Section Analysis

The nonlinear fiber section analysis in StructuralMind divides a section into many small pieces, assigns each piece its own strain and the stress that corresponds to it, then sums them and solves for equilibrium with the forces acting on the section. The capacity therefore comes out of the material curves themselves rather than out of a single closed relation. What that buys is the ability to choose how concrete and steel actually behave, and to see not only the moment a section carries but the curvature at which it gets there.

The purpose of fiber section analysis is not to issue a code verdict. This macro exists to analyse and present the expected behaviour of a section. That is why the constitutive models and the material factors are supplied by the user, both factors defaulting to 1, so the calculation runs on characteristic strengths. When a specific code design check is needed, you can use the Column Design macro. The interaction diagram that enters the strength check there and the diagram you see here come from the same engine.

What is computed#

Axial compression is taken as positive and must be entered that way. A bending angle of 0° is bending about the horizontal axis and 90° about the vertical axis. Angles in between give combined bending, and the three-dimensional interaction surface is swept from 0° to 360°.

Section and reinforcement#

Rectangular, circular and hollow circular sections can be analysed.

Reinforcement is defined in one of two ways.

In the edge-based layout the four corner bars need not share a diameter. The top and bottom counts include the corners.

Stirrups can be defined as rectangular, circular or spiral. A rectangular stirrup takes its leg count separately in each direction and can be single, double, triple, diamond or cross-tie.

The stirrup layout is not used for drawing alone. When a confined concrete curve is selected, the lateral confining pressure is computed from the stirrup diameter, spacing and leg count, so changing the stirrup also changes the core concrete curve.

Prestressing tendons can be defined on rectangular, circular and hollow circular sections. Tendon area, diameter and prestress force are entered, and the pre-strain enters the section analysis. On a rectangular section the tendons are placed either around the perimeter or as asymmetric layers.

Material curves#

Concrete and steel each take their own constitutive curve. The core and the cover concrete can be assigned different curves, and a confined core is solved together with an unconfined cover.

⚠️ The equivalent rectangular block is a step function and is defined only at the ultimate state, that is, for the condition where the extreme concrete fiber sits at its maximum strain. It cannot be used in a moment-curvature calculation, because a step function does not define the stiffness of the section up to yield.

The parabola-rectangle diagram is continuous and does run in a moment-curvature calculation. Its initial slope, however, is not tied to the modulus of elasticity. In the Hognestad curve the peak strain is derived from $\varepsilon_{c0} = 2f_c/E_c$, which makes the initial tangent exactly $E_c$. In the parabola-rectangle the peak strain $\varepsilon_{c2}$ is fixed (0.002 up to C50), so the initial tangent is $n f_{ck}/\varepsilon_{c2}$ and grows linearly with the concrete strength, while $E_c$ grows with its square root. The two therefore coincide only around one grade.

For pre-cracking stiffness or yield curvature, a behaviour curve should be selected. Ductility is the same story: $\varepsilon_{cu2} = 0.0035$ is a design limit set by the code, not the strain at which concrete crushes.

For steel, the elastoplastic, bilinear, trilinear and OpenSees Steel02 curves are available. When a curve carrying strain hardening is selected, the hardening onset and rupture strains are entered as well.

Materials are defined in one of two modes. In catalogue mode a code and a grade are selected and every property is derived from the code's relations. In custom mode the strength, modulus of elasticity and strain limits are entered directly.

Material factors#

The concrete factor $\gamma_c$ and the steel factor $\gamma_s$ come from the user and both default to 1. This macro never selects a code factor of its own.

The material factor is applied after the curve is built, to the stress read from it: at every strain the stress is divided by that factor. The modulus of elasticity, the peak strain and the crushing strain stay at the values belonging to the characteristic material strength.

When a result on the design strengths is wanted, the factors can be entered by hand. For TS 500 the values are $\gamma_c = 1.5$ and $\gamma_s = 1.15$.

Out of scope for this calculation#

Endpoints#

All three build the fiber mesh from the geometry in the request. When only the mesh itself is wanted, POST /api/v1/section-mesher/mesh can be called separately.

Adding audit_mode to the request returns a step-by-step breakdown of the calculation alongside the result. The language field sets the language of that generated text and does not affect the numeric results.

Which anchors the calculation is tested against, and the size and direction of each deviation, are on the Section Analysis verification page.