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### Introduction to Stress

In this article we will learn about the types of stresses i.e. normal stress, tensile stress, compressive stress and shear stress. We will discuss about the definition and formula of each stress in detail.

### Definition of Stress

Stress is defined as the internal resistance set up by a body when it is deformed. It is measured in N/m^2 and this unit is specifically called Pascal (Pa). A bigger unit of stress is the mega Pascal (MPa).

1 Pa = 1N/m^2,
1MPa = 106 N/m^2 =1N/mm^2.

The term stress is used to express the loading in terms of force applied to a certain cross-sectional area of an object. From the perspective of loading, stress is the applied force or system of forces that tends to deform a body. From the perspective of what is happening within a material, stress is the internal distribution of forces within a body that balance and react to the loads applied to it. The stress distribution may or may not be uniform, depending on the nature of the loading condition. For example, a bar loaded in pure tension will essentially have a uniform tensile stress distribution. However, a bar loaded in bending will have a stress distribution that changes with distance perpendicular to the normal axis.

Simplifying assumptions are often used to represent stress as a vector quantity for many engineering calculations and for material property determination. The word “vector” typically refers to a quantity that has a “magnitude” and a “direction”. For example, the stress in an axially loaded bar is simply equal to the applied force divided by the bar’s cross-sectional area.

Significant stress may exist even when deformation is negligible or non-existent (a common assumption when modeling the flow of water). Stress may exist in the absence of external forces; such built-in stress is important, for example, in pre-stressed concrete and tempered glass. Stress may also be imposed on a material without the application of net forces, for example by changes in temperature or chemical composition, or by external electromagnetic fields (as in piezoelectric and magnetostrictive materials).

### Types of Stress

A stress acts on a body may be normal stress or shear stress.

#### Normal Stress

Normal stress is a stress that acts perpendicular to the area. The formula for the normal stress is given by

The normal stress is again subdivided into two parts.

#### Tensile Stress

• The stress which induced in a body when it is subjected to two equal and opposite pulls as shown in the figure given below is called tensile stress.
• Due to the tensile stress there is an increase in the length of the body and decrease in the cross section area of the body.
• Tensile stress is a type of normal stress, so it acts at 90 degree to the area.
• The strain which is induced due to tensile stress is called tensile strain. It is equals to the ratio of increase in the length to the original length.

#### Compressive Stress

•  The stress which induced in a body when it is subjected to two equal and opposite pushes as shown in the figure given below is called compressive stress.
• Due to the compressive stress, there is a decrease in the length and increase in the cross section area of the body.
• Compressive stress is also a type of normal stress and so it also acts at 90 degree to the area.
• The strain which is induced due to compressive stress is called compressive strain. It is equals to the ratio of decrease in the length to the original length.

#### Shear Stress

Another simple type of stress occurs when a uniformly thick layer of elastic material like glue or rubber is firmly attached to two stiff bodies that are pulled in opposite directions by forces parallel to the layer; or a section of a soft metal bar that is being cut by the jaws of a scissors-like tool. Let F be the magnitude of those forces, and M be the mid plane of that layer. Just as in the normal stress case, the part of the layer on one side of M must pull the other part with the same force F. Assuming that the direction of the forces is known, the stress across M can be expressed by the single number Τ (tau) = F/A, where F is the magnitude of those forces and A is the area of the layer.

However, unlike normal stress, this simple shear stress is directed parallel to the cross-section considered, rather than perpendicular to it. For any plane S that is perpendicular to the layer, the net internal force across S, and hence the stress, will be zero.

As in the case of an axially loaded bar, in practice the shear stress may not be uniformly distributed over the layer; so, as before, the ratio F/A will only be an average (“nominal”, “engineering”) stress. However, that average is often sufficient for practical purposes. Shear stress is observed also when a cylindrical bar such as a shaft is subjected to opposite torques at its ends. In that case, the shear stress on each cross-section is parallel to the cross-section, but oriented tangentially relative to the axis, and increases with distance from the axis. Significant shear stress occurs in the middle plate (the “web”) of I-beams under bending loads, due to the web constraining the end plates (“flanges”).

• Shear stress induced in a body when it is subjected to two equal and opposite forces that acts tangential to the area.
• The strain produced due to the shear stress is called shear strain.
• The shear stress is denoted by the symbol τ (tau). It is a Greek letter.
• It is defined as ratio of shear resistance to the shear area.
• The formula for the shear stress is given below.
• Shear stress is responsible for the change in the shape of the body. It does on affect the volume of the body.

References

• https://en.wikipedia.org/wiki/Stress_(mechanics)
• http://www.mechanicalbooster.com/2016/09/types-of-stress.html
• http://www.mathalino.com/reviewer/mechanics-and-strength-of-materials/normal-stresses