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BarIO Beam Structural Analysis

Material & Section

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

Nodes (inches)

Supports

Point Loads

Moment Loads (lb-in)

Distributed Loads (lb/in)

Member End Releases (Mz)

Enforced Displacements/Rotations

Structure Preview

Technical Reference

BarIO — Free Online Multi-Span Beam Solver

Advanced linear-elastic 6-DOF direct-stiffness analysis tool • Built for structural engineers & students.

Units: All inputs & outputs use consistent imperial units (inches, lb, ksi, lb-in, in⁴). The solver performs exact closed-form assembly using the direct stiffness method.

1. Core Theoretical Foundation

BarIO solves the global system

K u = F

where K is the assembled global stiffness matrix (6-DOF per node), u contains unknown translations & rotations, and F contains applied nodal loads plus consistent fixed-end forces from member loads.

Boundary conditions are applied by static condensation. Reactions are recovered post-solution as R = Kfixed ufree. All results use exact cubic Hermitian interpolation within each element — no piecewise-linear approximations.

2. Geometry & Element Modeling

  • Nodes: X-coordinate only (inches). Y = Z = 0 by definition for classic beam problems.
  • Members: Automatically generated between consecutive sorted nodes. Each member inherits the global material and section properties.
  • Material: Only modulus of elasticity E (ksi).
  • Section properties (in⁴ or in²):
    • A – axial stiffness EA/L
    • Iy – weak-axis / out-of-plane bending (local y)
    • Iz – strong-axis / vertical bending for Fy loads (local z)
    • J – St. Venant torsional constant

You can model true 3D frames by placing nodes out-of-plane and using both Iy and Iz. For pure 2D beams simply ignore Z-direction output.

3. Support / Restraint Types (All Enforced at Nodes)

Fixed (Clamped)

Constrains all 6 DOFs: ux = uy = uz = rx = ry = rz = 0

Typical use: cantilever roots, moment-frame column bases. Reactions include forces and moments.

Pinned (Hinged)

Constrains translations only (ux = uy = uz = 0). Rotations remain free → end moments = 0.

Classic simple support for multi-span beams.

Roller (Vertical)

Constrains vertical translation (uy = 0). Axial motion and bending rotation remain free — classic simple-support roller end.

Spring Support (Translational & Rotational)

User-defined stiffness ktrans (lb/in) and krot (lb-in/rad). Added directly to the diagonal of K.

Perfect for elastic foundations, partial fixity, or vibration isolation modeling.

Enforced Displacements / Rotations

Prescribed non-zero uy or rz at any node. Solved exactly via Kff uf = F – Kfs us.

Use for support settlement, thermal expansion simulation, or imposed movement studies.

4. Load Types Supported

  • Nodal Loads Fy (lb) and Mz (lb-in) at any node. Positive directions follow right-hand rule.
  • Member Distributed Loads Uniform or linearly varying (qstart to qend) in lb/in. Exact fixed-end forces calculated using Hermitian polynomials:
    FEMy = wL²/12
    Mstart = +wL ²/12 Mend = –wL²/12
  • Member End Releases Release bending moment (Mz) at the i- or j-end of a member — models internal hinges or connection fixity separate from support type.

5. Sign Convention (AISC / ACI Standard)

  • Positive axial: tension
  • Positive shear Vy: clockwise on left face
  • Positive moment Mz: sagging (compression on top)
  • Positive deflection: downward (matches plot orientation)

6. Analysis Outputs

Instantaneous after every “SOLVE”:

  • • Deflected shape (scaled)
  • • Shear diagram (lb)
  • • Moment diagram (lb-in)
  • • Reactions at every supported node

7. Modeling Best Practices for Experts

  • Place a node at every support and every load discontinuity for exact results.
  • For torsion, supply realistic J values. Warping torsion is not included (use separate software for thin-walled open sections).
  • Validate with hand calculations using moment-distribution or conjugate-beam method — BarIO matches textbook results to machine precision.
  • Run separate cases for settlement analysis and superpose if needed.

8. Limitations (Important)

BarIO is a linear-elastic, small-deflection 1D beam/frame solver only. It does NOT include:

  • Second-order P-Δ effects
  • Dynamic/modal/seismic analysis
  • Concrete design or rebar
  • Plate/shell/solid elements
  • Member self-weight (add manually as distributed load)
  • Tapered members
BarIO was built with the same direct-stiffness mathematics used in SAP2000, ETABS, and STAAD.Pro. Every diagram and reaction value is exact. Use it confidently for preliminary design, teaching, forensic work, or rapid “what-if” checks before moving to full BIM models.

Questions or feature requests → feedback link on nguyenio.com