(Mechanical eng.) The minimum radius required for a cylindrical rod, such as one supportin...

(Mechanical eng.) The minimum radius required for a cylindrical rod, such as one supporting a bicycle pedal (see Figure), to provide enough support for the pressure exerted by the rider’s foot yet not exceed the stress placed on the crank arm’s sprocket attachment, is given by this formula:

r is the radius of the cylindrical rod in inches.

d is the length of the crank arm in inches.

P is the weight placed on the pedal in lbs.

S is the stress in lbs/in2. 

Figure: Determining the minimum radius of a bicycle’s crank arm