Source: https://guthlabs.ai/docs/instruments/column-buckling-euler-critical-load/

instrument / verified-clean

# Column Buckling — Euler Critical Load

The current ledger marks this instrument verified clean within the source-bound verification corpus.

Status: **VERIFIED_CLEAN**Lifecycle: **verified-clean**

## Inspectable records

[01**Overview**Purpose and lifecycle](<https://guthlabs.ai/docs/instruments/column-buckling-euler-critical-load/>)[02**Mechanism**Method and assumptions](<https://guthlabs.ai/docs/instruments/column-buckling-euler-critical-load/mechanism/>)[03**Implementation**Binding and validation](<https://guthlabs.ai/docs/instruments/column-buckling-euler-critical-load/implementation/>)[04**Qualification**Evidence and errata](<https://guthlabs.ai/docs/instruments/column-buckling-euler-critical-load/qualification/>)

## Ledger state

The current ledger marks this instrument verified clean within the source-bound verification corpus.

**Area**: Mechanical, Civil & Structural Engineering — Statics/Dynamics, Strength of Materials, Machine Design, Civil, HVAC, Vibration

**Tranche**: tranche-4

**Evidence ID**: t4-106

**Ledger rows**: 1

No ledger note is attached.

## Review findings

The core Euler formulas are standard and numerically verified, but the specification needs explicit unit contracts, complete input requirements for stress and slenderness, domain validation, and a more accurate description of Euler versus Johnson and crushing/yield behavior.

### Formula and scope findings

- The algebraic formulas are correct: Pcr = π²EI/(KL)² and σcr = π²E/(KL/r)², provided r = √(I/A) and all quantities use a consistent unit system.

- Stress and slenderness ratio cannot be computed from E, I, L, and K alone; r or both I and A are required.

- The honest-label statement that short columns need the Johnson formula is imprecise: Johnson's parabolic formula generally applies to an intermediate inelastic range, while short columns are typically checked for yielding or crushing; applicability depends on material and slenderness.

### Unit assumptions

- E, stress, and σcr must use the same stress unit; I and A must use mutually consistent length powers.

- For SI inputs, use E in Pa, I in m^4, A in m^2, L and r in m; Pcr is then in N and σcr in Pa.

- For US customary inputs, using E in ksi, I in in^4, A in in^2, and L and r in inches produces Pcr in kip and σcr in ksi.

- K is dimensionless and is the effective-length factor: approximately 0.5 fixed-fixed, 0.7 fixed-pinned, 1.0 pinned-pinned, and 2.0 fixed-free.

## Boundary hardening

**BREAK_CLAIMED** · SELF_FLAGGED

The specification has no numerical slender-column validity threshold or Johnson-formula branch, so it cannot reliably classify the formula's applicability near the slender/short-column transition. It also produces undefined results for zero length unless the input is rejected, and negative K has an unresolved convention that can cause either silent normalization or invalid lookup behavior.

## Errata and corrections

No applied erratum is attached to this unique-name record.

## Inspectable example

4 review vectors are recorded. One source-bound sample is shown below.

````
{
  "inputs": {
    "E_Pa": 200000000000,
    "I_m4": 0.000008,
    "A_m2": 0.004,
    "L_m": 3,
    "K": 1
  },
  "expected_outputs": {
    "Pcr_N": 1754596.34,
    "sigma_cr_Pa": 438649084.45,
    "slenderness_ratio": 67.08204
  },
  "working": "r = √(I/A) = √(0.000008/0.004) = √0.002 = 0.0447214 m. KL/r = (1×3)/0.0447214 = 67.08204. Pcr = π²EI/(KL)² = 9.8696044×200000000000×0.000008/(3)² = 9.8696044×1600000/9 = 1754596.34 N. σcr = Pcr/A = 1754596.34/0.004 = 438649084.45 Pa."
}
````

## Related workflows

[Beam & Column Structural Benchslender columns](<https://guthlabs.ai/docs/instrument-workflows/structural-bench/>)

## Sources and evidence

These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.

- `VERIFIED_LEDGER.json · VERIFIED_CLEAN`

- `evidence-tranche4/tranche4-results.json`

- `BOUNDARY_HAZARD_CATALOG.json`