3-D frames and section properties: torsion, biaxial bending and frame buckling

Proofline's 3-D frame cell solves space frames — every member carries axial force, torsion and bending about both of its axes — and the Section properties cell gives the numbers of a cross-section. Both run in your browser with the same engine as the Truss & Frame Solver (type “3-D frame”) and the Section Properties Calculator tool pages, so a cell and its tool page give identical results. They are linear-elastic checking models, not certified design.

1. Open the 3-D part of the Structures lab

Choose Notebook → Templates…, open Structures lab and press Run all. After the 2-D cells the note 3-D frames introduces three more cells: a beam section, a table frame and an Euler column.

2. Section properties

Beam section: IPE 200 without fillets uses Shape “I-section (b × h, tf, tw)” with Width b (mm) 100, Depth h (mm) 200, Flange thickness tf (mm) 8.5 and Web thickness tw (mm) 5.6. The result: A = 27.25 cm², Iy = 1,845.6 cm⁴, Iz = 141.93 cm⁴ and J = 5.165 cm⁴, with 21.39 kg/m in S235 steel. The local y axis runs across the width, z along the depth, so Iy is the strong axis.

The code block Line for the 3-D frame model holds section BEAM shape=i b=100 h=200 tf=8.5 tw=5.6. Use this section in a 3-D cantilever under the result adds a 3-D frame cell that uses it.

3. A table frame in 3-D

Table frame 4 × 3 m with frame buckling describes four fixed columns and a beam grid in the Space frame (one statement per line) box. Nodes have x, y and z (z is up); section COL shape=i … computes the section from its shape, material steel takes typical steel values, udl B1 qz=-12 loads two beams, load E Fx=4 pushes sideways and selfweight adds the members' weight.

The drawing shows the frame in an oblique view: tension members solid, compression dashed and the deformed shape exaggerated, with x, y and z arrows in the corner. The cell reports a largest displacement of 5.117 mm at the middle of B1, a highest utilisation of 0.349 in B1 and a Buckling load factor of 41.46: all loads together could grow 41 times before the frame buckles elastically. A third drawing shows that buckling mode.

The member table gives N, Vy, Vz, T, My and Mz with the extreme-fibre stress, the torsion shear and the von Mises value; Member end forces in local axes lists both ends of every member. Diagram chooses which internal force the second drawing shows.

4. Turn the view

Under the drawings, Turn the view 30° to the left and Turn the view 30° to the right rotate the frame about the vertical axis; View from higher up (15°) and View from lower down (15°) tilt it. Plan view looks straight down, Reset view returns to the start. Each press changes View azimuth (°) and View elevation (°) of the cell and runs it again — the forces stay the same, only the drawings turn.

5. Euler's load from the eigen solver

Euler column from the eigen solver is a pinned 4 m steel tube (88.9 × 4 mm) split into four elements under 100 kN. With Buckling analysis of the whole frame switched on it reports a buckling load factor of 1.249, so the column buckles at 124.9 kN — Euler's π²EI/L² is 124.8 kN. The member check of each 1 m element shows N/Pcr = 0.05 because it uses the element length; the frame analysis finds the real column.

6. Tips

• Hinges in 3-D: hinge=end releases both bending moments, release=start:t releases torsion.
• ref=0,1,0 or roll=90 on a member turns its section.
• Sagging with z up is a negative My (right-hand rule); diagrams are drawn on the tension side.
• Save the internal forces along C1 as a dataset (the first beam member) keeps N … Mz and the deflections along it for a Plot cell.
• Both tools are also JSON APIs and MCP tools: proofline-truss-frame-solver and proofline-section-properties.