Mechanical Engineering Design Notes

Design Contents

Preliminary Matters
Design Methodology
..brain storming
..evaluation matrix
Statistical Considerations
..variability in materials
..variability in dimensions
..variability in loading
..preferred sizes
Design Factor
Introduction to Failure
Failure Theories
Application of von Mises
..criterion in 2 D

Stress Concentration
..and notch sensitivity
Failure Under Combined Loading
..combined bending and torsion
Failure Under Cyclic Loading
..fracture mechanics
Instability - Buckling
Concentrically Loaded Strut
..slender columns
..Euler formula
..effective length
..short and intermediate columns
Eccentrically Loaded Strut
.. theory
Shock Loading

Design Factor - Factor of Safety - In Reality - Factor of Ignorance?

We do not know exactly:

Full Details of Load(s)
The Nature of Defects Introduced by Manufacturing

It is common practice to size components so the maximum design stress is below the UTS or yield stress by an appropriate factor - the Factor of Safety, based on UTS or Yield Strength (or in some cases involving fatigue, on the fatigue endurance strength).

Generally use a larger FoS if:

There is little information about one or more of the factors above.
Failure would have serious consequences, such as loss of life.

Increasingly now computers are being used to provide more accurate simulation of stresses that occur in components, particularly in the case of high value products where safety and saving weight is essential - aircraft and automotive.

In these critical applications, manufactured components will sometimes be tested to assess the reliability of the material and the manufacturing techniques. For some applications the efforts that go into large scale operations mean that much lower FoS are used for these than can be used for routine daily working - An example of this is lifting operations and cranes.

The FoS, also sometimes known as the design factor of safety, nd or n, may be determined in terms of the material's ultimate tensile stress (UTS) or the yield stress:

n = strength / stress, or FoS = UTS / design stress

It should be noted that the above disussion is satisfactory for linear systems where the stress is proportional to the load. However for situations where buckling or instability is a possibility, the stress and load are NOT linearly related, then the design factor or factor of safety MUST be based on loads, ie:

n or FoS = load to just cause failure/design load.

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