Questions and Answers of Machine Elements In Mechanical Design

Make a bar chart of $\mathrm{CO}_{2}$ footprint divided by embodied energy, using data from the data sheets of Appendix A, Table A10, fora. Cementb. Low carbon steelc. Copperd. Polyvinylchloride
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
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 $3.0 \mathrm{~kg}$
Aluminum 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
Use the $E-H_{p} ho$ 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.Data From Fig, 14.7 103 Young's
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
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 embodied-energy per unit
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
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
Use the indices for the crash barriers 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
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
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
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 kg of these materials.a. Use these data
The global population, $P$, is 7.5 billion, rising exponentially with a growth rate $\alpha=1.13 \%$ per year. At this growth rate, how long will it take to double to 15 billion?
Global biopolymer population, $P$, is currently 1 million tonnes per year and is said to be rising exponentially with a growth rate $\alpha=12 \%$ per year. At this growth rate, how long will it
The opening paragraph of this chapter contained the statement that at a global growth rate of 3% per year we will mine, process, use and dispose of more 'stuff' in the next 5 years than in the entire
The images show two contrasting coffee machines. Analyse the context for which these were designed by responding to the five W questions Who? What? Where? When? Why?
Today (2016) bagless vacuum cleaners vary in price by almost a factor of 10 an Argos VC 403 is priced at £38 ($$53),$ a Dyson DC23 is priced at £333 ($$466).$ There is a market for both, so a
Watches vary in price by a factor of over 10,000. I have a very cheap watch which I like because it has a stopwatch and is waterproof, so I can swim with it. It is extremely accurate and if I lose it
Carry out a comparison and analysis like that of the previous exercise fora. Suitcases (luggage)b. Refrigerators
Write down the first association that comes to your mind when you glance at each of the images of cars shown below. How has the designer suggested this association?
Look at the six car-images again and ponder on them for a moment. How do you perceive each one? How do they make you feel? If you had a choice of any one of these, which would you choose? Why?
What do people think of when they see something made of gold? They might – because of its expense – associate it with wealth and luxury; or perhaps – because it is a visible symbol of riches
Here is a little design exercise. You have acquired the rights to market a new biopolymer – one made from a fast-growing, prolific, crop. What are you going to call it? The name should carry the
Many very simple products have had (and continue to have) very long lives. The table lists some of these. Research the history of one of them, seeking the context (Who, What, Where, When, Why) the
A paperclip (invented 1899) is one of the simplest of products with one of the longest lives. Every office has them. They don’t normally arouse interest or amusement. Here is an example of a
Each of these mice is designed to fill a particular niche in the mouse-market. Apply the method of product analysis outlined in the previous exercise to explain the designer’s choices of materials,
Examine a product and ask the following:a. What does the product do?b. Who will use it? Where? When? Why?c. What are their aspirations? How do they see themselves?d. What aesthetics has the designer
A process is sought to make the rocker arm shown here. It is to be made from and aluminium–silicon alloy. The shape is ‘3-D solid’.The expected production run (batch size) is 2000. It weight
A camera body is shown on the right. The design requires that it be made of a magnesium alloy and that the initial production run will be 10,000 units. You are asked to suggest processes by which the
The car roof box shown in the image is to be made of glass-fibre reinforced polyester in a batch of 10,000. It is made up of two separate shell-like components – an upper and a lower half. What
Metal foams can be made by first making an open-cell polymer foam, then embedding this in plaster, burning out the polymer and finally forcing metal under pressure into the resulting mould to
A copper ingot is compressed between two anvils. If the yield strength $\sigma_{y}$ of copper is $80 \mathrm{MPa}$ and the coefficient of friction $\mu$ at the interface between the copper and
A cylindrical magnet is to be made from Alnico (an iron-aluminium-nickel-cobalt alloy) by powder compaction and sintering. The aspect ratio of the cylinder, $h / 2 r$, is 2. The coefficient of
The quadrant sketched here is part of the control system for the wing-elevator of a commercial aircraft. It is to be made of a light alloy (aluminium or magnesium) with the shape shown in the figure.
The electric plug is perhaps the commonest of electrical products. It has a number of components: the casing, the pins, connectors, a cable clamp, fasteners, and, in some plugs, a fuse. The task is
Few things are more irritating than a dripping tap. Taps drip because the rubber washer is worn or the brass seat is pitted by corrosion, or both. Ceramics have good wear resistance, and they have
Polyethylene bottles are used to contain fluids as various as milk and engine oil. A typical polyethylene bottle weighs about 30 grams and has a wall thickness of about $0.8 \mathrm{~mm}$. The
As weight-saving assumes greater importance in automobile design, the replacement of steel parts with polymer-composite substitutes becomes increasingly attractive. Weight can be saved by replacing a
This exercise and the next require the use of the CES Edu-Pack Materials Selection software.a. Use CES to select a joining process to meet the following requirements.b. Use CES to select a joining
This exercise, like the last, requires the use of the CES Edu-Pack Materials Selection software.a. Use CES to select a surface-treatment process to meet the following requirements.b. Use CES to
A method is sought to mould the wide-necked containers show in the image. It suggested that they might be blow-moulded, injection moulded or rotation moulded. The table lists approximate values for
A light, stiff, strong tie (Fig. E8.1). A tie, of length $L$ loaded in tension, is to support a load $F$, at minimum weight without failing (implying a constraint on strength) or extending
The best choice of material for a light strong column depends on its aspect ratio: the ratio of its height $H$ to its diameter $D$. This is because short, fat columns fail by crushing; tall
Fig. E8.4 shows a material chart with the two indices of Exercise E8.2 as axes. Identify and plot coupling lines for selecting materials for a column with $F=10^{6} \mathrm{~N}$ and \(H=3
In the US a typical family car covers 120,000 miles over its life and delivers, on average 25 miles per US gallon (6.6 miles per litre). Petrol in the US costs $\$ 0.63$ per litre, so the life cost
The makers of the car shown in Fig. 8.5 plan to market it in Europe. If the car covers 120,000 miles $(193,000 \mathrm{~km})$ over its life and consumes on average 9.5 litres per \(100
A Routemaster - a London bus - weighs 12 tonnes when empty, 18 tonnes with full. It does, on average, 6.6 miles $(11 \mathrm{~km})$ per imperial gallon of diesel, which cost $£ 5$ per imperial
Trucks rely on compressed air for braking and other power-actuated systems. The air is stored in one or a cluster of cylindrical pressure tanks like that shown here (length $L$, diameter $2 R$,
Explore the trade-off between relative cost and relative mass for the air cylinder of Exercise E8.7, considering the replacement of a mild steel tank with one made, first, of low alloy steel, and,
Fig. E8.8, below, is a chart with axes of $\mathrm{m} / \mathrm{m}_{o}$ and $C / C_{o}$ derived in Exercise E8.7 Mild steel (here labelled 'Low carbon steel') lies at the coordinates $(1,1)$.
Freezers and refrigerated trucks have panel walls that provide thermal insulation, and at the same time are stiff, strong and light (stiffness to suppress vibration, strength to tolerate rough
Evaluate the shape factor $\phi_{B}^{e}$ for stiffness-limited design in bending of a square box section of outer edgelength $h=100 \mathrm{~mm}$ and wall thickness $t=3 \mathrm{~mm}$. Is this
Evaluate the shape factor $\phi_{B}^{f}$ for strength-limited design in bending of a square box section of outer edge-length $h=100 \mathrm{~mm}$ and wall thickness $t=3 \mathrm{~mm}$. Is this
Derive the expression for the shape-efficiency factor $\phi_{B}^{e}$ for stiffness-limited design for a circular tube with outer radius $5 t$ and wall thickness $t$, loaded in bending (Fig.
Derive the expression for the shape-efficiency factor $\phi_{B}^{e}$ for stiffness-limited design for a channel section of thickness $t$, overall flange width $5 t$ and overall depth $10 t$,
Derive the expression for the shape-efficiency factor $\phi_{B}^{e}$ for stiffness-limited design for a square box section of wall thickness $t$, and height and width $h_{1}=10 t$ bent about
Determine the value of the shape-efficiency factor $\phi_{B}^{f}$ for strength-limited design in bending using the dimensions shown on the diagramsa. For the tube-section shown in Fig. E10.5(A)b.
A beam of length $L$, loaded in bending, must support a specified bending moment $M$ without failing and be as light as possible. Show that to minimize the mass of the beam per unit length, \(m /
The elastic shape factor measures the gain in stiffness by shaping, relative to a solid square section of the same cross-section area and thus mass per unit length. Shape factors can be determined by
A steel truss bridge shown in Fig. E10.7 has a span $L$ and is simply supported at both ends. It weighs $m$ tonnes. As a rule of thumb, bridges are designed with a stiffness $S_{B}$ such that
A beam, loaded in bending, must support a specified bending moment $M^{*}$ without failing and be as light as possible. Section shape is a variable, and 'failure' here means the first onset of
A shaft of length $L$, loaded in torsion, must support a specified torque $T^{*}$ without failing and be as cheap as possible. Section shape is a variable and 'failure' again means the first
A concept for a lightweight display stand. The stalk must support a mass $m$ of $100 \mathrm{~kg}$, to be placed on its upper surface at a height $h$, without failing by elastic buckling. It is
Cylindrical tubing is available from stock in the following materials and sizes. Use this information and the material index to identify the best stock material for the stalk of the stand shown in
Calculate the gain in bending efficiency, $\psi_{B}^{e}$, when a solid is formed into small, thin-walled tubes of radius $r$ and wall thickness $t$ that are then assembled and bonded into a
Calculate the change in structural efficiency for both bending stiffness and strength when a solid flat panel of unit area and thickness $t$ is foamed to give a foam panel of unit area and
Use the 4-segment chart for stiffness-limited design of Fig. 10.9 of the text to compare the mass per unit length, $m / L$, of a section with $E I=10^{5} \mathrm{Nm}^{2}$ made froma. structural
Show, by direct calculation, that the conclusion of Exercise 10.16 - that the CFRP beam with $E I=10^{5} \mathrm{Nm}^{2}$ and $\phi_{B}^{e}=10$ weighs less than the steel beam with the same
Use the 4-segment chart for strength-limited design of Fig. 10.12 of the text to compare the mass per unit length, $m / L$, of a section with $Z \sigma_{f}=10^{4} \mathrm{Nm}$ (where $Z$ is the
Show, by direct calculation, that the conclusion of Exercise E10.18 - that the titanium alloy beam with $Z \sigma_{f}=10^{4} \mathrm{Nm}$ and $\phi_{B}^{f}$ of 10 is much lighter than the 6061
The bcc and diamond cubic structures of Table 12.1 are stable only when the bonds linking the atoms depend on direction. When bonding is nondirectional (when spheres are allowed to pack in the earths
Nylon 66 has a tensile strength $\sigma_{m}$ of $55 \mathrm{MPa}$. It is to be reinforced with 12 micron diameter chopped S-glass fibres with a tensile strength $\sigma_{t s, f}$ of \(4750
The unit cell of the lattice shown on the right has:a. A mechanismb. An optimally rigid structure, free of self-stressesc. An over-constrained structure, with potential for self-stress. 12 bars that
Conducting carbon nanotubes with an aspect ratio of $\beta=200$ are dispersed in a polylactide matrix, a nonconducting biopolymer. If the dispersion is random (not an easy thing to achieve) what
The chart for exploring stiff composites with light alloy or polymer matrices is shown below. A construction like that of Fig. 12.11 of the text allows the potential of any given matrix-reinforcement
Density chart for light alloys and fibres shown as Fig. E12.2 to explore the relative potential of Magnesium - E-glass-fibre composites and Magnesium - Beryllium composites for light, stiff
The chart below allows exploration of components for composites with desired combinations of thermal conductivity and expansion, using light alloy or polymer matrices. Three possible matrices
The loss coefficient-modulus $(\eta-E)$ chart of Figure 3.9 is populated only along one diagonal band. (The loss coefficient $\eta$ measures the fraction of the elastic energy that is dissipated
An aircraft quality sandwich panel has the characteristics listed in the table.a. Use the data and Eqs (12.30)- (12.32) of the text to calculate the equivalent density, flexural modulus and
Plot aluminium alloys, steels, CFRP and GFRP onto a copy of the $E-ho$ chart for natural materials (Figure 13.15 of Chapter 13, Hybrids: Case Studies), where $E$ is Young's modulus and $ho$ is
Plot aluminum alloys, steels, CFRP and GFRP onto a copy of the strength-density chart for natural materials of Figure 13.16 of Chapter 13, Hybrids: Case Studies, using the flexural strength index
The table lists the moduli and strengths of spring materials. Plot these onto a copy of the ${ }^{E-\sigma_{f}}$ chart for natural materials of Figure 13.15 of Chapter 13, Hybrids: Case Studies,
Find an engineering material that most closely resembles the longitudinal strength of compact bone (cortical bone $(L)$ )in its strength and density characteristics by plotting data for this
The same materials appear on all the charts of Chapter 3, Materials Property Charts. These can be used as the starting point for 'what if...?' exercises. As a challenge, use any chart or combination
Use Fig. 3.3 to identify one metal and one polymer with a longitudinal wave speed close to $1000 \mathrm{~m} / \mathrm{s}$.Data From Fig. 3.3 Joung s modulusE GPAD 1000 Coungos modulus density 100
A component is at present made from a brass, a copper alloy. Use the Young's modulus - Density $(E-ho)$ chart of Fig. 3.3 to suggest three other metals that, in the same shape, would be stiffer.
Use the Young's modulus - Density $(E-ho)$ chart of Fig. 3.3 to identify materials with both a modulus $E>50 \mathrm{GPa}$ and a density \(hoFig.3.3 oungs modulusE GPa Coungos modulus density
Use the Young's Modulus - Density ( $E-ho$ ) chart of Fig. 3.3 to find(a) metals that are stiffer and less dense than steels and(b) materials (not just metals) that are both stiffer and less dense
Use the $(E-ho)$ chart of Fig. 3.3 to identify metals with both $E>100 \mathrm{GPa}$ and $E / ho>0.02 \mathrm{GPa} /\left(\mathrm{kg} / \mathrm{m}^{3}\right)$.Fig.3.3 oungs modulusE GPa
Use the $E / ho$ chart of Fig. 3.3 to identify materials with both $E>100 \mathrm{GPa}$ and $E^{1 / 3} / ho>0.003(\mathrm{GPa})^{1 / 3} /\left(\mathrm{kg} / \mathrm{m}^{3}\right)$.
Use the $E-ho$ chart of Fig. 3.3 to establish whether woods have a higher specific stiffness $E / ho$ than epoxies.Fig. 3.3 oungs modulusE GPa Coungos modulus density 1000 100 110 10-2
Do titanium alloys have a higher or lower specific strength (strength/density, $\sigma_{f} / ho$ ) than the best steels? This is important when you want strength at low weight (landing gear of
The design of a cycle safety helmet requires a lining that will crush at a stress of 8-12 MPa and be as light as possible. Use the $\sigma_{f}-ho$ chart of Fig. 3.4 to select an appropriate class
Use the modulus-strength $E-\sigma_{f}$ chart of Fig. 3.5 to find materials that have $E>10 \mathrm{GPa}$ and $\sigma_{f}>1000 \mathrm{MPa}$.Fig. 3.5 1000 Modulus strength Metals and
The undercarriage of a cargo plane requires a metal with a compressive strength above $200 \mathrm{MPa}$ and a high bending strength per unit weight, requiring a high value of the index
Transport systems require materials that are stiff and strong, but at the same time are light and have enough toughness to survive accidental overloads and stress concentrations. Use the Specific
Is the fracture toughness, $K_{l c}$, of the common polymers polycarbonate, $\mathrm{ABS}$, or polystyrene larger or smaller than the engineering ceramic alumina, \(\mathrm{Al}_{2}
The bumpers of cars have to be tough and light. Compare the use of aluminium and of polypropylene for car bumpers. First read the approximate toughness, $G_{1 c}$ for the two materials from the
Use the fracture toughness-modulus chart (Fig. 3.7) to find materials that have a fracture toughness $K_{1 c}$ greater than $40 \mathrm{MPa} \cdot \mathrm{m}^{1 / 2}$ and a toughness \(G_{1

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