96787207-Anderson.pdf

Safety Factor  The  The concept of sa safety factor has substantial ial his histtory behind ind it. it. In ancien ient Rom Rome, the design igner of a bridg idge was required required to stand under that bridge bridge after completion completion whil while chariots chariots drove over the top. This his method of acceptance testing put the bridge bridge designer’s r’ s lif li fe at risk risk as well as the lives of those who used the bridge bridge. The idea was obviousl obviously y to induce induce the bridge bridge designer to design and build a safe bridge bridge. Safe Safe designs were then copied copied.  The  The desire ire for for sa safe structures and machine ines is the same today as it was ancien iently. ly. Mod Modern engine ineering ing is based on predicting cting the performa rformance of structures and machines before before they are actually buil built. This his requires quires an assessment of how how well well the system performance performance can be predicted predicted for for the intended intended material terials, s, expected use, foreseeable ble abuse, the expected service rvi ce environme nvironment, and the expected lif li fe of the system. The transition transiti on from from engineering ring model to reality is is usually ally fa facil cilitate tated d by includi including ng a factor actor of safety ety in i n the design to accommodate uncertainty rtainty in in material rial properti properties es and the design process, process, the conseque consequences of fail f ailure, ure, risk ri sk to people, people, and degree of  characterizati cterization on of and control over over the service service environm environment. The safety factor for for structural systems, proposed rd Philon of Byzantium (3  century BC) [Shigley & Mischke, 2001], is defined as follows… N=

 capacity  strength load

=

stress

>1

(1) (1)

Notice otice that safety factor factor is is a sim simple ple ratio tio that is inten intended to be greater than one. That is, cap capacity acity must be greater than load and strength must be greater than stress. stress. A large safety factor factor usually means a safer design, however, more material rial is is used in the design with a corres corresponding ponding increase in cost and weight. weight. Therein lies li es one of the fundamental tal trade-off e-offs in in enginee engineering ring design – cost vs. safety. ety. Reducing cost is al always ways a busines business im imperative, whil while the publ public dem demands increased safety. ety. Prof Profes essional organiz organiza ations tions frequently specif cify minim minimum safety fact factors ors for for various various systems. I t is is incum incumbent on the design sign engine ngineer to choose an adequate safety factor factor to safeguard publi public safety at an affordable affordable cost. Aerospace systems require minima nimal weight weight structures, thus demanding low low safety factors. factors. Aerospace systems also undergo extensiv extensive e physical hysical tes testing ting of materials, terials, components, and structures to vali validate the design before producti production, which which is is a very costly costly and tim time consuming process. A military tary missil missile, for for example ple, may have have a safety factor of 1 because cause it is is inte intended for use only only once and has a relatively relatively short li life. A fighter aircraft aircraft may have a safety factor factor as low low as 1.2, but the air crews crews have ejection ection seats and parachutes and the airfram rframe undergoes regular inspection ction and maintenance. A commercial ercial aircr aircraft aft may have a safety factor factor as low low as 1.5, but it it also is is inspected and maintained ntained regularl regularly. y. On the other end of the the spectrum, a concrete concrete dam may have a safety factor factor as high high as 20 because the expected life is several decade decades and it is i s abrittl brittle e structure for for which which fail failure ure would be catastrophic. tastrophic.  The  The loa load bearing ing capacity ity or or st strength of a material ial is determine ined by ph physica ical te testing ing. The The properties ies of a specif cific material terial are random variables variables that are assumed to fol folllow a normal distri distributi bution on with with a mean value value and a standard deviation. viation. A material varies in composi compositi tion on from from factory actory to fa f actory and from batch atch to batch in production, with with a corresponding variation variation in in properties rties. Materi teria al properties rties also vary accordi according ng to the the processing rocessing appli applie ed to the material rial to shape and strengthen it as desired. sired. In some materials, rials, properti properties es may vary signi signifficantly over over time. Corrosi orrosive ve service rvi ce environme nvironments may attack the surface surface of the material rial and cause corrosi corrosion, on, erosion, erosion, and/or cracking cracki ng over tim time, thus reducing material terial strength. High temperature service rvi ce environme nvironments usually reduce material terial strength signif significantly. tly. Cycl Cycliic loading of a material aterial can lead to a fati atigue failure ailure over tim time. Impact (shock) (shock) loa loadi ding ng produces very high high transien nsient stresses which which can precipi cipitate tatefailure. ail ure.  The  The loa load and stress value lues for for the structure usually come fro from an engine ineering ing model an and depend on system geometry, inten i ntended use, forese foreseeable ble abuse, service service environme nvironment, antici anticipate pated material rial deteriorati deterioration on over tim ti me, etc.  The  The loa load on a member in in the structure is based on the external loa loads applied lied to the whole structure, th the reaction ions supporting supporting the structure, and and thegeometry of the structure. V ariatio ariations ns in external loads, reactions, and/or geometry result in in variations riations of calculate calcul ated load. Thus load, and therefore stress, is is also a random variab variable with with an expected mean value and a standard deviati deviation. on.

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Reliability Equation 1 is called the central safety factor if it is based on mean values of capacity, strength, load, and stress. This means, for example, that approximately 50% of the parts made out of a particular material will have a strength less than the mean value, and the rest will have a strength greater than or equal to the mean value. If one were to design a part for mass production using the mean strength value, approximately half of the parts produced would beof lower strength than desired. This might pose a problemover the service life of those systems. Suppose the loading on the system were actually greater than anticipated in the design and the strength of the system were less than expected, then the probability of failure of that system would be greater than expected. Figure 1 depicts normal probability distributions of both stress and strength which overlap. The region of overlap is also the region of greatest probability of system failure.

P( )

S Figure 1. The Probability Distributions of Stress and Strength Showing Substantial Overlap [J uvinall & Marshek, 1991, p. 225] Based on figure 1, we may modify the safety factor equation (1) to account for this overlap between stress and strength [Shigley & Mischke, 1989, p 259], [Shigley, 1972, p. 174] as follows…

 1 − aγ S  > 1  1 + a γ σ 

N R =  N

where NR N a

γ S γ σ

(2)

is thesafety factor based on reliability is thecentral safety factor based on mean or expected values (equation 1) is the number of standard deviations to produce thedesired confidencelevel a: 0 1.65 2.33 3 3.08 3.62 4.42 4.89 Reliability: 50% 95% 99% 99.87% 99.9% 99.99% 99.999% 99.9999% Failure Rate: 50% 5% 1% 0.13% 1/1,000 1/10,000 1/100,000 1/1,000,000 is thecoefficient of variation of thestrength value (published or estimated) is thecoefficient of variation of thestress value (estimated)

Notice that equation 2 is a relatively simple modification of the definition of central safety factor (equation 1) that compares thehighest expected stress against the lowest expected strength based on the specified level of reliability. 1.0

   l   a   r    t 0.8   :   n   o  e    i    t   C    / 0.6   a   y    t    R    i    l    i 0.4    F    b    S    i   a    l   e0.2    R

Coef. of Variation =0.01 Coef. of Variation =0.05 Coef. of V ariation =0.1 Coef. of Variation =0.15 Coef. of V ariation =0.2

0.0 0

1

2 3 Number of Standard Deviations

4

5

Figure 2. Ratio of the Reliability Safety Factor to the Central Safety Factor

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 The Visodic Safety Factor Model  Joseph P. Visodic developed and published recommendations for minimum central safety factor values in 1948 which were based on cumulative experience [Shigley and Mischke, 2001, p. 25], [Burr & Chetham, 1995, p. 308], [Juvinall & Marshek, 1991, p. 224], [J uvinall, 1983, p. 176]. These arepresented in table 1. Safety factors for ductile materials are based on yield strength. Safety factors for brittle materials are based on ultimate strength and are twice the recommended values for ductile materials. Safety factors for primarily cyclic loading are based on endurance limit. Impact loads require a safety factor of at least 2 multiplied by an “impact factor,” usually in the range of 1.1 to 2 [Shigley & Mischke, 2001, p. 28].  Table 1. Recommended Central Safety Factors for Ductile Materials based on Yield Strength [Shigley & Mischke, 2001, P. 25] Safety Factor 1.2-1.5 1.5-2.0 2.0-2.5 2.5-3.0 3.0-4.0 3.0-4.0

K nowledgeof  L oads Accurate Good Good Average Average Uncertain

K nowledgeof  Stress Accurate Good Good Average Average Uncertain

K nowledge of  Material Well Known Well Known Average Less Tried Untried Better Known

K nowledgeof  Environment Controllable Constant Ordinary Ordinary Ordinary Uncertain

 The Norton Safety Factor Model Robert L. Norton [1996, p. 21] stated “Clearly, where human safety is involved, high values of (safety factor) are justified.” His overall safety factor value is a combination of a safety factor based on material properties, one based on engineering model accuracy, and one based on expected service environment, as follows… Nductile ≥ max( N1, N2, N3 ); based on yield strength Nbrittle ≥ 2[ max( N1, N2, N3 ) ]; based on ultimate strength Where N1, N2, and N3 are selected from table 2

(3) (4)

Safety factors for ductile materials are based on yield strength, while those for brittle materials are based on ultimate strength. Table 2 shows recommended values of N 1, N2, and N3.  Table 2. Recommended Central Safety Factors for Ductile Materials based on Y ield Strength [Norton, 1996, p. 21] Safety Factor Value 1.3 2 3 5+

N1 Material Properties (from tests) Well known/characterized Good Approximation Fair Approximation Crude Approximation

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N2 Stress/L oad Model Accuracy Confirmed by testing Good Approximation Fair Approximation Crude Approximation

3

N3 Service Environment Same as material test conditions Controlled, room-temperature Moderately challenging Extremely challenging

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 The Pugsley Safety Factor Model Pugsley [1966] recommended that safety factors be determined as the product of two factors… N =N1N2 Where N1 =f( A, B, C ) -fromtable 3a N2 =f( D, E ) -from table 3b A is the quality of materials, workmanship, maintenance, and inspection B is control over applied loads C is accuracy of stress analysis, experimental data, or experience with similar parts D is danger to people E is economic impact

(5)

 Table 3a. Values for Safety Factor Characteristics A =quality of materials, workmanship, maintenance B =control over applied loads C =accuracy of stress analysis, experiment, experience (VG =Very Good, G =Good, F =Fair, P =Poor) B= Characteristic C =VG A =VG C =G C =F C =P C =VG A =G C =G C =F C =P C =VG A =F C =G C =F C =P C =VG A =P C =G C =F C =P

VG 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

G 1.30 1.45 1.60 1.75 1.55 1.75 1.95 2.15 1.80 2.05 2.30 2.55 2.15 2.35 2.65 2.95

F 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

P 1.70 1.95 2.20 2.45 2.05 2.35 2.65 2.95 2.40 2.75 3.10 3.45 2.75 3.15 3.55 3.95

 Table 3b. Values for Safety Factor Characteristics D =danger to people; E =economic impact (VS =Very Serious, S =Serious, NS =Not Serious)

Characteristic D =NS D =S D =VS

E= S 1.0 1.3 1.5

NS 1.0 1.2 1.4

VS 1.2 1.4 1.6

Misc. Safety Factor Models Lipson and Juvinall [1963, p. 165] presented the safety factor recommendation shown in tables 4 and 5, which were based on cumulative experience. In order to compare the values in these tables with the values in the

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previous tables, let us assume that the yield strength of hot rolled steel is half of the ultimate strength, therefore the safety factors can be cut in half (except for those listed for cast iron, which is brittle).  Table 4. Recommended Safety Factors based on UltimateStrength [M achinery’s Handbook]

K ind of L oad Dead (static) load Repeated, gradually applied in one direction with mild shock Repeated, gradually applied in reversed directions with mild shock Shock load

Steel (Ductile) 5 6

Cast iron (Brittle) 6 10

8

15

12

20

 Table 5. Recommended Safety Factors based on UltimateStrength [L ipson & J uvinall, 1963, p. 165] K ind of L oad Dead (static) load Ordinary duty Variable load Live load Fluid tight joint Shock load

(Ductile) 4 4 4 6 6 10

Discussion and Recommendations  The value of a central safety factor (equation 1) should not be less than two (2) for most structural applications and should routinely be set at three (3). Low safety factors are justified only where extensive physical testing of both materials and structural systems is done. Low safety factors also require routine periodic inspection and maintenance of the system if it is to have a useable life of more than a few years in an ordinary service environment. Uncertainty in loading, uncertainty in material properties, foreseeable abuse, and challenging service environments demand higher values of the safety factor. A long service life also requires a larger value of safety factor. High reliability applications require systems with a larger central safety factor value.  The reliability safety factor (equation 2) accommodates lower values than the central safety factor (equation 1) for the same probability of failure. Shigley [1972, p. 174] feels that given well known values and a reasonable reliability level (95% or higher) safety factor values between 1.3 and 2.0 are adequate. Again, lower safety factor values require physical testing, a predictable service environment, and periodic inspection and maintenance. Brittle materials require a higher safety factor than ductile materials because brittle failure is abrupt and not preceded by yielding. The consensus in the literature is that the safety factor for brittle materials should be at least twice that used for ductile materials and should be based on ultimatestrength. Service loads due to expected normal use and foreseeable abuse are usually difficult to establish. Well characterized loads justify a lower minimumsafety factor value, while uncertain loads require a larger value. Cyclic loading induces fatigue failure in structural components. The safety factor for primarily cyclic loading should be based on the endurance limit rather than on yield or tensile strength. Well characterized cyclic loads  justify a lower minimum safety factor value, while uncertain loads should have a larger value.

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Impact (shock) loading induces very high transient stresses in structural components that can precipitate failure. Therefore the safety factor for impact loading should be at least 2.0, and 1.5 to 2.5 times that used for static (dead) loads. The greater the impact force, the higher the safety factor needed.  The consequences of system failure must also be considered in the selection of a minimum safety factor value. If human life and health are not at risk and potential property damage is limited to the systemitself, then the minimum safety factor value may be lowered a little. However if human life and health are at risk and/or potential property damage caused by system failure is substantial, then a higher minimum safety factor value is required.  These are the situations in which failure precipitates liability litigation and therefore a higher safety factor should be viewed as relatively cheap liability insurance.  The service life of the system is important in the selection of a minimum safety factor value. A short expected service life justifies a lower minimum safety factor value, while a long expected service life demands a higher value.  The service environment also affects the selection of a minimum safety factor value. A controlled indoor environment may accommodate a lower minimum safety factor value, while a challenging environment involving temperature extremes, corrosion, earthquake, occasional high winds, etc. needs a substantially larger value.  Table 6. A Comparison of Safety Factor Models  Test Cases 1. Commercial aerospacestructure – Very well tested materials and structures. Well Characterized loads. Predictable service environment. Periodic inspection and maintenancethroughout long life. Failure usually results in high risk to many human lives. (A SF of 1.5 is expected.) 2. Trailer hitch coupler – Defined maximum loads by class. Occasional service loads 2-3 times defined maximums. Corrosive environment. Cyclic and impact loading. Very little inspection and maintenance during moderately long life. Failure may result in high risk to human life. 3. L argeutility power transformer – Well defined maximum loads. Occasional service loads 1-2 times normal. Cyclic and impact loading. Predictable but challenging service environment. Periodic inspection and maintenance throughout very long life. (A SF of 5 is customary.)

Visodic

Norton

Pugsley

1.2-1.5

1.3

1.4

4.5-6.0

4.0

4.0

3.8-5.0

4.0

3.8

References: Burr, Arthur H. and John B. Cheatham, 1995, Mechanical Analysis and Design, 2nd ed., Prentice Hall, Englewood Cliffs, New Jersey. (ISBN: 0-02-317265-7, Library of Congress: TJ230.B94) Dieter, George E., 1991, Engineering Design--A Materials and Processing Appr oach, 2nd. ed., McGraw Hill, Inc., New York. (ISBN 0-07-016906-3, LOC TA 174.D495)  Juvinall, Robert C. and Kurt M. Marshek, 1991, Fundamentals of Machine Component Design, 2nd Ed., John Wiley & Sons, New York. (ISBN: 0-471-62281-8, Library of Congress: TJ230.J88 1991)  Juvinall, Robert C., 1983, Fundamentals of Machine Component Design, John Wiley & Sons, New York. (ISBN: 0-471-06485-8, Library of Congress: TJ230.J88 1983) Lipson, Charles and Robert C. Juvinall, 1963, Handbook of Stress and Strength – Design and Material Applications, Macmillan, New Y ork. (Library of Congress: 63-10398) Norton, Robert L., 1996, Machine Design – An I ntegrated Approach, Prentice-Hall, Upper Saddle River, New  Y ork. (ISBN: 0-13-565011-9, Library of Congress: TJ230.N64) Pugsley, A. G., 1966, The Safety of Structures, Arnold, New Y ork.

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Shigley, J oseph E. and Charles R. Mischke, 2001, Mechanical Engineering Design, 6th ed., McGraw Hill, Inc., New Y ork. (ISBN: 0-07-365939-8, Library of Congress: TJ 320.S5 2001) Shigley, J oseph E. and Charles R. Mischke, 1989, Mechanical Engineering Design, 5th ed., McGraw Hill, Inc., New Y ork. (ISBN: 0-07-056899-5, Library of Congress: TJ 320.S5 1989) Shigley, J oseph E. and Larry D. Mitchell, 1983, Mechanical Engineering Design, 4th ed., McGraw Hill, Inc., New  Y ork. (ISBN: 0-07-056888-X, Library of Congress: TJ 320.S5 1983) Shigley, J oseph E., 1972, Mechanical Engineering Design, 2nd ed., McGraw Hill, Inc., New York. (ISBN: 07056869-3, Library of Congress: 74-167497) Visodic, J. P., 1948, “Design Stress Factors,” Proceedings of the ASME, Vol. 55, May, ASM E International, New  Y ork.

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