Hooke’s Law and Modulus of Elasticity ( ) - ppt video online download
To understand the relationship between the Young's modulus and the at equation () if it still doesn't make sense, look at equation (). Elasticity: Young's modulus & Hooke's Law doesn't obey (F/A)= Y (∆l/l).elastic limit: after this strain threshold which the equation is no longer applicable!. Objectives: ◇ Learn and constitutive relationship of linear materials. ◇ Know Shear stress distribution varies from zero at the member surfaces . Young's modulus = elastic modulus. (E) The Hooke's law is valid only in the elastic region.
Lecture Information In the late s, Robert Hooke stated that "The power of any springy body is in the same proportion with the extension. The law is explained by a direct proportionality between a spring's compression or expansion and the restoring force which ensues.
This law is valid within the elastic limit of a linear spring, when acting along a frictionless surface.
Hooke’s Law and Modulus of Elasticity ( )
Extending Hooke's exploration of springs, it becomes apparent that most materials act like springs with force being directly proportional to displacement. But as compared to springs, other materials possess an area which must be accounted for. We will now explore the measures of stress and strain.
The SI unit for stress is pascals Pa which is equal to 1 Newton per square meter. The Psi is an alternative unit which expresses pounds per square inch. The units of stress are equal to the units of pressure which is also a measure of force per unit area.
Stress cannot be measured directly and is therefore inferred from a measure of strain and a constant known as Young's modulus of elasticity. Statically indeterminate structure — there are more unknown reactions than equations of equilibrium. Where do the other equations needed to solve the unknown reactions come from? Equations of compatibility which are based on displacements. Here is a easy method to determine how many compatibility equations you need for any given problem: In this case, there is thermal strain but no thermal stress!
Deformations 24 Temperature Changes Thermal stresses occur when the bar is constrained such that it cannot deform freely. In this case there is thermal stress but no thermal strain! There is a relationship between them which is derived in section 2.
An isotropic material has two independent properties. More Mechanical Properties 35 More Mechanical Properties Example Problem A vibration isolation unit consists of two blocks of hard rubber bonded to a plate AB and to rigid supports as shown. However, Hooke's law is only valid under the assumption of an elastic and linear response.
Any real material will eventually fail and break when stretched over a very large distance or with a very large force; however all solid materials exhibit nearly Hookean behavior for small enough strains or stresses.
solid state physics - From the local Hooke's law to the global one - Physics Stack Exchange
If the range over which Hooke's law is valid is large enough compared to the typical stress that one expects to apply to the material, the material is said to be linear. Otherwise if the typical stress one would apply is outside the linear range the material is said to be non-linear. Steelcarbon fiber and glass among others are usually considered linear materials, while other materials such as rubber and soils are non-linear.Young's modulus and Hooke's Law
However, this is not an absolute classification: For example, as the linear theory implies reversibilityit would be absurd to use the linear theory to describe the failure of a steel bridge under a high load; although steel is a linear material for most applications, it is not in such a case of catastrophic failure.
In solid mechanicsthe slope of the stress—strain curve at any point is called the tangent modulus.