BarIO — Free Online Multi-Span Beam Solver

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

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 = K_fixed u_free. 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 – strong-axis bending (local y)
  • Iz – weak-axis bending (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)

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 (q_start to q_end) in lb/in. Exact fixed-end forces calculated using Hermitian polynomials:
  FEM_y = wL²/12
  M_start = +wL ²/12 M_end = –wL²/12
• Member Point Loads & Moments Applied at any location along a member → exact shear jump and moment kink.

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