Part 5 continues the theory given in Parts 1–4 in the February 1947 issue of the Journal (pp. 199–269). The present paper deals with the stresses and deformations of conical and cylindrical tubes under arbitrary loading, thus completing the analysis given in Part 4 which dealt only with pure torque.

A remarkable unification of the theory of bending and torsion is achieved. It is shown that the axial constraint stresses, i.e. the corrections to the engineers' stresses, may in general be calculated as if caused by torque about axes different in each mode. The analysis proves that it is in no circumstances correct to calculate the axial constraint stresses from the torque about the flexural axis.

Functions giving the cross-wise distribution of stress are fully worked out for the n-boom tube of arbitrary cross-section and for the singly symmetrical trapezoidal tube with continuous direct stress-carrying covers. The analysis is a considerable extension of the results given for the four-boom tube in Part 4.