Stress strain relations normal stresses produce normal strains. F kx, where k is a constant factor characteristic of the spring, its stiffness. Hookes law describes the experimentally observed linear relation bet ween stresses and. The force per unit area required to produce any elastic deformation is referred to as the stress. As said this stress may be of 2 types, tensile and compressive. Mathematically, hookes law is commonly expressed as. In mechanics, the force applied per unit area is known as stress and is denoted by the symbol the extent to which the material compresses or stretches is known as strain. In position a the spring is at rest and no external force acts on the block. Hooke s law is a principle of physics that states that the that the force needed to extend or compress a spring by some distance is proportional to that. Hooke s law elastic force occurs in the spring when the spring is being stretchedcompressed or deformed. For a given material, youngs modulus e is the ratio of stress to strain, provided the limit of. Hooke s law is a principle of physics that states that the force f needed to extend or compress a spring by some distance x is proportional to that distance.
Tensile stress tends to enhance length and compressive stress tries to decrease the length. For relatively small stresses, stress is proportional to strain. For this physics lesson, 11th graders perform a computer simulation on hooke s law. From the definitions of stress and strain, you should see that. The constant e is youngs modulus and represents the stiffness of the the material. Hookes law states that for small deformities, the stress and strain are proportional to each other. The law is named after 17th century british physicist robert hooke. Generalized hookes law the generalized hookes law for a material is given as. Quantify the linear elastic stress strain response in terms of tensorial quantities and in particular the fourthorder elasticity or sti ness tensor describing hookes law.
When stress and strain were covered in newtons third law of motion, the name was given to this relationship between force and displacement was hooke s law. In simple terms, hookes law says that stress is directly proportional to strain. Stress, strain and hookes law problem set solutions pdf. Cbse class 11 physics notes for mechanical properties of solid, hookes law, stress and strain. The displacements go as 1r, which means that the strain stress go as 1r2. This is much like the case of electrostatics, where the total energy of the. Beyond the elastic limit plastic deformation occurs and strains are not totally recoverable. Stress and stress are connected via a constitutive. Request pdf stress, strain, hookes law a system of forces with a common point of application can be replaced by a statically equivalent force. However, hookes law also relates shear strain and shear stress. Hookes law holds up to a maximum stress called the proportional limit.
If we apply a force to a rubber band, we find that the rubber band stretches. Hooke s law holds up to a maximum stress called the proportional limit. When the elastic materials are stretched, the atoms and molecules deform until stress is been applied and when the stress is removed they return to their initial state. It is important to note that hookes law is valid for most materials. Eleventh graders explore hooke s law through a variety of hands on activities. Elastic force acts in the opposite direction of the external force. George ferdinand becker, the finite elastic stressstrain function, the american. Strain is the relative deformation produced by stress. For example, k k size 12k is directly related to youngs modulus when we stretch a string.
The total strain in the xdirection is, the total strain in the ydirection is, and the total shear strain is. This law gives us a relation between stress and strain. Part of mechanics of materials for dummies cheat sheet. Hooke s law in terms of stress and strain is stress strain in terms of the definitions l l y a f the constant of proportionality is called the elastic modulus or youngs modulus. At pre16 level or earlier, most students will have carried out a springstretching. When force is applied to a material, we know that it either stretches or compresses in response to the applied force.
When stress and strain were covered in newtons third law of motion, the name was given to this relationship between force and displacement was hookes law. The graph will bend the same way to the hooke s law graph if tension is on the yaxis and extension on the xaxis. They depend on location within an elastic body, as well as time and temperature. Hooke s law can be expressed in 3d space or 6d space depending on whether the stress and the strain are tensors or column matrices. The left side of each equation is the magnitude of the force per unit area required to cause an elastic deformation. These expressions can be inverted to obtain stress in terms of strain. Cbse class 11 physics notes for mechanical properties of. Hookes law may also be expressed in terms of stress and strain. Hookes law can also be explained in the terms of strain and stress. As discussed in the previous lecture, it is important not to lose sight that the material element is a threedimensional body and we have only been considering a twodimensional view of it. Like stress, strain is also a 2 nd order tensor that can be represented as a 3 x 3 matrix. Stress is the force on unit areas within a material that develops as a result of the externally applied force. He first stated the law in 1660 as a latin anagram. Therefore the expression for hookes law in plane stress is given as.
The fractional change in a quantity d ll 0, d xl 0, or d vv 0 that results when a stress is applied is referred to as the strain. Applications of a recurring principle article pdf available in ajp advances in physiology education 334. It is the general question that is asked in the subject strength of materials. The units of k k size 12k are newtons per meter nm. In position c, a force f is used to stretch the spring by a length. Hookes law in terms of a loaddisplacement and b stressstrain. In mechanics of materials, hookes law is the relationship that connects stresses to strains. Model to demonstrate hooke s law and illustrate that physiological phenomena, such as lengthtension relationships of the heart starling mechanism, aortic recoil, and lung recoil, share.
Hookes law problems and solutions solved problems in. In position b a force f is used to compress the spring by a length equal to. Therefore the elastic energy density, which goes like 2, goes like 1r4 and its integral diverges. The limiting point b for this condition is termed the elastic limit. Stress, strain and hookes law lesson teachengineering. Hookes law may be also expressed in terms of stress and strain. Where, f is force, k is constant of proportionality and x is displacement. The generalized hooke s law also reveals that strain can exist without stress.
It tries to bring the deformed end of the spring to the original equilibrium position. There will thus be some permanent deformation or permanent set when load is removed. Hooke s law states that the extensionx of a spiral spring. That means these forces tend to cause change in length of the solid body and generates longitudinal stress.
Hookes law states that the applied force is equal to a constant times the change in length or displacement. Using a generalized hookes law for stress and strain. For most practical purposes it can often be assumed that points a and b are coincident. Hooke s law free download as powerpoint presentation. Let a force is applied on a body which can modify the shape and size of the object. When the scope of the law is confined to minute strains, hookes own law and that. As a material deforms along an axis due to an applied stress on that axis, the material also deforms along any axis lateral to the axis. A graph of force f versus elongation x shown in the figure below. They design a mechanism to test the stress and strain of certain materials. In this model, the strain energy density function is of the form of a polynomial in the two invariants, of the left cauchygreen deformation tensor the strain energy density function for the polynomial model is. Pdf an overview of stressstrain analysis for elasticity equations. Hookes law in terms of stress and strain is stress strain in terms of the definitions l l y a f the constant of proportionality is called the elastic modulus or youngs modulus.
Hooke s law in compliance form hooke s law for isotropic materials in compliance matrix form is given by, some literatures may have a factor 2 multiplying the shear modulii in the compliance matrix resulting from the difference between shear strain and engineering shear strain, where, etc. The only nonvanishing stress component is a constant tension or pull pdf aalong x, so that the complete symmetric stress tensor becomes. Here, f is the restoring force, x is the displacement from equilibrium or deformation, and k is a constant related to the difficulty in deforming the system. In continuous elastic materials hookes law implies that strain is a linear function. Materials for which hookes law is a useful approximation are known as linearelastic or hookean materials. The generalized form of hooke s law relating stress to strain is.
The polynomial hyperelastic material model is a phenomenological model of rubber elasticity. Units and dimension of the modulus of elasticity are same as those of stress. Strain where k is the constant of proportionality and is the modulus of elasticity. Although hookes original law was developed for uniaxial stresses, you can use a generalized version of hookes law to connect stress and strain in threedimensional objects, as well. Though his law was established for the case of springs alone, it has since been related to all. Hooke s law in the diagram below is shown a block attached to a spring. Students are introduced to hookes law as well as stressstrain relationships. Students are introduced to hooke s law as well as stress strain relationships. Hookean materials are broadly defined and include springs as well as muscular layers of the heart. To understand the hookes law its mandatory to understand 2 terms. Module 3 constitutive equations learning objectives understand basic stress strain response of engineering materials. It some engineering texts, the maximum shear stress determined by viewing the. Hooke s law quick reference the physical principle that the stress within a solid is proportional to the strain, so that the movement of an object is proportional to the pressure that is applied to it.
976 1079 1012 1359 732 1187 230 844 361 1473 406 775 442 401 588 1037 1482 844 444 1540 1092 775 1494 306 153 719 393 1161 1295 1214 299 552 17 1543 1148 126 1249 936 195 835 1087 729 64 30 813 1120 1316 972 1023