### STRENGTH OF MATERIALS

Introduction
Strength of materials deals with the relations between the external forces applied to elastic bodies and the resulting deformations and stresses. In the design of structures and machines, the application of the principles of strength of materials is necessary if satisfactory materials are to be utilized and adequate proportions obtained to resist functional forces.

Forces are produced by the action of gravity, by accelerations and impacts of moving
parts, by gasses and fluids under pressure, by the transmission of mechanical power, etc. In order to analyze the stresses and deflections of a body, the magnitudes, directions and points of application of forces acting on the body must be known. Information given in the Mechanics section provides the basis for evaluating force systems.

The time element in the application of a force on a body is an important consideration.

Thus a force may be static or change so slowly that its maximum value can be treated as if it were static; it may be suddenly applied, as with an impact; or it may have a repetitive or cyclic behavior.

The environment in which forces act on a machine or part is also important. Such factors as high and low temperatures; the presence of corrosive gases, vapors and liquids; radiation, etc. may have a marked effect on how well parts are able to resist stresses.

Throughout the Strength of Materials section in this Handbook, both English and
metric SI data and formulas are given to cover the requirements of working in either
system of measurement. Formulas and text relating exclusively to SI units are given
in bold-face type.

Mechanical Properties of Materials.—Many mechanical properties of materials are
determined from tests, some of which give relationships between stresses and strains as shown by the curves in the accompanying figures.

Stress is force per unit area and is usually expressed in pounds per square inch. If the
stress tends to stretch or lengthen the material, it is called tensile stress; if to compress or shorten the material, a compressive stress; and if to shear the material, a shearing stress.

Tensile and compressive stresses always act at right-angles to (normal to) the area being considered; shearing stresses are always in the plane of the area (at right-angles to compressive or tensile stresses).

Fig. 1. Stress-strain curves
In the SI, the unit of stress is the pascal (Pa), the newton per meter squared (N/m2).
The megapascal (newtons per millimeter squared) is often an appropriate sub-multiple for use in practice.

Unit strain is the amount by which a dimension of a body changes when the body is subjected to a load, divided by the original value of the dimension. The simpler term strain is often used instead of unit strain.

Proportional limit is the point on a stress-strain curve at which it begins to deviate from the straight-line relationship between stress and strain.

Elastic limit is the maximum stress to which a test specimen may be subjected and still return to its original length upon release of the load. A material is said to be stressed within the elastic region when the working stress does not exceed the elastic limit, and to be stressed in the plastic region when the working stress does exceed the elastic limit.

The elastic limit for steel is for all practical purposes the same as its proportional limit.

Yield point is a point on the stress-strain curve at which there is a sudden increase in strain without a corresponding increase in stress. Not all materials have a yield point. Some representative values of the yield point (in ksi) are as follows:

Yield strength, Sy, is the maximum stress that can be applied without permanent deformation of the test specimen. This is the value of the stress at the elastic limit for materials for which there is an elastic limit. Because of the difficulty in determining the elastic limit, and because many materials do not have an elastic region, yield strength is often determined by the offset method as illustrated by the accompanying.

Yield strength in such a case is the stress value on the stress-strain curve corresponding to a definite amount of permanent set or strain, usually 0.1 or 0.2 per cent of the original dimension.

Yield strength data for various materials are given in tables starting on pages 417, 419, 463, 464, 466, 468, 472, 554, 556, 560, 569, 570, 575, 580, 588, 590, 591, and elsewhere.

Ultimate strength, Su, (also called tensile strength) is the maximum stress value obtained on a stress-strain curve.
Modulus of elasticity, E, (also called Young's modulus) is the ratio of unit stress to unitstrain within the proportional limit of a material in tension or compression. Some representative values of Young's modulus (in 106 psi) are as follows:

Modulus of elasticity in shear, G, is the ratio of unit stress to unit strain within the proportional limit of a material in shear.
Poisson's ratio, μ, is the ratio of lateral strain to longitudinal strain for a given material
subjected to uniform longitudinal stresses within the proportional limit. The term is found in certain equations associated with strength of materials. Values of Poisson's ratio for common materials are as follows:

Aluminum, wrought, 2014-T6 60                            Titanium, pure 55–70
Aluminum, wrought, 6061-T6 35                                  Titanium, alloy, 5Al, 2.5Sn 110

Beryllium copper 140
Steel for bridges and buildings,ASTM A7-61T, all shapes 33

Brass, naval 25–50
Cast iron, malleable 32–45

Steel, castings, high strength, for structural purposes,
ASTM A148.60 (seven grades) 40–145

Cast iron, nodular 45–65
Magnesium, AZ80A-T5 38
Steel, stainless (0.08–0.2C, 17Cr, 7Ni) 1⁄4 hard 78
Aluminum, cast, pure 9 Magnesium, AZ80A-T5 6.5
Aluminum, wrought, 2014-T6 10.6 Titanium, pure 15.5
Beryllium copper 19 Titanium, alloy, 5 Al, 2.5 Sn 17
Brass, naval 15 Steel for bridges and buildings,
ASTM A7-61T, all shapes 29
Bronze, phosphor, ASTM B159 15
Cast iron, malleable 26 Steel, castings, high strength, for structural
purposes, ASTM A148-60 (seven grades) 29
Cast iron, nodular 23.5
Aluminum 0.334                                                           Nickel silver 0.322
Beryllium copper 0.285                                                Phosphor bronze 0.349
Brass 0.340                                                                  Rubber 0.500
Cast iron, gray 0.211                                                   Steel, cast 0.265
Copper 0.340                                                              high carbon 0.295
Inconel 0.290                                                               mild 0.303
Lead 0.431                                                                   nickel 0.291
Magnesium 0.350                                                         Wrought iron 0.278
Monel metal 0.320                                                       Zinc 0.331