1
Table 1-3
Factors Used to Determine a Safety Factor for Ductile Materials
Information
Quality of Information
Factor
F1
The actual material used was tested
1.3
Material-property data
Representative material test data are available
2
available from tests
Fairly representative material test data are available
3
Poorly representative material test data are available 5+
F2
Are identical to material test conditions
1.3
Environmental conditions
Essentially room-ambient environment
2
in which it will be used
Moderately challenging environment
3
Extremely challenging environment
5+
F3
Models have been tested against experiments
1.3
Analytical models for
Models accurately represent system
2
loading and stress
Models approximately represent system
3
Models are crude approximations
5+
ment of the quality of information used. The overall safety factor is then taken as the largest of the three factors chosen. Given the uncertainties involved, a safety factor typically should not be taken to more than 1 decimal place accuracy.
N
ductile MAX( F 1, F 2, F 3) (1.1 a)
The ductility or brittleness of the material is also a concern. Brittle materials are designed against the ultimate strength, so failure means fracture. Ductile materials under static loads are designed against the yield strength and are expected to give some visible warning of failure before fracture, unless cracks indicate the possibility of a fracture-mechanics failure (see Sections 5-3 and 6-5). For these reasons, the safety factor for brittle materials is often made twice that which would be used for a ductile material in the same situation:
N
brittle 2 * MAX( F 1, F 2, F 3) (1.1 b)
This method of determining a safety factor is only a guideline to obtain a starting point and is obviously subject to the judgment of the designer in selecting factors in each category. The designer has the ultimate responsibility to ensure that the design is safe. A larger safety factor than any shown in Table 1-3 may be appropriate in some circumstances.
Design and Safety Codes
Many engineering societies and government agencies have developed codes for specific areas of engineering design. Most are only recommendations, but some have the force of law. The ASME provides recommended guidelines for safety factors to be used in particular applications such as steam boilers and pressure vessels. Building codes are
20
MACHINE DESIGN -
An Integrated Approach
1
legislated in most U.S.A. states and cities and usually deal with publicly accessible structures or their components, such as elevators and escalators. Safety factors are sometimes specified in these codes and may be quite high. (The code for escalators in one state called for a factor of safety of 14.) Clearly, where human safety is involved, high values of N are justified. However, they come with a weight and cost penalty, as parts must often be made heavier to achieve large values of N. The design engineer must always be aware of these codes and standards and adhere to them where applicable.
The following is a partial list of engineering societies and governmental, industrial, and international organizations that publish standards and codes of potential interest to the mechanical engineer. Addresses and data on their publications can be obtained in any technical library or from the internet.
American Gear Manufacturers Association (AGMA) http://www.agma.org/
American Institute of Steel Construction (AISC) http://www.aisc.org/
American Iron and Steel Institute (AISI) http://www.steel.org/
American National Standards Institute (ANSI) http://www.ansi.org/
American Society for Metals (ASM International) http://www.asm-intl.org/
American Society of Mechanical Engineers (ASME) http://www.asme.org/
American Society of Testing and Materials (ASTM) http://www.astm.org/
American Welding Society (AWS) http://www.aws.org/
Anti-Friction Bearing Manufacturers Association (AFBMA)
International Standards Organization (ISO) http://www.iso.ch/iso/en
National Institute for Standards and Technology (NIST) * http://www.nist.gov/
Society of Automotive Engineers (SAE) http://www.sae.org/
Society of Plastics Engineers (SPE) http://www.4spe.org/
Underwriters Laboratories (UL) http://www.ul.com/
1.8
STATISTICAL CONSIDERATIONS
Nothing is absolute in engineering any more than in any other endeavor. The strengths of materials will vary from sample to sample. The actual size of different examples of the “same” part made in quantity will vary due to manufacturing tolerances. As a result, we should take the statistical distributions of these properties into account in our calculations. The published data on the strengths of materials may be stated either as minimum values or as average values of tests made on many specimens. If it is an average value, there is a 50% chance that a randomly chosen sample of that material will be weaker or stronger than the published average value. To guard against failure, we can reduce the material-strength value that we will use in our calculations to a level that will include a larger percentage of the population. To do this requires some understanding of statistical phenomena and their calculation. All engineers should have this un-
* Formerly the National Bureau
derstanding and should include a statistics course in their curriculum. We briefly discuss of Standards ( NBS).
some of the fundamental aspects of statistics in Chapter 2.
Chapter 1