## Tuesday, December 22, 2009

### Elasticity

An important property of many structural materials is their ability to regain their original shape after a load is removed. These materials are called elastic.

Steel, glass and rubber are elastic; putty or modeling clay are not elastic. Each of these materials is elastic to varying degrees; steel and glass are both more elastic than rubber. The degree of elasticity, or "stiffness" of a material is called its Modulus of Elasticity (E). Given the modulus of elasticity, possible deformations can be calculated for any material and loading.

All materials are assumed to be elastic except when indicated otherwise in this course.

Robert Hooke (1635 - 1703), a great English scientist, experimented with springs, clocks and watches. During his investigation of the spring he discovered that in elastic materials, stress and strain are proportional. He first presented this in a lecture in 1678 and it is known today simply as Hooke's Law.

Hooke's Law applies as long as the material stress does not pass a certain point known as its proportional limit. This is the point at which the physical properties of the material actually change. Any time an elastic material is loaded between zero and the proportional limit, the stress and strain are directly proportional and if the load is released the material will regain its initial dimensions. If the stress is doubled the strain is doubled; if the stress is tripled the deformation is three times as great, etc.

The English physician and physicist Thomas Young (1773 - 1829) noted that if stress is proportional to strain, then for any given material, stress divided by strain would be a constant. This constant is known today as Young's Modulus or the Modulus of Elasticity.

The Modulus of Elasticity is represented by E = Stress / Strain.

This relationship is found as the slope of the curve of the stress-strain curve from initial loading to the proportional limit. A higher value of the modulus indicates a more brittle material (i.e. glass, ceramics). A very low value represents a ductile material (i.e. rubber).

Modulus of Elasticity

The values of the modulus of elasticity for structural materials have been determined by tests and are readily available in references such as the AISC manual. Some of the more common values are:

* Steel: E=29,000 KSI (sometimes rounded to 30,000 KSI)
* Aluminum: E=10,000 KSI
* Wood: E=1,000 - 2,000 KSI (usual range)
* Concrete E=2,500 - 5,000 KSI (usual range)

It is often necessary to be able to determine the deformation of a structural member once the loads and physical properties of the structural member are known. This is simply derived and is developed from the stress/strain relationships that have already been established. 