← Verification — Linear (Frames & Trusses)
V1.1 — Cantilever beam with tip load
ExactDescription
A cantilever beam with a concentrated transverse load at the free end — the most basic bending and shear check for a frame member.
Reference
Euler–Bernoulli beam theory (closed form): δ = PL³/(3EI), M = PL, V = P.
Model
A single elastic frame member of rectangular section, fully fixed against translation and rotation at one end and free at the other. A point load is applied transverse to the member at the free end under a single linear static load case. No hinges or nonlinear materials are involved — the check is purely on the elastic frame element's stiffness and force recovery.
| Tip load, P | 10 kip |
| Span length, L | 240 in |
| Elastic modulus, E | 29,000 ksi |
| Section width, b | 12 in |
| Section depth, d | 24 in |
| Moment of inertia, I | 13,824 in⁴ |
Comparison
| Quantity | Reference | vfopro | % diff | Status |
|---|---|---|---|---|
| Tip vertical displacement (in) | -0.1149 | -0.1149 | +0.00% | Exact |
| Tip axial displacement (in) | 0 | 0 | n/a | Exact |
| Tip lateral displacement (in) | 0 | 0 | n/a | Exact |
| Base vertical reaction (kip) | 10 | 10 | 0.00% | Exact |
| Base moment, element end i (kip-in) | -2,400 | -2,400 | 0.00% | Exact |
| Base shear, element end i (kip) | 10 | 10 | 0.00% | Exact |
| Tip moment, element end j (kip-in) | 0 | 0 | n/a | Exact |
Conclusion
Every reported quantity matched the closed-form value to at least 6 significant figures.
Last updated September 22, 2026 · applies to vfopro 20260922.0.0 or later