Verification › V.02 Frames
V.02.5Fixed Portal Frame under a Beam Load
Within 0.9% (the formula ignores axial shortening)Problem
Find the corner and base moments of a fixed-base portal frame with a uniform load on the beam, for three column-to-beam stiffness ratios.
Reference
- Slope-deflection, no sway: corner moment MB = wL²k / (6(2k + 1)), base moment MA = MB / 2, with k = (Icol/h) / (Ibeam/L).
Model
- Span L = 10 m, height h = 5 m, fixed bases
- w = 1 kN/m on the beam; Ibeam = 2 × 10⁻⁴ m⁴; E 200 GPa
- k = 0.5, 1 and 2
Comparison
| Result | Slope-deflection | Sutranet | Difference |
|---|---|---|---|
| k = 0.5, corner MB | 4166.7 | 4162.9 | 0.091% |
| k = 0.5, base MA | 2083.3 | 2077.7 | 0.27% |
| k = 1, corner MB | 5555.6 | 5548.9 | 0.12% |
| k = 1, base MA | 2777.8 | 2764.4 | 0.48% |
| k = 2, corner MB | 6666.7 | 6657.1 | 0.14% |
| k = 2, base MA | 3333.3 | 3304.5 | 0.86% |
- The solver includes axial shortening of the members, which the formula leaves out, so it sits slightly below it: about 0.1% at the corners and up to 0.9% at the bases.
Reproduce
This is a closed-form or table check with no project file; it runs in the solver test portal_frame.rs (sutranet-analysis).
Automated test: portal_frame.rs (sutranet-analysis), run on every change.
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