# T N Jp LjTJJ

T = torque transmitted: lbs-ft

N = change in rotational speed of the drillcollars; rpm

Jp = polar moment of inertia of the drillpipe; in4

Jc = polar moment of inertia of the drill collars; in4

Roark published an equation which predicts the minimum torque required to buckle a tube. His equation is

BT = resistance to buckling of the tube; lbs-ft L = cross-sectional moment of inertia of the tube; in4

Lc = length of the tube; ft

P = axial load (compression is - and tension is +); lb

If the bit hangs-up while rotating at 100 rpm and the drill string is composed of 400' of 8" * 3" collars and 5" * 4.276" * 19.5 ppf drillpipe, can the drill collars and drillpipe torsionally buckle?

Compute the resistance to buckling of the collars and the drillpipe and compare these values with the torque created by the bit hang-up.

The drill collars would be normally axially compressed at a point near the bit by 40,000 lbs with this BHA. Thus, P is set to 40,000 for the collars and a value of zero for the drillpipe. The length of the drillpipe is set at 10,000 feet. The moments of the collars and drillpipe are leg" = * (84 " 34) Ip5" = * (54 - 4.2764)