# Factor of Safety - Definition, Formula, Importance [Gate Notes]

By Aina Parasher|Updated : August 23rd, 2022

The factor of safety increases safety and reduces the risk of failure of a structure. The safety factor is most important regarding safety equipment and fall protection. If a structure fails, there is a risk of injury and death and a company's financial loss.

The factor of safety is used by engineers while designing a structure. Practically there is some uncertainty in applied forces, material properties, and model assumptions. It is provided a design margin over a theoretical design capacity to overcome uncertainty parameters (like a manufacturing process and material strength). Let us discuss in detail factor of safety.

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## What is a Factor of Safety?

The factor of safety definition is considered by the following parameters:

• The factor of safety is a structure's absolute strength (structural capability) ratio to the actual applied load. FoS measures the reliability of a particular design.
• A constant required value is imposed by standard specification to which a structure must exceed. This can be referred to as a design factor, design factor of safety, or required factor of safety.
• When the factor of safety is equal to one, it means that the ultimate stress is equal to the working stress; therefore, the body can only support load up to the actual load and no more before failing.

### Importance of Factor of Safety

Importance of Factor of Safety 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 there were for the design to be a failure. Resulting in an uneconomical and nonfunctional design.

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## Formula For Factor of Safety

The factor of safety is defined as the ratio of ultimate stress of the component material to the working stress. Mathematically, the Factor of safety is the ratio of material strength to allowable stress. The factor of the safety equation depends on the type of material:

Factor of safety = Ultimate strength/Working stress -for brittle material (concrete)

Factor of safety = Yield strength/Working stress -for ductile material (steel)

Example:

FoS for steel = Yield strength (fy)/Working stress (0.87 fy)= 1.15 (approximately)

FoS for concrete = Yield strength (fck)/Working stress (0.67 fck / 1.5)= 3 (approximately)

(∵ 2 times factor of safety is taken for concrete as it has least quality control while preparing the concrete)

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## Factors Affecting Factor of Safety (FoS)

The structure's safety depends on two principal design factors, load and material strength, which are not a function of each other. Hence, two different factors, one for load and the other for material strength, are used. Each of the two safety factors contributes partially to safety; they are termed a partial safety factor.

As per Clause 36.4. 2 of IS 456, when assessing the strength and serviceability criteria of the structures or structural members employed in a limit state.

 Material Limit state method Collapse Deflection Cracking Steel 1.15 1.0 1.0 Concrete 1.5 1.0 1.3

∴ The factor of safety for steel is lower as compared to concrete. Because concrete is a brittle material and relatively less reliable than steel and steel is manufactured in industry. So, In steel, the quality control is better than in concrete (as it is prepared at the site with different atmospheric conditions).

## Examples of Factor of Safety

Here are a few examples of factor of safety of a few elements which can be used while design consideration:

 Elements Factor of Safety Bolts 8.5 Structural Members in building services 2 Automobiles 3 Structural steel work in buildings 4.0 to 6.0 Engine components 6.0 to 8.0 Spring, large heavy-duty 4.5 Pressure vessels 3.5 – 6 Aircraft components 1.5 to 2.5 Turbine components – rotating 2.0 to 3.0 Pressure Vessel 3.5 to 4 Brittle Material 1.0 to 6.0 Boilers 3.5 to 6 Cast-iron wheels 20 Turbine components static 6.0 to 8.0 Impact Forces 3.0 to 6.0 Heavy duty shafting 10.0 to 12.0 Lifting equipment – hooks .. 8.0 to 9.0 Structural steel work in bridges 5.0 to 7.0 Aircraft and Spacecraft 1.2 to 3.0 Wire ropes 8.0 to 9.0
 Important Topics for Gate Exam Composite Beams Compression Members Concurrent Force System Conditions for Deadlock in Operating System Conduction Heat Transfer Consensus Theorem Constants in C Convection Heat Transfer Coplanar Force System Cut Set Matrix

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## FAQs on Factor of Safety

• The factor of safety is defined as the ratio of ultimate stress to the working stress. It denotes the additional strength of the component than the required strength to carry that load.

• Ductile materials have a homogenous structure, and residual stresses are relieved with heat treatment in the component. To account for this, a small factor of safety is used.

Hence, The factor of safety for steel is 1.15.

• Concrete is heterogeneous in nature, and if there is a slight variation in mix design, it will affect concrete strength greatly, whereas steel is very stiff and possesses a high strength-to-weight ratio. It is easy to fabricate a steel structure, so it is generally used for mass construction.

∴ The factor of safety for concrete is higher than steel as concrete is a brittle material and relatively less reliable than steel.

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

• Factor of safety = Ultimate Load (Strength)/Allowable Load (Stress)

∴  FOS is a dimensionless quantity.

### ESE & GATE CE

Civil Engg.GATEGATE CEESE CEESEBARC CEAFCAT CE