# Relationship between stress strain and young modulus reference

### Young’s modulus | Description, Example, & Facts | changethru.info

3 days ago Explain the concepts of stress and strain in describing elastic Note that the relation between stress and strain is an observed relation, measured in These tables are valuable references for industry and for anyone involved. This kind of graph is called stress- strain curve. Young Modulus Instead of drawing a force - extension graph, if you plot stress against strain for an listed in the form of a table in reference books so scientists and engineers can look them up. Sometimes referred to as the modulus of elasticity, Young's modulus is equal to the longitudinal stress divided by the strain. Stress and strain may be described as follows in the case of a metal bar The ratio of the transverse strain to the longitudinal strain is called Poisson's ratio. 7 references found in Britannica articles.

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.

### Young's modulus of elasticity (video) | Khan Academy

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.

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.

## 12.3: Stress, Strain, and Elastic Modulus (Part 1)

Steelcarbon fiber and glass among others are usually considered linear materials, while other materials such as rubber and soils are non-linear.

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. It can be experimentally determined from the slope of a stress—strain curve created during tensile tests conducted on a sample of the material.

Directional materials[ edit ] Young's modulus is not always the same in all orientations of a material. Compressive Stress in a Pillar A sculpture weighing 10, N rests on a horizontal surface at the top of a 6.

Find the compressive stress at the cross-section located 3. The normal force that acts on the cross-section located 3. Once we have the normal force, we use Equation Thus, if the pillar has a uniform cross-sectional area along its length, the stress is largest at its base.

**Stress & Strain - Elastic Modulus & Shear Modulus Practice Problems - Physics**

Stretching a Rod A 2. Ignoring the weight of the rod, what is the tensile stress in the rod and the elongation of the rod under the stress? Strategy First we compute the tensile stress in the rod under the weight of the platform in accordance with Equation Then we invert Equation Unlike in the previous example, however, if the weight of the rod is taken into consideration, the stress in the rod is largest at the top and smallest at the bottom of the rod where the equipment is attached.

What is the tensile strain in the wire?