For drill pipe, Stiffness ratio (SR)= section modulus of lower section tube/ section modulus of upper section tube. SR= 5 for routine drilling and SR=3 for severe drilling.  

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Dear Eshag,

Various oilfield studies shows that almost all of the Drill Pipe fatigue failures are the result of an accumulation of fatigue damage occurring when the Drill Pipe joints were run in the Transition Zone, or were stressed above the endurance limit in crooked holes. Field tests indicated that fatigue build up in the Drill Pipe in the transition zone is related to the relative stiffness of the Drill Collars and the adjacent Drill Pipe. The stiffness ratio of two sections of pipe in the drill string is expressed by the equation,

SR= (I/C)Lower/ (I/C)Upper ,

Where I= moment of inertia= 31.4/64(OD4(to the power 4)- ID4(to the power 4),

C= External radius= OD/2,

ID= Internal Diameter, in and

OD= outside Diameter, in

The average field tests shows that the higher the stiffness ratio at the transition zone the greater the fatigue build up. Criteria for permissible stiffness ratio varies between different operators and areas. The following maximums are typical: For shallow or routine drilling or low failure rate experience, keep stiffness ratio below 5.5. For more severe drilling or for significant failure rate experience, keep SR below 3.5. In order to reduce the stiffness ratio and increase service life of the drill pipe, heavy weight drill pipe having the same OD as the drill pipe and a wall thickness of up to 1 in and weight up to 78 lb/ft is used between the drill pipe and the drill collars. The number of joints used varies between 15 to 21 joints.

Hope it is helpful to you.

Ashish