Complete Case Studies
, LIBRARY OF CASE STUDIES
PROBLEM SOLUTIONS
Materials Selection for a Torsionally Stressed Cylindrical Shaft
CS1.D1 (a) Using the procedure outlined in this case study, ascertain which of the metal alloys listed in
Appendix B (of the textbook) have torsional strength performance indices greater than 10.0 (for f and in units
of MPa and g/cm3, respectively), and, in addition, shear strengths greater than 350 MPa. (b) Also using the cost
database in Appendix C of the textbook, conduct a cost analysis in the same manner as in this case study. For those
materials that satisfy the criteria noted in part (a), and, on the basis of this cost analysis, which material would
you select for a solid cylindrical shaft? Why?
Solution
(a) This portion of the problem asks for us to determine which of the materials listed in the database of
Appendix B have torsional strength performance indices greater than 10.0 (for f and in units of MPa and g/cm3,
respectively) and, in addition, shear strengths greater that 350 MPa. To begin, it is noted in Section CS1.2 that the
shear yield strength, f = 0.6y. On this basis, and given that (Equation CS1.9), it follows that
It is possible to expedite the materials selection process for this criterion using the “Engineering Material
Properties” component of VMSE as follows:
1. Click on “Engineering Materials Properties” near the bottom of the opening window.
2. In the window that appears, click on the “Show Combination/Ratio/Product” box.
3. In the next window that appears click on the “Ratio” box.
4. Click on the “Select property:” pull-down menu, and select “y (Yield Strength)” item. Then click on
the “Add display of selected property” box. Yield strength values of all materials will be displayed in the database
portion of the window.
5. Next, from the “Select property” pull-down menu, select “ (Density)”, and then click on the “Add
display of selected property” box. Density values of all materials will be displayed in the second column database
portion of the window.
6. There are two “Power for” boxes at the bottom of the top portion window—default values in these
boxes are “1.0”. The in the "Power for next-to-right-most-column" box enter “0.667” (the decimal equivalent for
Excerpts from this work may be reproduced by instructors for distribution on a not-for-profit basis for testing or instructional purposes only
to students enrolled in courses for which the textbook has been adopted. Any other reproduction or translation of this work beyond that
permitted by Sections 107 or 108 of the 1976 United States Copyright Act without the permission of the copyright owner is unlawful.
Complete Case Studies
,2/3rds), which is the exponent to which the first column entries (i.e., the yield strength values) will be taken. Leave
the default “1.0” in the "Power for right-most-column" box, since the exponent to which the density is to be taken
is “1.0”.
7. Now click on the “Take Ratio” button. The ratio is then displayed in the third database
column.
8. Values that appear in this column may be sorted from highest to lowest value by clicking on the “Ratio”
heading at the top of this column.
9. We want all metal alloys with ratios greater than 10.0. This means that we want to
select from the values tabulated those metals with values greater than .
Fifteen metal alloys are found to have ratios greater than 14.06; these are listed along with their
(0.6y)2/3/ and y values in the table below. [Note: it is necessary to manually calculate the (0.6y)2/3/ ratios.]
Alloy Condition y
Ti-6Al-4V Aged 17.14 1103
7075 Al T6 16.11 505
7075 Al T651 16.11 505
AZ31B Mg Rolled 14.65 220
Ti-6Al-4V Annealed 14.18 830
AZ31B Mg Extruded 13.75 200
Ti-5Al-2.5Sn Annealed 13.22 760
440A Stainless Q/T, 315C 12.73 1650
2024 Al T3 12.63 345
4340 Steel Q/T, 315C 12.50 1620
4140 Steel Q/T, 315ºC 12.24 1570
2024 Al T351 12.13 325
6061 Al T6 11.16 276
6061 Al T651 11.16 276
17-7PH Stainless PH, 510ºC 11.13 1310
Excerpts from this work may be reproduced by instructors for distribution on a not-for-profit basis for testing or instructional purposes only
to students enrolled in courses for which the textbook has been adopted. Any other reproduction or translation of this work beyond that
permitted by Sections 107 or 108 of the 1976 United States Copyright Act without the permission of the copyright owner is unlawful.
Complete Case Studies
, Now, the second criterion calls for the material to have a shear strength greater than 350 MPa. Again,
since y = f /0.6, the minimum yield strength required is y = 350 MPa/0.6, or y = 583 MPa. Values of y from
the database are also given in this table. It is noted that all aluminum and magnesium alloys are eliminated on the
basis of this second criterion.
(b) This portion of the problem calls for us to conduct a cost analysis for these seven remaining alloys.
2/3
Below is given a tabulation of values for /(0.6y) , relative cost (as taken from Appendix C), and the product
of these two parameters. (It should be noted that no values of are given for five of these materials.) The three
remaining materials are ranked on the basis of cost, from least to most expensive.
Alloy Condition c
17-7PH Stain. PH 0.090 7.1 0.64
Ti-6Al-4V Annealed 0.0705 35.3 2.49
Ti-5Al-2.5Sn Annealed 0.0756 45.7 3.45
Thus, the 17-7PH stainless steel is the overwhelming choice of the three materials for which cost data are given
since it has the lowest value for the product.
It is up to the student to select the best metal alloy to be used for this solid cylindrical shaft (and then to
justify this selection).
Excerpts from this work may be reproduced by instructors for distribution on a not-for-profit basis for testing or instructional purposes only
to students enrolled in courses for which the textbook has been adopted. Any other reproduction or translation of this work beyond that
permitted by Sections 107 or 108 of the 1976 United States Copyright Act without the permission of the copyright owner is unlawful.
Complete Case Studies
, LIBRARY OF CASE STUDIES
PROBLEM SOLUTIONS
Materials Selection for a Torsionally Stressed Cylindrical Shaft
CS1.D1 (a) Using the procedure outlined in this case study, ascertain which of the metal alloys listed in
Appendix B (of the textbook) have torsional strength performance indices greater than 10.0 (for f and in units
of MPa and g/cm3, respectively), and, in addition, shear strengths greater than 350 MPa. (b) Also using the cost
database in Appendix C of the textbook, conduct a cost analysis in the same manner as in this case study. For those
materials that satisfy the criteria noted in part (a), and, on the basis of this cost analysis, which material would
you select for a solid cylindrical shaft? Why?
Solution
(a) This portion of the problem asks for us to determine which of the materials listed in the database of
Appendix B have torsional strength performance indices greater than 10.0 (for f and in units of MPa and g/cm3,
respectively) and, in addition, shear strengths greater that 350 MPa. To begin, it is noted in Section CS1.2 that the
shear yield strength, f = 0.6y. On this basis, and given that (Equation CS1.9), it follows that
It is possible to expedite the materials selection process for this criterion using the “Engineering Material
Properties” component of VMSE as follows:
1. Click on “Engineering Materials Properties” near the bottom of the opening window.
2. In the window that appears, click on the “Show Combination/Ratio/Product” box.
3. In the next window that appears click on the “Ratio” box.
4. Click on the “Select property:” pull-down menu, and select “y (Yield Strength)” item. Then click on
the “Add display of selected property” box. Yield strength values of all materials will be displayed in the database
portion of the window.
5. Next, from the “Select property” pull-down menu, select “ (Density)”, and then click on the “Add
display of selected property” box. Density values of all materials will be displayed in the second column database
portion of the window.
6. There are two “Power for” boxes at the bottom of the top portion window—default values in these
boxes are “1.0”. The in the "Power for next-to-right-most-column" box enter “0.667” (the decimal equivalent for
Excerpts from this work may be reproduced by instructors for distribution on a not-for-profit basis for testing or instructional purposes only
to students enrolled in courses for which the textbook has been adopted. Any other reproduction or translation of this work beyond that
permitted by Sections 107 or 108 of the 1976 United States Copyright Act without the permission of the copyright owner is unlawful.
Complete Case Studies
,2/3rds), which is the exponent to which the first column entries (i.e., the yield strength values) will be taken. Leave
the default “1.0” in the "Power for right-most-column" box, since the exponent to which the density is to be taken
is “1.0”.
7. Now click on the “Take Ratio” button. The ratio is then displayed in the third database
column.
8. Values that appear in this column may be sorted from highest to lowest value by clicking on the “Ratio”
heading at the top of this column.
9. We want all metal alloys with ratios greater than 10.0. This means that we want to
select from the values tabulated those metals with values greater than .
Fifteen metal alloys are found to have ratios greater than 14.06; these are listed along with their
(0.6y)2/3/ and y values in the table below. [Note: it is necessary to manually calculate the (0.6y)2/3/ ratios.]
Alloy Condition y
Ti-6Al-4V Aged 17.14 1103
7075 Al T6 16.11 505
7075 Al T651 16.11 505
AZ31B Mg Rolled 14.65 220
Ti-6Al-4V Annealed 14.18 830
AZ31B Mg Extruded 13.75 200
Ti-5Al-2.5Sn Annealed 13.22 760
440A Stainless Q/T, 315C 12.73 1650
2024 Al T3 12.63 345
4340 Steel Q/T, 315C 12.50 1620
4140 Steel Q/T, 315ºC 12.24 1570
2024 Al T351 12.13 325
6061 Al T6 11.16 276
6061 Al T651 11.16 276
17-7PH Stainless PH, 510ºC 11.13 1310
Excerpts from this work may be reproduced by instructors for distribution on a not-for-profit basis for testing or instructional purposes only
to students enrolled in courses for which the textbook has been adopted. Any other reproduction or translation of this work beyond that
permitted by Sections 107 or 108 of the 1976 United States Copyright Act without the permission of the copyright owner is unlawful.
Complete Case Studies
, Now, the second criterion calls for the material to have a shear strength greater than 350 MPa. Again,
since y = f /0.6, the minimum yield strength required is y = 350 MPa/0.6, or y = 583 MPa. Values of y from
the database are also given in this table. It is noted that all aluminum and magnesium alloys are eliminated on the
basis of this second criterion.
(b) This portion of the problem calls for us to conduct a cost analysis for these seven remaining alloys.
2/3
Below is given a tabulation of values for /(0.6y) , relative cost (as taken from Appendix C), and the product
of these two parameters. (It should be noted that no values of are given for five of these materials.) The three
remaining materials are ranked on the basis of cost, from least to most expensive.
Alloy Condition c
17-7PH Stain. PH 0.090 7.1 0.64
Ti-6Al-4V Annealed 0.0705 35.3 2.49
Ti-5Al-2.5Sn Annealed 0.0756 45.7 3.45
Thus, the 17-7PH stainless steel is the overwhelming choice of the three materials for which cost data are given
since it has the lowest value for the product.
It is up to the student to select the best metal alloy to be used for this solid cylindrical shaft (and then to
justify this selection).
Excerpts from this work may be reproduced by instructors for distribution on a not-for-profit basis for testing or instructional purposes only
to students enrolled in courses for which the textbook has been adopted. Any other reproduction or translation of this work beyond that
permitted by Sections 107 or 108 of the 1976 United States Copyright Act without the permission of the copyright owner is unlawful.
Complete Case Studies
