Structures: trusses, beams, frames and plates with holes

Proofline has two structural cells that run in your browser: Truss/frame analysis and Plate stress (2-D). They use the same engine as the Truss & Frame Solver and the Plate Stress tool pages, so a cell and its tool page give identical numbers. Both are linear-elastic models for checking and learning — not certified design.

1. Open the Structures lab

Choose Notebook → Templates… and open Structures lab, then press Run all. The notebook holds a note and six structural cells: a simply supported beam, the same beam fixed at one end, a Warren roof truss, a portal frame with a hinge and the same plate with a hole on a coarse and a fine mesh.

2. A beam you can check by hand

Open Simply supported IPE 200 beam, 6 m. The Structure (one statement per line) box describes it:

node A 0 0
node B 6 0
material steel E=210 fy=235
section IPE200 A=28.5 I=1943 W=194
member M1 A B
support A pin
support B roller
udl M1 qy=-5

Units are metres and kN; E is in GPa, fy in MPa, A in cm², I in cm⁴ and W in cm³, as printed in steel tables. The result shows a largest displacement of 20.68 mm at 3 m — exactly 5wL⁴/384EI — and a largest bending moment of 22.5 kN·m, wL²/8. The member table gives the bending stress and the utilisation against the yield strength; the beam deflection table compares the sag with the Deflection limit L/… you set.

The next cell changes one line to support A fixed. The beam becomes statically indeterminate: the displacement drops to 8.576 mm at 3.6 m, the reactions are 18.75 kN with a 22.5 kN·m fixed-end moment at A and 11.25 kN at B (5wL/8, wL²/8 and 3wL/8).

3. A roof truss and its buckling check

Warren roof truss, 12 m uses the Structure type “2-D truss (pin-jointed bars)”. In the diagram tension members are solid and compression members dashed; thicker lines carry more force. The member table shows 30 kN tension in the middle bottom chords and 30 kN compression in the top chord GH. The Euler buckling check table lists the slenderness and the critical load of every compression member: GH reaches N/Pcr = 0.46.

The equilibrium check adds loads and reactions in x, y and moment. All three should be practically zero; anything else points to a typing error in a support or load.

4. Hinges and frames

Portal frame with a hinge and wind joins two fixed columns with a beam that has hinge=end: the beam cannot carry a moment at C. The bending moment diagram draws the moments on the tension side of each member and drops to zero at the hinge. If you remove a support so the structure can move freely, the cell names the free direction instead of returning nonsense.

To keep a beam's internal forces, use Save the moment and deflection along M1 as a dataset under the result; you can then plot them with a Plot cell.

5. Plate with a hole and mesh refinement

Steel strip with a hole, coarse mesh is a 200 × 100 mm plate with a 30 mm hole, pulled with 50 MPa. The model uses rect, hole circle, thickness, material, fix and traction lines, in millimetres, newtons and MPa. The stress map colours each triangle; choose von Mises, σx, σy or τxy under Stress map and switch on Draw the element edges to see the mesh.

The coarse cell reports a peak von Mises stress of 157.5 MPa, 3.149 × the applied stress. The next cell, Same strip, fine mesh at the hole, sets Element size at the holes (mm, optional) to 1 and reaches 170.3 MPa, 3.405 × — the comparison block shows the change. Refining further barely changes the peak: the mesh has converged, close to the factor of about 3.37 from Peterson's charts. Refine the mesh at the holes halves the element size for you.

6. Tips

• Holes must lie completely inside the outline. For a symmetric quarter plate, draw the cut-out as part of the outline and fix ux on one symmetry line and uy on the other.
• Fix only what holds the real part; extra fixings add stiffness that is not there.
• The structural tools are also available as JSON APIs and MCP tools: proofline-truss-frame-solver and proofline-plate-stress.