Safety factors are very common in engineering design to reduce the risk of product failure. However, there are a many different ways to apply them as well as to report them. In this blog, we’ll explore these and clear up, once and for all, the differences between ‘safety factor’, ‘factor of safety’, ‘margin of safety’ and ‘unity check’.

## Why Use Safety Factors At All?

Safety factor(s) can be considered somewhat of a catch-all term for the concepts that we’ll be looking at in this post. No matter how accurately we try to design or analyze engineering components, there is always a level of uncertainty involved. There could be variability in the material properties or the service loads. Or perhaps nonlinearities are not considered when building the FEM or hand calculation. Including a safety factor in the design is a way to reduce risk when designing engineering components, especially for critical structures where lives could be at stake.

Imagine designing a platform that can hold exactly the weight of one person, and one person only (1x factor on yield). There will be variability in where exactly on the platform that one person stands. How heavy are they? What if that person falls over, causing a dynamic load? Without any safety factor, there’s no margin for error in the design and could possibly lead to dangerous failures.

One thing to keep in mind is that different engineering industries and codes use different terminology to refer to, what is basically, the same thing. I’ve summarized this as best as I could based on my experience. At the end of the day, a safety factor is simply a ratio of actual vs allowable, no matter how it’s actually implemented/reported.

## Safety Factors For Designing

A safety factor used in design, or a design factor, is a predefined factor of a component’s yield or ultimate stress. As the name implies, this is typically used when designing as a not-to-exceed value. Usually, industries or design standards will set these. For example, in Aluminum Design Manual 2015, the design factor for tensile yield is 1.65 on building type structures. This can sometimes also be called a safety factor.

One way to apply a design factor is to apply it to the allowable strength of the material, kind of like a not-to-exceed value. This is the principle of allowable strength design (ASD). So, for example, if the yield of the material is 35 ksi, and there’s a 2x design factor, the allowable stress becomes 17.5 ksi. This is a more straightforward approach.

Alternatively, we can apply design factors to the loads. For example, hoist load factors are very common to account for lifting dynamics. Fitting factors can be used to address uncertainties of load paths through bolted joints. Applying design factors to the loads is the fundamental tenet of load and resistance factor design (LRFD).

For fully linear analyses, applying the design factor to the load or the allowable would result in the exact same answer.

## Safety Factors For Reporting

Safety factors can also be used in reporting results to show how a design compares to its allowable. It’s especially useful to include these in summary tables so anyone can see at a glance which components pass or fail, and which are the most critical.

### Factor Of Safety (FOS)

A factor of safety is the ratio of the allowable load to the maximum design load (or capacity/demand). A factor of safety above one means the component passes with the specified design factor.

As an example, let’s take a 304 stainless steel with a yield strength of 205 MPa and a design factor of 3. This makes the maximum allowable stress = 68.33 MPa. If the maximum design stress is 50 MPa, the factor of safety is 68.33/50, or 1.37 – the part is good to go since the FOS > 1.

### Margin Of Safety (MOS)

Margin of safety is the factor of safety minus one. A positive margin of safety means the component passes with the specified design factor. Effectively, the margin of safety is the percentage a component exceeds the design criteria. This measure is very commonly used in the US government and in the aerospace industry.

Using our same example, our margin of safety would be 68.33/50 – 1, or 0.37. Here, MOS > 0, so, again, we’re good to go.

### Unity Check (UC)

Unity check is the inverse of the factor of safety, which is the ratio of the maximum design load to the allowable load. Another term for this is utilization ratio. A unity check below one means the component passes with the specified design factor.

Using our same example, our unity check would be 50/68.33, or 0.73. In the report we would show UC < 1, OK.

One advantage of the unity check is that it can be used to combine different modes of failure. For example, in AISC 360-16, the unity checks for axial, flexural, torsional, and shear loading can be added together to check for combined loading as shown below:

## Final Thoughts

As shown here in this blog, there are many ways to apply a safety factor and to report a part’s strength compared to its intended load. Various industries and codes will have different conventions for applying these in design and reporting; however, the most important thing is to design parts with a safety factor to account for variabilities and assumptions made during the analysis.

If you are looking for any help with FEA or simulation in general, **reach out to us at any time**! We have experience working in all of the above conventions!