Source: https://guthlabs.ai/docs/instruments/reinforced-concrete-beam-singly-reinforced-flexural-capacity/implementation/

instrument implementation / implementation-contract

# Reinforced Concrete Beam — Singly Reinforced Flexural Capacity implementation

A source-bound implementation contract for Reinforced Concrete Beam — Singly Reinforced Flexural Capacity; deployment and executable qualification remain separate.

Status: **VERIFIED_WITH_ERRATA**Lifecycle: **implementation-contract**

## Binding contract

This record describes what an executable surface must bind and validate. It does not claim that a public calculator, package, or production route is deployed.

**Record owner**: Guth Instruments

**Lifecycle**: verified-with-binding-errata

**Evidence ID**: t5-122

**Effect**: Computation or source lookup only

## Input and validation requirements

- Division by zero occurs if b is zero; d is also required to be positive for a meaningful section and steel ratio.

- Negative or inconsistent units can produce meaningless capacities; automatic unit validation is required.

- If a is greater than or equal to d, the simplified expression can produce zero or negative nominal moment and must not be presented as a valid tension-controlled design capacity.

- Applying φ=0.9 without checking tensile strain can overstate design capacity for over-reinforced sections.

- ρmin and ρmax cannot be checked because their formulas, ACI edition, and any required code parameters are absent.

- The zero-steel case computes arithmetically but is not a reinforced-concrete flexural design and would generally fail minimum-reinforcement requirements once those requirements are defined.

## Required corrections

````
[
  {
    "stress_correction": {
      "vector_inputs": {
        "As": 300,
        "fy": 500,
        "fc": 40,
        "b": 250,
        "d": 450
      },
      "wrong_outputs": {
        "a_mm": 14.823529,
        "Mn_kN_m": 66.388235,
        "phiMn_kN_m": 59.749412
      },
      "corrected_outputs": {
        "a_mm": 17.647059,
        "Mn_kN_m": 66.176471,
        "phiMn_kN_m": 59.558824
      },
      "method": "a = As*fy/(0.85*fc*b) = 150000/8500 = 17.647059 mm, not 14.823529 (a ~1000/8500 arithmetic slip). Mn and phiMn recomputed downstream from the corrected a. rho/rho_min/rho_max/check flags do not depend on a and were unaffected."
    }
  }
]
````

## Inspectable interface fixture

The sample below is evidence for interface and validation tests, not a production implementation.

````
{
  "inputs": {
    "As": 300,
    "fy": 420,
    "fc_prime": 28,
    "b": 300,
    "d": 500,
    "units": "As mm²; fy and fc_prime MPa; b and d mm"
  },
  "expected_outputs": {
    "a_mm": 17.6470588,
    "Mn_kN_m": 61.8882353,
    "phiMn_kN_m": 55.6994118,
    "rho": 0.002,
    "rho_min_check": "UNDETERMINED: rho_min formula/value not supplied",
    "rho_max_check": "UNDETERMINED: rho_max formula/value not supplied"
  },
  "working": "Asfy = 300 × 420 = 126000 N.\\n0.85fc'b = 0.85 × 28 × 300 = 7140 N/mm.\\na = 126000 ÷ 7140 = 17.6470588 mm.\\nMn = 126000 × (500 − 17.6470588 ÷ 2) = 126000 × 491.1764706 = 61888235.3 N·mm = 61.8882353 kN·m.\\nφMn = 0.9 × 61.8882353 = 55.6994118 kN·m.\\nρ = As/(bd) = 300/(300 × 500) = 300/150000 = 0.002."
}
````

## Other records

[01**Overview**](<https://guthlabs.ai/docs/instruments/reinforced-concrete-beam-singly-reinforced-flexural-capacity/>)[02**Mechanism**](<https://guthlabs.ai/docs/instruments/reinforced-concrete-beam-singly-reinforced-flexural-capacity/mechanism/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/reinforced-concrete-beam-singly-reinforced-flexural-capacity/qualification/>)

## Sources and evidence

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

- `VERIFIED_LEDGER.json`

- `evidence-tranche5/tranche5-results.json`

- `STRESS_TEST_CORRECTIONS_APPLIED.json`