INTRODUCTION TO DESIGN

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Factor of Safety*

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A factor of safety or safety factor can be expressed in many ways. It is typically a ratio of two quantities that have the same units, such as strength/stress, critical load/applied load, load to fail part/expected service overload, maximum cycles/applied cycles, or maximum safe speed/operating speed. A safety factor is always unitless.

 

The form of expression for a safety factor can usually be chosen based on the character of loading on the part. For example, consider the loading on the side wall of a cylindrical water tower that can never be “more than full” of a liquid of known density within a known temperature range. Since this loading is highly predictable over time, a comparison of the strength of the material to the stress in the wall of a full tank might be appropriate as a safety factor. Note in this example that the possibility of rust reducing the thickness of the wall over time must be considered. (See Section 4.17 for a discussion of stresses in cylinder walls and Section 7.6 for a discussion of corrosion.) If this cylindrical water tower is standing on legs loaded as columns, then a safety factor for the legs based on a ratio of the column’s critical buckling load over the applied load from a full water tower would be appropriate. (See Section 4.16 for a discussion of column buckling.)

 

 

If a part is subjected to loading that varies cyclically with time, it may experience fatigue failure. The resistance of a material to some types of fatigue loading can be expressed as a maximum number of cycles of stress reversal at a given stress level. In such cases, it may be appropriate to express the safety factor as a ratio of the maximum number of cycles to expected material failure over the number of cycles applied to the part in service for its desired life. (See Chapter 6 for a discussion of fatigue-failure phenomena and several approaches to the calculation of safety factors in such situations.) The safety factor of a part such as a rotating sheave (pulley) or flywheel is often expressed as a ratio of its maximum safe speed over the highest expected speed in service. In general, if the stresses in the parts are a linear function of the applied service loads and those loads are predictable, then a safety factor expressed as strength/stress or failure load/applied load will give the same result. Not all situations fit these criteria. Some require a nonlinear ratio. A column is one example, because its stresses are a nonlinear function of the loading (see Section 4.16). Thus a critical (failure) load for the particular column must be calculated for comparison to the applied load.

 

 

Another complicating factor is introduced when the magnitudes of the expected applied loads are not accurately predictable. This can be true in virtually any application in which the use (and thus the loading) of the part or device is controlled by humans. For example, there is really no way to prevent someone from attempting to lift a 10-ton truck with a jack designed to lift a 2-ton automobile. When the jack fails, the manufacturer (and designer) may be blamed even though the failure was probably due more to the “nut behind the jack handle.” In situations where the user may subject the device to overloading conditions, an assumed overload may have to be used to calculate a safety factor based on a ratio of the load that causes failure over the assumed service overload. Labels warning against inappropriate use may be needed in these situations as well.

 

Since there may be more than one potential mode of failure for any machine ele-

* Also called safety factor. We

will use both terms interchange-

ment, it can have more than one value of safety factor N. The smallest value of N for ably in this text.

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MACHINE DESIGN -

An Integrated Approach

 

 

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any part is of greatest concern, since it predicts the most likely mode of failure. When N becomes reduced to 1, the stress in the part is equal to the strength of the material (or the applied load is equal to the load that fails it, etc.) and failure occurs. Therefore, we desire N to be always greater than 1.

 

Choosing a Safety Factor

Choosing a safety factor is often a confusing proposition for the beginning designer. The safety factor can be thought of as a measure of the designer’s uncertainty in the analytical models, failure theories, and material-property data used, and should be chosen accordingly. How much greater than one N must be depends on many factors, including our level of confidence in the model on which the calculations are based, our knowledge of the range of possible in-service loading conditions, and our confidence in the available material-strength information. If we have done extensive testing on physical prototypes of our design to prove the validity of our engineering model and of the design, and have generated test data on the particular material’s strengths, then we can afford to use a smaller safety factor. If our model is less well proven or the material-property information is less reliable, a larger N is in order. In the absence of any design codes that may specify N for particular cases, the choice of factor of safety involves engineering judgment. A reasonable approach is to determine the largest loads expected in service (including possible overloads) and the minimum expected material strengths and base the safety factors on these data. The safety factor then becomes a reasonable measure of uncertainty.

If you fly, it may not give you great comfort to know that safety factors for commercial aircraft are in the range of 1.2 to 1.5. Military aircraft can have N < 1.1, but their crews wear parachutes. (Test pilots deserve their high salaries.) Missiles have N = 1 but have no crew and aren’t expected to return anyway. These small factors of safety in aircraft are necessary to keep weight low and are justified by sophisticated analytical modeling (usually involving FEA), testing of the actual materials used, extensive testing of prototype designs, and rigorous in-service inspections for incipient failures of the equipment. The opening photograph of this chapter shows an elaborate test rig used by the Boeing Aircraft Co. to mechanically test the airframe of full-scale prototype or production aircraft by applying dynamic forces and measuring their effects.

It can be difficult to predict the kinds of loads that an assembly will experience in service, especially if those loads are under the control of the end-user, or Mother Nature. For example, what loads will the wheel and frame of a bicycle experience? It depends greatly on the age, weight, and recklessness of the rider, whether used on- or off-road, etc. The same problem of load uncertainty exists with all transportation equipment, ships, aircraft, automobiles, etc. Manufacturers of these devices engage in extensive test programs to measure typical service loads. See Figures 3-16 (p. 106) and 6-7 (p. 315) for examples of such service-load data.

Some guidelines for the choice of a safety factor in machine design can be defined based on the quality and appropriateness of the material-property data available, the expected environmental conditions compared to those under which the material test data were obtained, and the accuracy of the loading- and stress-analysis models developed for the analyses. Table 1-3 shows a set of factors for ductile materials which can be chosen in each of the three categories listed based on the designer’s knowledge or judg-

 

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Chapter 1