Thursday, 29 December 2016

TYPES OF STRESS IN STRENGTH OF MATERIALS

TYPES OF STRESS IN STRENGTH OF MATERIALS

We were discussing the concept of stress and strain in our previous post; now we are going further to start our discussion for classifying the stress and strain. Hence, we will see here the types of stress and strain with the help of this post.

Types of stress

There are following type of stresses as displayed in figure here and we will discuss each type of stress in detail with the help of this post. Basically stresses are classified in to three types.
1. Direct stress or simple stress
2. Indirect stress
3. Combined stress

 
Further direct stress or simple stress is classified in two type i.e. normal stress and shear stress. As it is also displayed in figure, normal stress will be divided in two type i.e. tensile stress and compressive stress.

Similarly, indirect stress will also be divided in two type i.e. torsion stress and bending stress. Above figure displayed here indicates the brief introduction for the classification of stress in strength of material.

Normal stress

Normal stress is basically defined as the stress acting in a direction perpendicular to the area. Normal stress will be further divided, as we have seen above, in two types of stresses i.e. tensile stress and compressive stress.

Tensile stress

Let us see here the following figure; we have one bar of length L. There are two equal and opposite pulling type of forces P, acting axially and trying to pull the bar and this pulling action will be termed as tensile and stress developed in material of the bar will be termed as tensile stress.
Therefore we can define the tensile stress as the stress developed in a member due to the pulling action of two equal and opposite direction of forces. σt is the symbol which is used to represent the tensile stress in a member.

There will be increase in the length of the bar under the action of tensile loading, but diameter of the bar will be reduced under the action of tensile loading. Tensile stress will be determined with the help of following formula.

Tensile stress (σt) = Resisting force (R) / Cross sectional area (A)
Tensile stress (σt) =Tensile load or applied load (P) / Cross sectional area (A)
σt = P/A

Compressive stress

Let us see here the following figure; we have one bar of length L. There are two equal and opposite push type of loading P, acting axially and trying to push the bar and this pushing action will be termed as compression and stress developed in material of the bar will be termed as compressive stress.
Therefore we can define the compressive stress as the stress developed in a member due to the pushing action of two equal and opposite direction of forces. σc is the symbol which is used to represent the compressive stress in a member.

There will be decrease in the length of the bar under the action of compressive loading, but diameter of the bar will be increased under the action of compressive loading. Compressive stress will be determined with the help of following formula.

Compressive stress (σc) = Resisting force (R) / Cross sectional area (A)
Compressive stress (σc) = Compressive load or applied load (P) / Cross sectional area (A)
σc = P/A

Shear stress

 
Let us see here the following figure; we have two plates and these two plates are connected with each other with the help of a pin or a rivet as shown in figure. There are two equal and opposite forces (P) acting tangentially across the resisting section.

One force is acting on top plate towards left direction and second force is acting towards right side as shown in figure and hence such type of loading will try to shear off the body across the resisting section.

This type of loading action will be termed as shear loading and stress developed in material of the body will be termed as shear stress.
Therefore we can define the shear stress as the stress developed in a member, when member will be subjected with two equal and opposite forces acting tangentially across the resisting section. τ is the symbol which is used to represent the shear stress in a member. Shear resistance R will be equivalent to P here.

Shear stress (τ) = P/A

As we have seen above in figure, two plates are connected with each other with the help of a pin and therefore we can also say such type of loading as single shear. Let we have three plates and these three plates are connected with a pin or rivet, such type of loading will be termed as double shear. Shear resistance R will be P/2.

Shear stress (τ) = P/2A

Torsional stress

Torsional stress is one special type of stress in a member where one end of member will be secured and other end of member will be twisted. Let us see one example, let we have one shaft and its one end is supported by a ball bearing and other end of shaft is free to rotate.

 
Let if bearing is seized, then there will be twisting mechanism because one end of rotating shaft will be fixed due to seized bearing and other end of shaft will be twisted and therefore there will be produced stress in shaft and that stress will be termed as torsional stress.
From here, we can also say that torsional stress will exist in rotating members such as rotating shaft. Torsional stress will be indicated by symbol

Bending stress

Let we have one beam which one end is fixed at A and other end is loaded by force P and hence beam is deflected here as shown in figure.
Bending stress will be determined with the help of following formula as displayed here in following figure.
We will study and analyze each type of strain in detail in our next post.

Reference:

Strength of material, By R. K. Bansal
Image Courtesy: Google
We will see another important topic i.e. types of strain in the category of strength of material.

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