How large can we permit the stresses to be? Or conversely: How large must a part be to withstand a given set of loads? What are the overall conditions or limits that will determine the size and material for a part?

Design limits are based on avoiding failure of the part to perform its desired function. Because different parts must satisfy different functional requirements, the conditions which limit load-carrying ability may be quite different for different elements. As an example, compare the design limits for the floor of a house with those for the wing of an airplane.

If we were to determine the size of the wooden beams in a home such that they simply did not break, we would not be very happy with them; they would be too "springy. " Walking across the room would be like walking out on a diving board.

Obviously, we should be concerned with the maximum?"deflection" that we, as individuals, find acceptable. This level will be rather subjective, and different people will give different answers.?In fact, the same people may give different answers depending on whether they are paying for the floor or not!

An airplane wing structure is clearly different. If you look out an airplane window and watch the wing during turbulent weather, you will see large deflections; in fact you may wish that they were smaller.?However, you know that the important issue is that of " structural integrity,"?not deflection.

We want to be assured that the wing will remain intact. We want to be assured that no matter what the pilot and the weather do, that wing will continue to act like a good and proper wing. In fact, we really want to be assured that the wing will never fail under any conditions. Now that is a pretty tall order; who knows what the?"worst" conditions might be?

Engineers who are responsible for the design of airplane wing structures must know, with some degree of certainty, what the?" worst" conditions are likely to be. It takes great patience and dedication for many years to assemble enough test data and failure analyses to be able to predict the "worst" case. The general procedure is to develop statistical data which allow us to say how frequently a given condition is likely to be encountered-once every 1 000 hours, or once every 10 000 hours, etc.

As we said earlier, our object is to avoid failure. Suppose, however, that a part has failed in service, and we are asked: Why??"Error" as such can come from three distinctly different sources, any or all of which can cause failure:

(1) Error in design: We the designers or the design analysts may have been a bit too optimistic: Maybe we ignored some loads; maybe our equations did not apply or were not properly applied; maybe we overestimated the intelligence of the user; maybe we slipped a decimal point.

(2) Error in manufacture: When a device involves heavily stressed members, the effective strength of the members can be greatly reduced through improper manufacture and assembly: Maybe the wrong material was used; maybe the heat treatment was not as specified; maybe the surface finish was not as good as called for; maybe a part was?"out of tolerance"; maybe the surface was damaged during?machining; maybe the threads were not lubricated at assembly; or perhaps the bolts were not properly tightened.

(3) Error in use: As we all know, we can damage almost anything if we try hard enough, and sometimes we do so accidentally:?We went too fast; we lost control; we fell asleep; we were not watching the gages; the power went off; the computer crashed; he was taking a coffee break; she forgot to turn the machine off; you failed to lubricate it, etc.

Any of the above can happen: Nothing is designed perfectly; nothing is made perfectly; and nothing is used perfectly. When failure does occur, and we try to determine the cause, we can usually examine the design; we can usually examine the failed parts for manufacturing deficiencies; but we cannot usually determine how the device was used (or misused). In serious cases, this can give rise to considerable differences of opinion, differences which frequently end in court.

In an effort to account for all the above possibilities, we design every part with a safety factor. Simply put, the safety factor (SF) is the ratio of the load that we think the part can withstand to the load we expect it to experience. The safety factor can be applied by increasing the design loads beyond those actually expected, or by designing to stress levels below those that the material actually can withstand (frequently called "design stresses").

Safety factor = SF = failure load/design load

?????????????????= failure stress/design stress

It is difficult to determine an appropriate value for the safety factor. In general, we should use larger values when:

(1) The possible consequences of failure are high in terms of life or cost.

(2) There are large uncertainties in the design analyses.

Values of SF generally range from a low of about 1.5 to 5 or more. When the incentives to reduce structural weight are great (as in aircraft and spacecraft), there is an obvious conflict. Safety dictates a large SF, while performance requires a small value. The only resolution involves reduction of uncertainty. Because of extreme care and diligence in design, test, manufacture, and use, the aircraft industry is able to maintain very enviable safety records while using safety factors as low as 1.5.

We might note that the safety factor is frequently called the?"ignorance factor." This is not to imply that engineers are ignorant,?but to help instill in them humility, caution, and care. An engineer is responsible for his or her design decisions, both ethically and legally.?Try to learn from the mistakes of others rather than making your own.