Question

2. [10] A rod is made from a material with an ultimate strength of 200 MPa and an endurance limit of 100 MPa. Fully reversed stress at N cycles ($S_N$) is decreased by 20 MPa when N becomes 10 times larger(e.g. $S_{1000} = S_{100} - 20$ MPa). This rod is to be loaded axially with a mean tensile stress of $\sigma_m$ plus an alternating stress of $\sigma_a$. Use the Goodman relationship for the questions below. $\frac{\sigma_a}{S_e} + \frac{\sigma_m}{S_u} = 1$ ($S_e$: endurance limit, $S_u$: ultimate strength) (a) If $\sigma_a = 0.5\sigma_m$, how large $\sigma_m$ can be for the rod to never fail? (b) If $\sigma_m$ is fixed to the value calculated in (a), how large $\sigma_a$ can be in order to use the rod without failure at least for 1000 cycles? Assume the endurance limit corresponds to $10^6$ cycles.

          2. [10] A rod is made from a material with an ultimate strength of 200 MPa and an endurance limit of 100 MPa. Fully reversed stress at N cycles ($S_N$) is decreased by 20 MPa when N becomes 10 times larger(e.g. $S_{1000} = S_{100} - 20$ MPa). This rod is to be loaded axially with a mean tensile stress of $\sigma_m$ plus an alternating stress of $\sigma_a$. Use the Goodman relationship for the questions below.
$\frac{\sigma_a}{S_e} + \frac{\sigma_m}{S_u} = 1$
($S_e$: endurance limit, $S_u$: ultimate strength)
(a) If $\sigma_a = 0.5\sigma_m$, how large $\sigma_m$ can be for the rod to never fail?
(b) If $\sigma_m$ is fixed to the value calculated in (a), how large $\sigma_a$ can be in order to use the rod without failure at least for 1000 cycles? Assume the endurance limit corresponds to $10^6$ cycles.

2. [10] A rod is made from a material with an ultimate strength of 200 MPa and an endurance limit of 100 MPa. Fully reversed stress at N cycles (SN) is decreased by 20 MPa when N becomes 10 times larger(e.g. S1000 = S100 - 20 MPa). This rod is to be loaded axially with a mean tensile stress of plus an alternating stress of . Use the Goodman relationship for the questions below.
()/(Se) + ()/(Su) = 1
(Se: endurance limit, Su: ultimate strength)
(a) If = 0.5, how large can be for the rod to never fail?
(b) If is fixed to the value calculated in (a), how large can be in order to use the rod without failure at least for 1000 cycles? Assume the endurance limit corresponds to 10^6 cycles.

Added by Heather P.

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