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

 

20) A cylindrical specimen (diameter=54.7 mm; length=110mm) of basalt shows linear elastic behavior under uniaxial compression. At an axial stress of 100 mega Pascal (MPa) the absolute value of the measured axial strain is 0.2%. The young’s modules is calculated to be_____GigaPascal (GPa).

 (Thanks to Chandrasekhar, ANU)

Solution:

Given that the Axial stress= 100 Mega Pascal=100*10⁶ Pascal

                        Axial strain = 0.2%=0.002

 

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

 

$=\frac{100\times 10^{6}Pascal}{0.002}$

 

$=\frac{100\times 10^{6}Pascal}{2\times 10^{-3} }$

 

$=50\times 10^{9} Pascal$

 

$=50 Giga Pascal$