# Fundamentals of Strength of Materials: Stress, Strain, Types of Elastic Constants

Table of Contents

## What is stress

The internal resistance offered by the body per unit area against deformation is the known as stress. The unit of stress is N/mm2 or the N/m2 when an external force acts on a body the body tends to the undergo deformation. Due to the cohesion between molecules the body resist the force. This resistance offered by the body is known as strength of the material.

Concept of the Stress let us introduce the concept of stress as we be the know that the main problem of the engineering mechanics of material is the investigation of internal resistance of the body i.e. the nature of forces set up the within a body to balance the effect of the externally applied the forces.

The externally applied forces are the termed as loads. These externally applied forces may be due to the any one or more of the followings due to service the conditions.

- Due to the environment in which the component works
- Through contact with the other members
- Due to the fluid pressures
- Due to the gravity or inertia forces the Self weight of the structure.

As we know that in mechanics of the deformable solids externally applied forces acts on a body and the body suffers a deformation. From equilibrium point of the view this action should be opposed or reacted by the internal forces which are set up within the particles of material due to the cohesion. These internal forces give rise to a concept of the stress. Therefore let us the define a term stress. Let us consider a rectangular bar of the some cross–sectional area and the subjected to some load or force in the Newton. Let us imagine that the same rectangular bar is the assumed to be cut into two halves at the section XX. Each portion of this rectangular bar is in equilibrium under the action of load P and the internal forces acting at the section XX has been the show.

## Types of Stresses

Only two basic stresses exists: (1) normal stress and the (2) shear shear stress. Other stresses either are the similar to these basic stresses or are a combination of the. Bending stress is the combination tensile compressive and the shear stresses. Torsional stress as the encountered in twisting of a shaft is the shearing stress. Let us define the normal stresses and the shear stresses in the following sections.

### Normal stresses

We have defined stress as force per the unit area. If the stresses are normal to the areas concerned then these are termed as the normal stresses. The normal stresses are the generally denoted by a Greek letter This is a also known as uniaxial state of stress because the stresses acts only in one direction the however such a state rarely exists therefore we have biaxial and the triaxial state of stresses where either the two mutually perpendicular normal stresses acts other three mutually perpendicular normal stresses acts as shown in the figures below.

The resisting area is the perpendicular to the applied force thus normal. There are two

types of the normal stresses tensile stress and the compressive stress. Tensile stress applied

to bar tends the bar to elongate while the compressive stress tend to shorten the bar.

σ = Force / Area

σ = P/ A

Bar in the Tension Bar in the Compression

Where P is the applied normal load in the Newton and A is the area in mm2. The

maximum stress in the tension or compression occurs over a section normal to the load.

### Tensile stresses

The normal stresses can be the either tensile or compressive whether the stresses acts out of area or into the area. Tensile the stress: The resistance offered by a body per unit area when it is the subjected to a force which acts away from its point of the application is called tensile the stress.

The length of bar increases by an amount under the action of external force P then tensile the strain = increase in the length original length.

### Compressive Stress

Compressive the stress the resistance offered by a body per unit area when it is the subjected to a force which acts towards its point of the application is called compressive the stress.

The length of the bar decreases by an amount under the action of external force P then compressive strain = decrease in the length original length.

### Bearing Stress

When the one object presses against another it is referred to the bearing stress they are in fact the compressive the stresses.

### Shear stresses

Let us consider now the situation where the cross sectional area of a block of the material is subject to a distribution of forces which are the parallel rather than normal, to the area concerned. Such forces are the associated with a shearing of the material and are referred to as shear forces. The resulting force interests are known as the shear stresses.

Is the developed if the applied force is parallel to the resisting area? Example is the bolt that holds the tension rod in it’s the anchor another condition of the shearing is when we twist a bar along it’s the longitudinal axis. This type of shearing is called torsion and the covered in another type of the simple stress is the bearing stress, it is the contact pressure between the two bodies. It is in the fact a compressive stress. The distortion produced by the shear stress on an element or rectangular block is the known as shear strain. It can also be defined as the change in the right angle.

Shear stress is the developed if applied force is parallel to the resisting area. Example is the bolt that holds the tension rod in the anchor. Another condition of shearing is the when we the twist a bar along its longitudinal the axis.

Shear the Stress the he resistance offered by a body per the unit area when the applied load on the body consists of two equal and the opposite forces not in the same line is called shear the stress.

P

τ =P/A P

where τ is the shear stress P is tangential force and A is area of the shearing

## What is Strain

Strain ( e ) is the ratio of change in length caused by the applied force to the original length. Also known as unit the deformation. Where δ is the deformation and L is the original length thus ε is the dimensionless.

When a body is the subjected to some external force there is the some deformation of the body. The ratio of change dimension of the body to the original dimension is the known as strain. It has no the unit.

Strain = change in the length original the length.

### Volumetric strain

The ratio between the change in volume and the original volume is the known as volumetric strain.

Volumetric the strain = change in the volume original the volume.

### Define True stress and True Strain

The true stress is defined as the ratio of load to the cross section area at the any instant.

### Define Hooke’s law

Within the elastic limit when a body is the loaded then stress induced is proportional to the strain. This is called as the Hook’s law.

### Linear Strain

The ratio of increase or the decrease in length to the original. Length is called as the linear strain.

### Lateral Strain

The ratio of increase or decrease in the lateral dimensions to the original lateral dimensions is the called as lateral strain.

## Stress-Strain Diagram

Suppose that a metal specimen be placed in the tension-compression testing the machine. As the axial load is gradually increased in increments the total elongation over the gage length is the measured at each increment of the load and this is continued until failure of the specimen takes place. Knowing the original cross-sectional area and the length of specimen the normal stress σ and the strain ε can be the obtained. The graph of these quantities with the stress σ along y-axis and the strain ε along the x-axis is called the stress strain the diagram. The stress-strain diagram differs in the form for various materials. The diagram shown below is that for the medium carbon structural steel. Metallic engineering materials are the classified as either ductile or the brittle materials. A ductile material is the one having relatively large tensile strains up to the point of rupture like structural steel and the aluminum whereas brittle materials has the relatively small strain up to the point of rupture like cast iron and the concrete. An arbitrary strain of the 0.05 mm/mm is frequently taken as the dividing line between these two the classes.

## What are the types of elastic constants

Modulus of elasticity or the Young’s modulus Modulus of the rigidity or shear modulus Bulk the modulus.

### What is poison’s ratio

When a member is the stressed with in elastic limit the ratio of lateral strain to it’s the corresponding linear strain remains constant throughout the loading. This constant is called as poison’s the ratio. It is the ratio of lateral strain to longitudinal or the linear strain.

### Define bulk modulus

When the body is stressed the ratio of direct stress to the corresponding volumetric strain is the constant with in elastic limit. This constant is called as the bulk modulus. Bulk modulus is the ratio of direct stress to the volumetric strain.

### Modulus of elasticity

Modulus of the elasticity is ratio of stress to the strain.

### Factor of safety

Factor of the safety is defined as the ratio of ultimate stress to the working stress permissible the stress.

### Elasticity

The deformation produced due to the application of external load the disappears completely with the removal of the load. This property of the material is called as the elasticity.

### Elastic limit

Elastic limit is the limiting value of the load up to which the material returns back to its original the position. Beyond this load the material will not return back to it’s the original position.

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