# l_bracket

Family 1: shelf L-bracket. The back of the vertical flange is fixed to a wall (x = 0); a force pushes down on the
top of the horizontal flange; the inner corner has a fillet of radius R, where the stress concentrates.

Lengths are scaled by the flange length L (L = 80 mm in the solves). In linear elasticity with E, F and L scaled out
exactly (stress * L^2 / F and deflection * E * L / F depend only on the shape ratios and nu), each solve stands for
every size, material stiffness and load of the same shape: 5 dimensions instead of 9.

## 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) |
|---|---|---|---|
| `sigma_star` | 3.5 % / 4.4 % / 4.9 % | max 1.3 % | max 0.74 % |
| `delta_star` | 0.015 % / 0.044 % / 0.24 % | max 0.0083 % | max 0.00034 % |

## Checks

- points: 300 solved, 0 failed
- three-mesh studies: 30 (every 10th point); the band of each point is 1.25 x the largest standard-mesh error among its 3 nearest studies
- symmetry check (max): 0.003 %
- neighbour check: flagged 8, re-solved on a finer mesh 8, unresolved 0
- direction checks: sigma_star vs t_over_L ok (rho -0.912), sigma_star vs w_over_L ok (rho -0.349), sigma_star vs r_over_t ok (rho -0.148), delta_star vs t_over_L ok (rho -0.959), delta_star vs w_over_L ok (rho -0.261), delta_star vs h_over_L ok (rho 0.004)

## Against hand theory

| ratio | median | 95 % | max |
|---|---|---|---|
| `kt` | 1.024 | 1.467 | 1.604 |
| `beam_ratio` | 0.998 | 1.191 | 1.268 |
| `peak_angle_deg` | 15 | 21 | 24 |

## 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.