Physics - Stress and Strain
Hooke’s law provides that stress divided by strain equals a constant number. That number is different for different substances and even for one substance, it is different depending on what type of stress or strain we are talking about.
For our purposes, there are 2 types of strain: Tensile strain and shear strain.
Rule 17: Definition of Strain
Tensile strain equals change in length divided by original length. Shear strain equals distance moved divided by original height. When a solid is subjected to a stress, it changes shape, and we call the change in shape a strain.
Rule 18: Definition of Stress
Stress equals force divided by area or F/A. Stress is usually measured in pascals (Pa). One pascal equals one newton meter squared. So, stress creates strain. Tensile stress creates tensile strain and shear stress creates shear strain. Tensile stress is a measure of stretching or compressing force per area perpendicular to the force. So in order to measure the tensile stress applied to a metal bar, we take the force applied to it and divide it by the cross-sectional area of the metal bar. Shear stress is measured in pascals just like tensile stress. Shear stress is equal to the tangential force over the area of the surface to which it is applied.
Moduli
Modulus is the constant number that we talked about earlier. When objects undergo shear strain, the number is called shear modulus. When they undergo tensile strain, it is called Young’s modulus.
Rule 19:
For substances that obey Hooke’s law, shear modulus equals shear stress divided by shear strain. Young’s modulus equals tensile stress divided by tensile strain. So if you know the tensile stress that is imposed on an object and you know the Young’s modulus for the substance of which the object is made, you can figure out the tensile strain that results from the stress. Also, if you know the shear stress that is imposed on an object and you know the shear modulus for the substance of which the object is made, you can figure out the shear strain that results from the stress.
For our purposes, there are 2 types of strain: Tensile strain and shear strain.
Rule 17: Definition of Strain
Tensile strain equals change in length divided by original length. Shear strain equals distance moved divided by original height. When a solid is subjected to a stress, it changes shape, and we call the change in shape a strain.
Rule 18: Definition of Stress
Stress equals force divided by area or F/A. Stress is usually measured in pascals (Pa). One pascal equals one newton meter squared. So, stress creates strain. Tensile stress creates tensile strain and shear stress creates shear strain. Tensile stress is a measure of stretching or compressing force per area perpendicular to the force. So in order to measure the tensile stress applied to a metal bar, we take the force applied to it and divide it by the cross-sectional area of the metal bar. Shear stress is measured in pascals just like tensile stress. Shear stress is equal to the tangential force over the area of the surface to which it is applied.
Moduli
Modulus is the constant number that we talked about earlier. When objects undergo shear strain, the number is called shear modulus. When they undergo tensile strain, it is called Young’s modulus.
Rule 19:
For substances that obey Hooke’s law, shear modulus equals shear stress divided by shear strain. Young’s modulus equals tensile stress divided by tensile strain. So if you know the tensile stress that is imposed on an object and you know the Young’s modulus for the substance of which the object is made, you can figure out the tensile strain that results from the stress. Also, if you know the shear stress that is imposed on an object and you know the shear modulus for the substance of which the object is made, you can figure out the shear strain that results from the stress.
