3dIO — Free Online 6-DOF 3D Frame & Space Truss Analyzer
Full direct-stiffness 12×12 local / 6-DOF global assembly • No limits, no signup
Units (fixed): inches, lb, lb-in, ksi, in⁴. All loads and results use global Cartesian for nodes and local member coordinates for distributed loads and end forces.
1. Core Theoretical Foundation
3dIO solves the global equilibrium equation
K u = F
using the direct stiffness method with full 12×12 local stiffness matrices for each 6-DOF space-frame element. The solver assembles the global stiffness matrix, applies boundary conditions by static condensation, and recovers reactions and end forces exactly. Deflected shape is shown at user-controlled scale (default ×500) using exact cubic Hermitian interpolation.
DSM backend guarantees machine-precision results identical to commercial packages (SAP2000, STAAD.Pro, ETABS) for linear-elastic prismatic members.
2. Geometry & Element Modeling
- Nodes: Full 3D coordinates (X, Y, Z in inches). No limit on model size for typical browser use (<200 nodes recommended).
- Members: Defined by start (I) and end (J) node. Each member is a 6-DOF space beam element with user-defined end releases.
- Material: Young’s modulus E (ksi) only.
- Section properties:
- A – axial
- Iy / Iz – biaxial bending
- J – St. Venant torsion
Local member coordinate system follows right-hand rule: local x from I to J; local y and z defined by the global orientation (DSM auto-computes transformation matrix).
3. Member End Releases (Frame vs Truss Behavior)
Welded (Rigid) ends
Full moment transfer — 6 DOFs continuous. Classic space-frame behavior.
Pinned ends (I-end and/or J-end)
Moment releases about local y and z axes (My = Mz = 0 at pinned end). When both ends pinned → pure truss member (only axial force). This is how you model space trusses inside the same model.
4. Support / Restraint Types (Applied at Nodes)
Fixed
All 6 DOFs restrained (UX=UY=UZ=RX=RY=RZ=0).
Pinned
Translations restrained, rotations free.
Free
No restraints (useful for internal nodes or to override).
Spring
User-defined k_trans (lb/in) and k_rot (lb-in/rad) added to global K diagonal. Perfect for elastic supports or partial fixity.
Enforced displacements/rotations (UX…RZ) use the exact partitioned equation K_ff u_f = F – K_fs u_s — identical to commercial FEA.
5. Load Types Supported
- Nodal Loads (global): Full 6 components — FX, FY, FZ, MX, MY, MZ at any node.
- Distributed Loads (local member axes): Uniform or linearly varying in Fx, Fy, or Fz direction. Exact consistent nodal loads and fixed-end moments/torques computed by DSM.
- Enforced Displacements/Rotations: Any combination of UX…RZ for settlement, temperature, or prescribed movement studies.
6. Sign Convention (Standard Right-Hand Rule)
- Positive forces/moments follow global and local right-hand rule.
- Positive member end forces: tension axial (FX), shear in local y/z, torsion MX, bending My/Mz (sagging positive per local orientation).
- Deflection plots show true 3D displacement (green = deformed, dashed gray = original).
7. Analysis Outputs (Instant after SOLVE)
- • Interactive 3D deflected shape (original + deformed ×500)
- • Reactions at supported nodes only (FX…MZ)
- • Member end forces in local coordinates (I-end & J-end)
- • Full 6-DOF node displacements (inches & radians)
8. Modeling Best Practices for Experts
- Use pinned ends on both sides to create pure truss members within a frame model.
- Place nodes at every load discontinuity and support for exact results.
- For torsion, supply realistic J; warping is neglected (use specialized software for open thin-walled sections).
- Validate with hand calculations or known benchmarks.
- Run multiple load cases manually and superpose results (linear system).
9. Limitations (Important)
- Linear elastic, small-deflection theory only (no P-Δ, no cables, no geometric nonlinearity).
- No dynamic/modal/seismic analysis.
- No automatic self-weight (add as distributed load).
- No tapered members, no concrete/steel design checks.
- No plate/shell/solid elements — pure 1D frame/truss only.
3dIO gives you the same 6-DOF direct-stiffness mathematics used in professional practice, wrapped in a zero-install browser interface. Use it for rapid 3D frame verification, truss optimization, teaching, or forensic analysis before moving to full BIM/FEA suites.
Questions or feature requests → feedback on nguyenio.com