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We operate a bicycle whose crank is instrumented with strain gages in the ME 3221 "Fluctuating Stress" lab. The geometry of the pedal crank shaft is...

We operate a bicycle whose crank is instrumented with strain gages in the ME 3221
“Fluctuating Stress” lab. The geometry of the pedal crank shaft is shown below. The
worst stressed section is at the right shoulder. The dimensions of the shaft at that
section are shown.
Assume the shaft is made from I:AISI 4130 steel, water-quenched and tempered at
650◦C. The shaft surface is ground at the worst stressed section.
The stress elements below indicate the maximum nominal stress and the minimum
nominal stress expected at the worst stressed point. The normal stress is attributable
to bending. The shear stress is attributable to torque.
Determine if the shaft would have infinite life at 99% reliability if the stress varies
sinusoidally between these two states.
(a) Use the Goodman criteria.

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