Fig. . ) is of great importance for structural and manufacturing engineering designs. The ratio of stress and strain, called modulus of elasticity , is found to be a characteristic of the material.
. . Young’s Modulus Experimental observation show that for a given material, the magnitude of the strain produced is same whether the stress is tensile or compressive. The ratio of tensile (or compressive) stress ( σ ) to the longitudinal strain ( ε ) is defined as Young’s modulus and is denoted by the symbol Y .
Y = σ ε ( . ) From Eqs. ( . ) and ( .
), we have Y = ( F/A )/( ∆ L/L ) = ( F × L ) /( A × ∆ L) ( . ) Since strain is a dimensionless quantity, the unit of Young’s modulus is the same as that of stress i.e. , N m – or Pascal (Pa). Table .
gives the values of Young’s moduli and yield strengths of some material. From the data given in Table . , it is noticed that for metals Young’s moduli are large. Fig.
. Stress-strain curve for the elastic tissue of Aorta, the large tube (vessel) carrying blood from the heart. Table . Young’s moduli and yield strenghs of some material # Substance tested under compression u u Therefore, these materials require a large force to produce small change in length.
To increase the length of a thin steel wire of . cm cross- sectional area by . %, a force of N is required. The force required to produce the same strain in aluminium, brass and copper wires having the same cross-sectional area are N, N and N respectively.
It means that steel is more elastic than copper, brass and aluminium. It is for this reason that steel is preferred in heavy-duty machines and in structural designs. Wood, bone, concrete and glass have rather small Young’s moduli. Example .
A structural steel rod has a radius of mm and a length of . m. A kN force stretches it along its length. Calculate (a) stress, (b) elongation,