Flexibility and member orientation
Piping

The member is the simplest element of the piping system. It is delimited by two numbered neighboring points, and is designated by the higher number.

In general, the limb can be subjected to three forces and three moments directed along three mutually perpendicular axes. To each force, it responds with three displacements and three rotations. Consequently, the total flexibility of a limb is described by a square flexibility matrix A _m of format 6.

It's easy to show that this matrix is symmetrical with respect to the diagonal; this property follows from Maxwell's law of reciprocity (see articles in the Structural Calculus section of the Basic Sciences treatise)....