# l_bracket_modal

Family 21: the first natural frequency of the shelf L-bracket of family 1 (the back of the vertical flange fixed).

Hand anchor: the horizontal flange as a clamped-free beam of length L - t. The vertical flange is held over its whole back,
so it moves little; the corner and a short wide flange are what the ratio to the beam shows. Studio's own mesh sizes set the
levels here: the mode lives in the whole flange, not at the fillet.

## Parameters (nondimensional)

| parameter | range |
|---|---|
| `h_over_L` | 0.4 - 1.0 |
| `t_over_L` | 0.04 - 0.15 |
| `w_over_L` | 0.25 - 0.75 |
| `r_over_t` | 0.25 - 1.5 |
| `nu` | 0.25 - 0.35 |

## Answers and their error bands

| answer | error band (median / 95 % / max) | similarity x2 / x4 | CalculiX (same mesh) |
|---|---|---|---|
| `f_star` | 0.9 % / 1.9 % / 1.9 % | max 0.045 % | max - |

## Checks

- points: 80 solved, 0 failed
- three-mesh studies: 16 (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: f_star vs t_over_L ok (rho 0.992)

## Against hand theory

| ratio | median | 95 % | max |
|---|---|---|---|
| `f_over_beam` | 1.001 | 1.08 | 1.088 |

## 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.