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3dIO 3D Frame & Truss Analysis

Material & Section

E (ksi)
A (in²)
Iy (in⁴)
Iz (in⁴)
J (in⁴)

Nodes (inches)

Members

Supports

Point Loads & Moments

Distributed Loads (lb/in, local)

Enforced Displacements/Rotations

Structure Preview (3D)

Drag to rotate • Scroll to zoom
Technical Reference

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 uses auto-scaled visualization (typically ×50–×5000) so both original and deformed geometry stay visible after solve.

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)

Bending releases via PyNite def_releases (local My/Mz = 0 at released ends). One member end per pinned node is rotationally tethered for solver stability (standard PyNite truss practice). When both ends pinned → truss action (axial force dominates). XY-plane models auto-restrain UZ and RX/RY for 2D-in-3D stability.

4. Support / Restraint Types (Applied at Nodes)

Fixed

All 6 DOFs restrained (UX=UY=UZ=RX=RY=RZ=0).

Pinned

Translations restrained, rotations free.

Roller

Translation free along the selected global axis (X, Y, or Z); other translations restrained. Rotations free in 3D; XY-plane models also restrain out-of-plane motion (UZ, RX, RY). Use with a pin support to stabilize 2D trusses and frames.

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 + auto-scaled deformed)
  • • 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