Answer
(A)$u=43.1 \frac{in.lb}{in^{3}}$
(B)$u= 72.8 \frac{in.lb}{in^{3}}$
(C)$u= 172.4 \frac{in.lb}{in^{3}}$
Work Step by Step
We will just replace the units in the formula to determine the module of resilience.
Modulus of elasticity :
$E= 29. 10^{6} psi$
$σy$ : The uniaxiaxl tensile yield strength :
$σy= 50 ksi$
u= The modules of resilence is defined as the maximum energy that can be absorbed per unit volume without creating permanent distortions:
Modules of resilience
$u= \frac{σ^{2}_{y}}{2E}$
$u = \frac{(50.10^{3})^{2}}{2.(29.10^{6})}$
$u=43.1 \frac{in.lb}{in^{3}}$
(B)
Modulus of elasticity
E=$29.10^{6} psi$
Yield strength :
$σ_{y}=65 ksi$
Modulus of resilience :
$u= \frac{σ^{2}_{y}}{2E}$
$u=\frac{(65.10^{3})^{2}}{2.(29.10^{6})}$
$u= 72.8 \frac{in.lb}{in^{3}}$
c) Modulus of elasticity :
$E= 29.10^{6}$
Yield strength
$σ_{y}= 100 ksi$
Modulus of resilience
$u= \frac{σ^{2}_{y}}{2E}$
$u=\frac{(100.10^{3})^{2}}{2.(29.10^{6})}$
$u= 172.4 \frac{in.lb}{in^{3}}$
