Prove that strain has no unit
from its mathematical expression?
Answers
Answer:
Strain has no units because it is a ratio of lengths.
We can use the above definitions of stress and strain for forces causing tension or compression. If we apply compressive force we have compressive stress and compressive strain.
Explanation:
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Strain Formula
This article deals with the strain formula and its derivation. When a particular force acts on an object, individuals usually concern themselves about how the object would move afterward. However, what such individuals fail to consider is how the force might affect the structure of the object. A good example can be bridges. When vehicles move on a bridge, they tend to create a downward force due to their weight. The bridge undergoes stress test to withstand without breaking under heavy pressure. Stress certainly refers to the internal force per unit area. Most noteworthy, the amount of strain applied to an object ultimately determines the level of strain determined by it.What is Strain?
Strain refers to the amount of deformation an object undergoes due to the application of stress. In simple words, stress refers to the internal force, while strain refers to the physical effect on the object due to that force. Strain refers to a measure of the amount of deformation that takes place on an object due to force. The three main types of strain are the longitudinal strain, shearing strain, and the volumetric strain.
Strain happens to be a unitless quantity. This is because, the value in the numerator and denominator always have the same units. Furthermore, strain refers to a description of deformation in terms of the relative displacement of particles in a particular body.
However, this description excludes the rigid body motions. There certainly is a possibility to make different equivalent choices for the expression of a strain field. Moreover, this depends on whether it is defined with respect to final or initial configuration of the body.SIGNUP
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Strain Formula
This article deals with the strain formula and its derivation. When a particular force acts on an object, individuals usually concern themselves about how the object would move afterward. However, what such individuals fail to consider is how the force might affect the structure of the object. A good example can be bridges. When vehicles move on a bridge, they tend to create a downward force due to their weight. The bridge undergoes stress test to withstand without breaking under heavy pressure. Stress certainly refers to the internal force per unit area. Most noteworthy, the amount of strain applied to an object ultimately determines the level of strain determined by it.
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Two rods of different materials having coefficients of thermal expansion $$\alpha_1$$ and $$\alpha_2$$ and Young's moduli $$Y_1$$ and $$Y_2$$ respectively are fixed between two rigid massive walls. The rods are heated such that they undergo the same increase in temperature. There is no bending of the rods. If $$\alpha_1$$ and $$\alpha_2$$ are in the ratio $$2:3$$, the thermal stresses developed in the two rods are equal provided $$Y_1:Y_2$$ is equal to?
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A clock which keeps correct time at $$20^{\circ}C$$, is subjected to $$40^{\circ}C$$. If coefficient of linear expansion of the pendulum is $$12\times 10^{-6}/ ^{\circ}C$$, then how much will it gain or loss in time?
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A thin uniform film of refractive index $$1.75$$ is placed on a sheet of glass of refractive index $$1.5$$. At room temperature $$(20^{\circ}C)$$, this film is just thick enough for light with wavelength $$600nm$$ reflected off the top of the film to be canceled by light reflected from the top of the glass. After the glass is placed in an oven and slowly heated to $$170{|circ}C)$$, the film concels reflected light wavelength $$606nm$$. The coefficient of linear expansion of the film is (Ignore any changes in the refractive index of the film due to the temperature change.)
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strain formula
What is Strain?
Strain refers to the amount of deformation an object undergoes due to the application of stress. In simple words, stress refers to the internal force, while strain refers to the physical effect on the object due to that force. Strain refers to a measure of the amount of deformation that takes place on an object due to force. The three main types of strain are the longitudinal strain, shearing strain, and the volumetric strain.
Strain happens to be a unitless quantity. This is because, the value in the numerator and denominator always have the same units. Furthermore, strain refers to a description of deformation in terms of the relative displacement of particles in a particular body.
However, this description excludes the rigid body motions. There certainly is a possibility to make different equivalent choices for the expression of a strain field. Moreover, this depends on whether it is defined with respect to final or initial configuration of the body.
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