Relation Between The Stress And The Strain example essay topic

Simple Stress and Strain The strength of materials are expressed from the point of view of machine designer. A machine designer needs to know the properties of different materials so that he can select the most suitable material for each part of a machine. A machine designer uses his information of stress to make sure that the stress is reasonable and that each part of the machine is sufficiently strong. Strength of materials is the scientific area of applied mechanics for the study of the strength of engineering materials and their mechanical behavior in general (such as stress, deformation, strain and stress-strain relations). Strength is considered in terms of compressive strength, tensile strength, and shear strength, namely the limit states of compressive stress, tensile stress and shear stress respectively. One can see the importance of stress and strain.

They are an indication of how severely the part in machine is loaded and how it is a factor that determines whether the forces applied are reasonable. Stress and strain always occur together. When a material is subjected to stress, it deforms, and when a material is deformed there must be strain. If the stress and strain are not the same for all materials, then it is found by experiments There is a relation between the stress and the strain for any given material. It said, when the relationship between the two are given, the stress and the strain can be found in one another.

All materials deform when subjected to stress and it is necessary to be able to calculate the deformation of a body under load, because in most cases the deformation is more momentous than the stress. Stress is in all probability the most imperative word in the subject matter of strength of materials. Stress is defined as force per unit area. It has the same units as pressure, and in fact pressure is one special variety of stress.

However, stress is a much more complex quantity than pressure because it varies both with direction and with the surface it acts on. The simple stress are: compression (stress that acts to shorten an object), tension (stress that acts to lengthen an object), and shear (stress that acts parallel to a surface). Shear can cause one object to slide over another. It also tends to deform originally rectangular objects into parallelograms. The most general definition is that shear acts to change the angles in an object. Strain is defined as the amount of deformation an object experiences compared to its original size and shape.

For example, if a block 10 cm on a side is deformed so that it becomes 9 cm long, the strain is (10-9) /10 or 0.1 (sometimes expressed in percent, in this case 10 percent.) Note that strain is dimensionless. Strain in addition can be express further in these familiar terms: compression (longitudinal strain that shortens an object), tension (longitudinal strain that lengthens an object) and shear (strain that changes the angles of an object). Shear can also causes lines to rotate in strain. These stresses can further be said to be a member of a machine or structure that indicates how severely it is loaded; a stress is said to be a failure if the machine part is loaded to heavy. Tensile stress is the stress that can be applied to an object by pulling on it, or attempting to stretch it. Further, it is a loading that tends to produce stretching on a material by the application of axially directed pulling forces.

Materials can withstand some tensile loading, but if enough force is applied, they will eventually break into two parts. Steel is an example of a material with high tensile strength. Its opposite is compressive stress and compression stress. Compressive is the stress applied to materials resulting to their compaction (decrease of volume).

When a material is subjected to compressive stress then this material is under compression. Usually compressive stress applied to bars, and columns. In architecture and structural engineering, a column is that part of a structure whose purpose is to transmit through compression the weight of the structure. Other compression members are often termed columns because of the similar stress conditions. Columns can be either compounded of parts or made as a single piece. In addition, a material is compression stress when the forces acting on it tend to shorten it.

The forces have a propensity to squeeze the material together and this predisposition is resisted by interior forces or stresses. Stress is plotted vertically and strain is plotted horizontally. After it is plotted, the line then is drawn trough the plotted points to give the stress-strain curve. It is understood that it is not always a straight line but straight enough for practical purposes.

The stress is related to the external force you put on an object. The strain is resulting deformation of the object's shape or size. Stress and strain can be thought of as cause' and effect'. If you put a force on something, it changes.

This sort of deformation is called elastic deformation. The word elastic' means that after you removed the external force (i.e. remove the stress), the object returns to its original shape and size. When the stress is not too large, there is a simple law relating stress and strain, which gets the name of Hooke's Law. Hooke's Law states that in an elastic material strain is proportional to stress. The point at which a material ceases to obey Hooke's Law is known as its elastic limit. The first part is very easy.

It means that the bigger the weight (stress) you hang on the string the more it will stretch (strain). The second part is also straightforward. While the elastic limit is not exceeded, the string will go back to its original length when you take the weights off it, but if you add too much weight, the string will stretch without going back to its original length when you take the weights off it. If you leave a very large weight hanging on the string, it will gradually get longer and longer until it breaks. In this state the wire is behaving as if it were a fluid instead of a solid. For this investigation, one also need to know about Young's modulus.

This is the coefficient of elasticity of stretching. It is the ratio of the stress or stretching force per unit cross sectional area to the strain or amount of stretching per unit of length. Forces obeying Hooke's Law can be thought of as restoring forces. That means that if you disturb the system from rest, the forces act to restore the initial situation. However, what happens is that the system overshoots its initial situation. For example, if you stretch a string and let it go, it does go back to its initial position, but then it keeps on going and compresses. it then uncompressed, but again overshoots.

The simpler form of Hooke's law is the spring relation: F = k "Ax where k is the spring constant. Elasticity describes the state where the work offered by the application of external agents (forces), is stored in the material in form of elastic energy and it is recovered in form of displacement when external agents are removed. Working stress is the stress to which it is planned to subject the material and is the stress used in design calculations. Working stress is less than ultimate strength of the material, do to the fact that the machine will break if the stress reaches the ultimate.

Ultimate strength is an attribute directly related to a material, rather than just specific specimen of the material, and as such is quoted force per unit of cross section area (N / mm 2). For example, Ultimate Tensile Strength (UTS) of mild steel is 470 N / mm 2. It is useful to remember that 1 MPa = 1 N / mm 2. Factor of safety is a designed constraint that an engineered component or structure must achieve.

FS = UTS / R, where FS: the Factor of Safety, R: The acting force (or stress) and UTS: the Ultimate force (or stress). For example to achieve a factor of safety of 4, the allowable stress in a mild steel component can be worked out as R = UTS / FS = 117.5 MPa. In conclusion, stress is the ratio of applied load to the cross-sectional area of element in tension and expressed in pounds per square (psi). And strain is a measure of the deformation of the material that is dimensionless. Since stress is proportional to load and strain is proportional to deformation, this applies stress is proportional to strain.

Hooke's Law is the statement of that proportionality..