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Materials Selection in Mechanical Design

Michael F. Ashby

Chapter 4

Materials Selection - The Basics - all with Video Answers

Educators

Chapter Questions

00:17

Problem 1

What is meant by an objective and what by a constraint in the requirements for a design? How do they differ? How are they used?

AG
Ankit Gupta
Numerade Educator
02:12

Problem 2

What is meant by a free variable? Give examples of free variables.

Christopher Stanley
Christopher Stanley
Numerade Educator
00:42

Problem 3

You are asked to design a cooking pan for camping. What constraints would you apply in selecting a material for the pan? What objectives would you use to rank the materials that meet the constraints?
FIGURE E4.3 Credi the image to Varga

Aadit Sharma
Aadit Sharma
Numerade Educator
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Problem 4

Bikes come in many forms, each aimed at a particular sector of the market:
- Sprint bikes
- Touring bikes
- Mountain bikes
- Shopping bikes
- Children's bikes
- Folding bikes
Use your judgement to identify the primary constraints and objective that you would apply in selecting a material for the frame for the differing bike types.

Victor Salazar
Victor Salazar
Numerade Educator
03:36

Problem 5

A material is required for the windings of an electric heater for a sauna. The heating coils must be capable of temperatures up to $800^{\circ} \mathrm{C}$. Think out what attributes a material must have if it is to be made into windings and function properly when exposed to air. List the function and the constraints; set the objective to 'minimize material price' and the free variables to 'choice of material'.

Supratim Pal
Supratim Pal
Numerade Educator
03:36

Problem 6

A material is required to manufacture office scissors. Paper is an abrasive material, and scissors sometimes encounter hard obstacles like staples. List function and constraints, set the objective to 'minimize material price' and the free variables to 'choice of material'.

Supratim Pal
Supratim Pal
Numerade Educator
03:36

Problem 7

A material is required for a heat exchanger for cooling a small marine engine, saline, water at $120^{\circ} \mathrm{C}$ (and thus under pressure). List function and constraints, set the objective to 'minimize material price' and the free variables to 'choice of material'.

Supratim Pal
Supratim Pal
Numerade Educator
01:35

Problem 8

A material is required for a disposable fork for a fast food chain that is conscious of its environmental image. List the objective and the constraints that you would see as important in this application.

Courtney Burson
Courtney Burson
Numerade Educator
00:58

Problem 9

Formulate the constraints and objective you would associate with the choice of material to make the forks of a racing bicycle.

Katelyn Chen
Katelyn Chen
Numerade Educator
02:57

Problem 10

The standard CD ('Jewel' case) cracks easily and, if broken, can scratch the CD. Jewel cases are made of injection moulded polystyrene, chosen because it is transparent, cheap and easy to injection mould. A material is sought to make CD cases that do not crack so easily. The case must still be transparent, able to be injection moulded, and able to compete with polystyrene in cost.

Arpit Gupta
Arpit Gupta
Numerade Educator
00:43

Problem 11

Ultraprecise bearings that allow a rocking motion make use of knifeedges or pivots. As the bearing rocks, it rolls, translating sideways by a distance that depends on the radius of contact. The further it rolls, the less precise is its positioning, so the smaller the radius of contact $R$ the better. But the smaller the radius of contact, the greater is the contact pressure $(F / A)$. If this exceeds the hardness $H$ of either face of the bearing, it will be damaged. Elastic deformation is bad too: it flattens the contact, increasing the contact area and the roll. Translate the requirements for the bearing, listing function, constraints, objective and free variable.

Yujie Wang
Yujie Wang
College of San Mateo
02:37

Problem 12

Material indices for elastic beams with differing constraints. Start each of the four parts of this problem by listing the function, the objective and the constraints. You will need the equations for the deflection of a cantilever beam with a square cross-section $t \times t$, given in Appendix B, Section B3. The two that matter are that for the deflection $\delta$ of a beam of length $L$ under an end load $\mathrm{F}$ :
a. Show that the best material for a cantilever beam of given length $L$ and given (i.e., fixed) square cross-section $(t \times t)$, that will deflect least under a given end load $F$, is that with the largest value of the index $M=E$, where $E$ is Young's modulus (neglect self-weight) Fig. E4.12A.
b. Show that the best material choice for a cantilever beam of given length $L$ and with a given section $(t \times t)$ that will deflect least under its own selfweight is that with the largest value of $M=E / \rho$, where $\rho$ is the density Fig. E4.12B.
c. Show that the material index for the lightest cantilever beam of length $L$ and square section (not given, i.e., the area is a free variable) that will not deflect by more than $\delta$ under its own weight is $M=E / \rho^{2}$ Fig. E4.12C.
d. Show that the lightest cantilever beam of length $L$ and square section (area free) that will not deflect by more than $\delta$ under an end load $F$ is that made of the material with the largest value of $M=E^{1 / 2} / \rho$ (neglect selfweight) Fig. E4.12D.

Chai Santi
Chai Santi
Numerade Educator
07:57

Problem 13

$$
F_{f}=\frac{\sigma_{f}}{\gamma_{m} L}
$$
where $y_{m}$ is the distance between the neutral axis of the beam and its outer filament and $I=t^{4} / 12=A^{2} / 12$ is the second moment of the cross-section. The table given in this exercise itemizes the design requirements.
Plot the criterion on a copy of the $\left(\sigma_{f}-\rho\right)$ chart of Figure $3.4$ and use it to identify promising candidate materials. (If you have access to the CES Edu software, make the chart and apply the index to find candidate materials.)Material index for a light, strong beam. In stiffness limited applications, it is elastic deflection that is the active constraint: it limits performance. In strength limited applications, deflection is acceptable provided the component does not fail; strength is the active constraint. Derive the material index for selecting materials for a beam of length $L$, specified strength and minimum weight. For simplicity, assume the beam to have a solid square cross-section $t \times t$. You will need the equation for the failure load of a beam (Appendix B, Section B4). It is

Ajay Singhal
Ajay Singhal
Numerade Educator
05:02

Problem 14

Material index for a cheap, stiff column. In the last two exercises the objective has been that of minimizing weight. There are many others. In the selection of a material for a spring, the objective is that of maximizing the elastic energy it can store. In seeking materials for thermal-efficient insulation for a furnace, the best are those with the lowest thermal conductivity and heat capacity. However, most common of all is the wish to minimize cost. So here is an example involving cost.

Banhishikha Sinha
Banhishikha Sinha
Numerade Educator