# Types Of Stress And Strain Pdf

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## Stress and Strain-Definition, Curve or Diagram, Formula, PDF

If a cylindrical bar is subjected to a direct pull or push along its axis as shown in Fig In the SI system of units load is measured in newtons, although a single newton, in engineering terms, is a very small load. In most engineering applications, therefore, loads appear in SI multiples, i. There are a number of different ways in which load can be applied to a member. Typical loading types are: a Static or dead loads, i. If, therefore, a bar is subjected to a uniform tension or compression, i.

Direct strain 8 If a bar is subjected to a direct load, and hence a stress, the bar will change in length. A particular form of elasticity which applies to a large range of engineering materials, at least over part of their load range, produces deformations which are proportional to the loads producing them. Since loads are proportional to the stresses they produce and deformations are proportional to the strains, this also implies that, whilst materials are elastic, stress is proportional to strain.

Whilst a material is elastic the deformation produced by any load will be completely recovered when the load is removed;there is no permanent deformation. Other classifications of materials with which the reader should be acquainted are as follows:A material which has a uniform structure throughout without any flaws or discontinuities is termed a homogeneous material.

Non-homogeneous or inhomogeneous materials such as concrete and poor-quality cast iron will thus have a structure which varies from point to point depending on its constituents and the presence of casting flaws or impurities. If a material exhibits uniform properties throughout in all directions it is said to be isotropic; conversely one which does not exhibit this uniform behaviour is said to be nonisotropic or anisotropic. An orthotropic material is one which has different properties in different planes.

A typical example of such a material is wood, although some composites which contain systematically orientated "inhomogeneities" may also be considered to fall into this category. EIn most common engineering applications strains do not often exceed 0. The actual value of Young's modulus for any material is normally determined by carrying out a standard tensile test on a specimen of the material as described below.

Tensile testIn order to compare the strengths of various materials it is necessary to carry out some standard form of test to establish their relative properties.

One such test is the standard tensile test in which a circular bar of uniform cross-section is subjected to a gradually increasing tensile load until failure occurs. Measurements of the change in length of a selected gauge length of the bar are recorded throughout the loading operation by means of extensometers and a graph of load against extension or stress against strain is produced as shown in Fig.

Some point A is eventually reached, however, when the linear nature of the graph ceases and this point is termed the limit of proportionality. For a short period beyond this point the material may still be elastic in the sense that deformations are completely recovered when load is removed i. The limiting point B for this condition is termed the elastic limit. For most practical purposes it can often be assumed that points A and B are coincident.

Beyond the elastic limit plastic deformation occurs and strains are not totally recoverable. There will thus be some permanent deformation or permanent set when load is removed. After the points C, termed the upper yield point, and D, the lower yield point, relatively rapid increases in strain occur without correspondingly high increases in load or stress.

The graph thus becomes much more shallow and covers a much greater portion of the strain axis than does the elastic range of the material. The capacity of a material to allow these large plastic deformations is a measure of the so-called ductility of the material, and this will be discussed in greater detail below.

For certain materials, for example, high carbon steels and non-ferrous metals, it is not possible to detect any difference between the upper and lower yield points and in some cases no yield point exists at all. In such cases a proof stress is used to indicate the onset of plastic strain or as a comparison of the relative properties with another similar material.

This involves a measure of the permanent deformation produced by a loading cycle; the 0. From P draw a line parallel with the initial straight line portion of the tensile test curve to cut the curve in N. The stress corresponding to N is then the 0. A material is considered to satisfy its specification if the permanent set is no more than 0. Beyond the yield point some increase in load is required to take the strain to point E on the graph.

Between D and E the material is said to be inthe elastic-plastic state, some of the section remaining elastic and hence contributing to recovery of the original dimensions if load is removed, the remainder being plastic. Beyond E the cross-sectional area of the bar w 1. This necking takes place whilst the load reduces, and fracture of the bar finally occurs at point F. The nominal stress at failure, termed the maximum or ultimate tensile stress, is given by the load at E divided by the original cross-sectional area of the bar.

This is also known as the tensile strength of the material of the bar. Owing to the large reduction in area produced by the necking process the actual stress at fracture is often greater than the above value. Since, however, designers are interested in maximum loads which can be carried by the complete cross-section, the stress at fracture is seldom of any practical value.

If load is removed from the test specimen after the yield point C has been passed, e. Thus, despite the fact that loading to S comprises both elastic OC and partially plastic CS portions, the unloading procedure is totally elastic.

A second load cycle, commencing with the permanent elongation associated with the strain OT, would then follow the line TS and continue along the previous curve to failure at F. It will be observed, however, that the repeated load cycle has the effect of increasing the elastic range of the material, i. The procedure could be repeated along the line PQ, etc.

In fact, careful observation shows that the material will no longer exhibit true elasticity since the unloading and reloading lines will form a small hysteresis loop, neither being precisely linear. Repeated loading and unloading will produce a yield point approaching the ultimate stress value but the elongation or strain to failure will be much reduced.

Typical stress-strain curves resulting from tensile tests on other engineering materials are shown in Figs 1. After completing the standard tensile test it is usually necessary to refer to some "British Standard Specification" or "Code of Practice" to ensure that the material tested satisfies the requirements, for example: BS Ductile materialsIt has been obset.

Thus the extension of the material over this range is considerably in excess of that associated with elastic loading. The capacity of a material to allow these large extensions, i. Materials with high ductility are termed ductile materials, members with low ductility are termed brittle materials. A quantitative value of the ductility is obtained by measurements of the percentage elonoation or percentag e reduction in area, both being defined below.

A property closely related to ductility is malleability, which defines a material's ability to be hammered out into thin sheets. A typical example of a malleable material is lead. This is used extensively in the plumbing trade where it is hammered or beaten into corners or joints to provide a weatherproof seal.

Malleability thus represents the ability of a material to allow permanent extensions in all lateral directions under compressive loadings. Brittle materialsA brittle material is one which exhibits relatively small extensions to fracture so that the partially plastic region of the tensile test graph is much reduced Fig. Whilst Fig. There is little or no necking at fracture for brittle materials.

The bar will also exhibit, however, a reduction in dimensions laterally, i. This ratio is termed Poisson's ratio. It must be remembered, however, that the longitudinal strain induces a lateral strain of opposite sign, e. For most engineering materials the value of v lies between 0.

From the work of w 1. This lateral strain will be compressive and will result in a compression or reduction of length on this axis. Consider, therefore, an element of material subjected to two stresses at right angles to each other and let both stresses, r and ay, be considered tensile, see Fig. Simple two-dimensional system of direct stresses. The following strains will be produced: The total strain in the X direction will therefore be given by: If any stress is, in fact, compressive its value must be substituted in the above equations together with a negative sign following the normal sign convention.

Shear stressConsider a block or portion of material as shown in Fig. Such a system could be realised in a bicycle brake block when contacted with the wheel. There is then a tendency for one layer of the material to slide over another to produce the form of failure shown in Fig. Shear strainIf one again considers the block of Fig. The block will in fact change shape or "strain" into the form shown in Fig.

The angle of deformation 7 is then termed the shear strain. Shear strain is measured in radians and hence is non-dimensional, i. The constant G is termed the modulus of rigidity or shear modulus and is directly comparable to the modulus of elasticity used in the direct stress application.

The term modulus thus implies a ratio of stress to strain in each case. Double shearConsider the simple riveted lap joint shown in Fig. When load is applied to the plates the rivet is subjected to shear forces tending to shear it on one plane as indicated.

In the butt joint with two cover plates of Fig. In such cases twice the area of metal is resisting the applied forces so that the shear stress set up is given by Allowable working stress-factor of safetyThe most suitable strength or stiffness criterion for any structural element or component is normally some maximum stress or deformation which must not be exceeded. In the ease of stresses the value is generally known as the maximum allowable working stress.

Because of uncertainties of loading conditions, design procedures, production methods, etc. In this case a factor of safety of 3 implies that the design is capable of carrying three times the maximum stress to which it is expected the structure will be subjected in any normal loading condition.

There is seldom any realistic basis for the selection of a particular safety factor and values vary significantly from one branch of engineering to another.

## Stress (mechanics)

In continuum mechanics , stress is a physical quantity that expresses the internal forces that neighbouring particles of a continuous material exert on each other, while strain is the measure of the deformation of the material. For example, when a solid vertical bar is supporting an overhead weight , each particle in the bar pushes on the particles immediately below it. When a liquid is in a closed container under pressure , each particle gets pushed against by all the surrounding particles. The container walls and the pressure -inducing surface such as a piston push against them in Newtonian reaction. These macroscopic forces are actually the net result of a very large number of intermolecular forces and collisions between the particles in those molecules. Strain inside a material may arise by various mechanisms, such as stress as applied by external forces to the bulk material like gravity or to its surface like contact forces , external pressure, or friction.

the material is loaded, both stress and strain increase, and the plot proceeds from Point 1 to Point. 2. This type of behavior is termed Elastic and the region between Points Examples of brittle materials include glass, cast iron, high carbon.

## Book on Mechanics of Materials(Simple Stress and Strain)

A model of a rigid body is an idealized example of an object that does not deform under the actions of external forces. It is very useful when analyzing mechanical systems—and many physical objects are indeed rigid to a great extent. The extent to which an object can be perceived as rigid depends on the physical properties of the material from which it is made.

The Tensile stress is like pulling the material on each side or might one side as figures shown below,. The Compressive stress is like pushing the material on each side or might one side as figures shown below,. The figure is shown below,.

In this article, we discuss three types of stress: Acute stress, episodic acute stress, and chronic stress.

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These forces are called stress. In response to stress, the rocks of the earth undergo strain , also known as deformation. Strain is any change in volume or shape. There are four general types of stress. One type of stress is uniform, which means the force applies equally on all sides of a body of rock. The other three types of stress, tension, compression and shear, are non-uniform, or directed, stresses.

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The simplest type of load (P) is a direct pull or push, known technically as tension or compression. Foxit Advanced PDF Editor · To remove this notice, Modules of rigidity. For elastic material shear strain is proportional to the shear stress.

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