Performance Indices

Engineering elements perform a physical function which can be defined, they have to satisfy a functional requirement. In the example below, a structural element, length L, is required to carry a tensile load, P, which will not cause the stress to exceed:
material failure stress / specified factor of safety.

A minimum mass is required.

There are three aspects to this design:

The functional requirement, F - carrying the specified load P
The geometry, G - the length of the strut
The properties of the material, M

Then the performance index, p, is a function of F, G and M. p = f (F, G, M)
F, G and M are normally independent and separable so the optimum material properties, M, are independent of F and G. The optimum choice of M is therefore the optimum for any value of F and G.

Looking at the example where a minimum mass is required, the maximum allowable working stress is given by:

P/A = Sigma_failure / factor of safety

A = FoS P / Sigma_failure

mass, m = FoS P L R_o / Sigma_failure

rearranging: m = (FoS P)(L)(R_o / Sigma_failure)

(functional requirement - the load that can be carried safely)(specified geometry - length)(material properties)

The highest performance index, p, is given by minimum mass which is given by maximum of the ratio:
Sigma_failure / R_o
A preliminary choice of material may now be made by examining plots of failure stress (yield strength or possibly UTS) against density.

Other functional requirements, to resist buckling, internal pressure etc., result in different ratios to be maximised and a wide range of charts are published.

Further information about this approach can be found in ASM Handbook, Vol 20 - Materials Selection and Design, 1997.

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David J Grieve, 14th May 2002.