Hook's Law. Elastic, shear and bulk modulus. assistancedogseurope.info Def. Robert Hooke ( - ) in performing such experiments as the above arrived at Hook's Law: . we die and it comes time for God to judge us, He will .. for the stress leads to Hooke's law, which is a linear relationship between the stress and the .. (), strain stiffening is defined as increase in a material's elastic modulus with applied . 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modulus & Hooke's Law doesn't obey (F/A)= Y (∆l/l).elastic limit: after this strain threshold which the equation is no longer applicable!.
Because window glass is itself very stiff, the windows were unable to flex along with the building frame, and they simply popped out of their mountings. It is important to note that the structural design was, in fact, safe.
The stresses in the structural 9 members were within allowable limits. Nonetheless, the building failed to fulfill its intended function because of excessive deformations.
Elasticity: Young's modulus & Hooke's Law - SchoolWorkHelper
A deformation is simply a change in the dimensions or shape of a body. Deformations can be caused by applied loads or by changes in temperature. Deformations are important to engineers for four principal reasons: Deformation is a measure of performance. As the case of the John Hancock tower illustrates, when structural elements deform excessively, an entire structure may fail to function as intended. The tendency to deform under load is one of several methods commonly used to characterize materials.
Unlike stresses, deformations can be directly measured. And because there is a clear mathematical relationship between stress and deformation, measured deformations can be used to indirectly determine the stresses in a body. Thus deformations are very important to our understanding about how structures work. Deformations are particularly valuable for analyzing statically indeterminate structures. A statically indeterminate structure is one for which the equations of equilibrium alone are not sufficient to solve for all unknown reactions and internal forces.
In such problems, deformations are used as the basis for formulating the additional equations necessary to analyze the structure. We will not analyze statically indeterminate structures in CE, but civil engineering majors will do so in a later course. It is important to note that, while there are two different expressions for lateral strain, a given axially loaded member with a given applied load has just one value of lateral strain.
The lateral deformations might be different in the two lateral directions—but the lateral strain is always the same in both directions. In all cases, the general expression for normal strain is the deformation divided by the original length.
Because this calculation is always a length divided by a length, strain is actually a dimensionless quantity. The Young's modulus directly applies to cases of uniaxial stress, that is tensile or compressive stress in one direction and no stress in the other directions.
Young's modulus is also used in order to predict the deflection that will occur in a statically determinate beam when a load is applied at a point in between the beam's supports. Other elastic calculations usually require the use of one additional elastic property, such as the shear modulusbulk modulus or Poisson's ratio. Any two of these parameters are sufficient to fully describe elasticity in an isotropic material.
Linear versus non-linear[ edit ] Young's modulus represents the factor of proportionality in Hooke's lawwhich relates the stress and the strain.
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.
Young's modulus - Wikipedia
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. Stress or intensity of stress at a point. Stress per unit of area at the point. Its value at any particular point of a section is the stress on an infinitesimally small element of area about the point divided by the area of the element.
In general, it varies from point to point in the section. Stresses are expressed in pounds per square foot, tons per square foot, kilograms per square centimeter, etc. External forces that tend to change the length or shape of a body create resistive internal forces that resist the action.
Elasticity: Young’s modulus & Hooke’s Law
Tensile stress or tension. The internal force that resists the action of external forces tending to increase the length or dimensions of a body. Compressive stress or compression. The internal force that resists the action of external forces tending to decrease the length or dimensions of a body.
Three types of stress. At any point in a body there can be any one of the following three types of stress: Tensile stress is caused by forces that stretch. Compressive stress is caused by forces that compress. The upper side is in tension and the lower side is in compression.
Here two equal and opposite forces F act on a rectangular block so as to push the top one way and the bottom the other, thus creating shear stress in the block. Shear stresses are forces that resist a tendency for one part of a body to slide over another.
Force F represents the weight of the beam and any loads on the beam at the wall. Force R is the reaction of the wall pushing upward. A normal stress on a section is one that acts in a direction perpendicular to the section considered.