Cartesian Plane ⚠ Tap Set Origin (key O) to show the X & Y axes — needed for centroid distances
Section Properties ★ Sample — not charged
Solve this section
Set the origin, then solve to reveal the area, centroid, the common-shapes (Varignon's theorem) breakdown, and every detailed value.
🎯 Set the origin first — tap Set Origin and click a corner so centroid distances are measured from a known point.
Common Shapes — finding x̄ & ȳ (Varignon's Theorem) ★ Sample — not charged
The section is split into simple shapes the way you would solve it by hand — rectangles, triangles, and circular parts (circle, semicircle, quarter-circle, or sector). Each colored piece matches its color on the drawing. x̄ᵢ, ȳᵢ are each piece's centroid measured from the origin axes; multiply by its area, sum, and divide by the total area to get the section centroid (Varignon's theorem).
⚠ This solver only handles straight edges and circular arcs (which break down into the shapes above). It does not support parabolas, ellipses, or other curves — don't use it for sections with those.
| Part | Shape | Area Aᵢ | x̄ᵢ | ȳᵢ | Aᵢ·x̄ᵢ | Aᵢ·ȳᵢ |
|---|
Solve to see the common-shapes breakdown
Every common shape, its area, centroid, and the Varignon sums for x̄ and ȳ — shown once you solve.
Detailed Values ★ Sample — not charged
| Property | Symbol | Value | Unit |
|---|
Detailed section values
Every centroidal moment of inertia, principal axes, radii of gyration, and section moduli — shown once you solve.
The AI scanner is a learning aid, not a perfect tool. It can misread dimensions or miss small features on busy diagrams. Always check the numbers in the Edit panels after a scan, especially for complicated cross-sections.
Each scan costs Ebora Points whether the result is right or wrong — so a clean, well-labeled photo is worth the extra moment to set up.
The idea
Build the cross-section from nodes (points) and the lines / arcs / circles that connect them. The solver computes its area, centroid, moments of inertia, and section modulus values. Any closed loop you draw inside another closed loop is treated as a hollow cut-out automatically — you never have to "close" a shape by hand.
Skipping the drawing — the scanner
Tap Open scanner in the sidebar, photograph or upload the cross-section from your textbook, and the AI builds the geometry for you. Make sure the dimension labels (B, H, t, r) are visible and readable. Use the Nodes and Edges & curves panels to fix any dimensions the AI got wrong.
The five tools
- Node V — tap empty space to place a point, or tap an existing node / edge / curve to select it. Then use 🗑 Delete selected (or the Delete key) to remove it.
- Line L — tap a node (or empty space to drop one), then tap the next node to connect them with a straight edge. Keep tapping to chain around the perimeter; the shape closes itself when you return to the start.
- Arc A — tap the start node, then a point the curve passes through, then the end node. Arcs are circular only — the app splits them into circles, semicircles, quarter-circles, or sectors. It does not handle parabolas, ellipses, or other curves.
- Circle C — tap the centre, then any point on the circumference (or type the radius and press Enter).
- Set Origin O — tap the point you want as (0, 0). Use it after drawing so you can read x̄ and ȳ from any reference corner.
Solid vs. hollow
You don't tag anything — the app looks at how loops are nested.
- A loop not inside any other loop → solid.
- A loop inside one other loop → hollow (subtracted).
- A loop inside two others → solid again (an island inside a hole).
The shaded blue area is the solid part. The unshaded interior of a nested loop is the hollow part.
Typing exact distances (works on phones too)
The Distance + Angle panel above the canvas is the primary way to enter precise dimensions.
- Distance only — type the length, leave Angle blank. The line goes from the last point toward wherever the cursor is pointing, at exactly that length. Useful for axial segments (combine with Ortho).
- Distance + Angle — type both. The line goes at exactly that angle
(0° = right / +X axis, 90° = up / +Y axis, counter-clockwise positive) for that
length. Polar entry, like AutoCAD's
@dist<angle. - Tap Apply (or press Enter while a field is focused) to commit. On desktop you can also just type digits on the canvas — the distance field fills automatically. Hit Enter or click to commit.
- Hold Shift for one-off Ortho, or click the Ortho button (or press F8) to lock it on.
Point labels & editing
Every node you place gets an automatic label (A, B, C, …). Use the Nodes panel to change a node's exact (X, Y) — every edge connected to it follows along automatically. Use Edges & curves to set a line's length numerically (the end node slides along the existing direction) or a circle's radius, and to delete any single edge or curve. You can also tap a node/edge/curve on the canvas with the Node tool to select it, then Delete.
Navigating the canvas
- Pan — hold the middle mouse button and drag on a desktop, or use a two-finger drag on a phone or tablet.
- Zoom — mouse wheel on a desktop, pinch on touch, or the + / − buttons.
- Fullscreen — tap the ⛶ Full button on the canvas toolbar to expand the drawing area to the whole screen. Tap again or press Esc to exit.
- The X and Y coordinate axes start hidden. They appear after you use Set Origin so the coordinate system reflects the reference point you chose. You can toggle them in Grid & display.
Tips
- Lines and arcs chain together: an arc continues from the last point of the previous segment, so you can mix straight edges and curved fillets in one continuous loop.
- Use Type exact point (X, Y) to place a node at exact coordinates — then switch to Line to connect it to others.
- Snap to grid is on by default. Turn it off in Grid & display for fine adjustments.
- Press Esc to cancel the current sketch, Enter to close it.
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