GATE-2018 (24) :Wyllie – Time average equation

17. A cylindrical sample of granite (diameter = 54.7 mm; length = 137 mm) shows a linear relationship between axial stress and axial strain under uniaxial compression up to the peak stress level at which the specimen fails. If the uniaxial compressive strength of this sample is 200 MPa and the axial strain corresponding to this peak stress is 0.005, the Young’s modulus of the sample in GPa is _______ (in integer).

 

Solution:

Given that the Axial stress= 200 Mega Pascal=200*10⁶ Pascal

                            Axial strain =0.005

 

Then the Young’s modulus (E) = $\frac{Axial Stress}{Axial Starin}$

 

$=\frac{200\times 10^{6}Pascal}{0.005}$

 

$=\frac{200\times 10^{6}Pascal}{5\times 10^{-3} }$

 

$=40\times 10^{9} Pascal$

 

Young’s modulus (E) =40 Giga Pascal