We were discussing the concept of stress and strain and also we have discussed the different types of stress and also different types of strain in our previous posts. Now we are going further to start our discussion to understand the “Hooke’s Law”, in subject of strength of material, with the help of this post.
Before going further, let us recall the concept of elasticity and elastic limit first. As we have already discussed that if an external force is applied over the object, there will be some deformation or changes in the shape and size or simply dimensions of the object. Body will secure its original shape and size after removal of external force if deformation due to external force is within certain limit.
Therefore, there will be some specific value of force for each material up to which, strain will be temporary or elastic i.e. deformation will be disappeared after removal of load and corresponding value of stress will be termed as elastic limit of that material.
According to Hook’s law
Within elastic limit, stress applied over an elastic material will be directionally proportional to the strain produced due to external loading. Mathematically we can say as displayed here in figure.
Let us remove the proportionality sign and therefore we will have to use one constant value in order to remove the proportionality sign.
Where E is basically Modulus of elasticity or young modulus and we can define modulus of elasticity as the ratio of stress to strain. Modulus of elasticity will have same unit as that for stress because strain is unit less parameter and therefore modulus of elasticity unit in S.I. system will be N/m2.
Let us draw here the curve between stress and strain for an elastic material. Stress value is provided here at Y-axis and strain value at X-axis. We may notice here that as stress value increases strain value will also be increased and similarly strain value will be decreased with decrease in stress value and we must note it here that this relationship will be linear, as shown in curve, up to elastic limit.
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Strength of material, By R. K. Bansal
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We will see another important topic in the category of strength of material.