Two pieces of shafting (1-in. diameter) are in line with each other and are join

Question

Two pieces of shafting (1-in. diameter) are in line with each other and are joined
together at the point where their ends meet by a sleeve that fits over the adjoining
ends. The sleeve is attached to each bar by a quarter inch diameter pin that goes
through the sleeve and shaft at right angles to the axis of the shaft. If the torque
transmitted by the shaft is 300 in-lb, what is the shear stress in the pins?

Note: to offer a clearer image, imagine the two shafts connected end to end, with a sleeve over them where the connection is. From outside of the sleeve, two pins, one on each side of the connection, is passed through the sleeve to the center of the shaft. the pin does not go all the way through, just to the center, so there is only 1 shear point per side of the connection.

Explanation / Answer

T = 300 in-lb

The shear force in the pin is caused by the tortion of the ahsft, and can calculated from

V = T/dshaft = 300/1 = 300 lb

shear stress is = V/Apin = 300/(*0.252/4) = 6111.55 psi

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