Elements, materials & sections

The beam element

EduBeam has one element type: a 2D Timoshenko beam in the x–z plane with three degrees of freedom at each end (Dx, Dz, Ry). It carries axial force, shear and bending, and includes shear deformation (which is why the cross section has a shear coefficient). The full formulation is in the theory manual.

2D beam element – three DOFs per node

Results along an element are exact for the linear model, so one element per member is enough. Add intermediate nodes only where you need a support, a hinge, a change of section, or a node to attach a load to.

Adding elements

Method	How
Dialog	Elements tab → Add element (or canvas menu → Add element): choose Initial node, End node, material and cross section.
Mouse	Elements tab → Add using mouse (or hold Ctrl with the canvas menu item). Click a node to start, then click the next node to connect—clicking empty canvas creates a new node there. Keep clicking to draw a polyline; press Esc to finish. The first material and cross section in the model are assigned automatically.

Materials and sections first

An element cannot exist without a material and a cross section. If none are defined the viewer shows No materials defined / No cross sections defined with an Add new shortcut.

Element direction

The local x axis runs from the initial node to the end node. This matters for:

• local-coordinate loads (fx, fz in LCS),
• the Load position from start node of concentrated loads,
• the order of end forces (X12, Z12, M12 at the start, X21, Z21, M21 at the end) in the results table.

Use Swap nodes in the Elements table to reverse an element.

End hinges

Each element has two End hinges checkboxes (start / end) in the Elements table. A ticked hinge releases the bending moment at that end (static condensation of the rotational DOF), so:

• one hinge → a pin inside a frame or a continuous beam (moment is zero there);
• both hinges → a truss bar that carries axial force only.

Both ends hinged → truss element

When two elements meet at a node and only one of them is hinged, the other still transfers moment into the node—so hinge the element you want released, not "the node".

Editing and deleting

Click an element and use the popover (Edit element, Add load, Stiffness matrix, Delete), or edit directly in the Elements table. Deleting an element also removes its loads. Stiffness matrix opens a floating window with the 6 × 6 element matrix in local and global coordinates—handy when checking hand assembly.

Materials

Materials tab → Add material:

Field	Symbol	Unit	Notes
Young's modulus	$E$	pressure unit (MPa by default)	Steel ≈ 210 000 MPa, concrete ≈ 30 000 MPa, timber ≈ 11 000 MPa
Shear modulus	$G$	pressure unit	$G = E / (2(1+\nu))$; steel ≈ 81 000 MPa. Only affects the Timoshenko shear term.
Density	$\rho$	kg/m³	Stored with the project; not used by the static solver (there is no self-weight load).
Coefficient of thermal expansion	$\alpha$	1/K	Used by temperature loads. Steel 12 × 10⁻⁶.

Material library offers ready-made presets: structural steels (S235, S275, S355, stainless), aluminium alloys, copper/brass/bronze, titanium, concrete classes, timber (C24, GL24h, GL32h), glass, GFRP/CFRP and common polymers. Pick one from the library dialog or from Or choose from library inside the Add material dialog.

Cross sections

Cross sections tab → Add cross section:

Field	Symbol	Unit	Notes
Area	$A$	area unit	Axial stiffness $EA$
Second moment of area	$I_y$	m⁴ (or the selected unit)	Bending stiffness $EI_y$ about the in-plane bending axis
Height	$h$	length unit	Used by temperature-gradient loads (curvature $= \alpha\,\Delta T / h$)
Shear coefficient	$k$	–	Timoshenko shear correction factor: effective shear area $= kA$. Use 1 to (almost) ignore shear deformation; ≈ 0.83 for rectangles; for I-sections use $A_{web}/A$.

Section library provides approximate values for rectangles, squares, circles, IPE and HEA profiles, RHS and CHS tubes. Treat them as starting points and check the values against a section table before relying on them.

Polygonal sections. Cross sections tab → Polygonal section (or Or define a polygonal shape inside the Add cross section dialog) opens a shape editor. Start from a preset (rectangle, I, T, L, channel, rectangular/circular hollow, circle), then drag vertices, click an edge midpoint to insert a vertex, double-click a vertex to remove it, or type coordinates directly; holes are added as extra contours. The editor computes $A$, the centroid, the centroidal second moments $I_y$, $I_z$, $I_{yz}$ (about axes through the centroid, regardless of where the shape is drawn), the principal moments $I_1$, $I_2$ with the principal-axis angle $\alpha$ (from $y$ to axis 1), the radii of gyration, and draws the ellipse of inertia. On save $A$, $I_y$ and $h$ are filled in from the shape (they show as read-only in the table – use the polygon button in the Actions column to edit the shape); the shear coefficient $k$ is still entered by hand. Section coordinates are local and right-handed with $x$ pointing out of the screen: $y$ points to the left, $z$ downwards.

Quick sanity values

For a rectangle $b \times h$: $A = bh$, $I_y = bh^3/12$. For a solid circle of diameter $d$: $A = \pi d^2/4$, $I_y = \pi d^4/64$.

Materials and sections can be shared by any number of elements; changing a value updates every element that uses it and re-solves the model.