Chapter 14, Materials and the Environment Video Solutions, Materials Selection in Mechanical Design

Problem 1

Carbon footprint and embodied energy of materials. Make a bar chart of $\mathrm{CO}_{2}$ footprint divided by embodied energy, using data from the data sheets of Appendix A, Table A10, for
a. Cement
b. Low carbon steel
c. Copper
d. Polyvinylchloride (PVC)
e. Aluminium alloys and
f. Softwood
Which material has the highest ratio? Why? Note the median value of this ratio for most of the materials - it is almost constant and is useful when estimating carbon footprints from embodied energies and vice versa.

James Kiss

Numerade Educator

01:12

Problem 2

Embodied energies.
a. Window frames are made from extruded aluminium. It is argued that making them instead from extruded PVC would give a product with a lower embodied energy and carbon footprint. If the section shape and thickness of the aluminium and the PVC windows are the same and both are made from virgin material, is the claim justified? You will find embodied energies and densities for the two materials in the data sheets of Appendix A, Tables A2 and A10. Use the mean values of the ranges given there.
b. Products like window frames would more usually be made from recycled aluminium. If the embodied energy of recycled aluminium is $30 \mathrm{MJ} / \mathrm{kg}$, does the conclusion change?

Ajay Singhal

Numerade Educator

02:05

Problem 3

Embodied energy.
a. A range of office furniture includes a chunky hardwood table weighing $18 \mathrm{~kg}$ and a much lighter table with a $3.0 \mathrm{~kg}$ virgin aluminium frame and a $3.0 \mathrm{~kg}$ glass top. Which of the two tables has the lower embodied energy? Use data from the data sheets of Appendix A to find out.
b. If the alumina-glass table is made from recycled aluminium with an embodied energy of $30 \mathrm{MJ} / \mathrm{kg}$, does the conclusion change?

Supratim Pal

Numerade Educator

03:40

Problem 4

Getting a feel for embodied energies. Aluminium is made by the electrolysis of bauxite. The embodied energy of virgin aluminium is approximately (all embodied energies are approximate) $210 \mathrm{MJ} / \mathrm{kg}$. What else could you do with this much electrical energy? Explore
a. How much water would it boil?
b. How far would it drive an electric car if the average at-wheel energy to propel a small car is $0.6 \mathrm{MJ} / \mathrm{km}$ ?

Bin Chen

Numerade Educator

01:41

Problem 5

Minimizing embodied energy. Use the $E-H_{\rho} \rho$ chart of Fig. $14.7$ to find the polymer with a modulus $E$ greater than $1 \mathrm{GPa}$ and the lowest embodied energy per unit volume.

Sai Chaitanya Tadepalli

Numerade Educator

02:43

Problem 6

Comparing products by embodied energy. A maker of polypropylene (PP) garden furniture is concerned that the competition is stealing market share by claiming that the 'traditional' material for garden furniture, cast iron, is less energy and $\mathrm{CO}_{2}$ intensive than the PP. A typical PP chair weighs $1.6 \mathrm{~kg}$; one made of cast iron weighs $8.5 \mathrm{~kg}$.
a. Use the data for these two materials in Appendix A, Table A10, to find out who is right - are the differences significant if the data for embodied energy are only accurate to $\pm 25 \%$ ?
b. If the PP chair lasts 5 years and the cast iron chair lasts 25 years, does the conclusion change?

Sheryl Ezze

Numerade Educator

04:18

Problem 7

Materials with low embodied energy. Identical casings for a power tool could be die-cast in aluminium or moulded in acrylonitrile butadiene styrene or polyester glass-fibre reinforced polymers (GFRP). Use the embodiedenergy per unit volume bar chart of Figure $3.21$ to decide which choice minimizes the embodied energy of the casing, assuming the same volume of material is used for each casing.

Jayashree Behera

Numerade Educator

07:37

Problem 8

Disposable knives and forks. Disposable knives and forks are ordered by an environmentally-conscious pizza house. The shape of each (and thus the length, width and profile) are fixed, but the thickness is free: it is chosen to give enough bending-stiffness to cut and impale the pizza without excessive flexure. The pizzeria proprietor wishes to enhance the greenness of his image by minimizing the energy content of his throw-away tableware, which could be moulded from polystyrene (PS) or stamped from aluminium sheet.

Regina Hays

Numerade Educator

07:57

Problem 9

Materials for low embodied energy structures. Show that the index for selecting materials for a strong panel with the dimensions shown in the figure, loaded in bending, with minimum embodied energy content is that with the largest value of $$
M=\frac{\sigma_{Y}^{1 / 2}}{H_{p} \rho}
$$
where $H_{p}$ is the embodied energy of the material, $\rho$ its density and $\sigma_{y}$ its yield strength. To do so, rework the panel derivation in Chapter 4, Materials Selection - The Basics (Eq. 4.9) replacing the stiffness constraint with a constraint on failure load $F$ requiring that it exceed a chosen value $F^{*}$ where
$$
F=C_{2} \frac{I \sigma_{y}}{h L}>F
$$
where $C_{2}$ is a constant and $I$ is the second moment of area of the panel, $I=\frac{b h^{5}}{12}$.

Ajay Singhal

Numerade Educator

02:28

Problem 10

Indices for selection to minimize embodied energy. Use the indices for the crash barriers (Eqs $14.9$ and 14.10) with the charts for strength and density (Fig. 3.4) and strength and embodied energy (Fig. 14.8) to select materials for each of the barriers. Position your selection line to include one metal for each. Reject ceramics and glass on the grounds of brittleness. List what you find for each barrier.

Narayan Hari

Numerade Educator

01:46

Problem 11

Energy-efficient materials for transport. The makers of a small electric car wish to make bumpers out of a moulded thermoplastic. Which index is the one to guide this selection if the aim is to maximize the range for a given battery storage capacity? Plot it on the appropriate chart selected form the text and make a selection.

Mayukh Banik

Numerade Educator

02:17

Problem 12

Energy-efficient floor joists: embodied energy and shape. Floor joists are beams loaded in bending. They can be made of wood, of steel, or of steelreinforced concrete, with the shape factors listed below. For a given bending
stiffness and strength, which of these carries the lowest production-energy burden? The relevant data, drawn from the tables of Appendix A, are listed.
a. Start with stiffness. Locate from Eq. ( $10.20)$ of the text the material index for stiffness-limited, shaped beams of minimum mass. Adapt this to make the index for stiffness-limited, shaped beams of embodied energy by multiplying density $\rho$ by the embodied energy/kg, $H_{p}$. Use the modified index to rank the three beams.
b. Repeat the procedure, this time for strength, creating the appropriate index for strength-limited shaped beams at minimum energy content by adapting Eq. (10.28).
What do you conclude about the relative energy-penalty of design with wood and with steel?

Chai Santi

Numerade Educator

08:38

Problem 13

Power systems: energy pay-back time. The table below shows data for the main materials used in a wind turbine: the approximate mass used per $\mathrm{kW}$ installed and the embodied energy per $\mathrm{kg}$ of these materials.

Saman Zulfiqar

Numerade Educator