Documented ratio · one limit state · non-normative arithmetic

Documented Capacity-to-Demand Ratio Worksheet

Calculate a dimensionless ratio from one documented resistance, capacity or limit and one compatible documented demand for the same limit state, condition and unit.

no universal FoSno material presetsone shared unitno SAFE verdict

A ratio greater than one is not, by itself, proof of safety or code compliance. Codes may apply factors to loads, resistance, material properties, test levels or service conditions in different ways. Buckling, fatigue, fracture, instability, connections, deflection, creep, temperature and other limit states require their own controlled checks.

Controlled ratio inputs

Use values already derived on a compatible basis. This worksheet does not select a design factor or transform nominal strength into an allowable.

Ratio basis

Nominal basis: the quotient is only a nominal capacity-to-demand ratio; it is not a code-selected factor of safety.

Documented numerator RPositive resistance, strength, capacity, allowable or rated limit selected above.

Documented denominator DPositive demand/effect on the identical physical-quantity basis.

Shared quantity and unit labelOne shared label prevents silent conversion or mixing of force, stress, moment, pressure or different reference areas.

Limit state / failure mode

Numerator source, revision and statistical/material basis

Demand source, load combination and analysis revision

Applicable code, standard, edition and jurisdiction

Geometry, reference area, environment and service-condition record

Calculation ID and intended decision boundary

Required compatibility confirmation R and D have the same physical dimension, unit, reference area/geometry, direction, sign convention and limit-state definition. The selected basis correctly records which load, resistance, material and test factors are already included; no factor is silently applied twice. I will not use this arithmetic ratio as a substitute for all required limit states, uncertainty treatment, code checks or competent engineering review.

Reference arithmetic result

Capacity/limit-to-demand ratio Q = R/D

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Dimensionless quotient on the user-documented basis.

Arithmetic utilization U = D/R

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Not a code utilization unless the supplied basis is a valid code resistance/effect pair.

Signed difference R − D

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Ratio minus one Q − 1

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Pure arithmetic; not automatically a code-defined margin of safety.

No universal minimum, PASS/FAIL, SAFE/UNSAFE, fatigue life, reliability or code-compliance conclusion is produced.

Formula and model boundary

For positive, compatible quantities R and D expressed in the same unit and defined for the same limit state:

Q = R/D · U = D/R = 1/Q · Δ = R−D · q = Q−1

Q and U are dimensionless. Δ retains the shared unit. The quotient contains no information about how R and D were derived, so their provenance, factors, load combinations, material state, statistical basis and applicability must remain attached to the result.

Terminology boundary. A nominal-strength ratio, allowable-stress check, load-and-resistance-factor check, proof-test ratio and rated-capacity comparison are not interchangeable merely because each contains a division. If an allowable already includes a safety factor, dividing it by demand does not recover the original design factor.

Exact numerical checks

Intrări	Q	U	R−D	Q−1
R=235 MPa; D=120 MPa	47/24 = 1.95833333333	2400/47 = 51.0638297872%	115 MPa	23/24 = 0.958333333333
R=10 kN; D=4 kN	2.5	40%	6 kN	1.5

Why no universal recommended factor is shown

NIST’s structural-safety overview explains that allowable-stress design and probability-based limit-state design organize strength, loads and factors differently. The applicable factors reflect uncertainty and consequences through a specific code framework; an isolated generic range cannot replace that framework.

NASA-STD-5001B with Change 3 is an active, public example of a controlled factor standard. Its official scope is structural design and testing of spaceflight hardware, and its factors are minimum acceptable values within that scope unless justified by engineering risk assessment. Those values are not imported into this general worksheet.

OSHA 29 CFR 1926.1417 is a separate application example: crane equipment may not be operated above rated capacity and load weight must be established by recognized data or calculation. This does not create a universal material FoS for unrelated designs.

Source classification

Claim	Clasificare	Inspected source
Q=R/D and U=D/R	Dimensionless arithmetic identity; not a normative design rule	Direct dimensional analysis
Allowable-stress and load/resistance-factor design differ	Authoritative structural-safety overview	NIST SP 958, pp. 283–288 web edition
NASA factor values are application-specific	Active standard scope/status; no NASA values reused	NASA-STD-5001B with Change 3, active; revalidated 2022-10-24
Rated lifting capacity and load verification are application controls	Federal regulation example; not a general FoS formula	OSHA 29 CFR 1926.1417(o)

NASA-STD-5001 official status/scope page — active B with Change 3; public scope and review data.

NIST SP 958 structural-safety overview — allowable-stress and limit-state context.

OSHA 29 CFR 1926.1417 — rated-capacity and load-verification example.

Accessed: 15 July 2026. No closed-code factor, material property, allowable table or acceptance threshold was inferred.

Engineering review required. Before a safety or compliance decision, verify every applicable failure mode and serviceability limit, load combination, material specification, statistical basis, fabrication/inspection requirement, environment, duration/cycles, geometry, stress concentration, degradation mechanism and consequence of failure under the controlling code and jurisdiction.