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inputted image and question large double torus stiffness problem over long spans need analyzing
You’re poking right at the hard part of these forms—global stiffness over long, curved spans is where they get sneaky.
Key stiffness issues in a large double-torus truss
Global ring flexibility (hoop modes):
The toroidal geometry wants to “ovalize” under asymmetric loads.Problem: Low in-plane bending stiffness of the ring → large lateral deflections, especially midspan between supports.
Watch for: First few modes being global ovalization or “breathing” of the torus rather than local member bending.
Torsional softness of the ring:
If the torus is essentially a single-layer truss ring, its torsional stiffness is often weak.Problem: Eccentric loads (lighting, rigging, façade panels) twist the ring, causing out-of-plane rotations and secondary bending in chords.
Mitigation: Use a closed box-like section at the macro level—e.g., double chord top/bottom with diagonals forming a tube, or two concentric rings tied with radial webs.
Span-to-depth ratio of the truss:
Long spans with shallow truss depth are inherently flexible.Rule of thumb: For a primary long-span truss, depth ≈ span/15–20 is comfortable; much shallower and deflections dominate.
In a torus: “Depth” is the radial distance between inner and outer chords (or top/bottom chords if vertical). Too small → poor bending stiffness around the ring.
Local member buckling vs. global stability:
Compression chords: Long, lightly braced chords around the torus are prone to elastic buckling if panel lengths are large.
Bracing density: Panel length and diagonal layout control effective buckling length; large toroidal spans often need tighter panelization than straight trusses.
Support conditions and continuity:
Discontinuous rings: If the double torus is segmented (e.g., four quadrants bolted together), joint flexibility can dominate global stiffness.
Support layout: Few supports → large bending in the ring between them; many supports → more statically indeterminate, but stiffer and more redundant.
How to analyze stiffness (conceptual workflow)
Idealize as a ring/torus beam first (macro model):Model: Treat each torus as a curved beam with equivalent ?? (bending) and ?? (torsion) derived from the truss.
Goal: Quickly see global deflections, ovalization, and sensitivity to support layout and span.
Derive equivalent section properties from the truss:
Axial stiffness of chords:??eq=∑???cos2(??)
Bending stiffness: Use chord separation (depth) and chord areas to get an equivalent ? about the ring’s local axes.Torsional stiffness: If you have a closed truss tube, approximate ? from the chord layout; if it’s open, accept that ?? is small and design bracing accordingly.
Refine with a 3D truss FE model:
Nodes: At each panel point along the torus; include both toroids if it’s a “double” system.
Members: Chords, diagonals, verticals, and any cross-ties between the two tori.
Check:
Nodal displacements under worst-case load patterns.
Member forces and utilization.
Buckling factors (linear eigen-buckling) for global modes.
Pay attention to load patterns that “break symmetry”:
Partial loading: Half-ring or quarter-ring loads often govern deflection and member forces.
Eccentric loads: Loads offset from the ring centroid to excite torsion and out-of-plane bending.
Strategies to increase stiffness over long spans
Increase structural depth:Radial depth: Separate inner and outer chords more; larger radius difference → higher in-plane bending stiffness.
Vertical depth: If the torus is vertical, increase distance between top and bottom chords.
Create a true closed tube:
Double torus as a box: Tie the two tori together with regular radial frames so they act as a single closed section.
Benefit: Huge gain in torsional stiffness and resistance to ovalization.
Densify bracing:
Shorter panels: More nodes, shorter members → higher buckling capacity and better distribution of forces.
Diagonal patterns: Use X-bracing or K-bracing patterns that stabilize both chords effectively.
Stiffen joints and segment connections:
Bolted flanges / sleeves: Ensure segment joints are not the weak link; rotational slop here kills global stiffness.
Pre-tensioned connections: Where possible, use preloaded bolts or clamps to reduce slip.
Optimize support scheme:
More supports: If feasible, add intermediate supports to reduce effective span between supports.
Support stiffness: Model support flexibility (e.g., base plates, anchors) realistically—soft supports can negate gains in the truss.
A quick gut-check for your design
If you tell me:Major radius (centerline of torus), Minor radius / truss depth, Number of panels, Chord sizes, and Support locations,
I can walk through a rough equivalent ??, estimate deflections over the longest span, and flag where the double-torus concept is likely to feel “soft” versus robust.
What’s the approximate diameter and depth of the double torus you’re thinking about, and is it for a stage, a roof, or something more permanent?
it indicates that the secondary members made from 30×2 mm is fine. but the primary need to be Much larger chord tubes (think on the order of 150–400 mm OD, with sensible wall thickness), and Real truss depth between chords and between the two tori to build up ?eff.
That is an ouch to support the regolith mass...
150–400 mm OD 4–12mm wall thickness
Truss depth (within each torus) 1–3m between inner/outer or top/bottom chords
Separation between the two tori 20–30m center‑to‑center (this is the single biggest lever on global stiffness)
Panel length 5–10m spacing between nodes
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