The solid round bar shown in the figure is not rotating. The bar is loaded with a repeated bending load that cause the maximum bending moment to fluctuate between $0$ and $4000lbf.in.$ The bar was machined of steel with $Sy=71$ksi and Sut $=85$ ksi $.$ Determine the fatigue life of the bar at room temperature and $99\%$ reliability.

Question $1(1$ point$)$

The part will fail where the fatigue stress is maximum. Sections $A,B,C$ and $D$ need to be investigated. Section $B$ is located at maximum moment. At this location there is no stress concentration. Points A$,$ C and D will experience lesser moments but have higher stress concentrations. Calculate the maximum fatigue stress at each location to determine at what section do you estimate the part failure? $($A$,$ B$,$ C or D$?)$

Section A

Section B

Section C

Section D

Question $2(1$ point$)$

The mean stress different from zero suggests the use of the Goodman diagram for fatigue life calculations. $S_e,$ the fatigue endurance at ${10}^6$cycles is needed to construct the Goodman diagram. Calculate the fatigue endurance, $S_e,$ at ${10}^6$cycles :

$q,$ ksi$).$

$q,$ ur Answer:

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Answer

Question $3(1$ point$)$

Use the following relations to determine the zone in the Goodman Diagram. $($G$1,$ G$2$ G$3$ or G$4?)$

$\frac{{}_{fa}}{S_e}+\frac{{}_{fm}}{S_{ut}}=$

${}_{fa}-{}_{fm}=$

G$1-$ infinite life

G$2-$ eventual failure

G$3-$ finite life

G$4-$ yield before fatigue

Question $4(1$ point$)$

Calculate the amplitude of the equivalent completely reversed stress which should be used together with the SN diagram to determine the finite fatigue life : $($ Xssi $)$

Your Answer:

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Answer

Question $5(1$ point$)$

Based on the results we will need $f{S}_{ut}.$ Verify with the diagram presented in the lecture that the $f$ factor is $0\mathrm{.}87$ ; Use this f factor to calculate $f{S}_{ut}$: $($ X ksi $)$

Your Answer:

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Answer

Question $6(1$ point$)$

Use the Basquin equation to calculate the finite life: $($X E$5$ cycles$)$

Your Answer:

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Answer