TECHNICAL NOTES · STRUCTURES
Margin of safety, done right: a worked bracket check
Margin of safety is the number a stress report is judged on — and one of the easiest to get subtly wrong. Here is a complete check on one bracket, with every factor applied in the open, so each step can be audited.
The definition
Margin of safety compares what a part can carry with what it must carry, after every factor has been applied:
MS = allowable / (applied × FS × other factors) − 1
A margin of zero means the part just meets the requirement; positive means reserve; negative
means it cannot be signed off. Note the − 1: a ratio of 1.23 is a margin of +0.23,
and confusing the two is one of the most common reporting errors.
Limit, ultimate and the 1.5 factor
For transport aircraft, 14 CFR 25.301 defines limit loads as the maximum loads expected in service, and 25.303 applies a factor of safety of 1.5 to them, unless otherwise specified, to give ultimate loads. Two checks follow from 25.305: the structure must carry limit load without detrimental permanent deformation, and ultimate load without failure for at least three seconds. In stress terms that usually means yield at limit and ultimate strength at ultimate. Space programmes take their factors from their own standards, such as NASA-STD-5001 — the method is the same, the numbers are not.
The bracket
An aluminium-alloy fitting carries a limit load case whose analysis gives a peak applied stress of 260 MPa at the critical section. The design allowables are taken as Ftu = 480 MPa and Fty = 410 MPa. These are illustrative: real allowables come from MMPDS, or your programme's own data, for the actual alloy, temper, product form, thickness and grain direction, at the statistical basis your rules require.
| CHECK | CALCULATION | MARGIN |
|---|---|---|
| Yield at limit | 410 / (1.0 × 260) − 1 | +0.58 |
| Ultimate | 480 / (1.5 × 260) − 1 | +0.23 |
| Ultimate, with fitting factor | 480 / (1.5 × 1.15 × 260) − 1 | +0.07 |
The factor that changes the answer
This part is a fitting, and 14 CFR 25.625 requires a fitting factor of at least 1.15 unless the fitting's strength is proven by limit and ultimate load tests that simulate the actual stress conditions. Applied on top of the 1.5, it cuts the ultimate margin from +0.23 to +0.07 — the difference between a comfortable part and one with almost nothing left for a later load increase. Bearing factors, casting factors and any special factors in your certification basis work the same way. Each one belongs in the denominator, where a reviewer can see it.
Mistakes that hide a thin margin
- Reporting the ratio as the margin. 1.07 is not a margin of +1.07; it is +0.07.
- Applying the factor of safety twice — once in the loads and again in the stress check. State in every report whether the input loads are limit or ultimate.
- Typical instead of allowable properties. Handbook typical strengths sit well above design allowables, and using them inflates every margin.
- Rounding up. A margin of −0.004 is negative, not zero. Never round a margin in the favourable direction.
- Single-stress checks on combined loading. Tension with shear, or bending with axial load, needs an interaction check; checking each stress alone overstates the margin.
- Margins without a load case. A margin only means something alongside the load case, location and allowable that produced it.
Show the work
A margin a reviewer can trust carries its inputs with it: load case, section, applied stress, allowable and its source, every factor, and the arithmetic. ARITHMOS executes structural checks like this one as code and reports each factor in the open, so the +0.07 above traces straight back to the 1.15 that produced it.
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Published · 3 October 2026 · All technical notes