MecMovies 4.0 : M1.6: Shear Stress in Bolted Flanges

The figure on the left shows a shaft with a flange at one end. The axis of the shaft is along the x axis. The torque at the end of the shaft has a magnitude T and is directed counterclockwise. The force on each of the bolt is F subscript bolt directed opposite to the torque T. The figure on the right shows the front view of the flange. The bolt circle has a diameter of 250 millimeters.

The bolts are installed on a $250 mm -$ diameter bolt circle, which means that each bolt is located at a radial distance of $125 mm$ from the centerline of the flange and shaft.

Sum moments about the $x$ axis to find the bolt force:

$\sum_{} M_{x} = T - (4 bolts) (125 mm) F_{bolt} = 0$
$∴ F_{bolt} = \frac{(10 kN - m) (1, 000 mm / m)}{(4 bolts) (125 mm)}$
$= 20 kN / bolt$