Modulus of elasticity (Young’s Modulus)

Elasticity is a property of an object or material indicating how it will restore it to its original shape

after distortion.

An elastic material is one in which the change in length is proportional to the load applied and in which the strain is proportional to the stress. Furthermore, a perfectly elastic material will immediately return to its original length when the load is removed.

A spring is an example of an elastic object - when stretched, it exerts a restoring force which

tends to bring it back to its original length. This restoring force is in general proportional to the

stretch described by Hooke's Law.

A graph of stress 𝜎, against strain 𝛆, is a straight line whose gradient is always found to be the same for a given material.

Figure 1 shows typical graphs for steel, copper and aluminium. The value of the gradient is a measure of the elasticity or ‘stiffness’ of the material, and is known as its Modulus of Elasticity, E.

FIG 1

Direct stress

Consider a component of original length l, and cross-sectional area A, which is subjected to a direct tensile load F as shown in Figur 2. Let the change of length be x.

FIG 2

It is assumed that the load in the material is distributed evenly over the cross-sectional area A, of the component. The direct stress 𝜎 in the material is the load carried by each square millimetre or

square metre of cross-sectional area.

the load and the stress are tensile and these are sometimes given a positive sign. Compressive loads produce compressive stress and these are sometimes given a negative sign. You

Direct strain 𝛆, is a measure of the deformation which the load produces. It is the change in length given as a fraction of the original length.