Strength of material

For machines, plant and buildings to work and give an economic life, their component parts must be capable of resisting the various forces to which they are subject during normal working. Any load applied to a component induces stresses and strains in it. The type of stress depends on the manner in which the load is applied. Stress is force per unit area (N/m ). Strain is the proportional distortion when subject to stress (6//Z) and is often quoted as a percentage. The ratio of stress to strain is constant and known as Hooke s Laws after its discoverer, thus  

E is called Yoxmg s modulus or modulus of elasticity and its value depends on the material and the t5qje of stress to which it is subjected. 

A cross sectional area V o distance from neutral axis f = moment of inertia M = torsion moment (torque) d -diameter of shaft 

The calculation of tensile, compressive and shear stresses is relatively easy, but to obtain bending stresses it is necessary to know the moment of inertia of the section of the beam and in the case of torsion, although it is a shear stress, because it is spread along the length of the shaft its calculation is complex. V tith bending moments, a tensile stress is induced in the outer surface of the beam and an equal and opposite compressive stress occurs in the inner surface. 

For further information on this subject refer to Reference 1 and References 6-9. 

The principles of strength of materials are applied to the design of structures to assure that the elements of the structures will operate reliably under a known set of loads. Thus the field encompasses both the calculation of the strength and deformation of members and the measurement of the mechanical properties of engineering materials. 

If the load acts to elongate the bar, the stress is said to be tensile (+), and if the load acts to compress the bar, the stress is said to be compressive (-). For all real materials. 

In the region where the relationship between stress and strain is linear, the material is said to be elastic, and the constant of proportionality is E, Young s modulus, or the elastic modulus. 

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Yield strengths listed are not included in A8TM specifications. The value shown is based on yield strengths of materials with similar characteristics. 

The method adopted to calculate the sectional modulus is therefore simple and on the safe side. However, to calculate the sectional modulus more accurately or to derive it for any other section of the support than considered here reference may be made to a textbook on the strength of materials or a machine handbook. 

Novikov, S.A., Shear Stress and Spall Strength of Materials Under Shock Loads (Review), J. Appl. Mech. Tech. Phys. 22 (3), 385-394 (1981). 

As well as being a good way of measuring the yield strengths of materials like ceramics, as we mentioned above, the hardness test is also a very simple and cheap nondestructive test for (Ty. There is no need to go to the expense of making tensile specimens, and the hardness indenter is so small that it scarcely damages the material. So it can be used for routine batch tests on materials to see if they are up to specification on without damaging them. 

Timoshenko, S. P. 1966 Strength of Materials Part II - Advanced Theory and Practice, 3rd Edition. NY D. van Nostrand. 

Timoshenko, S., Strength of Materials Adranced Theory Problems, 3rd ed. Van Nostrand Reinhold Pub., 1956. 

Most materials scientists at an early stage in their university courses learn some elementary aspects of what is still miscalled strength of materials . This field incorporates elementary treatments of problems such as the elastic response of beams to continuous or localised loading, the distribution of torque across a shaft under torsion, or the elastic stresses in the components of a simple girder. Materials come into it only insofar as the specific elastic properties of a particular metal or timber determine the numerical values for some of the symbols in the algebraic treatment. This kind of simple theory is an example of continuum mechanics, and its derivation does not require any knowledge of the crystal structure or crystal properties of simple materials or of the microstructure of more complex materials. The specific aim is to design simple structures that will not exceed their elastic limit under load. 

From strength of materials one can move two ways. On the one hand, mechanical and civil engineers and applied mathematicians shift towards more elaborate situations, such as plastic shakedown in elaborate roof trusses here some transient plastic deformation is planned for. Other problems involve very complex elastic situations. This kind of continuum mechanics is a huge field with a large literature of its own (an example is the celebrated book by Timoshenko 1934), and it has essentially nothing to do with materials science or engineering because it is not specific to any material or even family of materials. 

Absorption of heat (auto-refrigeration) and eonsequent temperature reduetion on flashing may have a serious effeet on assoeiated heat transfer media, upon the strength of materials of eonstruetion, and result in frosting at the point of leakage. Exposure of personnel eandes a risk of frostbite. 

Table 1.4. Flange Ratings for Different Materials Strength of Materials...

The first step in the analysis of this situation is the transformation of the applied stresses on to the fibre axis. Referring to Fig. 3.10 it may be seen that Ox and Oy may be resolved into the x, y axes as follows (the reader may wish to refer to any standard Strength of Materials text such as Benham, Crawford and Armstrong for more details of this stress transformation) ... 

Just as there must be some rationale for selecting a particular stiffness and/or strength of material for a specific structural application, there must also be a rationale for determining how best to achieve that stiffness and strength for a composite of two or more materials. That is, how can the percentages of the constituent materials be varied so as to arrive at the desired composite stiffness and strength ... 

The mechanics of materials (or strength of materials or resistance of materials) approach embodies the usual concept of vastly simplifying assumptions regarding the hypothesized behavior of the mechanical system. The elasticity approach actually is at least three approaches (1) bounding principles, (2) exact solutions, and (3) approximate solutions. 

Using Table 52 the variables are El(FL ), L(L), d(L), (d - d,)(L), T(FL), and P(F). Note that this I is moment-area which is in the units of ft (not to be confused with I given in Table 52 which is moment of inertia, see Chapter 2, Strength of Materials, for clarification). The number of FI ratios that will describe the problem is equal to the number of variables (6) minus the number of fundamental dimensions (F and L, or 2). Thus, there will be four FI ratios (i.e., 6-2 = 4), FI, flj, fl, and FI. The selection of the combination of variables to be included in each n ratio must be carefully done in order not to create a complicated system of ratios. This is done by recognizing which variables will have the fundamental dimensions needed to cancel with the fundamental dimensions in the other included variables to have a truly dimensionless ratio. With this in mind, FI, is... 

Timoshenko, S., and MacCullough, Gleason, H., Elements of Strength of Materials, Van Nostrand, Princeton, 1957. 

Knowing the stretch L and the forces applied Fj and Fj and using Hooke s law (see the section titled Strength of Materials in Chapter 2), the length to the free point is... 

Rowe, M. E., Heavy wall drill pipe, a key member of the drill stem, Publ. No. 45, Drilco, Division of Smith International, Inc., Houston, 19XX. Timoshenko, S., and D. H. Young, Elements of Strength of Materials, Fifth Edition, D. Van Nostrand Co., New York, 1982. 

Analysis of the above formulas leads one to conclusion that ultimate attainable strength of material increases with the increasing scatter of the strength of fine fibers characterized by good adhesion to the matrix and is lower for fibers with larger diameters and poorer adhesion. 

Jensen, A., et al., Applied Strength of Materials, McGraw-Hill, 1975. 

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