For an axially loaded rod, prove that b 5 1 for the Ebyr

Determine the tensile and yield strengths for the following materials: (a) UNS G10200 hot-rolled steel. (b) SAE 1050 cold-drawn steel. (c) AISI 1141 steel quenched and tempered at 540C. (d) 2024-T4 aluminum alloy. (e) Ti-6Al-4V annealed titanium alloy.

Assume you were specifying an AISI 1060 steel for an application. Using Table A21, (a) how would you specify it if you desired to maximize the yield strength? (b) how would you specify it if you desired to maximize the ductility?

Determine the yield strength-to-density ratios (specific strength) in units of kN ? m/kg for AISI 1018 CD steel, 2011-T6 aluminum, Ti-6Al-4V titanium alloy, and ASTM No. 40 gray cast iron

Determine the stiffness-to-weight density ratios (specific modulus) in units of inches for AISI 1018 CD steel, 2011-T6 aluminum, Ti-6Al-4V titanium alloy, and ASTM No. 40 gray cast iron.

Poissons ratio n is a material property and is the ratio of the lateral strain and the longitudinal strain for a member in tension. For a homogeneous, isotropic material, the modulus of rigidity G is related to Youngs modulus as G 5 E 2(1 1 n) Using the tabulated values of G and E in Table A5, calculate Poissons ratio for steel, aluminum, beryllium copper, and gray cast iron. Determine the percent difference between the calculated values and the values tabulated in Table A5.

A specimen of steel having an initial diameter of 0.503 in was tested in tension using a gauge length of 2 in. The following data were obtained for the elastic and plastic states:

Compute the true stress and the logarithmic strain using the data of Prob. 26 and plot the results on log-log paper. Then find the plastic strength coefficient s0 and the strain-strengthening exponent m. Find also the yield strength and the ultimate strength after the specimen has had 20 percent cold work.

The stress-strain data from a tensile test on a cast-iron specimen are

A part made from annealed AISI 1018 steel undergoes a 20 percent cold-work operation. (a) Obtain the yield strength and ultimate strength before and after the cold-work operation. Determine the percent increase in each strength. (b) Determine the ratios of ultimate strength to yield strength before and after the cold-work operation. What does the result indicate about the change of ductility of the part?

Repeat Prob. 29 for a part made from hot-rolled AISI 1212 steel.

Repeat Prob. 29 for a part made from 2024-T4 aluminum alloy.

A steel member has a Brinell of HB 5 275. Estimate the ultimate strength of the steel in MPa.

A gray cast iron part has a Brinell hardness number of HB 5 200. Estimate the ultimate strength of the part in kpsi. Make a reasonable assessment of the likely grade of cast iron by comparing both hardness and strength to material options in Table A24.

A part made from 1040 hot-rolled steel is to be heat treated to increase its strength to approximately 100 kpsi. What Brinell hardness number should be expected from the heat-treated part?

Brinell hardness tests were made on a random sample of 10 steel parts during processing. The results were HB values of 230, 232(2), 234, 235(3), 236(2), and 239. Estimate the mean and standard deviation of the ultimate strength in kpsi.

Repeat Prob. 215 assuming the material to be cast iron.

For the material in Prob. 26: (a) Determine the modulus of resilience, and (b) Estimate the modulus of toughness, assuming that the last data point corresponds to fracture.

Some commonly used plain carbon steels are AISI 1010, 1018, and 1040. Research these steels and provide a comparative summary of their characteristics, focusing on aspects that make each one unique for certain types of application. Product application guides provided on the Internet by steel manufacturers and distributors are one source of information.

Repeat Prob. 218 for the commonly used alloy steels, AISI 4130 and 4340.

An application requires the support of an axial load of 100 kips with a round rod without exceeding the yield strength of the material. Assume the current cost per pound for round stock is given in the table below for several materials that are being considered. Material properties are available in Tables A5, A20, A21, and A24. Select one of the materials for each of the following additional design goals. (a) Minimize diameter. (b) Minimize weight. (c) Minimize cost. (d) Minimize axial deflection

A 1-in-diameter rod, 3 ft long, of unknown material is found in a machine shop. A variety of inexpensive nondestructive tests are readily available to help determine the material, as described below: (a) Visual inspection. (b) Scratch test: Scratch the surface with a file; observe color of underlying material and depth of scratch. (c) Check if it is attracted to a magnet. (d) Measure weight (60.05 lbf). (e) Inexpensive bending deflection test: Clamp one end in a vise, leaving 24 in cantilevered. Apply a force of 100 lbf (61 lbf). Measure deflection of the free end (within 61y32 in). ( f) Brinell hardness test. Choose which tests you would actually perform, and in what sequence, to minimize time and cost, but to determine the material with a reasonable level of confidence. The table below provides results that would be available to you if you choose to perform a given test. Explain your process, and include any calculations. You may assume the material is one listed in Table A5. If it is carbon steel, try to determine an approximate specification from Table A20.

A 1-in-diameter rod, 3 ft long, of unknown material is found in a machine shop. A variety of inexpensive nondestructive tests are readily available to help determine the material, as described below: (a) Visual inspection. (b) Scratch test: Scratch the surface with a file; observe color of underlying material and depth of scratch. (c) Check if it is attracted to a magnet. (d) Measure weight (60.05 lbf). (e) Inexpensive bending deflection test: Clamp one end in a vise, leaving 24 in cantilevered. Apply a force of 100 lbf (61 lbf). Measure deflection of the free end (within 61y32 in). ( f) Brinell hardness test. Choose which tests you would actually perform, and in what sequence, to minimize time and cost, but to determine the material with a reasonable level of confidence. The table below provides results that would be available to you if you choose to perform a given test. Explain your process, and include any calculations. You may assume the material is one listed in Table A5. If it is carbon steel, try to determine an approximate specification from Table A20.

A 1-in-diameter rod, 3 ft long, of unknown material is found in a machine shop. A variety of inexpensive nondestructive tests are readily available to help determine the material, as described below: (a) Visual inspection. (b) Scratch test: Scratch the surface with a file; observe color of underlying material and depth of scratch. (c) Check if it is attracted to a magnet. (d) Measure weight (60.05 lbf). (e) Inexpensive bending deflection test: Clamp one end in a vise, leaving 24 in cantilevered. Apply a force of 100 lbf (61 lbf). Measure deflection of the free end (within 61y32 in). ( f) Brinell hardness test. Choose which tests you would actually perform, and in what sequence, to minimize time and cost, but to determine the material with a reasonable level of confidence. The table below provides results that would be available to you if you choose to perform a given test. Explain your process, and include any calculations. You may assume the material is one listed in Table A5. If it is carbon steel, try to determine an approximate specification from Table A20.

Search the website noted in Sec. 220 (http://composite.about.com/cs/software/) and report your findings. Your instructor may wish to elaborate on the level of this report. The website contains a large variety of resources. The activity for this problem can be divided among the class.

Research the material Inconel, briefly described in Table A5. Compare it to various carbon and alloy steels in stiffness, strength, ductility, and toughness. What makes this material so special?

Consider a rod transmitting a tensile force. The following materials are being considered: tungsten carbide, zinc alloy, polycarbonate polymer, and aluminum alloy. Using the Ashby charts, recommend the best material for a design situation in which failure is by exceeding the strength of the material, and it is desired to minimize the weight.

Repeat Prob. 226, except that the design situation is failure by excessive deflection, and it is desired to minimize the weight

Consider a cantilever beam that is loaded with a transverse force at its tip. The following materials are being considered: tungsten carbide, high-carbon heat-treated steel, polycarbonate polymer, and aluminum alloy. Using the Ashby charts, recommend the best material for a design situation in which failure is by exceeding the strength of the material and it is desired to minimize the weight.

Repeat Prob. 228, except that the design situation is failure by excessive deflection, and it is desired to minimize the weight

For an axially loaded rod, prove that b 5 1 for the Eb yr guidelines in Fig. 216

For an axially loaded rod, prove that b 5 1 for the Sb yr guidelines in Fig. 219

For a cantilever beam loaded in bending, prove that b 5 1y2 for the Eb yr guidelines in Fig. 216.

For a cantilever beam loaded in bending, prove that b 5 2y3 for the Sb yr guidelines in Fig. 219.

Consider a tie rod transmitting a tensile force F. The corresponding tensile stress is given by s 5 FyA, where A is the area of the cross section. The deflection of the rod is given by Eq. (43), which is d 5 (Fl)y(AE), where l is the length of the rod. Using the Ashby charts of Figs. 216 and 219, explore what ductile materials are best suited for a light, stiff, and strong tie rod. Hint: Consider stiffness and strength separately.

Repeat Prob. 113. Does the data reflect the number found in part (b)? If not, why? Plot a histogram of the data. Presuming the distribution is normal, plot Eq. (14) and compare it with the histogram

Determine the tensile and yield strengths for the following materials: (a) UNS G10200 hot-rolled steel. (b) SAE 1050 cold-drawn steel. (c) AISI 1141 steel quenched and tempered at \(540^{\circ} \mathrm{C}\). (d) 2024-T4 aluminum alloy. (e) Ti-6 \(\mathrm{Al}-4 \mathrm{~V}\) annealed titanium alloy.

Assume you were specifying an AISI 1060 steel for an application. Using Table A-21, (a) how would you specify it if you desired to maximize the yield strength? (b) how would you specify it if you desired to maximize the ductility?

Determine the yield strength-to-density ratios (specific strength) in units of \(\mathrm{kN} \cdot \mathrm{m} / \mathrm{kg}\) for AISI 1018 CD steel, 2011-T6 aluminum, Ti-6Al-4V titanium alloy, and ASTM No. 40 gray cast iron.

Determine the stiffness-to-weight density ratios (specific modulus) in units of inches for AISI 1018 CD steel, 2011-T6 aluminum, Ti-6Al-4V titanium alloy, and ASTM No. 40 gray cast iron.

Poisson's ratio \(\nu\) is a material property and is the ratio of the lateral strain and the longitudinal strain for a member in tension. For a homogeneous, isotropic material, the modulus of rigidity G is related to Young's modulus as \(G=\frac{E}{2(1+\nu)}\) Using the tabulated values of G and E in Table A-5, calculate Poisson's ratio for steel, aluminum, beryllium copper, and gray cast iron. Determine the percent difference between the calculated values and the values tabulated in Table A-5.

A specimen of steel having an initial diameter of 0.503 in was tested in tension using a gauge length of 2 in. The following data were obtained for the elastic and plastic states: Note that there is some overlap in the data. (a) Plot the engineering or nominal stress-strain diagram using two scales for the unit strain \(\epsilon\), one scale from zero to about 0.02 in/in and the other scale from zero to maximum strain. (b) From this diagram find the modulus of elasticity, the 0.2 percent offset yield strength, the ultimate strength, and the percent reduction in area. (c) Characterize the material as ductile or brittle. Explain your reasoning. (d) Identify a material specification from Table A-20 that has a reasonable match to the data.

Compute the true stress and the logarithmic strain using the data of Prob. 2-6 and plot the results on log-log paper. Then find the plastic strength coefficient \(\sigma_0\) and the strain-strengthening exponent m. Find also the yield strength and the ultimate strength after the specimen has had 20 percent cold work.

The stress-strain data from a tensile test on a cast-iron specimen are Plot the stress-strain locus and find the 0.1 percent offset yield strength, and the tangent modulus of elasticity at zero stress and at 20 kpsi.

A part made from annealed AISI 1018 steel undergoes a 20 percent cold-work operation. (a) Obtain the yield strength and ultimate strength before and after the cold-work operation. Determine the percent increase in each strength. (b) Determine the ratios of ultimate strength to yield strength before and after the cold-work operation. What does the result indicate about the change of ductility of the part?

Repeat Prob. 2-9 for a part made from hot-rolled AISI 1212 steel.

Repeat Prob. 2-9 for a part made from 2024-T4 aluminum alloy.

A steel member has a Brinell of \(H_B=275\0. Estimate the ultimate strength of the steel in MPa.

A gray cast iron part has a Brinell hardness number of \(H_B=200$\). Estimate the ultimate strength of the part in kpsi. Make a reasonable assessment of the likely grade of cast iron by comparing both hardness and strength to material options in Table A-24.

A part made from 1040 hot-rolled steel is to be heat treated to increase its strength to approximately 100 kpsi. What Brinell hardness number should be expected from the heat-treated part?

Brinell hardness tests were made on a random sample of 10 steel parts during processing. The results were \(H_B\) values of 230,232(2), 234,235(3), 236(2), and 239 . Estimate the mean and standard deviation of the ultimate strength in kpsi.

Repeat Prob. 2-15 assuming the material to be cast iron.

For the material in Prob. 2-6: (a) Determine the modulus of resilience, and (b) Estimate the modulus of toughness, assuming that the last data point corresponds to fracture.

Some commonly used plain carbon steels are AISI 1010, 1018, and 1040. Research these steels and provide a comparative summary of their characteristics, focusing on aspects that make each one unique for certain types of application. Product application guides provided on the Internet by steel manufacturers and distributors are one source of information.

Repeat Prob. 2-18 for the commonly used alloy steels, AISI 4130 and 4340.

An application requires the support of an axial load of 100 kips with a round rod without exceeding the yield strength of the material. Assume the current cost per pound for round stock is given in the table below for several materials that are being considered. Material properties are available in Tables A-5, A-20, A-21, and A-24. Select one of the materials for each of the following additional design goals. (a) Minimize diameter. (b) Minimize weight. (c) Minimize cost. (d) Minimize axial deflection.

A 1-in-diameter rod, 3 ft long, of unknown material is found in a machine shop. A variety of 2-23 inexpensive nondestructive tests are readily available to help determine the material, as described below: (a) Visual inspection. (b) Scratch test: Scratch the surface with a file; observe color of underlying material and depth of scratch. (c) Check if it is attracted to a magnet. (d) Measure weight \((\pm 0.05 \mathrm{lbf})\). (e) Inexpensive bending deflection test: Clamp one end in a vise, leaving 24 in cantilevered. Apply a force of \(100 \mathrm{lbf}(\pm 1 \mathrm{lbf})\). Measure deflection of the free end (within \(\pm 1 / 32 \mathrm{in})\). (f) Brinell hardness test. Choose which tests you would actually perform, and in what sequence, to minimize time and cost, but to determine the material with a reasonable level of confidence. The table below provides results that would be available to you if you choose to perform a given test. Explain your process, and include any calculations. You may assume the material is one listed in Table A-5. If it is carbon steel, try to determine an approximate specification from Table A-20.

A 1-in-diameter rod, 3 ft long, of unknown material is found in a machine shop. A variety of 2-23 inexpensive nondestructive tests are readily available to help determine the material, as described below: (a) Visual inspection. (b) Scratch test: Scratch the surface with a file; observe color of underlying material and depth of scratch. (c) Check if it is attracted to a magnet. (d) Measure weight \((\pm 0.05 \mathrm{lbf})\). (e) Inexpensive bending deflection test: Clamp one end in a vise, leaving 24 in cantilevered. Apply a force of \(100 \mathrm{lbf}(\pm 1 \mathrm{lbf})\). Measure deflection of the free end (within \(\pm 1 / 32 \mathrm{in})\). (f) Brinell hardness test. Choose which tests you would actually perform, and in what sequence, to minimize time and cost, but to determine the material with a reasonable level of confidence. The table below provides results that would be available to you if you choose to perform a given test. Explain your process, and include any calculations. You may assume the material is one listed in Table A-5. If it is carbon steel, try to determine an approximate specification from Table A-20.

A 1-in-diameter rod, 3 ft long, of unknown material is found in a machine shop. A variety of 2-23 inexpensive nondestructive tests are readily available to help determine the material, as described below: (a) Visual inspection. (b) Scratch test: Scratch the surface with a file; observe color of underlying material and depth of scratch. (c) Check if it is attracted to a magnet. (d) Measure weight \((\pm 0.05 \mathrm{lbf})\). (e) Inexpensive bending deflection test: Clamp one end in a vise, leaving 24 in cantilevered. Apply a force of \(100 \mathrm{lbf}(\pm 1 \mathrm{lbf})\). Measure deflection of the free end (within \(\pm 1 / 32 \mathrm{in})\). (f) Brinell hardness test. Choose which tests you would actually perform, and in what sequence, to minimize time and cost, but to determine the material with a reasonable level of confidence. The table below provides results that would be available to you if you choose to perform a given test. Explain your process, and include any calculations. You may assume the material is one listed in Table A-5. If it is carbon steel, try to determine an approximate specification from Table A-20.

Search the website noted in Sec. 2-20 (http://composite.about.com/cs/software/) and report your findings. Your instructor may wish to elaborate on the level of this report. The website contains a large variety of resources. The activity for this problem can be divided among the class.

Research the material Inconel, briefly described in Table A-5. Compare it to various carbon and alloy steels in stiffness, strength, ductility, and toughness. What makes this material so special?

Consider a rod transmitting a tensile force. The following materials are being considered: tungsten carbide, zinc alloy, polycarbonate polymer, and aluminum alloy. Using the Ashby charts, recommend the best material for a design situation in which failure is by exceeding the strength of the material, and it is desired to minimize the weight.

Repeat Prob. 2–26, except that the design situation is failure by excessive deflection, and it is desired to minimize the weight.

Consider a cantilever beam that is loaded with a transverse force at its tip. The following materials are being considered: tungsten carbide, high-carbon heat-treated steel, polycarbonate polymer, and aluminum alloy. Using the Ashby charts, recommend the best material for a design situation in which failure is by exceeding the strength of the material and it is desired to minimize the weight.

Repeat Prob. 2-28, except that the design situation is failure by excessive deflection, and it is desired to minimize the weight.

For an axially loaded rod, prove that \(\beta=1\) for the \(E^\beta / \rho\) guidelines in Fig. 2-16.

For an axially loaded rod, prove that \(\beta=1\) for the \(S^\beta / \rho\) guidelines in Fig. 2-19.

For a cantilever beam loaded in bending, prove that \(\beta=1 / 2\) for the \(E^\beta / \rho\) guidelines in Fig. 2-16.

For a cantilever beam loaded in bending, prove that \(\beta=2 / 3\) for the \(S^\beta / \rho\) guidelines in Fig. 2-19.

Consider a tie rod transmitting a tensile force F. The corresponding tensile stress is given by \(\sigma=F / A\), where A is the area of the cross section. The deflection of the rod is given by Eq. (4-3), which is \(\delta=(F l) /(A E)\), where l is the length of the rod. Using the Ashby charts of Figs. 2-16 and 2-19, explore what ductile materials are best suited for a light, stiff, and strong tie rod. Hint: Consider stiffness and strength separately.

Repeat Prob. 1-13. Does the data reflect the number found in part (b)? If not, why? Plot a histogram of the data. Presuming the distribution is normal, plot Eq. (1-4) and compare it with the histogram.