*This article talks explains the concept of safety factor and how it is calculated. It’s a fundamental notion that every mechanical engineer have to understand well.*

How do I know if the design of my part is «safe» enough?

That’s a difficult question that many designers asked themselves.

One of the potential answers involves the measure of the **safety factor**.

For certain people, this notion is still not well understood, so I decided to write about it!

**Important note**: This article talks mainly about “stress-based” safety factors, but you should know that there are different definitions of “safety factor” margins, which are not all necessarily related to the state of stress. Additionally, stress definitions can vary… there is Von Mises Stress, but also Tresca, etc…. (Thanks to **Boyd McKay** for his contribution in improving that article by mentioning those)

**Getting safe designs**

First of all, I think it is not too much to remind that one of the purpose of simulation is to get safe designs…

When a part fails, it involves of course a **risk for the life of people**, but also a **huge financial loss for the company** who created this part (just think about the explosive Samsung batteries and you will understand what I am talking about)

FEA simulation helps to understands **why a design fails**, **where it failed** and **how to improve it**.

That’s why FEA is so important for companies who design products.

To assess the safety of a design, designers need a simple factor which will help in understanding if a design is safe enough.

This factor is called the safety factor.

**How is the safety factor calculated**

The definition of the safety factor is simple. It is defined as the ratio between the strength of the material and the maximum stress in the part.

When the stress in a specific position becomes superior to the strength of the material, the safety factor ratio becomes inferior to 1, this when there is danger

What it tells us basically is that in a specific area of the model, the stress is higher than the strength the material can bear.

When the stress in the model remains much inferior to the strength of the material, the safety factor stays superior to 1 and the model is «safe».

Keep in mind that if the safety factor is way superior to 1 everywhere in your model, this is also indicating that your part may be over-engineered. In this case, this is not desirable either, because you are just wasting material resources and increasing the cost.

Now, let’s talk about the 2 important values that you need to calculate this safety factor: Stress and Strength

**What is stress ?**

If you still have some doubts about that, no shame, it’s not a concept easy to grasp for beginners, but it is an essential one.

In short, stress is a value that mesure the inner pressure inside a solid which is cause by an external loading. If stress is too high inside a part, the part may fail.

The notion of stress is not so different with what we experience everyday at work… When we receive a load of work, we become stressed. If we are too stressed, we may experience a nervous breakdown and many health problems.

If you want to understand more about stress and how stress is actually calculated, I wrote a full article about that few months ago.

**Read the article**:What is stress

**What is the strength of a material?**

Stress and Strength are different and that’s where many people don’t get it.

Stress in a body is always a function of the applied loading and cross-section, whereas strength is an inherent property of the body’s material/ manufacturing process.

Strength is obtained similarly to other material properties, by doing for example a standard tensile test which subjects a sample bar to uniaxial stress. Then we can draw the material stress-strain curve by extracting the deformation data and plotting it in function of the load data.

Note that if you need some high accuracy, the test should be performed under conditions similar to the operating conditions of the part or the system (Temperature, strain rate, material grain, flow direction,…)

There are several important points to understand on this curve:

- The point P is the proportional limit, it limits the portion of the curve which governed by Hooke’s law
- The point E is the elastic limit. The material will continue to behave elastically up to point E, but stress and strain won’t be proportional anymore.
- The point Y is the yield point which corresponds to the yield strength of the material
- The point U indicates the maximum stress that can be achieved by the material. It corresponds to its ultimate or tensile strength.
- The point F is the fracture point.

Note that the points E and Y may coincide for some types of materials such as ferrous materials.

The yield point is not necessarily very clear, and it is generally obtained by an offset method:

Y is considered to be the intersection of an offset line, parallel to the linear portion of the stress-strain curve typically at 0.002 axial strain, and the plastic portion of the curve.

As you read, there are several material strength values: the yield strength, the ultimate strength and the fracture strength.

The safety factor is calculated with the yield strength so this is the parameter you need to know in priority.

**Is this ratio a perfect indicator of a model safety?**

I’d like to say that nothing is really perfect… As engineers, we have to learn to live with errors ;-)

Errors are everywhere:

- In the testing process that will provide you with the stress-strain material curve and the yield strength used to calculate the safety factor
- In the FE model that you build, it is probable that the boundary conditions and/or the meshing will cause a certain amount of error
- In the FEA software itself and the algorithms it uses, error is included (and hopefully controlled)

That’s why it’s always better to consider a safety factor which is not exactly 1, but maybe a little higher (2-3) depending on the hypothesis you take.

**Additional note:**The safety factor only describe material failure. In some designs, it is sufficient, but if you are designing a slender element some form of stability failure (i.e. buckling) may occur. Such safety factor do not take that into account since buckling can happen when stress is much smaller than limit stress of the material.

## Comments worth mentionning from other FEA specialists

**David Backhouse** (Backhouse Technical Service LTD):

*There is no set ‘safety factor’ as such. That is too simple a concept as there are many modes of failure. There are instances, for example, where stresses above yield are acceptable. You should really refer to the appropriate design standard for the structure, its use, and the classification of the stresses.*

**Karl Van Aswegen** (Fluid Codes FZ LLE):

*Safety Factors are not necessarily max stress/yield. Many times the industry you work in will dictate how you calculate design safety factors. More often than not fatigue is your biggest problem not yield.*

**Eric Lee** (Austal):

*In my opinion, safety factors are really only important in certain cases. In the industries that I’ve worked in (shipbuilding/offshore) safety factors are hardly the criteria we work to. We do have our allowable stresses, but safety factors never govern because there are always stress concentrations that are allowed to be waived because of the geometry, mesh size/aspect ratio, loading conditions, etc.**The only real place where safety factors absolutely drive the design is in lifting applications where you need a SF of 3 to 5.That said, it’s always a good thing to check, especially if you’re doing approximate hand calculations.*

**Jeff Finlayson** (Boeing):

*It is best to understand what a safety factor really is and understand what the requirements actually state.**In general, the ultimate safety factor is Ultimate load/applied load, and for yield SF is Yield load/applied load. Stresses may not be linearly related to the load due to local plasticity effects. Static preloads may receive no safety or a small one depending on requirements for uncertainties.*

**Vlad Kerchman**(Independent Consultant):

*In evaluating the possible ultimate *loads/stresses* people frequently look for quasi-static or steady-state conditions with extreme overload or bias. In real service/ life it typically happens under drastic change of loading – in *dynamics, say,* vehicle impacting a road obstacle or *bump,* or seismic loading on a structure, explosion, etc.. That’s where FEA can really help to replace difficult and expensive testing.*

**Neil Grant** (Allen-Vanguard):

*I think safety factor needs to be expressed with respect to something. For a one time use, it can be with respect to ultimate strength. Similarly, for many cycles, it can be expressed with respect to the fatigue limit strength.*

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## FAQs

### How do you calculate factor of safety in FEA? ›

The Factor of Safety of the structure is defined as **F = C/D** and failure is assumed to occur when F is less than unity.

**What does safety factor mean in FEA? ›**

The definition of the safety factor is simple. It is defined as **the ratio between the strength of the material and the maximum stress in the part**. When the stress in a specific position becomes superior to the strength of the material, the safety factor ratio becomes inferior to 1, this when there is danger.

**How do you calculate safety factor percentage? ›**

As an example, if we have a system that requires 80 psi and the available city pressure of 88 psi, a 10% safety factor on the required pressure would be **80 psi x 10% = 8 psi safety required**. In this case the minimum is met.

**What should my factor of safety be? ›**

A usually applied Safety Factor is **1.5**, but for pressurized fuselage it is 2.0, and for main landing gear structures it is often 1.25. In some cases it is impractical or impossible for a part to meet the "standard" design factor.

**What does a 2 to 1 safety factor mean? ›**

When considering safety factors, **if a rescuer can only hold 30 pounds of force and the force exiting a belay device has 15 pounds of force, the system safety factor is only 2:1 regardless of the strength of the equipment**.

**What is a 4 to 1 safety factor? ›**

In the section covering leaf chain, the Machinery Directive states that the minimum safety factor when lifting a weight should be 4:1. In other words, **the leaf chain should be able to lift four times the maximum weight it will be lifting in its working life**.

**What does a safety factor of 1.5 mean? ›**

1.3 – 1.5. **For use with reliable materials where loading and environmental conditions are not severe**. 1.5 – 2. For use with ordinary materials where loading and environmental conditions are not severe. 2 – 2.5.

**What is a safety factor of 4? ›**

2.5 - 3 | For less tried materials or for brittle materials under average conditions of environment, load and stress. |

3 - 4 | For untried materials used under average conditions of environment, load and stress. |

**What is factor of safety with example? ›**

In mechanical engineering, mathematically Factor of safety is **the ratio of material strength and allowable stress**. For example, if the required specification of a shaft is to withstand a 100 kg load. But if our shaft design is for a 200 kg load. The Shaft safety factor value is “two”.

**How do you calculate FoS? ›**

A very basic equation to calculate FoS is to **divide the ultimate (or maximum) stress by the typical (or working) stress**. A FoS of 1 means that a structure or component will fail exactly when it reaches the design load, and cannot support any additional load.

### Can factor of safety be less than 1? ›

The factor of safety is the ratio of the allowable stress to the actual stress: A factor of safety of 1 represents that the stress is at the allowable limit. **A factor of safety of less than 1 represents likely failure**. A factor of safety of greater than 1 represents how much the stress is within the allowable limit.

**What is safety factor in Ansys? ›**

In Ansys, the safety factor is always shown **between 15 and -15**. My design shows both maximum and minimum value as 15 with overall red coloured model. Certain literature says that ansys is not capable of producing result if the safety factor is more than 15 and thus it shows like that.

**Why do we need factor of safety? ›**

A factor of safety **increases the safety of people and reduces the risk of failure of a product**. When it comes to safety equipment and fall protection, the factor of safety is extremely important. If a structure fails there is a risk of injury and death as well as a company's financial loss.

**Why factor of safety is used in design? ›**

The Factor of Safety is essentially used **to assure the structural designing does not occur any unexpected failure or presence of deformation or defect**. The smaller the Factor of Safety, the higher chances was there for the design to be a failure. Resulting in an uneconomical and nonfunctional design.

**What is factor of safety on what basis is its value selected? ›**

Factor of safety: It is defined as **the ratio of the maximum stress to the working stress**. Factors to be considered while selecting the factor of safety: The properties of the material and the possible change of these properties during operation. Type of applied load, whether it is Gradual or Impact.

**What is the safety factor of steel? ›**

The current safety factor for steel is **γM = 1**.

**What does a high factor of safety mean? ›**

In general, a high factor of safety means **a heavier component, more upscale material and an improved design**. A factor of one means that the stress is at the allowable limit. Less than one means likely failure.

**How do you calculate static safety factor? ›**

Static safety factor the static equivalent radial load (P 0 ) is obtained as follows. **P0 = X0 • Fr + + Y0 • Fa = 1 • 4442.1 + + 0.44 • 0 = 10866 N 2M dp 2 ×891315 277.5** Using the value of P 0 above, the static safety factor (f s ) is calculated to be 13.8.

**What is factor of safety in engineering? ›**

Factor of safety (FoS) is **ability of a system's structural capacity to be viable beyond its expected or actual loads**.

**How does solidworks calculate factor of safety? ›**

To access the Factor of Safety Wizard: After you run a static study, **right-click Results and click Define Factor of Safety Plot, or**. **Click the down arrow on Results Advisor (Simulation CommandManager) and click New Plot > Factor of Safety**.

### How do you calculate safe working load? ›

Once you know the diameter of the rope, you can apply it to the formula, which is **SWL = D ^{2} x 8**. D represents the diameter of the rope in inches. If you're working with a 1.5-inch diameter cable, for example, then the formula would be SWL = 1.5

^{2}x 8 or SWL = 2.25 x 8.

**Where does safety factor of 1.5 come from? ›**

The 1.5 Ultimate Factor of Safety covers: **Inadvertent In-Service Loads greater than the design limit**. Structural deflections above limit load that could compromise vehicle structural integrity. As-built part thickness within tolerance but less than that assumed in the stress analysis.

**What does FoS mean in engineering? ›**

**Factor of Safety** (FoS) is a measure used in engineering design to represent how much greater the resisting capacity of a structure or component is relative to an assumed load.

**What is the factor of safety of mild steel? ›**

Partial safety factor for steel and concrete should be considered as **1.15** and 1.5 respectively.

**What is margin of safety? ›**

Margin of safety is **a principle of investing in which an investor only purchases securities when their market price is significantly below their intrinsic value**. In other words, when the market price of a security is significantly below your estimation of its intrinsic value, the difference is the margin of safety.

**How is margin of safety calculated in engineering? ›**

The margin of safety is defined as the factor of safety minus one; that is **margin of safety = FS-1.0**. The margin of safety allows extra load range in the event the material is weaker than expected or an allowable load that may be higher than anticipated.

**What is the difference between design factor and factor of safety? ›**

The design factor is defined for an application (generally provided in advance and often set by regulatory code or policy) and is not an actual calculation, the safety factor is a ratio of maximum strength to intended load for the actual item that was designed.

**What is the factor of 50? ›**

The factors of 50 are the natural numbers that divide the original number, evenly. They are **1,2,5,10,25 and 50**.

**How do you calculate the factor of safety against sliding? ›**

The factor of safety against sliding is defined as **the resisting forces (friction + passive) divided by the driving lateral force**, and the minimum value should be 1.50. Where seismic loads are included, the minimum safety factor should be 1.10.

**What is safety factor in Ansys? ›**

In Ansys, the safety factor is always shown **between 15 and -15**. My design shows both maximum and minimum value as 15 with overall red coloured model. Certain literature says that ansys is not capable of producing result if the safety factor is more than 15 and thus it shows like that.

### What is factor of safety with example? ›

In mechanical engineering, mathematically Factor of safety is **the ratio of material strength and allowable stress**. For example, if the required specification of a shaft is to withstand a 100 kg load. But if our shaft design is for a 200 kg load. The Shaft safety factor value is “two”.

**What does a safety factor of 1.5 mean? ›**

1.3 – 1.5. **For use with reliable materials where loading and environmental conditions are not severe**. 1.5 – 2. For use with ordinary materials where loading and environmental conditions are not severe. 2 – 2.5.

**What is a safety factor of 4? ›**

2.5 - 3 | For less tried materials or for brittle materials under average conditions of environment, load and stress. |

3 - 4 | For untried materials used under average conditions of environment, load and stress. |

**What is the maximum safety factor? ›**

Factor of Safety Equation

For a structure to be considered safe, its factor of safety must be **greater than 1**. A factor of safety that is equal to 1 means that the structure's maximum strength or capacity is equal to its determined design load. This means that the structure would fail if any additional load was applied.

**What does a factor of safety of 1 mean? ›**

A FoS of 1 means that **a structure or component will fail exactly when it reaches the design load, and cannot support any additional load**. Structures or components with FoS < 1 are not viable; basically, 1 is the minimum.

**What is a safety factor in engineering? ›**

Factor of safety (FoS) is ability of a system's structural capacity to be viable beyond its expected or actual loads.

**Why do we consider factor of safety? ›**

A factor of safety **increases the safety of people and reduces the risk of failure of a product**. When it comes to safety equipment and fall protection, the factor of safety is extremely important. If a structure fails there is a risk of injury and death as well as a company's financial loss.

**Why factor of safety is used in design? ›**

The Factor of Safety is essentially used **to assure the structural designing does not occur any unexpected failure or presence of deformation or defect**. The smaller the Factor of Safety, the higher chances was there for the design to be a failure. Resulting in an uneconomical and nonfunctional design.

**What is factor of safety on what basis is its value selected? ›**

Factor of safety: It is defined as **the ratio of the maximum stress to the working stress**. Factors to be considered while selecting the factor of safety: The properties of the material and the possible change of these properties during operation. Type of applied load, whether it is Gradual or Impact.

**What does a factor of safety less than 1 mean? ›**

The factor of safety is the ratio of the allowable stress to the actual stress: A factor of safety of 1 represents that the stress is at the allowable limit. A factor of safety of less than 1 represents **likely failure**. A factor of safety of greater than 1 represents how much the stress is within the allowable limit.

### Where does safety factor of 1.5 come from? ›

The 1.5 Ultimate Factor of Safety covers: **Inadvertent In-Service Loads greater than the design limit**. Structural deflections above limit load that could compromise vehicle structural integrity. As-built part thickness within tolerance but less than that assumed in the stress analysis.

**Is higher factor of safety good? ›**

In general, a high factor of safety means a heavier component, more upscale material and an improved design. A factor of one means that the stress is at the allowable limit. Less than one means likely failure.

**What is the safety factor of steel? ›**

The current safety factor for steel is **γM = 1**.

**How does solidworks calculate factor of safety? ›**

To access the Factor of Safety Wizard: After you run a static study, **right-click Results and click Define Factor of Safety Plot, or**. **Click the down arrow on Results Advisor (Simulation CommandManager) and click New Plot > Factor of Safety**.

**What is margin of safety? ›**

Margin of safety is **a principle of investing in which an investor only purchases securities when their market price is significantly below their intrinsic value**. In other words, when the market price of a security is significantly below your estimation of its intrinsic value, the difference is the margin of safety.