Question

Chapter 06, Problem 6.38 An alloy to be used for a spring application must have a modulus resilience of at least 0.80 x 106 J/m3 (0.80 x 106 Pa). What must be its minimum yield strength (in MPa)? Assume that the modulus of elasticity for this alloy is 109 GPa. MPa

Answer 1

Resilience is given as;

$U_r = \frac{\sigma_y^2}{2E}$

$\Rightarrow \sigma_y = \sqrt{2U_rE}$

$\Rightarrow \sigma_y = \sqrt{2(0.80\times10^6)(109\times10^9)}$

$\Rightarrow \sigma_y =417.6(10^6)\;\;Pa$

$\Rightarrow \sigma_y =417.6\;\;MPa$

....(Answer)