Reinforced Concrete Beam — Singly Reinforced Flexural Capacity mechanism

Model scope

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.

• 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.

Units and conventions

• 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.

Inspectable vector

One of 4 source-bound review vectors:

{
  "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."
}

Failure boundary

• 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.

Other records

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