Rebar Area / Spacing Calculator mechanism

Model scope

The area formula is correct for a specified integer bar count and a valid lookup-table area. The instrument is not complete as specified because the spacing-input path, target-area path, integer rounding rule, bars-per-meter definition, boundary placement convention, and US-versus-metric unit behavior are not defined. The honest label should state that this is a nominal steel-area and geometric spacing calculator, not a complete reinforcement design or code-compliance checker.

• As = n·Ab is correct when n is the integer number of identical bars and Ab is the nominal cross-sectional area for the selected bar size.
• spacing = width/(n−1) is valid only for n >= 2 and only when the first and last bar are located at the two width boundaries with equal center-to-center spacing. It is not a general rebar spacing formula.
• The specification accepts spacing as an input but provides no formula for deriving the number of bars or total steel area from spacing. A stated boundary convention is required; commonly n = floor(width/spacing) + 1, but other detailing conventions are possible.
• The claimed required-spacing calculation for a target As is not specified. It needs an integer-bar rule such as n = ceil(target_As/Ab) for a minimum-area requirement, followed by spacing = width/(n−1).
• The bars-per-meter formula is missing and ambiguous. It may mean 1/spacing, n/width, or a code-specific effective bar density; these are not generally equal.
• The specification mixes US bar-size areas in square inches with metric dimensions and bars-per-meter without defining unit conversion and output units.

Units and conventions

• US rebar sizes and nominal areas are used; #4 = 0.20 in², #5 = 0.31 in², and #8 = 0.79 in².
• Width and spacing are in inches unless explicitly stated otherwise.
• For vectors with a defined spacing, bars-per-meter is interpreted as 1/spacing after converting spacing from inches to meters.
• The spacing formula assumes bars are placed at both width boundaries, so there are n−1 equal spaces.
• For the target-area vector, target As is interpreted as a minimum required area and the bar count is rounded up to the next whole bar.
• As outputs are reported in square inches unless otherwise stated.

Inspectable vector

One of 4 source-bound review vectors:

{
  "inputs": {
    "mode": "area_and_spacing_from_count",
    "bar_size": "#4",
    "number_of_bars": 10,
    "width_in": 108
  },
  "expected_outputs": {
    "As_total_in2": 2,
    "spacing_in": 12,
    "bars_per_meter": 3.280839895
  },
  "reference_data": {
    "rebar_nominal_area_in2": {
      "#4": 0.2
    },
    "inch_to_meter": 0.0254,
    "source_convention": "US rebar nominal-area table, widely tabulated standard value consistent with ASTM A615/ACI practice; inch-to-meter conversion is the exact SI definition."
  },
  "working": "As = n·Ab = 10·0.20 in² = 2.00 in². Spacing = width/(n−1) = 108 in/(10−1) = 108/9 = 12.00 in. Convert spacing: 12.00 in·0.0254 m/in = 0.3048 m. Bars per meter = 1/0.3048 m = 3.280839895 bars/m."
}

Failure boundary

BREAK_CLAIMED · SELF_FLAGGED

Zero width produces zero spacing and an undefined bars-per-meter result; one bar produces division by zero in spacing; negative width has conflicting signed versus geometric interpretations; and the two calculation modes require explicit selection.

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-tranche7/tranche7-results.json
• BOUNDARY_HAZARD_CATALOG.json