appropriate for a symmetric point load. A different load arrangement, multiple loads, or an opening in the web needs a different truss that this tool does not build for you.

Because the method is lower bound, it guarantees strength but says nothing about serviceability. Crack width and deflection are not checked here, and a deep beam with a heavily utilised strut can still be unserviceable. Detailing matters as much as the numbers: the tie must be fully anchored past the node, which usually means bends or bearing plates rather than a straight bar stopped at the support.

Distributed reinforcement to control cracking in the web is required in addition to the main tie, and the tool does not size it. Fatigue, fire and seismic detailing are outside the scope.

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