Factors of Safety
Dateline: 12/29/97I had planned to present a software review this week, but a ski accident last week has left my leg in a brace and I can't sit at my computer desk for more than a few minutes at a time. Instead, I'll give a brief overview of safety factors and some special considerations for applying them to composites.
Uncertainties
Any engineer designing a new structure faces several uncertainties:
- Loads are not known to an exact value.
- Material properties have some variation.
- Analytical models are usually a rough approximation of the structure.
- Numerical models, though a better geometric representation of the structure, are still mathematical abstractions of the real world.
- The model may not be a good representation of the structure.
- The designer or analyst may have missed a load case.
- Defects may be introduced in the manufacturing process.
- Unknowns: Some physical events will have an effect on the structure, but the magnitude of that effect is unkown.
- Unknown unknowns: There will always be something you didn't think of.
To help account for these uncertainties, engineers apply a factor of safety, or FS, to the design. Most often, the FS appears as a number by which all loads are multiplied. For example, if a bridge is required to carry a 10 ton truck, it may be designed to carry a 50 ton truck, providing a safety factor of 5.
Typical Values
Actual safety factors used depend on the industry and the amount of risk which can be tolerated. Civil engineering structures support people and weight is not very critical, so safety factors may be in the range of 5 to 10.
I primarily work with unmanned aerospace structures--launch vehicles and satellites. Physical safety is not much of an issue, but structural weight is very expensive. Typical safety factors are 1.10 for yield and 1.25 for ultimate failure. (For manned systems, these numbers might be 1.25 and 1.40, or 1.40 and 2.00--still fairly risky.)
In fact, for most aerospace programs, military standards (MIL-SPECS) specify the safety factors. Limit loads are defined as the expected flight loads. Safety factors are applied to the limit loads. At yield, the structure is allowed to permanently deform, but must not lose any load-carrying capability. The structure is never expected to reach ultimate loads, but should be capable of surviving if it does (though it probably can't be flown again without some repair work).
Margins
Most designs can actually support loads somewhat above the ultimate loads. The extra load-carrying capability is called the margin of safety, or simply the margin. Margins are reported in different ways.
Civil engineers typically report the actual safety factor. If the bridge above could actually carry a 65 ton truck, the factor of safety is reported as 6.5.
Aerospace engineers, on the other hand, report an actual margin of safety, or MS. The MS is defined as the percentage of load above the ultimate which can be carried:
MS = Load Capability / Ultimate Load - 1A margin of 0 means the structure is predicted to fail at the ultimate loads; a margin of 0.10 means the structure is predicted to fail at 10% over the ultimate loads.
When weight is very critical, a zero margin is desired. In practice, margins will be positive for a number of reasons:
- Materials or stock profiles may only be available in finite sizes.
- Multiple failure modes cannot be optimized simultaneously. A zero margin for bending stresses may give a positive margin for buckling.
- Some failure modes require positive margins because of greater uncertainty.
- Management may decide they are uncomfortable with the initial level of risk.
Two common cases where positive margins are required are buckling and fastened joints. Buckling models are notoriously inaccurate, and it is common to see a minimum required margin of 0.15 (or loads must be multiplied by an additional factor of 1.15 for buckling calculations). For fastened joints with large numbers of fasteners, it is unrealistic to expect all fasteners to carry the load. This is primarily because the holes are a bit oversized. The additional margin required, also usually 0.15, is called a fitting factor.
Test Loads
Aerospace structures will be tested to some level at or above limit loads. A dedicated test structure is called a qualification unit and is usually tested to ultimate loads.
Flight units are sometimes tested to limit loads (this is called an acceptance test), but these tests are often skipped for metallic structures. Because of the greater uncertainties in composite manufacturing processes, composite flight structures are almost always acceptance tested, and the levels are often bumped up to 1.10 times limit loads.
If a program can't afford a dedicated qual unit, the flight unit will be tested to protoflight levels, or 1.10 times limit loads. This is true for both metallic and composite structures. Furthermore, without a qualification test, the flight structures must always be tested to protoflight levels.
Composites
Composites require some special considerations when defining safety factors. The case of flight structure testing has already been described above.
The most obvious difference, though, is in the definition of yield loads. Composites, being brittle materials, do not yield. This is one of the few situations where analysis of composite structures is simpler than analysis of metallic structures. Because composites do not yield, it is not necessary to design for both a yeild and an ultimate safety factor.
Some people consider the first ply failure point to be similar to yield in metals. However, it is not common practice to design to both a first ply failure and a last ply failure load. In fact, some programs define ultimate failure as the onset of first ply failure.
Another case that requires special treatment is buckling of composite shells. For launch structures, the standard model is defined in NASA SP-8007. This document describes analytical models for calculating buckling loads of composite cylindrical and conical shells.
The NASA models contain empirical knockdown factors to account for observed variations in real structures. These knockdown factors range from about 0.8 to about 0.5. Add to that a safety factor of 1.25 and a minimum margin requirement of 0.15, and the allowable buckling load may be much less than one-half the "predicted" load.
At some point, one must begin to question the utility of a model that can't claim to be accurate within even 50%. The NASA document actually states that the knockdown factors are preliminary and deserve further investigation. Although this document was written in the mid-1960s, I have yet to find any additional research on these empirical factors.
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