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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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