PROBLEMS ON VOLUMETRIC STRAIN,LATERAL STRAIN,LONGITUDINAL STRAIN AND POISSON’S RATIO

      

      1)    Determine the changes in length, width and thickness of a steel bar which is 4m long, 30 mm wide and 20mm thick and is subjected to an axial pull 30KN in the direction of length. E=2x10⁵N/mm² and poison’s ratio=0.3.Also determine the volumetric strain, change in volume and final volume.

      

            Step 1: Data

          Length: 4m = 4000 mm

            Width = 30mm

Thickness = 20mm

Load = 30KN

E=2x10⁵N/mm²

poison’s ratio= 0.3

volumetric strain, change in volume and final volume = ??

Step 2: Calculation of area of the material

A= b X d

A = 30 X 20

A = 600mm²

Step 3: Calculation of stress:

Stress = Load/area of cross section

Stress = 30 X 1000 /600

Stress= 50 N/mm²

Step 4: Calculation of longitudinal strain:

E = σ/e

2x10⁵ = 50/e

Longitudinal strain = 0.25X10^-3

Step 5: Calculation of lateral strain:

ϻ = lateral strain/ longitudinal strain

0.3 = lateral strain / 0.25X10^-3 

lateral strain = 0.075X10^-3 

Step 6: Calculation of change in volume

e_v = (dl/l)(1-2ϻ)

e_v=(0.25X10^-3)(1-2(0.3))

e_v= 0.1X10^-3    

Step 7 Calculation of change in volume:

e_v = dv/v

Volume = lbd

             = (4000) (30) (20)

             = 24x10⁵ mm³

0.1X10^-3 = dv/24x10⁵ 

dv= 240 mm³