# column_buckling

Family 18: the linear buckling load of a clamped-free box column (built-in eigenvalue solver).

Anchors: Euler, P_cr = (pi / 2)^2 E I / L^2, and Engesser's shear correction, P = P_e / (1 + P_e / (5/6 G A)). The ratio to
Engesser's value is the part of the answer no formula gives (the fixed root, a stubby column). Buckling is about the weak
axis (w > t).

## Parameters (nondimensional)

| parameter | range |
|---|---|
| `t_over_L` | 0.02 - 0.15 |
| `w_over_t` | 1.2 - 4.0 |
| `nu` | 0.2 - 0.4 |

## Answers and their error bands

| answer | error band (median / 95 % / max) | similarity x2 / x4 | CalculiX (same mesh) |
|---|---|---|---|
| `p_star` | 0.26 % / 0.58 % / 0.58 % | max 2.3e-08 % | max - |

## Checks

- points: 100 solved, 0 failed
- three-mesh studies: 20 (every 5th point); the band of each point is 1.25 x the largest standard-mesh error among its 3 nearest studies
- symmetry check (max): 0 %
- neighbour check: flagged 0, re-solved on a finer mesh 0, unresolved 0
- direction checks: p_star vs w_over_t ok (rho 0.595), p_star vs nu ok (rho 0.689)

## Against hand theory

| ratio | median | 95 % | max |
|---|---|---|---|
| `p_over_euler` | 1.006 | 1.021 | 1.032 |
| `p_over_engesser` | 1.011 | 1.032 | 1.044 |

## Columns of points.csv

parameters, the answers, `<answer>_band` (relative), the hand-theory ratios, `mirror_err`, `equilibrium_err` (where a single reaction exists), `<answer>_loo_err` / `_neighbour_flag` (leave-one-out prediction from all other points), `<answer>_recheck_diff` / `_flag_resolved` (finer re-solve of a flagged point), `has_gci` / `has_similarity` / `has_calculix`, `nodes`, `solve_s`, `studio` (version).

Solved with NovaSolver Studio through the same commands an AI client uses over MCP; the first section says which solver and mesh. The claim is verification (the equations are solved within the band), not validation against tests.

## License

This data is licensed under CC BY 4.0: https://creativecommons.org/licenses/by/4.0/
Credit: NovaSolver, https://novasolver.jp/studio/verified/
Provided as is, without warranty. Design decisions remain the user's responsibility.