Worked example: composite section

Build a steel-on-concrete composite section in GCS — a 200 × 50 mm concrete slab with a 100 × 150 mm steel beam stacked on top — and walk through both the geometric and stiffness-weighted (transformed) property output.

Problem statement

We want to analyse a simple composite cross-section: a 200 × 50 mm concrete slab with a 100 × 150 mm steel beam stacked on top of it. This is the textbook composite-beam configuration — the concrete bears in compression while the steel carries tension (and bending stiffness). The two regions are touching at the slab–beam interface but do not overlap.

We want:

The geometric section properties — treating both regions as a single 2D shape, with no material weighting
The stiffness-weighted (transformed) properties — referenced to the concrete

This example walks through the adjacent regions composite layout — two outlines of different materials that share a boundary but no interior area. The embedded inclusion layout (inclusion strictly inside an outline — rebar inside concrete) is also supported, and its modular-ratio bookkeeping is worked through at the end of this page.

Given data

Region	Role	Geometry (mm)	Material	$E$ (MPa)
1	Outline	Concrete slab — 200 × 50 with bottom-left at $(0, 0)$	AS 3600 Grade 32	30,100
2	Outline	Steel beam — 100 × 150 with bottom-left at $(50, 50)$	AS/NZS 3678 Grade 350	200,000

The concrete’s $E_c$ is not a stored catalogue figure: it is derived from $f'_c = 32$ MPa under the concrete design standard of this project’s jurisdiction, which for an Australian project is AS 3600:2018 Table 3.1.2 — 30,100 MPa. The same section in a US or European project would use ACI 318-19 Cl 19.2.2 or EN 1992-1-1 Cl 3.1.3 and land on a different $E_c$ , and therefore a different transformed set.

Modular ratio of steel to concrete: $n_s = E_s / E_c = 200{,}000 / 30{,}100 \approx 6.645$ .

Step 1 — Draw the concrete slab

Open GCS for a new design option. Press P to enter Draw Polygon mode and draw the 200 × 50 rectangle at the origin.

Two independent aids give you exact dimensions, and they are separate mechanisms rather than one combined gesture:

Distance lock — type the number. With a segment in progress, typing digits (and .) builds a locked length; it appears as a blue "{n} mm" chip in the status bar. Backspace edits it, Esc clears it, Enter commits the segment at exactly that length.
SHIFT — angle snap. Holding SHIFT constrains the segment to horizontal / vertical (and 45°). It does not prompt for a dimension.

The editor’s own hint says it: “Click to add points. Hold SHIFT for H/V snap. Click start or press Esc to finish.” Use both together for an axis-aligned rectangle of a known size — SHIFT for the direction, typed digits for the length.

In the Elements list set the Role of the new element to Outline and assign AS 3600 Grade 32 as the material.

The Role select offers three options — Outline, Void and Inclusion. This example uses the first and the third; Void carves a hole out of an enclosing outline and is out of scope here (see Section properties).

Step 2 — Draw the steel beam

Press P again and draw the 100 × 150 rectangle starting at $(50, 50)$ . Set its role to Outline and assign AS/NZS 3678 Grade 350 as the material.

The two rectangles meet along the segment from $(50, 50)$ to $(150, 50)$ . The validator allows shared boundaries; what it rejects for two outlines is any interior overlap. This boundary-touching is the adjacent condition this layout is built around.

The composite section after drawing both regions — the concrete slab on the bottom and the steel beam stacked on top, sharing the interface line at y = 50.

Step 3 — Read the analysis output

Once the auto-save lands and the server returns properties for the saved geometry, the badge in the sidebar header flips from Preview to Calculated. The properties panel now shows two groups: the geometric properties at the top (which sum both rectangles as one shape with no material weighting), and the transformed properties below (which scale the steel’s contribution by the modular ratio).

The right-sidebar Section Properties panel showing the geometric properties at the top and the stiffness-weighted (transformed) properties below — each group has its own area, centroid, and second moments.

Geometric properties (what the canvas shows as the section)

These properties treat both regions as a single shape — material assignments do not enter the calculation here.

Property	Symbol	Value
Total area	$A$	25000 mm²
Perimeter	$P$	1000 mm
Centroid $x$	$\bar{x}$	100 mm
Centroid $y$	$\bar{y}$	85 mm
Second moment about $x$	$I_{xx}$	9.02e7 mm⁴
Second moment about $y$	$I_{yy}$	4.58e7 mm⁴

$P$ is the wetted perimeter, not the outer boundary. GCS sums every region’s own closed boundary, so the 100 mm slab–beam interface is counted twice — once as part of the slab, once as part of the beam. That is the “wetted perimeter” convention engineers expect for a hollow tube, and it is what Section properties means by “total length of all edges across all regions”. The composite’s outer boundary is 800 mm. Both figures are correct answers to different questions; this is the one place on the page where your own arithmetic will contradict a reported number, so it is worth knowing which is which before you reach for the hand check below.

Hand check — area and centroid

$A = A_\mathrm{slab} + A_\mathrm{beam} = (200)(50) + (100)(150) = 10{,}000 + 15{,}000 = 25{,}000 \text{ mm}^2$

The two regions are both symmetric about $x = 100$ , so the geometric centroid sits on that axis: $\bar{x} = 100$ mm.

For the $y$ centroid, take area-weighted moments about the bottom edge:

$\bar{y} = \frac{A_\mathrm{slab}\,\bar{y}_\mathrm{slab} + A_\mathrm{beam}\,\bar{y}_\mathrm{beam}}{A_\mathrm{slab} + A_\mathrm{beam}} = \frac{(10{,}000)(25) + (15{,}000)(125)}{25{,}000} = \frac{250{,}000 + 1{,}875{,}000}{25{,}000} = 85 \text{ mm}$

The reported value matches.

Hand check — second moment $I_{xx}$

Apply the parallel-axis theorem for each region about the composite centroid ( $\bar{y} = 85$ mm):

$I_{xx,\mathrm{slab}} = \frac{b h^3}{12} + A\,d^2 = \frac{(200)(50)^3}{12} + (10{,}000)(25 - 85)^2 = 2.083 \times 10^6 + 3.60 \times 10^7 = 3.808 \times 10^7$

$I_{xx,\mathrm{beam}} = \frac{(100)(150)^3}{12} + (15{,}000)(125 - 85)^2 = 2.813 \times 10^7 + 2.40 \times 10^7 = 5.213 \times 10^7$

$I_{xx} = 3.808 \times 10^7 + 5.213 \times 10^7 \approx 9.02 \times 10^7 \text{ mm}^4$

Matches the reported value.

Hand check — perimeter

Both readings, so the 1000 is not mistaken for an error. The wetted perimeter sums each region’s own closed boundary:

P = \underbrace{2(200 + 50)}_{\text{slab} = 500} + \underbrace{2(100 + 150)}_{\text{beam} = 500} = 1000 \text{ mm}

The outer boundary walks the composite’s silhouette once, which skips the shared interface in both directions:

200 (slab bottom) + 50 (slab right) + 50 (slab top, x=200 -> 150)
+ 150 (beam right) + 100 (beam top) + 150 (beam left)
+  50 (slab top, x=50 -> 0) + 50 (slab left)                    = 800 mm

The difference is exactly $2 \times 100$ mm — the interface, counted on both sides. GCS reports the first.

Transformed (stiffness-weighted) properties

The first outline (the concrete slab) sets the reference material. Its $E_c$ is derived from $f'_c = 32$ MPa under AS 3600:2018 Table 3.1.2, giving 30,100 MPa, so the steel beam’s contributions are scaled by the modular ratio $n_s = 200{,}000 / 30{,}100 = 6.645$ .

Property	Path	Notes
Reference material	`transformed.referenceMaterial`	AS 3600 Grade 32, $E_c = 30{,}100$ MPa (AS 3600 Table 3.1.2, derived from $f'_c = 32$ MPa)
Transformed area	109668 mm²	$A_c + n_s\,A_s = 10{,}000 + 6.645(15{,}000)$
Transformed centroid $y$	115.88 mm	Steel pulls the elastic neutral axis upward toward the steel beam
Transformed second moment $I_{xx}$	2.798e8 mm⁴	Much larger than $I_{xx}$ above because the heavily weighted steel is far from the transformed centroid

Hand check — transformed centroid

Take E-weighted moments about the bottom edge:

$\bar{y}_t = \frac{A_c \bar{y}_c + n_s\,A_s\,\bar{y}_s}{A_c + n_s\,A_s} = \frac{(10{,}000)(25) + (6.645)(15{,}000)(125)}{109{,}668} = \frac{250{,}000 + 12{,}458{,}472}{109{,}668} \approx 115.88 \text{ mm}$

Notice how much the centroid shifts compared with the geometric one ( $\bar{y} = 85$ mm). The steel’s stiffness pulls the elastic neutral axis toward it by about 31 mm — and this is exactly why composite design uses transformed properties: stress and strain at any fibre are governed by the transformed centroid and transformed $I$ , not by the geometric values.

Plastic modulus is null

Both plasticModulus and shapeFactor are null in the response, with plasticModulusReason explaining why. Composite plastic capacity depends on per-material yield, not on modular ratio — GCS refuses to substitute a meaningless value. See Materials — Plastic modulus is null for composite sections. For plastic capacity of this composite as a real structural element, use a material-specific designer.

What this example demonstrates

This is the adjacent-regions layout — two outlines sharing a boundary but no interior area. The embedded-inclusion layout (next section) is the other supported composite shape; what the validator rejects is the partial overlap in between, with overlapping_regions.
Geometric and transformed properties answer different questions. Geometric properties describe the shape; transformed properties capture how the composite responds to bending under linear-elastic behaviour.
The reference material is explicit in the response. You never have to guess what stiffness the transformed properties are expressed in.
Plastic capacity is not in scope for composite sections in this tool — see the scope statement for the reasoning.

Embedded inclusions — rebar inside concrete

The second supported composite layout puts the inclusion strictly inside an outline rather than beside it. Consider a single concrete outline with a steel inclusion contained within it:

Draw a 200 × 100 concrete Outline at the origin.
Draw a 20 × 20 steel Inclusion with its centre at the outline’s centre — for example bottom-left at $(90, 40)$ . Set the role to Inclusion and assign AS/NZS 3678 Grade 350.
The section properties panel’s Preview figures update immediately; the Calculated figures update once the auto-save lands and the server returns properties for the saved geometry.

The geometric properties are unchanged from the bare outline — the inclusion displaces the host material at its footprint rather than adding to it. The transformed properties pick up the extra stiffness of the embedded steel:

Property	Symbol	Value
Geometric area	$A$	20000 mm²
Transformed area	$A_t$	22258 mm²

$A = 200 \times 100 = 20{,}000\ \text{mm}^2$

$A_t = A_\mathrm{outline} + (n_s - 1)\,A_\mathrm{inclusion} = 20{,}000 + (6.645 - 1)(400) \approx 22{,}258\ \text{mm}^2$

The inclusion is centred, so neither centroid moves — only the magnitudes. (Its own boundary is counted in the wetted perimeter too, giving $2(200+100) + 4(20) = 680$ mm.)

Equivalently: the host material owns the displaced footprint at modular ratio 1, the inclusion replaces it at modular ratio $n_s$ , and the difference is $(n_s - 1)\,A_\mathrm{inclusion}$ . Internally this is exactly what the calculator does — it injects a synthetic “ghost void” of the inclusion’s shape carrying the outline’s material, so no special case is needed in the integrals. The same arithmetic carries through the second-moment and centroidal integrals.

As with the adjacent layout, plasticModulus stays null — the section is still composite.

Only strict containment is accepted. An inclusion whose boundary crosses the outline’s is a partial overlap and returns overlapping_regions; it is neither adjacent nor embedded, and there is no unambiguous reading of which material owns the shared area.

This is the right tool for the linear-elastic stiffness-weighted properties of a reinforced section. For full RC design (concrete cracking, rebar yielding, $M$ – $N$ interaction, biaxial bending), the Advanced Concrete Section is the right destination — the modular-ratio method here cannot capture post-elastic behaviour. The two tools complement each other rather than substitute.

Where to go next

Section properties reference — the full output catalogue with formulas
ACS — for reinforced concrete design (post-elastic, code-capacity)
Limitations — what the analyser deliberately does not do