Section analysis

Run ultimate and serviceability limit state checks, prestress analysis, fire design, and moment-curvature analysis on concrete sections.

Overview

Once you have defined the section geometry, reinforcement, and materials, ACS runs design checks automatically as you enter or modify design actions. Results appear in the right panel, organised by limit state.

All calculations re-run with a short debounce delay after any input changes. You can also force a full refresh with Ctrl+Shift+Enter.

Applied loads

Open the Applied Loads panel to define design actions. Select the member type to control which load fields are visible:

Load combinations

ACS supports multiple load combinations, each tagged with a limit state:

Add combinations using the + button under each limit state tab. Each combination has a name, active/inactive toggle, and a set of load values.

The governing combination for each check type is identified automatically in the Design Summary.

Ultimate limit state (ULS)

Flexure

The flexure panel reports uniaxial bending capacity about the major ($x$) and minor ($y$) axes.

Key results:

Ductility checks by code:

N-M interaction

For members under combined axial force and bending, the interaction diagram shows the full capacity envelope.

Uniaxial interaction plots the $N$-$M_x$ curve with key points:

• Squash load: Pure compression capacity ($M = 0$)
• Balanced point: Simultaneous concrete crushing and steel yielding
• Pure bending: Moment capacity at zero axial load
• Pure tension: Tensile capacity (reinforcement only)

Your design point ($N^*, M^*$) is plotted on the diagram. If it falls inside the envelope, the section is adequate.

Biaxial interaction generates a 3D $N$-$M_x$-$M_y$ surface and checks the design point using:

• Rigorous method: 3D surface interpolation
• Bresler reciprocal (AS 3600 Cl. 10.6.4): $1/N_u = 1/N_{ux} + 1/N_{uy} - 1/N_{u0}$
• Bresler load contour (ACI 318): $(M_x/M_{ux})^\alpha + (M_y/M_{uy})^\alpha \leq 1.0$

The interaction diagram can also be viewed as a 3D surface in the canvas Interaction tab.

Shear

The shear panel computes capacity per the code truss model:

Where:

• $V_{uc}$ = concrete contribution (depends on $f'_c$, $b_w$, $d$, axial force)
• $V_{us}$ = steel contribution ($A_{sv} \cdot f_{sy} \cdot d / s$)

The design capacity $\phi V_u$ is compared against $V^*$.

Serviceability limit state (SLS)

SLS checks use the first active SLS load combination.

Stress check

Verifies that concrete and steel stresses under service loads remain within allowable limits:

Crack width

Computes the characteristic crack width $w_k$ and compares it against the allowable width for the exposure class:

Where:

• $s_{r,max}$ = maximum crack spacing
• $\varepsilon_{sm}$ = mean steel strain
• $\varepsilon_{cm}$ = mean concrete strain between cracks

Typical limits: 0.3 mm for sheltered environments, 0.2 mm for exposed, 0.1 mm for water-retaining.

Deflection parameters

Computes the effective moment of inertia $I_{ef}$ for deflection calculation:

Where:

• $I_g$ = gross moment of inertia
• $I_{cr}$ = cracked moment of inertia
• $M_{cr}$ = cracking moment
• $M_s$ = service moment

Long-term factors account for creep and shrinkage effects.

Prestressing

For sections with tendons, the PT tab provides:

Prestress losses

All loss components are computed individually:

The effective prestress $f_{pe}$ after all losses is used for subsequent capacity and stress checks.

Transfer and service stresses

Concrete stresses are checked at two stages:

• Transfer: immediately after prestressing (using $f_{ci}$, the concrete strength at transfer)
• Service: long-term under sustained loads (using $f'_c$)

PT ultimate capacity

The moment capacity of the prestressed section accounts for tendon stress increase beyond the effective prestress:

Where $\varepsilon_{ps}$ is the additional strain at the tendon level at ultimate, capped at $f_{pu}$.

Fire design

See the dedicated Fire design page for detailed documentation.

Moment-curvature analysis

The Moment-curvature tab traces the full nonlinear response of the section:

1. Uncracked elastic phase
2. Cracking (concrete tensile strength exceeded)
3. Post-cracking (tension stiffening)
4. Steel yielding
5. Ultimate (concrete crushing or steel rupture)

The M-$\kappa$ curve shows ductility capacity and energy absorption. You can run curves at multiple axial load levels and view the results overlaid on the same plot.

The M-$\kappa$ interaction surface (triggered by button) generates a 3D surface by sweeping the bending angle from 0$^\circ$ to 360$^\circ$ at multiple axial load levels. This provides a rigorous biaxial interaction check based on the full nonlinear material response.

Design summary

The Summary tab presents all checks in a single table, showing the governing utilisation ratio and load combination for each check type (flexure, shear, crack width, deflection).

For batch analysis with multiple load combinations, the summary identifies:

• The governing combination per check type
• The overall governing utilisation ratio
• Pass/fail status for each check

Related pages

• Fire design — fire rating analysis
• Moment-curvature theory — mathematical background
• M-N interaction theory — interaction diagram theory
• RC beam worked example — step-by-step design