RC Section Analyser

Define a reinforced-concrete section and its longitudinal reinforcement, then calculate gross, transformed, cracked, service, axial-moment, and moment-curvature response. The analyser is intended for transparent section studies and engineer-reviewed calculations.

Open the RC Section Analyser

What the Analyser Does

Models rectangular, Tee, and solid circular concrete sections with an explicit longitudinal reinforcement cage.
Reports transformed elastic properties based on the displayed concrete and reinforcement. The detailed PDF also records gross geometric reference properties.
Calculates primary-axis cracked-section properties and service reinforcement stress for the entered service moment. At an explicit angle it instead reports cracked bending-axis Iuu, perpendicular neutral-axis depth, and cracking moment.
Generates a nominal, unfactored P-M envelope and a nonlinear moment-curvature response at the entered axial force.
Displays the biaxial section-response boundary at the entered axial force on every successful run.
Reports uncracked elastic stress extrema at entered N + Mx + My, labelled P-M control points, exact nominal moment at entered N, and cracking curvature.
Recalculates a selected point on the moment-curvature curve so you can inspect its strain plane, neutral axis, concrete response, reinforcement stresses and forces, and equilibrium residuals.

These are section-level results. The analyser does not perform a design standard check or provide a compliance certificate.

Quick Start

Choose Metric (mm) or Imperial (in) display units.
Select Rectangle, Tee, or Circle and enter the section dimensions.
Enter the concrete and reinforcement strengths, clear cover, and tie or stirrup size.
Choose a reinforcement catalogue, bar sizes, and the number of longitudinal bars. Confirm the cage in the cross-section preview.
Review the Analysis material model. Use the displayed stress-strain curves and parameters to confirm the intended material response.
Enter axial force and section moments. The service moment and counter-clockwise neutral-axis angle are optional.
Select Calculate section response, then review the properties, response curves, and calculation notes.
Select a point on the moment-curvature chart, then select Inspect selected point to run that nonlinear state. Pro users can save the current validated results as a detailed PDF.

Access and Daily Solves

Sign in before running the solver. Signed-in Free accounts include three RC section solves per UTC day, while Pro accounts have unlimited solves. This allowance is separate from Structural FEA analysis runs.

Each Calculate section response action and each Inspect / Recompute selected point action uses one solve. Selecting or moving between chart points alone uses none. For signed-in Free accounts, the analyser shows today's usage beside the calculation action. After a successful calculation, the primary action stays disabled while the displayed response matches the current inputs, so the same request cannot spend another solve accidentally.

While Your Calculation Runs

Detailed section responses can take a little while to calculate. Keep the page open and the analysis will continue automatically. When demand is high, your calculation may wait its turn; the page will let you know if it is taking longer than usual. There is no need to submit it again.

Section and Reinforcement Inputs

Input group	What to enter
Section geometry	Width and depth for rectangles; web width, total depth, flange width, and flange thickness for Tee sections; diameter for solid circles.
Concrete and cage	Concrete compressive strength, longitudinal steel yield strength, clear cover, tie or stirrup size, and schematic tie spacing.
Rectangular and Tee reinforcement	Main bar size, top and bottom bar counts, and optional side bars on each face. A separate side-bar size is available when side bars are used.
Circular reinforcement	Main bar size and the number of bars equally distributed around the perimeter at the displayed cage radius.
Reinforcement catalogue	EN metric or ASTM bar and tie sizes. This is a physical bar-size selection and is independent of the display unit system.

The section preview uses the same bar coordinates as the calculation. Hover or focus a bar in the cross-section to identify its size and position. Tie spacing is shown in the member-elevation sketch only; it does not change the nonlinear section response.

Analysis Material Models

The material model controls the nonlinear section response and is separate from the section geometry, reinforcement catalogue, and display units. The analyser provides two defined models:

Parabolic concrete + elastic-plastic steel: parabolic concrete compression response with tension cracking and a symmetric elastic-plastic reinforcement response.
Parabolic concrete + strain-hardening steel: the same concrete response with a symmetric bilinear steel hardening branch. This model also requires an entered steel ultimate strength that is not less than the steel yield strength and a fracture strain greater than the yield strain fy / Es.

The response families use those parameters in different ways. Gross properties are geometric. The linear no-tension / ultimate family uses the entered elastic moduli for transformed and uncracked results, removes concrete tension from cracked/service response, and uses the ultimate concrete compression profile for the P-M sweep. The sampled parabolic service family is used for moment-curvature and selected-state response: parabolic compression plus linear-elastic concrete tension up to the entered tensile strength, followed by loss of tensile stress. No tension stiffening or cyclic unloading model is included.

Expand Analysis material model to review or edit the concrete elastic modulus, concrete tensile strength, peak and ultimate concrete strains, parabola exponent, steel elastic modulus, steel fracture strain and, for the hardening model, steel ultimate strength. The plotted stress-strain curves show the response defined by the current values. They are stacked at the full input-panel width with stress and strain scales, key limit strains, and a short explanation of how each curve is used. The small concrete tension range is widened and labelled in the plot so cracking remains visible without implying a uniform strain scale across that widened region.

Section Response Actions and Sign Conventions

Input or result	Convention
Axial force, N	Positive in compression. It sets the entered-N level for the moment-curvature calculation, biaxial response boundary, exact nominal solve, and uncracked stress calculation. The P-M envelope remains a sweep across axial force.
Moment Mx (horizontal x-x axis)	When the neutral-axis angle is blank, its sign selects the P-M, moment-curvature, and exact nominal response orientation for every section shape. This is material for an asymmetric cage or geometry, such as a Rectangle with unequal top and bottom reinforcement or a Tee. The P-M and moment-curvature charts report moment magnitude; the biaxial chart retains signed Mx and My components.
Moment My (vertical y-y axis)	Used with the entered Mx to place the demand point against the biaxial boundary at entered N. It does not change that calculated boundary. A non-zero My intentionally removes the demand marker from the uniaxial P-M chart; use the biaxial chart for the complete demand vector.
Service moment	Optional input whose sign sets the primary-axis cracked and service orientation and whose magnitude drives the reinforcement- stress result. Leave it blank to omit the separate service result; cracked properties then follow the Mx orientation. Service stress is calculated at zero service axial force. Leave the neutral-axis angle blank for automatic orientation, or use 0 degrees for non-negative service moment and +/-180 degrees for negative service moment. Other explicit angles are incompatible. Steel stress is an elastic cracked-section estimate; values above fy are flagged as outside the steel elastic range.
Neutral-axis angle	Optional counter-clockwise angle from the horizontal section axis, in degrees. Leave it blank for the primary-axis response. The chosen angle applies to the P-M envelope, moment-curvature, exact nominal solve, cracked reference, and selected-state calculations and is recorded in the PDF. A rotated response reports cracked bending-axis Iuu, perpendicular d_n, and Mcr, not a fake top-depth Icr or top-depth neutral-axis depth.
Coordinates	Section x points right and y points up. Moments act about the gross section centroid: positive Mx compresses the top face and positive My compresses the right face. These axes stay fixed for wide and deep sections. Bar depth is measured downward from the top concrete face.
Stress and strain	Positive in compression and negative in tension.

Analysis-Domain Guards

Actions are checked in canonical SI units at both the page and analysis service boundaries. The axial range is derived from the entered gross concrete area, displaced reinforcement area, concrete compression strength, and the largest declared reinforcing-steel stress. Major, minor, and service moment limits use that material-force envelope with the full corresponding section dimension as a conservative lever arm. Values outside these bounds are rejected with the applicable kN and kN·m limits (or converted kip and kip·ft limits in Imperial display) before nonlinear analysis.

Understanding the Results

Geometry and Transformed Elastic Section

The on-screen calculated-property summary reports equivalent-concrete transformed area, net concrete area after bar displacement, axial rigidity EA, transformed centroid, x-x, y-y, product, and principal-axis inertias, top-face x-x section modulus, and the reference concrete modulus. These values include the longitudinal steel using the displayed concrete elastic modulus; they are not gross-section properties. The detailed PDF also records gross geometric area, centroid, inertias, and section modulus as reference values.

Nominal Extrema, Exact Points, Cracked, and Elastic Results

Sweep maximum compression, tension, and peak moment are plotting summaries, not design resistance. The analyser separately reports solver-labelled squash, balanced, and pure-bending controls and a single exact nominal ultimate solve at the entered axial force. It also reports uncracked elastic concrete and steel stress extrema at entered N + Mx + My. Primary-axis cracked/service results retain top-depth quantities; an explicit angle uses bending-axis Iuu and perpendicular d_n. All values are code-neutral, nominal, and unfactored.

Response Curves

P-M envelope: nominal axial force versus moment magnitude for the primary response orientation or the explicitly entered neutral-axis angle. No uniaxial demand marker is shown for an explicit angle because the neutral-axis angle alone does not define a compatible Mx/My moment vector; use the biaxial boundary to compare both entered moment components. Member slenderness and global second-order effects are not included.
Moment-curvature: nonlinear section response at the entered axial force and selected neutral-axis orientation. The curve includes the zero state, elastic-region sampling, and a point near the calculated cracking curvature before using bounded adaptive steps.
Biaxial response boundary: always returned at the entered axial force. It is a section-response boundary, not a member-capacity surface.

Selected Nonlinear Section State

Select a plotted moment-curvature point with the mouse or keyboard, then select Inspect selected point. Chart navigation moves the marker without starting background analyses. The explicit action recalculates that exact state and displays the neutral axis, linear strain plane, signed concrete normal stress, every longitudinal bar, concrete compression, tension, and net force resultants, steel compression and tension resultants, and force and moment residuals. The bar table reports each bar's position, diameter, strain, stress, force, and response state.

For a primary-axis response, the selected state reports neutral-axis depth from the top face. At an explicit angle, the displayed scalar is the neutral axis's vertical intercept from the top; the rotated cracked result d_n is instead a perpendicular depth from the extreme compression fibre.

Where the selected-state response contains a bounded valid analysis mesh, the diagram fills its returned triangles and interpolates stress only within each triangle for display. It does not refine the mesh, bridge separate concrete regions, run another analysis, or calculate von Mises stress. Compression uses warm colours, tension uses blue, and the zero-stress neighbourhood is grey. When a valid display mesh is not returned, including when the service omits an oversized or unsafe- topology mesh, the bounded concrete calculation-point view is retained. A malformed mesh included in a returned response fails response validation rather than being trusted or drawn. If the selected state cannot be matched to the current response or does not satisfy the calculation checks, it is not displayed as a valid state.

Units and Input Changes

Metric display uses mm, MPa, kN, and kN·m. Imperial display uses in, ksi, kip, and kip·ft. Switching units converts the displayed values but preserves the physical section, material parameters, actions, reinforcement sizes, bending angle, and the validated calculated response. It does not switch between EN metric and ASTM reinforcement catalogues.

Changing the geometry, cage, actions, or material model makes the previous response out of date and enables a new calculation. While the displayed response still matches the current physical inputs, the calculation action remains disabled and explains that state on hover. Calculate the revised inputs before relying on or exporting their results.

Exports

Pro users can generate a detailed PDF from the validated response currently displayed. It records the current geometry, cage, material parameters and curves, section properties, response curves, calculation notes, and a selected nonlinear state when one has been recomputed.

Scope and Limitations

Results are nominal, unfactored section response, not design resistances or code-compliance results.
The analyser covers parametric Rectangle, Tee, and solid Circle sections only. Arbitrary geometry and voided sections are not supported.
It does not model member slenderness, global frame behavior, second-order member effects, shear, torsion, punching, prestressing, or staged construction.
Slabs, walls, seismic detailing, deep beams, strut-and-tie behavior, and project-specific reinforcement detailing checks are outside its scope.
A confined concrete core is not modelled. The entered concrete response applies to the section without separate core and cover regions.
Concrete tension stiffening, cyclic loading and unloading, creep, shrinkage, and other time-dependent effects are not modelled.
Tie spacing is schematic and does not contribute to section response.

Independently verify loads, geometry, reinforcement placement, construction tolerances, material data, applicable design requirements, and the suitability of the selected material model. Final design and detailing remain the responsibility of a competent engineer.