# (a) stiffness and strength

Calladine, C. R. (1983), "Theory of shell structures", Cambridge University Press. ISBN 0-521-36945-2

Young, W. C. (1989), "Roark’s formulas for stress and strain", 6th ed, McGraw-Hill. ISBN 0-07-072541-1. (A “yellow pages" for results for calculations of stress and strain in loaded components.)

Solutions to standard problems: (b) heat flow

Hollman, J. P. (1981), "Heat transfer", 5th ed, McGraw Hill. ISBN 0-07-029618-9

Carslaw, H. S. and Jaeger, J. C. (1959), "Conduction of heat in solids", 2nd ed, Oxford University Press. ISBN 0-19-853303-9

9.8 Exercises

E.9.1. The materials of the drink containers of Figure 9.1 are recycled to different degrees. How does the ranking of Table 9.2 change if the contribution of recycling is included? To do so, multiply the energy per liter in the last column of the table by the factor where frc is the recycle fraction in current supply, Hm is the embodied energy for primary material production, and Hrc is that for recycling of the material. You will find data for all three attributes in the data sheets of Chapter 12.

E.9.2. Derive the correction factor to allow for recycle content cited in Exercise E.9.1.

E.9.3. Repeat the analysis of Table 9.2 and Section 9.2, applying it to industrial fluid containers of the sort you find in automobile supply stores: those for antifreeze, oil, cleaning fluids, and gasoline. Weigh them, record their volume, identify the material of which they are made (recycle mark? magnetic? non-magnetic?), retrieve their embodied ener­gies from the data sheets of Chapter 12, and rank them by embodied energy per unit volume of fluid contained.

E.9.4. Use the indices for the crash barriers (Equations 9.1 and 9.2) with the charts for strength and density (Figure 8.12) and strength and embodied energy (Figure 8.14) 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.

E.9.5. Complete the selection of materials for light, stiff shells of Section

8.5 by plotting the stiffness index

p

e1 12

onto a copy of the modulus-density chart of Figure 8.11. Reject ceram­ics and glass on the grounds of brittleness and foams on the grounds that the shell would have to be very thick. Which materials do you find? Which of these would be practical for a real shell?

E.9.6. In a faraway land, refrigerators cost the same as they do here, but electrical energy costs 10 times more than here—that is, it costs \$2/ kWhr. Make a copy of the tradeoff plot for fridges (Figure 9.8) and plot a new set of penalty lines onto it, using this value for the exchange con­stant, ae. If you had to choose just one fridge, which would it be?

E.9.7. You are asked to design a large heated workspace in a cold cli­mate, making it as ecofriendly as possible by using straw-bale insula­tion. Straw, when compressed, has a density of 600 kg/m3, a specific heat capacity of 1670 J/kg. K, and a thermal conductivity of 0.09 W/m. K. The space will be heated during the day (12 hours) but not at night. What is the optimum thickness of straw to minimize the energy loss?

E.9.8. The makers of a small electric car want to make bumpers out of a molded thermoplastic. Which index is the one to guide this selection? Plot it on the appropriate chart from the set shown in Figures 8.11-8.14 and make a selection.

E.9.9. Car bumpers used to be made of steel. Most cars now have extruded aluminium or glass-reinforced polymer bumpers. Both materials have a much higher embodied energy than steel. Take the mass of a steel bumper set to be 20 kg and that of an aluminum one to be 14 leg. Find an equa­tion for the energy consumption in MJ/km as a function of weight for petrol engine cars using the data plotted in Figure 9.11 of the text.

■ Work out how much energy is saved by changing the bumper set of a 1500 kg car from steel to aluminium over an assumed life of 200,000 km.

■ Calculate whether the switch from steel to aluminum has saved energy over life. You will find the embodied energies of steel and aluminum in the datasheets of Chapter 12. Ignore the differences in energy in manufacturing the two bumpers; it is small.

■ The switch from steel to aluminum increases the price of the car by \$60. Using current pump prices for gasoline, work out whether,

over the assumed life, it is cheaper to have the aluminum bumper or the steel one.

Exercises Using the CES Edu Software

E.9.10. Refine the selection for shells using Level 3 of the CES software. Make a chart with the two indices

as axes, using the Advanced facility to make the combination of proper­ties. Then add a Tree stage, selecting only metals, polymers, and com­posites and natural materials. Which ones emerge as the best choice? Why?

E.9.11. Tackle the crash-barrier case study using CES Level 2 following the requirements set out in Table 9.3 . Use a Limit stage to apply the constraints on fracture toughness Klc > 18 MPa. m and the requirement of recyclability. Then make a chart with density P on the x axis and yield strength ay on the y axis, and apply a selection line with the appropriate slope to represent the index for the mobile barrier:

P

2/3

y

List what you find to be the best candidates. Then replace Level 2 with Level 3 data and explore what you find.

E.9.12. Repeat the procedure of Exercise E.9.11, but this time make a chart using CES Level 2 on which the index for the static barrier

can be plotted. You will need the Advanced facility to make the prod­uct Hmp. List what you find to be the best candidates. Then, as before, dump in Level 3 data and explore what you find.

Sustainability is one of those words that has come to mean whatever the speaker wants it to mean. To large corporations it means staying in busi­ness and continuing to grow; sustainability to an oil company, for instance, means adequate reserves of oil in the short term and a stake in the energy technology that replaces it when the time comes. To those who think on a broader scale, sustainability means using technology to decouple gross domestic product (GDP)[39] from environmental damage (carbon emissions,

Renewable and nonrenewable energy. (Image of wind turbine courtesy of Leica Geosystems, Switzerland. Image of oil rig courtesy of the U. S. National Park Service.)

for instance), allowing the first to grow while reducing the second, using market forces such as carbon trading as a mechanism. There are people, however, who have no faith in this approach, seeing the free market as the cause of the problem, not the solution; it is the relentless drive for growth that threatens the planet. Sustainability, to them, means capping or redu­cing capital GDP. And there are all shades of viewpoints in between.

Here we examine the meaning of sustainability. The view you take of it depends on scale—on the time frame and spatial scope of the examination. We start with these and then explore sustainable and quasi-sustainable sources of energy and of materials.