1. Chapter 9 Selection of Material and Shape
Materials Selection in Mechanical Design, 4th Edition, © 2010 Michael Ashby

2. Section shape is important for certain modes of loading
Section shape is important for certain modes of loading. When shape is a variable, a new term – the shape factor Φ – appears in some of the material indices.
Figure 9.1
Materials Selection in Mechanical Design, 4th Edition, © 2010 Michael Ashby

3. Figure 9.2
Mechanical efficiency is obtained by combining material with macroscopic shape. The shape is characterized by the dimensionless shape factor Φ.
Materials Selection in Mechanical Design, 4th Edition, © 2010 Michael Ashby

4. Materials Selection in Mechanical Design, 4th Edition, © 2010 Michael Ashby

5. Figure 9.3
The best material-shape combination depends on the mode of loading. Certain structural elements are specially designed to carry specific types of loads.
Materials Selection in Mechanical Design, 4th Edition, © 2010 Michael Ashby

6. Elastic Bending of Beams
Figure 9.4
The bending stiffness of a beam is proportional to the product EI
Figure 9.4 shows the effect of shape on bending stiffness. A square-section beam compared: left, with a tube of the same area (but 2.5X stiffer); right, with a tube with the same stiffness (but 4X lighter).
Materials Selection in Mechanical Design, 4th Edition, © 2010 Michael Ashby

7. Materials Selection in Mechanical Design, 4th Edition, © 2010 Michael Ashby

8. Shape factor for various structural elements subject to bending loads
Figure 9.5
Shape factor for various structural elements subject to bending loads
Materials Selection in Mechanical Design, 4th Edition, © 2010 Michael Ashby

9. Materials Selection in Mechanical Design, 4th Edition, © 2010 Michael Ashby

10. Elastic Twisting of Shafts
Shapes that resist bending well may not be so good when twisted
Materials Selection in Mechanical Design, 4th Edition, © 2010 Michael Ashby

11. Materials Selection in Mechanical Design, 4th Edition, © 2010 Michael Ashby

12. Figure 9.6
Efficient structures have high values of the ratio I/A2; inefficient structures (ones that bend easily) have low values. Real structural sections have values of I and A that lie in the shaded zones.
Materials Selection in Mechanical Design, 4th Edition, © 2010 Michael Ashby

13. Figure 9.7
When looking at plastic bending it is better to compare the section modulus compared with the section area. Optimal materials have higher values of the ratio Z/A3/2 .
Materials Selection in Mechanical Design, 4th Edition, © 2010 Michael Ashby

14. Materials Selection in Mechanical Design, 4th Edition, © 2010 Michael Ashby

15. Materials Selection in Mechanical Design, 4th Edition, © 2010 Michael Ashby

16. If you wish to make stiff, strong structures that are efficient (using as little material as possible), make the shape-efficiency factor as large as possible. However, there are limits.
Materials Selection in Mechanical Design, 4th Edition, © 2010 Michael Ashby

17. Contours of shape factor illustrate their upper limit.
Figure 9.8
Contours of shape factor illustrate their upper limit.
Materials Selection in Mechanical Design, 4th Edition, © 2010 Michael Ashby

18. Each chart shares its axes with its neighbors
Figure 9.9
Charts explore structural sections for stiffness-limited design during bending.
Each chart shares its axes with its neighbors
Materials Selection in Mechanical Design, 4th Edition, © 2010 Michael Ashby

19. 4-Quadrant Chart Figure 9.10
Materials Selection in Mechanical Design, 4th Edition, © 2010 Michael Ashby

20. How the 4-quadrant chart is used
Figure 9.10
How the 4-quadrant
chart is used
Materials Selection in Mechanical Design, 4th Edition, © 2010 Michael Ashby

21. Comparison of steel, aluminum, and wood sections for a stiffness-limited design.
Figure 9.11
Materials Selection in Mechanical Design, 4th Edition, © 2010 Michael Ashby

22. 4-quadrant chart for strength-limited design
Figure 9.12
4-quadrant chart for strength-limited design
Materials Selection in Mechanical Design, 4th Edition, © 2010 Michael Ashby

23. Material Indices That Include Shape
Elastic bending of beam:
Torsion of shaft:
Failure of beam:
Failure of shaft:
Materials Selection in Mechanical Design, 4th Edition, © 2010 Michael Ashby

24. Materials Selection in Mechanical Design, 4th Edition, © 2010 Michael Ashby

25. Materials Selection in Mechanical Design, 4th Edition, © 2010 Michael Ashby

26. Graphical Coselecting Using Indices
Figure 9.13
Materials Selection in Mechanical Design, 4th Edition, © 2010 Michael Ashby

27. Architectured Materials
Figure 9.14
Mechanical efficiency can be obtained by combining material with microscopic, or internal, shape, which repeats itself to give an extensive structure. The shape is characterized by microscopic shape factors, Ψ.
Materials Selection in Mechanical Design, 4th Edition, © 2010 Michael Ashby

28. Figure 9.15
Figure 9.16
Microstructural shape can be combined with macroscopic shape to give efficient structures. The overall shape factor is the product of microscopic and macroscopic shape factors.
Materials Selection in Mechanical Design, 4th Edition, © 2010 Michael Ashby

29. Materials Selection in Mechanical Design, 4th Edition, © 2010 Michael Ashby