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engineering
machine elements in mechanical design

Materials Selection In Mechanical Design 5th Edition Michael F. Ashby - Solutions

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 thickness \(h\), at constant mass. The modulus \(E\) and strength \(\sigma_{f}\) of foams scale with
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 steel with a shape factor \(\phi_{B}^{e}\) of 20 , modulus \(E=210 \mathrm{GPa}\) and density
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 \(\phi_{B}^{e}=20\) is consistent with the idea that to minimize mass for a given stiffness one should
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 section modulus) made froma. 6061 grade aluminium alloy with a shape factor \(\phi_{B}^{f}\) of 3 ,
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 aluminium alloy beam of the same strength and \(\phi_{B}^{f}-\) is consistent with the idea that to
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 gravitational field, for example) packing can be loose-random, dense-random or close packed. Plot
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 \(4750 \mathrm{MPa}\). What is the maximum length \(\ell\) of fibre for useful strengthening?
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 are unique to the cell 24 bars that are shared between 2 cells } thus 24 bars, b, per cell 6 joints
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 volume fraction of nanotubes would be required to first allow conduction?
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 combination to be assessed. Four matrix materials are shown, highlighted in red. The materials
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 structures.Data From Fig, 12.2 LANSET FIGURE 12.2 Four configurations for a bridge. The design variables
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 -aluminium, magnesium and titanium - are shown in red. The materials shown in green are available as fibres
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 during a load-unload cycle.) Monolithic materials with low \(E\) have high \(\eta\), those with high
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 strength.b. Plot these on a copy of a modulus-density, a Strength-Density and Modulus-Strength chart (Figures
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 the density. How do they compare, using the flexural stiffness index \(E^{1 / 2} / ho\) as criterion
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 \(\sigma_{f}^{2 / 3} / ho\) (where \(\sigma_{f}\) is the failure stress) as criteria of excellence. The
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, and compare their energy-storing performance with that of natural materials, using the
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 material, read from Figure 13.15 of Chapter 13, Hybrids: Case Studies, onto a copy of the strength-density
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 of charts to explore what might be possible by hybridizing any pair of the materials listed below,
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 10 10 Longitudinal wave speed 10 ms 1 Rigid polymer foams 10-1 3x10 10-2 Foams 10 ms-1 10-33x102
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. 'Stiffer' means a higher value of Young's modulus.Data From Fig.3.3 Counges modulus density 1000
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 1000 100 110 10-2 Longitudinal wave speed 10 ms 3x103 Foams 10 ms- Rigid polymer foams 10-33x102
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 than steel.Fig.3.3 oungs modulusE GPa Coungos modulus density 1000 100 110 10-2 Longitudinal wave
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 Coungos modulus density 1000 100 110 10-2 Longitudinal wave speed 10 ms 3x103 Foams 10 ms- Rigid
Use the \(E / ho\) chart of Fig. 3.3 to identify materials with both \(E>100 \mathrm{GPa}\) and \(E^{1 / 3} / ho>0.003(\mathrm{GPa})^{1 / 3} /\left(\mathrm{kg} / \mathrm{m}^{3}\right)\). Remember that, on taking logs, the index \(M=E^{1 / 3} / ho\) becomes\[\log (E)=3 \log (ho)+3 \log
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 Longitudinal wave speed 10 ms 3x103 Foams 10 ms- Rigid polymer foams 10-33x102 10-4 10 10 ms 100 Diamond Al2Os
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 aircraft, mountain bikes). Use the \({ }_{f} / ho\) chart of Fig. 3.4 to decide.Fig. 3.4 10,000 T
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 of material to meet this need.Fig. 3.4 10,000 T Strength-density Metals and polymers: yield strength,
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 polymers: yield strength, dy Ceramics, glasses: modulus of rupture, MOR Elastomers: tensile tear
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 \(\sigma_{f}^{2 / 3} / ho\). What metals does the chart of Fig. 3.4 suggest?Fig. 3.4 10,000 Strength-density
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 modulus \(E / ho_{-}\)Specific strength \(\sigma_{f} / ho\) chart (Fig. 3.6) to identify materials that
Is the fracture toughness, \(K_{l c}\), of the common polymers polycarbonate, \(\mathrm{ABS}\), or polystyrene larger or smaller than the engineering ceramic alumina, \(\mathrm{Al}_{2} \mathrm{O}_{3}\) ? Are their toughness qualities \(G_{1 c}=K_{1 c}^{2} / E\) larger or smaller? The \(K_{l c}-E\)
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 chart of Fig. 3.7. Then divide each of these by the density of the material (read from any of 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 \(G_{1 c}=K_{1 c}^{2} / E\) (shown as contours on Fig. 3.7) greater than \(10 \mathrm{~kJ} /
The elastic deflection at fracture (the 'resilience') of an elastic-brittle solid is proportional to the failure strain, \(\varepsilon_{f r}=\sigma_{f r} / E\), where \(\sigma_{f r}\) is the stress that will cause a crack to propagate:\[\sigma_{f \mathrm{r}}=\frac{K_{1 c}}{\sqrt{\pi c}}\]Here
One criterion for design of a safe pressure vessel is that it should leak before it breaks: the leak can be detected and the pressure released. This is achieved by designing the vessel to tolerate a crack of length equal to the thickness \(t\) of the pressure vessel wall, without failing by fast
A material is required for the blade of a rotary lawnmower. Cost is a consideration. For safety reasons, the designer specified a minimum fracture toughness for the blade: it is \(K_{1 c}>30 \mathrm{MPa} \mathrm{m}^{1 / 2}\). The other mechanical requirement is for high hardness, \(H\), to
Bells ring because they have a low loss (or damping) coefficient, \(\eta\); a high damping gives a dead sound. Use the Loss coefficient-Modulus \((\eta-E)\) chart of Fig. 3.9 to identify material that should make good bells.Fig. 3.9 Loss coefficient, 17, at 30C 10 10 Neoprene Butyl rubber
A foundation is needed on which to mount vibration-sensitive measuring equipment. It is suggested that the foundation be made from concrete because of its ability to damp vibration. Is this assumption justified? Use Fig. 3.9 to find out.Fig. 3.9 Loss coefficient, 17, at 30C 10 10 Neoprene Butyl
The track of a tracked vehicle is made up of hardened steel segments bonded to rubber connectors. When the vehicle is in motion the rubber is subjected to a tension-compression cycle as the track passes over the front and rear drive sprockets. If the vehicle travels at \(20 \mathrm{kph}\), each
Use the Loss coefficient-Modulus ( \(\eta-E\) ) chart (Fig. 3.9) to find metals with the highest possible damping.Fig. 3.9 Loss coefficient, 17, at 30C 10 10 Neoprene Butyl rubber Elastomers Silicone Isoprene elastomers E = 0.04 GPa 10-1 Flexible polymer foams Foams 10-3 10-4 10-5 MFA 15 10-3
Use the Thermal conductivity-Electrical resistivity \(\left(\lambda-ho_{e}\right)\) chart (Fig. 3.10) to find three materials other than diamond with high thermal conductivity, \(\lambda\), and high electrical resistivity, \(ho_{e}\).Fig. 3.10 1012 1016 1020 10-8 1000 10-4 Electrical resistivity,
It is easier to measure the electrical resistivity of a metal than to measure its thermal conductivity. A new alloy has an electrical resistivity \(ho_{e}\) of \(55 \mu \Omega \mathrm{cm}\). Use the Wiedemann-Franz relationship, plotted on Fig. 3.10, to estimate its thermal conductivity,
A novel strontium-silica glass has a thermal conductivity \(\lambda\) of \(2.1 \mathrm{~W} / \mathrm{m} \mathrm{K}\) (exceptionally high for a glass). What, approximately, would you expect its thermal diffusivity \(a\) to be? Use the empirical relationship between \(\lambda\) and \(a\) to find out,
A new design of frying pan is made from glass ceramic 9606, a material with excellent thermal shock resistance originally developed for missile radomes. The pan bottom is \(4.2 \mathrm{~mm}\) thick. When placed on a gas cooker with a pat of butter in it, it is observed that it takes 7 seconds
The window through which the beam emerges from a high-powered laser must obviously be transparent to light. Even then, some of the energy of the beam is absorbed in the window and can cause it to heat and crack. This problem is minimized by choosing a window material with a high thermal
An external panel of a satellite is made of the Grade 9 titanium alloy Ti\(3 \mathrm{Al}-2 \mathrm{~V}\), with a yield strength \({ }_{\gamma}\) of \(550 \mathrm{MPa}\) and Poisson's ratio \(u\) of 0.36 . The panel heats up when the face of the satellite is directly exposed to the sun and cools
Use the Maximum service temperature ( \(T_{\max }\) ) chart (Fig. 3.14) to find polymers that can be used above \(200^{\circ} \mathrm{C}\).Fig. 3.14 Maximum service temperature (C) 2000 Max service temperature 1500 Tungsten alloys Nickel based superalloys 1000 500 Stainless steel Low alloy steel
Which class of magnets has the highest energy product? Which has the lowest? Use the chart of Remanent induction and Coercive force, Fig. 3.18, to find out.Fig. 3.18 Remanentinduction Br (7) 0.5 Remanent induction and coercive field Amorphous iron alloys Permalloy Ni-45% Fe Silicon iron Low carbon
If magneto strictive strain is a linear function of the field \(H\), what strain would appear in a Galfenol rod if it was subjected to a field of \(100 \mathrm{~A} / \mathrm{m}\) ? Use data read from the chart of Fig. 3.19 to find out.\(2.5 \times 10^{-4}(0.025 \%)\). A field of \(100 \mathrm{~A} /
a. Use the Young's modulus-Relative cost ( \(\left.E-C_{v, R}\right)\) chart (Fig. 3.26) to find the cheapest materials with a modulus, \(E\), greater than \(100 \mathrm{GPa}\).Fig. 3.26 1000 Modulus relative cost/vol 100 Young's modulus, E (GPa) 10 0.1 10 10 0.01 0.001 Nontechnical ceramics
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?
What is meant by a free variable? Give examples of free variables.
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?
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
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
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'.
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'.
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.
Formulate the constraints and objective you would associate with the choice of material to make the forks of a racing bicycle.
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 \(\mathrm{CD}\) cases that do not crack so easily. The case must
Ultraprecise bearings that allow a rocking motion make use of knife-edges 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
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
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
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
Aircraft and space structures make use of plates and shells. The index depends on the configuration. Here you are asked to derive the material index fora. a circular plate of radius \(a\) carrying a central load \(W\) with a prescribed stiffness \(S=W / \delta\) and of minimum mass andb. a
A furnace is required to sinter powder-metal parts. It operates continuously at \(650^{\circ} \mathrm{C}\) while the parts are fed through on a moving belt. You are asked to select a material for furnace insulation to minimize heat loss and thus to make the furnace as energy-efficient as possible.
A storage heater captures heat over a period of time, and then releases it, usually to an air stream, when required. Those for domestic heating store solar energy or energy from cheap off-peak electricity and release it slowly during the cold part of the day. What is a good material for the core of
Rework the storage heater of Exercise 4.17 to minimize the cost of the core instead of its volume.a. List the function, constraints, objective and free variable.b. Derive a material index for selecting the material for the heat storage material.Data From Exercise 4.17 E4.17. A storage heater
A clamp is required for processing of electronic components. The clamp has a square cross-section of width \(x\) and given depth \(b\). It is essential that the clamp have low thermal inertia so that it reaches temperature quickly. The time \(t\) it takes a component of thickness \(x\) to reach
In vehicle suspension design it is desirable to minimize the mass of all components. You have been asked to select a material and dimensions for a light spring to replace the steel leaf spring of an existing truck suspension. The existing leaf spring is a beam, shown schematically in the figure.
Long ago in the days of cathode-ray technology there were two types of cathode ray tube. In the older technology, colour separation was achieved by using a shadow mask: a thin metal plate with a grid of holes that allow only the correct beam to strike a red, green or blue phosphor. A shadow mask
This chapter introduced the families of processes with schematics of some of them. Good images of many processes can be found on the internet. Use the internet to find images for the following:a. Plastic film blowingb. Filament windingc. Additive manufactured. Metal spinninge. Spot weldingf.
The table lists properties of copper-nickel alloys from pure copper to pure nickel. Plot a trajectory of thermal conductivity against copper content. How do you explain the shape of the trajectory? Copper-Nickel Alloy Yield Strength (MPa) Fracture Toughness (MP a-m1/2) T-conductivity (W/mK) 100%
The table in Exercise E6.2 lists properties of copper-nickel alloys from pure copper to pure nickel. Plot trajectory of fracture toughness against yield strength.Data From Exercise E6.2 E6.2. Making property trajectories (1). The table lists properties of copper-nickel alloys from pure copper to
An aluminium alloy is sought for a demanding application. For safety reasons the designer has specified a minimum fracture toughness of \(30 \mathrm{MPa} \cdot \mathrm{m}^{1 / 2}\) and the highest possible strength. Use the property trajectory of Fig. 6.19 to select an alloy and a heat treatment
An approximate measure of the energy-absorbing capability of a metal is the product \(\sigma_{\gamma} \varepsilon_{f}\) of its yield strength \(\sigma_{y}\) and its elongation to fracture \(\varepsilon_{f}\). These two properties for copper and coppernickel alloys are the axes of Fig. 6.17. Plot
The CES EduPack ' 16 software contains sets of records for making process property charts. If this tool is available, use these record sets to plot the process-property trajectory fora. Thermal conductivity versus electrical resistivity for solution hardened copper as a function of solute
Even if you shut the windows and doors dust settles in rooms like gentle snow. The need: a device to remove dust from household floors. Here are three established concepts:1. human-powered bellows pump with cloth filter;2. axial-flow electric fan with muslin filter; 3. centrifugal fan with
Make a function-structure diagram for the Electrolux cleaner of Fig. E1.1.Data From Fig E1.1. FIGURE E1.1 Vacuum cleaners: a hand-powered cleaner from 1880, the Electrolux cylinder cleaner of 1960 and the Dyson centrifugal cleaner of 2010. Early cleaner courtesy Worcester News.
Microchips, particularly those for power electronics, get hot. If they get too hot they cease to function. The need: a scheme for removing heat from power microchips. One such scheme is sketched in Fig. E1.2. Its working principle is that of thermal conduction to fins from which heat is removed by
Make a function-structure diagram for the heat sinks.
The need: documents consisting of several pages can become confused if the pages are loose. Use the internet to explore alternative concepts for attaching a small number of pages together in a way that still allows them to be read. Record, as far as possible, the materials of the attachment and the
The speed of sound in Pyrex (borosilicate) glass is 5610 m/s. Find the density of this glass from Appendix A and use it to estimate the modulus E of Pyrex.
A cantilever beam has a length L=50 mm. It has a rectangular cross-section width b=5 mm and a thickness t=1 mm. It is made of an aluminium alloy. By how much will the end deflect under an end-load of F=5 N (roughly that exerted by the weight of 5 apples)? Use data from Appendix A4 for the (mean)
The wings of a glider are each 4 m long. The loadbearing member is the wing spar, a tubular beam running the length of the wing. The wing spar in this glider has a diameter of 140 mm and a wall thickness of 6 mm. It is made of an aluminum alloy. In flight the wing spar is loaded in bending with (we
A cantilever beam with length L=200 mm, width b=12 mm and thickness t=2 mm weighs 38 grams and has a natural vibration frequency of f=42 hertz. What is the modulus of the material of the beam? You will find equations for natural frequencies of vibration and moments of area in Appendix B, Tables B12
Exercise E2.4 used a natural vibration frequency to measure the modulus of a beam. Use the information in E2.4 to calculate the density of the beam, and then use this and the result of the exercise (the modulus of the beam) as a forensic tool. Scan the modulus values in Table A3 of Appendix A
A spring, wound from stainless steel wire with a wire diameter d=1 mm, has n=20 turns of radius R=10 mm. How much will it extend when loaded with a mass M of 1 kg? Assume the shear modulus G of stainless steel to be 3/8E where E is Young’s modulus, retrieve this from Appendix A3, and use the
A thick-walled tube has an inner radius ri = 10 mm and an outer radius r0 = 15 mm. It is made from polycarbonate, PC. What is the maximum torque Tf that the tube can carry without the onset of yield? Retrieve the (mean) yield strength of PC from Appendix A3, the expression for the torque at onset
A round bar, 20 mm in diameter, has a shallow circumferential notch with a depth with a root radius .The bar is made of a low carbon steel with a yield strength of . It is loaded axially with a nominal stress, (the axial load divided by the un-notched area). At what value of will yield first
An acrylic (PMMA) window is clamped in a thick low carbon steel frame at . The temperature falls to , putting the window under tension because the thermal expansion coefficient of PMMA is larger than that of steel. If the window was stress-free at 20°C, what stress does it carry at −20°C?
A flywheel with a radius R=200 mm is designed to spin up to 8000 rpm. It is proposed to make it out of ductile (nodular) cast iron, but the casting shop can guarantee only that it will have no crack-like flaws greater than 2a=2 mm in length. Use the expression for the maximum stress in a spinning
Liberty ships, thousands of which were constructed during World War II, were welded rather than riveted. Many were mistakenly made from a steel that became brittle at the temperatures of the Atlantic in winter. They had square hatches with sharp corners from which a crack could start and propagate
A clamp has a hemispherical contact face of radius R = 10mm to allow for misorientation. It is used to clamp a heavy lead archaeological treasure for X-ray examination. How much clamping force, F, can be applied without damage (meaning plastic deformation) to the treasured object? You will find the
You wish to measure, approximately, the thermal conductivity of polyethylene (PE). To do so you block one end of a PE pipe with a wall thickness of and diameter of 30 mm and fill it withboiling water while clutching the outside with your other hand. You note that the outer surface of the pipe first
A power transistor with an area of A of 1 mm2 dissipates 10 watts. It is attached to a heat sink 2 mm thick, effectively cooled to 30°C on the back face by forced airflow. If the heat sink is made of aluminium nitride, how hot will the microchip be at steady state? You will find equations of heat
The capacitance C of a condenser with two plates each of area A separated by a dielectric of thickness t iswhere is the permittivity of free space and is the dielectric constant of the material between the plates. Select a dielectric by scanning data in Appendix A, Tables A7 and Table A8, first
Piezoelectric materials respond to an electric field by change of shape. The strain induced by a field E is where is the piezoelectric charge coefficient, listed in Table A8. Its units are pm/V. A sample of soft PZT (lead zirconium titanite) is exposed to a field of 10 MV/m. How large is the
Remote, noncontact, temperature sensing is possible by focusing radiation from the source onto a pyroelectric material and by using the charge that appears on its surface as a measure of temperature. A sensor is required to measure temperature in the range 100–200°C. To work in this range the

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