Question
Download Solution PDFLinear strains along X, Y and Z directions in an object with homogenous material are given as 0.05, 0.10 and 0.10, respectively. The size of the object before deformation was 20 cm × 10 cm × 10 cm. Determine the volumetric strain and change in volume of the material after deformation.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFSolution:
Given:
- Linear strain along X direction, \(\epsilon_x\) = 0.05
- Linear strain along Y direction, \(\epsilon_y\)= 0.10
- Linear strain along Z direction, \(\epsilon_z\) = 0.10
- Original dimensions of the object: 20 cm, 10 cm and 10cm
Original volume of the object, V
V= 20 × 10 × 10 = 2000 cm3Volumetric Strain:
Volumetric strain, \(\epsilon_v\) is the sum of the linear strains:
\(\epsilon_x\) + \(\epsilon_y\) + \(\epsilon_z\)= 0.05 + 0.10 + 0.10 = 0.25Change in Volume:
The change in volume δV, can be calculated using the volumetric strain and the original volume:
\({δV \over V} = \epsilon_v\)= 0.25 × 2000 cm3= 500 cm3Since 1 cm3 = 1000 mm3, the change in volume in mm3 is: 5 × 105 mm3
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