Source: https://guthlabs.ai/docs/instruments/reinforced-concrete-beam-singly-reinforced-flexural-capacity/
instrument / verified-with-binding-errata
# Reinforced Concrete Beam — Singly Reinforced Flexural Capacity
The current ledger marks this instrument verified with errata that must be applied at binding time.
Status: **VERIFIED_WITH_ERRATA**Lifecycle: **verified-with-binding-errata**
## Inspectable records
[01**Overview**Purpose and lifecycle]()[02**Mechanism**Method and assumptions]()[03**Implementation**Binding and validation]()[04**Qualification**Evidence and errata]()
## Ledger state
The current ledger marks this instrument verified with errata that must be applied at binding time.
**Area**: Mechanical, Civil & Structural Engineering — Statics/Dynamics, Strength of Materials, Machine Design, Civil, HVAC, Vibration
**Tranche**: tranche-5
**Evidence ID**: t5-122
**Ledger rows**: 1
No ledger note is attached.
## Review findings
The nominal-strength equations are standard under the stated Whitney-block assumptions, but the instrument cannot honestly claim complete ACI 318 design capacity or reinforcement checks without an ACI edition, rho-min/rho-max definitions, and a tension-controlled strain verification. The exact unresolved ambiguity is whether φ=0.9 is to be applied unconditionally or only after calculating the tensile strain and confirming the applicable ACI tension-controlled limit.
### Formula and scope findings
- The formulas for steel ratio ρ, ρmin, and ρmax are not provided even though the instrument claims to check them.
- φ=0.9 is valid only when the tensile strain satisfies the applicable ACI 318 tension-controlled limit; the spec does not calculate c, εt, or otherwise verify that condition.
- The formula uses the Whitney equivalent rectangular compression block and is valid only for a singly reinforced rectangular section with a valid positive compression-block depth a less than d.
- ACI 318 edition is unspecified; strength-reduction factors and tension-controlled criteria can vary by edition and design provision.
- No explicit input constraints are specified for positive b and d, nonnegative As, fy, and f'c, or for preventing an over-reinforced/non-tension-controlled section from being labeled with φ=0.9.
### Unit assumptions
- Inputs must use one coherent unit system: As and b·d in the same area units, fy and f'c in the same stress units, and d and a in the same length units.
- With As in mm², dimensions in mm, and stresses in MPa (N/mm²), a is in mm and Mn is in N·mm; reported kN·m equals Mn divided by 1,000,000.
- With As in in², dimensions in inches, and stresses in ksi, a is in inches and Mn is in kip·in; reported kip·ft equals kip·in divided by 12.
- The coefficient 0.85 is treated as the ACI equivalent rectangular concrete compression-block factor.
- The value φ=0.9 is assumed only after verifying the applicable ACI tension-controlled strain requirement; that verification is not possible from the supplied inputs alone.
## Boundary hardening
### Recorded hazards
- 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.
## Errata and corrections
### Stress-test 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 example
4 review vectors are recorded. One source-bound sample is shown below.
````
{
"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."
}
````
## Related workflows
No source-defined multi-instrument workflow membership is recorded.
## Sources and evidence
These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.
- `VERIFIED_LEDGER.json · VERIFIED_WITH_ERRATA`
- `evidence-tranche5/tranche5-results.json`
- `STRESS_TEST_CORRECTIONS_APPLIED.json`