Relationship between stress strain hookes law apparatus

Stress, Strain and Hooke's Law - Lesson - TeachEngineering

relationship between stress strain hookes law apparatus

[link] shows the Hooke's law relationship between the extension \Delta L . Note that this stress-strain curve is nonlinear, since the slope of the line changes .. In , a kg physicist placed himself and kg of equipment at the top of. Hooke's law, law of elasticity discovered by the English scientist Robert Hooke in , Hooke's law may also be expressed in terms of stress and strain. Illustration of Hooke's Law, showing the relationship between force and it possible to deduce the relationship between strain and stress for.

You will also practice graphing prepared data to depict cancerous tissue. After we have mastered this material, we will have a quiz on stress, strain and Hooke's law. Please take careful notes and be sure to ask any questions you have about the example problems we will be working through.

Referring back to the legacy cycle which we discussed in the previous lesson, today's lesson constitutes the research and revise phase.


Refer back to your initial thoughts notes and record any new information that applies to solving the challenge. Your goal today is to review, revise and expand your current knowledge!

relationship between stress strain hookes law apparatus

Now, let's learn how to detect cancer. Students begin to learn the basic concepts required for creating a strain graph to depict cancerous tissue. Following this lesson, have students revise their initial thoughts and at the conclusion of the associated activity, students should have the skills necessary to Go Public with a solution.

The quiz serves as a formative assessment while the next lesson's Go Public phase provides a summative assessment.

  • What is Hooke's Law?
  • Mechanics of Materials: Strain
  • Hooke's Law - Stress And Strain

Just like stress, there are two types of strain that a structure can experience: When a force acts perpendicular or "normal" to the surface of an object, it exerts a normal stress. When a force acts parallel to the surface of an object, it exerts a shear stress. Let's consider a rod under uniaxial tension.

Hooke's law

The rod elongates under this tension to a new length, and the normal strain is a ratio of this small deformation to the rod's original length. Strain is a unitless measure of how much an object gets bigger or smaller from an applied load. Shear strain occurs when the deformation of an object is response to a shear stress i. Mechanical Behavior of Materials Clearly, stress and strain are related.

Stress and strain are related by a constitutive law, and we can determine their relationship experimentally by measuring how much stress is required to stretch a material. This measurement can be done using a tensile test.

relationship between stress strain hookes law apparatus

In the simplest case, the more you pull on an object, the more it deforms, and for small values of strain this relationship is linear. This linear, elastic relationship between stress and strain is known as Hooke's Law. If you plot stress versus strain, for small strains this graph will be linear, and the slope of the line will be a property of the material known as Young's Elastic Modulus.

This value can vary greatly from 1 kPa for Jello to GPa for steel. In this course, we will focus only on materials that are linear elastic i. From Hooke's law and our definitions of stress and strain, we can easily get a simple relationship for the deformation of a material. Intuitively, this exam makes a bit of sense: If the structure changes shape, or material, or is loaded differently at various points, then we can split up these multiple loadings using the principle of superposition.

Generalized Hooke's Law In the last lesson, we began to learn about how stress and strain are related — through Hooke's law. But, up until this point we've only considered a very simplified version of Hooke's law: In this lesson, we're going to consider the generalized Hooke's law for homogenousisotropicand elastic materials being exposed to forces on more than one axis.

Hooke’s law | Description & Equation |

First things first, even just pulling or pushing on most materials in one direction actually causes deformation in all three orthogonal directions. Let's go back to that first illustration of strain. This law had many important practical applications, with one being the creation of a balance wheel, which made possible the creation of the mechanical clock, the portable timepiece, the spring scale and the manometer aka.

Also, because it is a close approximation of all solid bodies as long as the forces of deformation are small enoughnumerous branches of science and engineering as also indebted to Hooke for coming up with this law. These include the disciplines of seismology, molecular mechanics and acoustics. However, like most classical mechanics, Hooke's Law only works within a limited frame of reference.

Because no material can be compressed beyond a certain minimum size or stretched beyond a maximum size without some permanent deformation or change of state, it only applies so long as a limited amount of force or deformation is involved. In fact, many materials will noticeably deviate from Hooke's law well before those elastic limits are reached. Still, in its general form, Hooke's Law is compatible with Newton's laws of static equilibrium. Together, they make it possible to deduce the relationship between strain and stress for complex objects in terms of the intrinsic materials of the properties it is made of.

For example, one can deduce that a homogeneous rod with uniform cross section will behave like a simple spring when stretched, with a stiffness k directly proportional to its cross-section area and inversely proportional to its length.


Another interesting thing about Hooke's law is that it is a a perfect example of the First Law of Thermodynamics. Any spring when compressed or extended almost perfectly conserves the energy applied to it. The only energy lost is due to natural friction.