SpanProof — continuous beam laboratory
Beam + spring supports (x = 0 at left end)
Hover a diagram for Δ, M, V at x · click to copy
Equilibrium holdsK symmetricTable 3-23 matched
Built-in identities
Vertical equilibrium ΣR = w × total length. Hermitian stiffness is symmetric by construction. Free cantilever tips must have zero shear and moment.
- |ΣR − (wL)| / |wL|
- 0
- max |Kᵢⱼ − Kⱼᵢ|
- 0
Three equal spans — all spans loaded
AISC Table 3-23 · 3 equal spansAISC pins: rigid simple supports, no cantilevers. Interior M = −wL²/10; end-span +M = 0.080 wL² at 0.400L; Δmax = 0.0069 wL⁴/EI at 0.446L.
| Quantity | AISC | This solver | Rel. err. | |
|---|---|---|---|---|
| End reaction R₁ = Rₙ | 4.000 | 4.000 | 0.00% | Pass |
| Interior reaction R₂ = R₃ | 11.00 | 11.00 | 0.00% | Pass |
| Shear just left of first interior | 6.000 | 6.000 | 0.00% | Pass |
| Shear just right of first interior | 5.000 | 5.000 | 0.00% | Pass |
| Max +M (end span) | 8.000 | 8.000 | 0.00% | Pass |
| End-span +M station (from A) | 4.000 | 4.000 | 0.00% | Pass |
| Max −M (first interior) | 10.00 | 10.00 | 0.00% | Pass |
| Center-span +M | 2.500 | 2.500 | 0.00% | Pass |
| Δmax (end span) | 6.90e-2 | 6.88e-2 | 0.24% | Pass |
| Δmax station (from A) | 4.460 | 4.500 | 0.90% | Pass |