# Coefficient of safety

Determination of the corresponding coefficient of safety is a complicated and responsible task. A high coefficient of safety usually results in a safer design, however with a higher weight and thus a higher price and vice versa. It is the basic engineering compromise of "price vs.safety". Profession organizations often specify minimum coefficients of safety for various systems; however, it is the responsibility of the designer to determine such coefficient of safety that ensures corresponding safety at an acceptable price. At the same time, the coefficient of safety can vary within a wide range. A coefficient close to 1.0 (one-off use, short service life) may be sufficient for a military missile; a coefficient at 1.2 for military aircraft (it is equipped with a parachute, it passes through an inspection process); in civil aviation it is about 1.5 (inspection process, regular maintenance). A dam with a coefficient of safety higher than 20 can be found at the other end of the range (service life of many decades, faults have catastrophic consequences).

For a simple orientation we give here some models for determining the corresponding coefficient of safety, which are published in specialized literature. . For thorough understanding of problems of safety and reliability we recommend you study specialized literature.

### Joseph P. Visodic.

In 1948 he published his recommendations for determining the minimum coefficient of safety, which are mentioned in the table below. The coefficient of safety for tensile materials is based on the yield strength. For fragile materials it is based on the ultimate strength and is double those values given for tensile materials. The coefficient of safety for cyclical loading is based on the fatigue limit. Shock loading requires min. coefficient of safety 2, multiplied by the coefficient of shock - usually in the range from 1.1 to 2.0.

Recommended coefficient of safety for tensile materials based on the yield strength.

 Coefficient of safety Knowledge of loading Knowledge of permitted stress Knowledge of properties of material Knowledge of environment 1.2-1.5 exact exact very good fully under control 1.5-2.0 good good very good invariable 2.0-2.5 good good average common 2.5-3.0 average average randomly tested common 3.0-4.0 average average not tested common 3.0-4.0 indefinite indefinite indefinite

### Robert L. Norton.

The total value of the coefficient of safety is a combination of coefficients of safety based on material properties, accuracy of the calculation model and knowledge of working environment.

Coefficient of safety SF

• SF (tensile materials) = max (SF1, SF2, SF3) ; based on the yield strength
• SF (fragile materials) = 2*[max (SF1, SF2, SF3)] ; based on yield point

where SF1, SF2, SF3 are selections from the following table.

 Coefficient of safety SF1 - Material properties (from tests) SF2 - Loading conditions (knowledge) SF3 - Working environment 1.3 Well known / characteristic Verified by testing Same as material testing conditions 2 Well approximated Well approximated Checked, room temperature 3 Fairly approximated Fairly approximated Slightly demanding 5+ Roughly approximated Roughly approximated Extremely demanding

### Pugsley, A.G.

He recommends determining the coefficient of safety as a product of two coefficients.

SF = SF1 * SF2

where:

• SF1 is a function of parameters A, B, C from the first table
• SF2 is a function of parameters D, E from the second table

Meaning of parameters:

1. Quality of material, level of processing, maintenance, service inspections
2. Control over possible overloading
3. Accuracy of analysis, knowledge of experimental data of experience with similar parts
4. Threat to people when a failure of the part occurs
5. Financial impact when a failure of the part occurs
 Parameter A Parameter C Parameter B B=1 B=2 B=3 B=4 A=1 C=1   C=2 C=3 C=4 1.10   1.20 1.30 1.40 1.30   1.45 1.60 1.75 1.50   1.70 1.90 2.10 1.70   1.95 2.20 2.45 A=2 C=1   C=2 C=3 C=4 1.30   1.45 1.60 1.75 1.55   1.75 1.95 2.15 1.80   2.05 2.30 2.55 2.05   2.35 2.65 2.95 A=3 C=1   C=2 C=3 C=4 1.50   1.70 1.90 2.10 1.80   2.05 2.30 2.55 2.10   2.40 2.70 3.00 2.40   2.75 3.10 3.45 A=4 C=1   C=2 C=3 C=4 1.70   1.95 2.20 2.45 2.15   2.35 2.65 2.95 2.40   2.75 3.10 3.45 2.75   3.15 3.55 3.95

Where the evaluation means: 1=Very good; 2=Good; 3=Sufficient; 4=Bad

 Parameter D Parameter E E=1 E=2 E=3 D=1   D=2 D=3 1.0   1.2 1.4 1.0   1.3 1.5 1.2   1.4 1.6

Where the evaluation means: 1=Minimum; 2=Mean; 3=Very serious

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