67
Important Equations Used in This Chapter
See the referenced sections for information on the proper use of these equations.
2
Axial tensile stress (Section 2.1):
P
=
(2.1 a)
Ao
Axial tensile strain (Section 2.1):
l − l
=
o
(2.1 b)
lo
Modulus of elasticity (Young’s modulus) (Section 2.1):
E =
(2.2)
Modulus of rigidity (Section 2.1):
E
G =
(2.4)
2(1 + )
Ultimate shear strength (Section 2.1):
steels :
S
us 0.80 Sut
(2.5 b)
other ductile metals :
S
us 0.75 Sut
Shear yield strength (Section 2.1):
U = d
(2.6)
0
Modulus of resilience (Section 2.1):
1 S 2
y
U
(2.7)
R
2 E
Modulus of toughness (Section 2.1):
S +
y Sut
U
(2.8)
T
2
f
Arithmetic mean (Section 2.2):
n
1
= x
(2.9b)
i
n i =1
Standard deviation (Section 2.2):
n
1
2
Sd =
( x −
(2.9c)
i )
n - 1 i =1
68
MACHINE DESIGN -
An Integrated Approach
Ultimate tensile strength as a function of Brinell hardness (Section 2.4): S
ut 500 HB 30 HB psi
2
(2.10)
S
ut 3.45 HB 0.2 HB MPa
2.10 REFERENCES
1 E. B. Haugen and P. H. Wirsching, “Probabilistic Design.” Machine Design, v. 47, nos.
10-14, Penton Publishing, Cleveland, Ohio, 1975.
2 H. E. Boyer and T. L. Gall, eds. Metals Handbook. Vol. 1. American Society for Metals: Metals Park, Ohio, 1985.
3 M. F. Ashby, Materials Selection in Mechanical Design, 2ed., Butterworth and Heinemann, 1999.
2.11 WEB REFERENCES
The web is a useful resource for up-to-date material property information at these and other sites that can be found with a search engine.
Properties data sheets for over 41,000 metals, plastics, ceramics, and composites.
Material properties and data.
2.12 BIBLIOGRAPHY
For general information on materials, consult the following: Metals & Alloys in the Unified Numbering System. 6th ed. ASTM/SAE: Philadelphia, Pa., 1994.
Brady, ed. Materials Handbook. 13th ed. McGraw-Hill: New York. 1992.
H. E. Boyer, ed. Atlas of Stress-Strain Curves. Amer. Soc. for Metals: Metals Park, Ohio, 1987.
K. Budinski, Engineering Materials: Properties and Selection. 4th ed. Reston-Prentice-Hall: Reston, Va., 1992.
M. M. Farag, Selection of Materials and Manufacturing Processes for Engineering Design. Prentice-Hall International: Hertfordshire, U.K., 1989.
I. Granet, Modern Materials Science. Reston-Prentice-Hall: Reston, Va., 1980.
H. W. Pollack, Materials Science and Metallurgy. 2nd ed. Reston-Prentice-Hall: Reston, Va., 1977.
S. P. Timoshenko, History of Strength of Materials. McGraw-Hill: New York, 1983.
L. H. V. Vlack, Elements of Material Science and Engineering. 6th ed. Addison-Wesley: Reading, Mass., 1989.
M. M. Schwartz, ed. Handbook of Structural Ceramics. McGraw-Hill: New York. 1984.