← Verification — Linear (Frames & Trusses)
V1.2 — Simply supported beam, uniform load
ExactDescription
A beam on two simple supports under a uniform load along its full length — midspan deflection, end reactions and midspan moment.
Reference
Standard simply-supported beam formulas (closed form): δmid = 5wL⁴/(384EI), R = wL/2, Mmid = wL²/8.
Model
An elastic frame member on a pin support at one end and a roller at the other, meshed into 8 equal elements so the uniform load and midspan response are captured smoothly. The uniform load is applied along the member's full length under a single linear static load case.
| Uniform load, w | 0.1 kip/in |
| 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 |
| Elements | 8 |
Comparison
| Quantity | Reference | vfopro | % diff | Status |
|---|---|---|---|---|
| Midspan deflection (in) | -0.0108 | -0.0108 | +0.00% | Exact |
| Left reaction (kip) | 12 | 12 | 0.00% | Exact |
| Right reaction (kip) | 12 | 12 | 0.00% | Exact |
| Midspan moment, sagging (kip-in) | -720 | -720 | 0.00% | Exact |
| Support moment (kip-in) | 0 | -1.677e-12 | n/a | Exact |
| End shear at left support (kip) | 12 | 12 | 0.00% | Exact |
Conclusion
Every reported quantity matched the closed-form value to at least 6 significant figures.
Was this page helpful?
Last updated September 22, 2026 · applies to vfopro 20260922.0.0 or later