YOUR AIMS

On completion of this lesson you should be able to:

- say what a performance index is, and what it measures
- describe the meanings of the terms primary function, constraint and objective
- use primary functions, constraints and objectives in deriving performance indices for given mechanical situations
- distinguish between the terms stiffness-limited and strength-limited in the context of mechanical design
- understand that changes in primary function, constraint and/or objective are likely to affect the performance index relevant to the situation

1. When deriving performance indices it is vital to be clear as to the (i) primary function of the component, (ii) the objective(s) of the design/selection and (iii) the constraints on design and performance.

With the aid of suitable examples, distinguish between these three criteria.

2. In deflection-limited (stiffness-limited) design for minimum mass components, a change in the loading regime on the component can have a major effect on the appropriate performance index and, therefore, on the materials selection process.

Demonstrate the truth of this statement by deriving performance indices for (i) a bar in tension, and (ii) a bar in bending, as illustrated below in FIGURE 6. In each case, we need to design for deflection-limited performance at minimum mass. The width of the bar, b, is fixed in each case but the depth, d, is free. Rank the materials in the table on the next page in order of suitability and comment on the results.

3. A cylindrical column is subjected to a compressive load, F, as in FIGURE 7 It will buckle elastically when the Euler load, Fcrit, is exceeded. The design is safe if F < (F_crit/S) where S is a safety factor.

For the geometry and end constraints shown in the diagram:

F_crit = 9Π³Er⁴/4L²

If the shape, load and length of the column are specified, but the cross sectional area is free, derive performance indices to select (i) the lightest and (ii) the cheapest column from among the following materials. Comment on your findings.