What the Ratio of Operating to Inventory Load Ratings Reveals: Exact Factor Identities and an Audit of 174,335 Bridges in the 2025 National Bridge Inventory

Every US highway bridge carries two load ratings: an inventory rating, the load it can carry indefinitely, and an operating rating, the maximum permissible load. I prove that when the same member and limit state govern both, their ratio is fixed by the code factors: 2.17 over 1.30, or 1.6692, under load factor rating; 1.75 over 1.35, or 1.2963, under load and resistance factor rating; and, for steel under allowable stress rating, (0.75 minus delta) over (0.55 minus delta), which is at least 15 over 11 and rises with the dead-load stress ratio delta. These identities give a check on reported ratings that needs no structural model. I apply it to 174,335 bridges in six states (California, Iowa, New York, Ohio, Pennsylvania, Texas) from the 2025 National Bridge Inventory. No bridge has an operating rating below its inventory rating. For LRFR ratings reported as rating factors, 60.1% sit at the nominal ratio within rounding, 32.5% above and 7.4% below; for LFR rating factors only 40.1% do, and the most common ratio is 1.299, the LRFR value. 2,278 of 14,094 LFR and ASD rating-factor records carry exactly 32.4 and 42.1 tonnes, the pattern of an inventory factor of 1.00 and an operating factor of 1.30. Ratios therefore flag records whose method code and values are inconsistent, a cheap first step in auditing inventory data.