Smallest cross-sectional area of rod-end?

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SUMMARY

The discussion focuses on calculating the smallest cross-sectional area of a rod-end under stress in structural mechanics. A force of 50 kN is applied at pin C on rod BC, with the stress calculated using the formula 4P/πd² for the circular cross-section and P/wt for the rectangular end. The discussion highlights that the effective width is reduced due to material being cut out for the pin, leading to an increased stress calculation of P/(w-d)t at that section. This emphasizes the importance of considering geometric changes in stress analysis.

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samtrix
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i was doing some reading on structural mechanics and i stumbled across this example:

01.gif


i don't really get the highlighted part. anyone care to explain?

02.gif


:)
 
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The pin at C exerts a force of 50kN on rod BC. In the middle of the rod, the cross section is circular, and we calculate the stress as 4P/\pi d^2 (diameter d). At the end of the rod, the cross section is flattened into a rectangle, so the stress is P/wt (width w, thickness t). BUT the width is reduced where material is cut out to fit the pin. At this cross section the stress is higher, P/(w-d)t. Does this make sense?
 

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